============================== prooftrans (BV) ======================= Prover9 (64) version Aug-2007, Aug 2007. Process 26411 was started by veroff on titan, Sat Jan 19 14:40:38 2008 The command was "prover9 -f 4.3_alt.in". ============================== end of head =========================== op(400,infix,[^,v,"->","=>",*]). op(200,prefix,[~,-]). ============================== end of input ========================== ============================== PROOF ================================= % -------- Comments from original proof -------- % Proof 1 at 0.03 (+ 0.00) seconds: "(4.8)". % Length of proof is 17. % Level of proof is 8. % Maximum clause weight is 11. % Given clauses 43. 4 x ^ (~ x => y) = x # label("(4.8)") # label(non_clause) # label(goal). [goal]. 12 1 => x = x # label("(BCK2)"). [assumption]. 20 x ^ ((x => y) => y) = x # label("(3.7)"). [assumption]. 25 ~ x = x => 0 # label("(~ def)"). [assumption]. 26 x => 0 = ~ x. [copy(25),flip(a)]. 32 ~ ~ x = x # label("(DN)"). [assumption]. 37 x => (y => x) = 1 # label("(3.17)"). [assumption]. 38 x => (y => z) = y => (x => z) # label("(3.18)"). [assumption]. 48 c8 ^ (~ c8 => c9) != c8 # label("(4.8)") # answer("(4.8)"). [deny(4)]. 250 ~ x => 0 = x. [para(32(a,1),26(a,2))]. 373 x => (y => 0) = y => ~ x. [para(26(a,1),38(a,1,2)),flip(a)]. 649 ~ x => ~ y = y => x. [para(250(a,1),373(a,1,2)),flip(a)]. 667 ~ x => y = ~ y => x. [para(32(a,1),649(a,1,2))]. 714 x => (~ x => y) = 1. [para(667(a,1),37(a,1,2))]. 737 x ^ (1 => (~ x => y)) = x. [para(714(a,1),20(a,1,2,1))]. 764 x ^ (~ x => y) = x # label("(4.8)"). [para(12(a,1),737(a,1,2))]. 765 $F # answer("(4.8)"). [resolve(764,a,48,a)]. ============================== end of proof ========================== ============================== PROOF ================================= % -------- Comments from original proof -------- % Proof 2 at 0.04 (+ 0.00) seconds: "(3.13)". % Length of proof is 20. % Level of proof is 10. % Maximum clause weight is 11. % Given clauses 45. 1 (x => y) ^ y = y # label("(3.13)") # label(non_clause) # label(goal). [goal]. 8 x ^ y = y ^ x # label("(D4)"). [assumption]. 12 1 => x = x # label("(BCK2)"). [assumption]. 20 x ^ ((x => y) => y) = x # label("(3.7)"). [assumption]. 25 ~ x = x => 0 # label("(~ def)"). [assumption]. 26 x => 0 = ~ x. [copy(25),flip(a)]. 32 ~ ~ x = x # label("(DN)"). [assumption]. 37 x => (y => x) = 1 # label("(3.17)"). [assumption]. 38 x => (y => z) = y => (x => z) # label("(3.18)"). [assumption]. 44 (c1 => c2) ^ c2 != c2 # label("(3.13)") # answer("(3.13)"). [deny(1)]. 250 ~ x => 0 = x. [para(32(a,1),26(a,2))]. 373 x => (y => 0) = y => ~ x. [para(26(a,1),38(a,1,2)),flip(a)]. 649 ~ x => ~ y = y => x. [para(250(a,1),373(a,1,2)),flip(a)]. 667 ~ x => y = ~ y => x. [para(32(a,1),649(a,1,2))]. 714 x => (~ x => y) = 1. [para(667(a,1),37(a,1,2))]. 737 x ^ (1 => (~ x => y)) = x. [para(714(a,1),20(a,1,2,1))]. 764 x ^ (~ x => y) = x # label("(4.8)"). [para(12(a,1),737(a,1,2))]. 792 x ^ (y => x) = x. [para(649(a,1),764(a,1,2))]. 796 (x => y) ^ y = y # label("(3.13)"). [para(792(a,1),8(a,1)),flip(a)]. 797 $F # answer("(3.13)"). [resolve(796,a,44,a)]. ============================== end of proof ========================== ============================== PROOF ================================= % -------- Comments from original proof -------- % Proof 3 at 0.04 (+ 0.00) seconds: "(4.6)". % Length of proof is 12. % Level of proof is 4. % Maximum clause weight is 13. % Given clauses 48. 2 (x v y) => y = x => y # label("(4.6)") # label(non_clause) # label(goal). [goal]. 7 x v y = y v x # label("(D3)"). [assumption]. 8 x ^ y = y ^ x # label("(D4)"). [assumption]. 19 x ^ 1 = x # label("(D10)"). [assumption]. 36 x => x = 1 # label("(3.16)"). [assumption]. 42 (x => y) ^ (z => y) = (x v z) => y # label("(4.4)"). [assumption]. 45 (c3 v c4) => c4 != c3 => c4 # label("(4.6)") # answer("(4.6)"). [deny(2)]. 112 1 ^ x = x. [para(19(a,1),8(a,1)),flip(a)]. 528 (x v y) => x = 1 ^ (y => x). [para(36(a,1),42(a,1,1)),flip(a)]. 883 (x v y) => x = y => x. [para(528(a,2),112(a,1))]. 898 (x v y) => y = x => y # label("(4.6)"). [para(7(a,1),883(a,1,1))]. 899 $F # answer("(4.6)"). [resolve(898,a,45,a)]. ============================== end of proof ========================== ============================== PROOF ================================= % -------- Comments from original proof -------- % Proof 4 at 0.05 (+ 0.00) seconds: "(4.7)". % Length of proof is 10. % Level of proof is 5. % Maximum clause weight is 13. % Given clauses 51. 3 x -> (y => z) = y => (x -> z) # label("(4.7)") # label(non_clause) # label(goal). [goal]. 23 x -> y = x => (x => y) # label("(-> def)"). [assumption]. 24 x => (x => y) = x -> y. [copy(23),flip(a)]. 38 x => (y => z) = y => (x => z) # label("(3.18)"). [assumption]. 46 c6 => (c5 -> c7) != c5 -> (c6 => c7) # label("(4.7)") # answer("(4.7)"). [deny(3)]. 47 c5 -> (c6 => c7) != c6 => (c5 -> c7) # answer("(4.7)"). [copy(46),flip(a)]. 372 x => (y => (x => z)) = y => (x -> z). [para(24(a,1),38(a,1,2)),flip(a)]. 1061 x => (x => (y => z)) = y => (x -> z). [para(38(a,1),372(a,1,2))]. 1120 x -> (y => z) = y => (x -> z) # label("(4.7)"). [para(1061(a,1),24(a,1)),flip(a)]. 1121 $F # answer("(4.7)"). [resolve(1120,a,47,a)]. ============================== end of proof ==========================