TSTP Solution File: LCL109-6 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : LCL109-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:42:27 EDT 2022
% Result : Unsatisfiable 3.16s 1.10s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL109-6 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.12/0.31 % Computer : n016.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 600
% 0.12/0.31 % DateTime : Mon Jul 4 04:24:01 EDT 2022
% 0.16/0.31 % CPUTime :
% 0.16/0.31 16322: Facts:
% 0.16/0.31 16322: Id : 2, {_}: not ?2 =<= xor ?2 truth [2] by axiom_1 ?2
% 0.16/0.31 16322: Id : 3, {_}: xor ?4 falsehood =>= ?4 [4] by axiom_2 ?4
% 0.16/0.31 16322: Id : 4, {_}: xor ?6 ?6 =>= falsehood [6] by axiom_3 ?6
% 0.16/0.31 16322: Id : 5, {_}: and_star ?8 truth =>= ?8 [8] by axiom_4 ?8
% 0.16/0.31 16322: Id : 6, {_}: and_star ?10 falsehood =>= falsehood [10] by axiom_5 ?10
% 0.16/0.31 16322: Id : 7, {_}: and_star (xor truth ?12) ?12 =>= falsehood [12] by axiom_6 ?12
% 0.16/0.32 16322: Id : 8, {_}:
% 0.16/0.32 xor ?14 (xor truth ?15) =?= xor (xor ?14 truth) ?15
% 0.16/0.32 [15, 14] by axiom_7 ?14 ?15
% 0.16/0.32 16322: Id : 9, {_}:
% 0.16/0.32 and_star (xor (and_star (xor truth ?17) ?18) truth) ?18
% 0.16/0.32 =?=
% 0.16/0.32 and_star (xor (and_star (xor truth ?18) ?17) truth) ?17
% 0.16/0.32 [18, 17] by axiom_8 ?17 ?18
% 0.16/0.32 16322: Id : 10, {_}:
% 0.16/0.32 xor ?20 ?21 =?= xor ?21 ?20
% 0.16/0.32 [21, 20] by xor_commutativity ?20 ?21
% 0.16/0.32 16322: Id : 11, {_}:
% 0.16/0.32 and_star (and_star ?23 ?24) ?25 =?= and_star ?23 (and_star ?24 ?25)
% 0.16/0.32 [25, 24, 23] by and_star_associativity ?23 ?24 ?25
% 0.16/0.32 16322: Id : 12, {_}:
% 0.16/0.32 and_star ?27 ?28 =?= and_star ?28 ?27
% 0.16/0.32 [28, 27] by and_star_commutativity ?27 ?28
% 0.16/0.32 16322: Id : 13, {_}: not truth =>= falsehood [] by false_definition
% 0.16/0.32 16322: Id : 14, {_}:
% 0.16/0.32 implies ?31 ?32 =<= xor truth (and_star ?31 (xor truth ?32))
% 0.16/0.32 [32, 31] by implies_definition ?31 ?32
% 0.16/0.32 16322: Goal:
% 0.16/0.32 16322: Id : 1, {_}:
% 0.16/0.32 implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
% 0.16/0.32 [] by prove_wajsberg_mv_4
% 3.16/1.10 Statistics :
% 3.16/1.10 Max weight : 28
% 3.16/1.10 Found proof, 0.780804s
% 3.16/1.10 % SZS status Unsatisfiable for theBenchmark.p
% 3.16/1.10 % SZS output start CNFRefutation for theBenchmark.p
% 3.16/1.10 Id : 5, {_}: and_star ?8 truth =>= ?8 [8] by axiom_4 ?8
% 3.16/1.10 Id : 13, {_}: not truth =>= falsehood [] by false_definition
% 3.16/1.10 Id : 6, {_}: and_star ?10 falsehood =>= falsehood [10] by axiom_5 ?10
% 3.16/1.10 Id : 7, {_}: and_star (xor truth ?12) ?12 =>= falsehood [12] by axiom_6 ?12
% 3.16/1.10 Id : 14, {_}: implies ?31 ?32 =<= xor truth (and_star ?31 (xor truth ?32)) [32, 31] by implies_definition ?31 ?32
% 3.16/1.10 Id : 9, {_}: and_star (xor (and_star (xor truth ?17) ?18) truth) ?18 =?= and_star (xor (and_star (xor truth ?18) ?17) truth) ?17 [18, 17] by axiom_8 ?17 ?18
% 3.16/1.10 Id : 155, {_}: and_star (and_star ?219 ?220) ?221 =>= and_star ?219 (and_star ?220 ?221) [221, 220, 219] by and_star_associativity ?219 ?220 ?221
% 3.16/1.10 Id : 10, {_}: xor ?20 ?21 =?= xor ?21 ?20 [21, 20] by xor_commutativity ?20 ?21
% 3.16/1.10 Id : 12, {_}: and_star ?27 ?28 =?= and_star ?28 ?27 [28, 27] by and_star_commutativity ?27 ?28
% 3.16/1.10 Id : 3, {_}: xor ?4 falsehood =>= ?4 [4] by axiom_2 ?4
% 3.16/1.10 Id : 4, {_}: xor ?6 ?6 =>= falsehood [6] by axiom_3 ?6
% 3.16/1.10 Id : 2, {_}: not ?2 =<= xor ?2 truth [2] by axiom_1 ?2
% 3.16/1.10 Id : 8, {_}: xor ?14 (xor truth ?15) =<= xor (xor ?14 truth) ?15 [15, 14] by axiom_7 ?14 ?15
% 3.16/1.10 Id : 11, {_}: and_star (and_star ?23 ?24) ?25 =>= and_star ?23 (and_star ?24 ?25) [25, 24, 23] by and_star_associativity ?23 ?24 ?25
% 3.16/1.10 Id : 218, {_}: implies ?350 ?351 =<= xor truth (and_star ?350 (xor truth ?351)) [351, 350] by implies_definition ?350 ?351
% 3.16/1.10 Id : 226, {_}: implies (and_star ?372 ?373) ?374 =<= xor truth (and_star ?372 (and_star ?373 (xor truth ?374))) [374, 373, 372] by Super 218 with 11 at 2,3
% 3.16/1.10 Id : 46, {_}: xor ?70 (xor truth ?71) =>= xor (not ?70) ?71 [71, 70] by Demod 8 with 2 at 1,3
% 3.16/1.10 Id : 48, {_}: xor ?75 falsehood =<= xor (not ?75) truth [75] by Super 46 with 4 at 2,2
% 3.16/1.10 Id : 55, {_}: ?75 =<= xor (not ?75) truth [75] by Demod 48 with 3 at 2
% 3.16/1.10 Id : 56, {_}: ?75 =<= not (not ?75) [75] by Demod 55 with 2 at 3
% 3.16/1.10 Id : 227, {_}: implies ?376 ?377 =<= xor truth (and_star (xor truth ?377) ?376) [377, 376] by Super 218 with 12 at 2,3
% 3.16/1.10 Id : 120, {_}: not ?148 =<= xor truth ?148 [148] by Super 2 with 10 at 3
% 3.16/1.10 Id : 930, {_}: implies ?376 ?377 =<= not (and_star (xor truth ?377) ?376) [377, 376] by Demod 227 with 120 at 3
% 3.16/1.10 Id : 931, {_}: implies ?376 ?377 =<= not (and_star (not ?377) ?376) [377, 376] by Demod 930 with 120 at 1,1,3
% 3.16/1.10 Id : 937, {_}: and_star (not ?886) ?887 =>= not (implies ?887 ?886) [887, 886] by Super 56 with 931 at 1,3
% 3.16/1.10 Id : 1113, {_}: and_star (not (implies ?1083 ?1084)) ?1085 =>= and_star (not ?1084) (and_star ?1083 ?1085) [1085, 1084, 1083] by Super 11 with 937 at 1,2
% 3.16/1.10 Id : 1145, {_}: not (implies ?1085 (implies ?1083 ?1084)) =<= and_star (not ?1084) (and_star ?1083 ?1085) [1084, 1083, 1085] by Demod 1113 with 937 at 2
% 3.16/1.10 Id : 1146, {_}: not (implies ?1085 (implies ?1083 ?1084)) =<= not (implies (and_star ?1083 ?1085) ?1084) [1084, 1083, 1085] by Demod 1145 with 937 at 3
% 3.16/1.10 Id : 1384, {_}: implies (and_star ?1399 ?1400) ?1401 =<= not (not (implies ?1400 (implies ?1399 ?1401))) [1401, 1400, 1399] by Super 56 with 1146 at 1,3
% 3.16/1.10 Id : 1411, {_}: implies (and_star ?1399 ?1400) ?1401 =>= implies ?1400 (implies ?1399 ?1401) [1401, 1400, 1399] by Demod 1384 with 56 at 3
% 3.16/1.10 Id : 3520, {_}: implies ?373 (implies ?372 ?374) =<= xor truth (and_star ?372 (and_star ?373 (xor truth ?374))) [374, 372, 373] by Demod 226 with 1411 at 2
% 3.16/1.10 Id : 3521, {_}: implies ?373 (implies ?372 ?374) =<= not (and_star ?372 (and_star ?373 (xor truth ?374))) [374, 372, 373] by Demod 3520 with 120 at 3
% 3.16/1.10 Id : 3522, {_}: implies ?373 (implies ?372 ?374) =<= not (and_star ?372 (and_star ?373 (not ?374))) [374, 372, 373] by Demod 3521 with 120 at 2,2,1,3
% 3.16/1.10 Id : 1109, {_}: and_star ?1073 (not ?1074) =>= not (implies ?1073 ?1074) [1074, 1073] by Super 12 with 937 at 3
% 3.16/1.10 Id : 3523, {_}: implies ?373 (implies ?372 ?374) =<= not (and_star ?372 (not (implies ?373 ?374))) [374, 372, 373] by Demod 3522 with 1109 at 2,1,3
% 3.16/1.10 Id : 3524, {_}: implies ?373 (implies ?372 ?374) =<= not (not (implies ?372 (implies ?373 ?374))) [374, 372, 373] by Demod 3523 with 1109 at 1,3
% 3.16/1.10 Id : 3525, {_}: implies ?373 (implies ?372 ?374) =?= implies ?372 (implies ?373 ?374) [374, 372, 373] by Demod 3524 with 56 at 3
% 3.16/1.10 Id : 59, {_}: and_star (not (and_star (xor truth ?17) ?18)) ?18 =?= and_star (xor (and_star (xor truth ?18) ?17) truth) ?17 [18, 17] by Demod 9 with 2 at 1,2
% 3.16/1.10 Id : 60, {_}: and_star (not (and_star (xor truth ?17) ?18)) ?18 =?= and_star (not (and_star (xor truth ?18) ?17)) ?17 [18, 17] by Demod 59 with 2 at 1,3
% 3.16/1.10 Id : 160, {_}: and_star (and_star (not (and_star (xor truth ?237) ?238)) ?238) ?239 =?= and_star (not (and_star (xor truth ?238) ?237)) (and_star ?237 ?239) [239, 238, 237] by Super 155 with 60 at 1,2
% 3.16/1.10 Id : 171, {_}: and_star (not (and_star (xor truth ?237) ?238)) (and_star ?238 ?239) =?= and_star (not (and_star (xor truth ?238) ?237)) (and_star ?237 ?239) [239, 238, 237] by Demod 160 with 11 at 2
% 3.16/1.10 Id : 1714, {_}: not (implies (and_star ?238 ?239) (and_star (xor truth ?237) ?238)) =?= and_star (not (and_star (xor truth ?238) ?237)) (and_star ?237 ?239) [237, 239, 238] by Demod 171 with 937 at 2
% 3.16/1.10 Id : 1715, {_}: not (implies (and_star ?238 ?239) (and_star (xor truth ?237) ?238)) =?= not (implies (and_star ?237 ?239) (and_star (xor truth ?238) ?237)) [237, 239, 238] by Demod 1714 with 937 at 3
% 3.16/1.10 Id : 1716, {_}: not (implies ?239 (implies ?238 (and_star (xor truth ?237) ?238))) =?= not (implies (and_star ?237 ?239) (and_star (xor truth ?238) ?237)) [237, 238, 239] by Demod 1715 with 1411 at 1,2
% 3.16/1.10 Id : 1717, {_}: not (implies ?239 (implies ?238 (and_star (xor truth ?237) ?238))) =?= not (implies ?239 (implies ?237 (and_star (xor truth ?238) ?237))) [237, 238, 239] by Demod 1716 with 1411 at 1,3
% 3.16/1.10 Id : 1718, {_}: not (implies ?239 (implies ?238 (and_star (not ?237) ?238))) =?= not (implies ?239 (implies ?237 (and_star (xor truth ?238) ?237))) [237, 238, 239] by Demod 1717 with 120 at 1,2,2,1,2
% 3.16/1.10 Id : 1719, {_}: not (implies ?239 (implies ?238 (and_star (not ?237) ?238))) =?= not (implies ?239 (implies ?237 (and_star (not ?238) ?237))) [237, 238, 239] by Demod 1718 with 120 at 1,2,2,1,3
% 3.16/1.10 Id : 1720, {_}: not (implies ?239 (implies ?238 (not (implies ?238 ?237)))) =?= not (implies ?239 (implies ?237 (and_star (not ?238) ?237))) [237, 238, 239] by Demod 1719 with 937 at 2,2,1,2
% 3.16/1.10 Id : 1721, {_}: not (implies ?239 (implies ?238 (not (implies ?238 ?237)))) =?= not (implies ?239 (implies ?237 (not (implies ?237 ?238)))) [237, 238, 239] by Demod 1720 with 937 at 2,2,1,3
% 3.16/1.10 Id : 943, {_}: implies ?906 ?907 =<= not (and_star (not ?907) ?906) [907, 906] by Demod 930 with 120 at 1,1,3
% 3.16/1.10 Id : 945, {_}: implies ?911 (not ?912) =>= not (and_star ?912 ?911) [912, 911] by Super 943 with 56 at 1,1,3
% 3.16/1.10 Id : 1722, {_}: not (implies ?239 (not (and_star (implies ?238 ?237) ?238))) =?= not (implies ?239 (implies ?237 (not (implies ?237 ?238)))) [237, 238, 239] by Demod 1721 with 945 at 2,1,2
% 3.16/1.10 Id : 1723, {_}: not (implies ?239 (not (and_star (implies ?238 ?237) ?238))) =?= not (implies ?239 (not (and_star (implies ?237 ?238) ?237))) [237, 238, 239] by Demod 1722 with 945 at 2,1,3
% 3.16/1.10 Id : 1724, {_}: not (not (and_star (and_star (implies ?238 ?237) ?238) ?239)) =?= not (implies ?239 (not (and_star (implies ?237 ?238) ?237))) [239, 237, 238] by Demod 1723 with 945 at 1,2
% 3.16/1.10 Id : 1725, {_}: not (not (and_star (and_star (implies ?238 ?237) ?238) ?239)) =?= not (not (and_star (and_star (implies ?237 ?238) ?237) ?239)) [239, 237, 238] by Demod 1724 with 945 at 1,3
% 3.16/1.10 Id : 1726, {_}: and_star (and_star (implies ?238 ?237) ?238) ?239 =?= not (not (and_star (and_star (implies ?237 ?238) ?237) ?239)) [239, 237, 238] by Demod 1725 with 56 at 2
% 3.16/1.10 Id : 1727, {_}: and_star (and_star (implies ?238 ?237) ?238) ?239 =?= and_star (and_star (implies ?237 ?238) ?237) ?239 [239, 237, 238] by Demod 1726 with 56 at 3
% 3.16/1.10 Id : 1728, {_}: and_star (implies ?238 ?237) (and_star ?238 ?239) =?= and_star (and_star (implies ?237 ?238) ?237) ?239 [239, 237, 238] by Demod 1727 with 11 at 2
% 3.16/1.10 Id : 1729, {_}: and_star (implies ?238 ?237) (and_star ?238 ?239) =?= and_star (implies ?237 ?238) (and_star ?237 ?239) [239, 237, 238] by Demod 1728 with 11 at 3
% 3.16/1.10 Id : 189, {_}: and_star ?283 (and_star ?284 ?285) =?= and_star ?284 (and_star ?285 ?283) [285, 284, 283] by Super 11 with 12 at 2
% 3.16/1.10 Id : 3068, {_}: and_star ?238 (and_star ?239 (implies ?238 ?237)) =?= and_star (implies ?237 ?238) (and_star ?237 ?239) [237, 239, 238] by Demod 1729 with 189 at 2
% 3.16/1.10 Id : 3069, {_}: and_star ?238 (and_star ?239 (implies ?238 ?237)) =?= and_star ?237 (and_star ?239 (implies ?237 ?238)) [237, 239, 238] by Demod 3068 with 189 at 3
% 3.16/1.10 Id : 65, {_}: and_star (not (and_star (xor truth ?95) ?96)) ?96 =?= and_star (not (and_star (xor truth ?96) ?95)) ?95 [96, 95] by Demod 59 with 2 at 1,3
% 3.16/1.10 Id : 43, {_}: xor ?14 (xor truth ?15) =>= xor (not ?14) ?15 [15, 14] by Demod 8 with 2 at 1,3
% 3.16/1.10 Id : 68, {_}: and_star (not (and_star (xor truth ?102) (xor truth ?103))) (xor truth ?103) =?= and_star (not (and_star (xor (not truth) ?103) ?102)) ?102 [103, 102] by Super 65 with 43 at 1,1,1,3
% 3.16/1.10 Id : 558, {_}: and_star (xor truth ?103) (not (and_star (xor truth ?102) (xor truth ?103))) =?= and_star (not (and_star (xor (not truth) ?103) ?102)) ?102 [102, 103] by Demod 68 with 12 at 2
% 3.16/1.10 Id : 559, {_}: and_star (xor truth ?103) (not (and_star (xor truth ?102) (xor truth ?103))) =?= and_star ?102 (not (and_star (xor (not truth) ?103) ?102)) [102, 103] by Demod 558 with 12 at 3
% 3.16/1.10 Id : 560, {_}: and_star (not ?103) (not (and_star (xor truth ?102) (xor truth ?103))) =?= and_star ?102 (not (and_star (xor (not truth) ?103) ?102)) [102, 103] by Demod 559 with 120 at 1,2
% 3.16/1.10 Id : 561, {_}: and_star (not ?103) (not (and_star (not ?102) (xor truth ?103))) =?= and_star ?102 (not (and_star (xor (not truth) ?103) ?102)) [102, 103] by Demod 560 with 120 at 1,1,2,2
% 3.16/1.10 Id : 562, {_}: and_star (not ?103) (not (and_star (not ?102) (not ?103))) =?= and_star ?102 (not (and_star (xor (not truth) ?103) ?102)) [102, 103] by Demod 561 with 120 at 2,1,2,2
% 3.16/1.10 Id : 377, {_}: xor ?14 (not ?15) =<= xor (not ?14) ?15 [15, 14] by Demod 43 with 120 at 2,2
% 3.16/1.10 Id : 563, {_}: and_star (not ?103) (not (and_star (not ?102) (not ?103))) =?= and_star ?102 (not (and_star (xor truth (not ?103)) ?102)) [102, 103] by Demod 562 with 377 at 1,1,2,3
% 3.16/1.10 Id : 380, {_}: implies ?31 ?32 =<= not (and_star ?31 (xor truth ?32)) [32, 31] by Demod 14 with 120 at 3
% 3.16/1.10 Id : 381, {_}: implies ?31 ?32 =<= not (and_star ?31 (not ?32)) [32, 31] by Demod 380 with 120 at 2,1,3
% 3.16/1.10 Id : 564, {_}: and_star (not ?103) (implies (not ?102) ?103) =?= and_star ?102 (not (and_star (xor truth (not ?103)) ?102)) [102, 103] by Demod 563 with 381 at 2,2
% 3.16/1.10 Id : 565, {_}: and_star (not ?103) (implies (not ?102) ?103) =?= and_star ?102 (not (and_star (not (not ?103)) ?102)) [102, 103] by Demod 564 with 120 at 1,1,2,3
% 3.16/1.10 Id : 566, {_}: and_star (not ?103) (implies (not ?102) ?103) =?= and_star ?102 (not (and_star ?103 ?102)) [102, 103] by Demod 565 with 56 at 1,1,2,3
% 3.16/1.10 Id : 956, {_}: implies (not (and_star ?942 (not ?943))) ?943 =?= not (and_star (not ?942) (implies (not (not ?943)) ?942)) [943, 942] by Super 943 with 566 at 1,3
% 3.16/1.10 Id : 978, {_}: implies (implies ?942 ?943) ?943 =?= not (and_star (not ?942) (implies (not (not ?943)) ?942)) [943, 942] by Demod 956 with 381 at 1,2
% 3.16/1.10 Id : 979, {_}: implies (implies ?942 ?943) ?943 =?= implies (implies (not (not ?943)) ?942) ?942 [943, 942] by Demod 978 with 931 at 3
% 3.16/1.10 Id : 9513, {_}: implies (implies ?11364 ?11365) ?11365 =?= implies (implies ?11365 ?11364) ?11364 [11365, 11364] by Demod 979 with 56 at 1,1,3
% 3.16/1.10 Id : 1221, {_}: not (implies (and_star ?1208 ?1209) ?1210) =<= and_star ?1208 (and_star ?1209 (not ?1210)) [1210, 1209, 1208] by Super 11 with 1109 at 2
% 3.16/1.10 Id : 1245, {_}: not (implies (and_star ?1208 ?1209) ?1210) =<= and_star ?1208 (not (implies ?1209 ?1210)) [1210, 1209, 1208] by Demod 1221 with 1109 at 2,3
% 3.16/1.10 Id : 1246, {_}: not (implies (and_star ?1208 ?1209) ?1210) =>= not (implies ?1208 (implies ?1209 ?1210)) [1210, 1209, 1208] by Demod 1245 with 1109 at 3
% 3.16/1.10 Id : 1515, {_}: not (implies ?1651 (implies ?1652 ?1653)) =?= not (implies ?1652 (implies ?1651 ?1653)) [1653, 1652, 1651] by Demod 1246 with 1411 at 1,2
% 3.16/1.10 Id : 178, {_}: and_star ?12 (xor truth ?12) =>= falsehood [12] by Demod 7 with 12 at 2
% 3.16/1.10 Id : 228, {_}: implies ?379 ?379 =?= xor truth falsehood [379] by Super 218 with 178 at 2,3
% 3.16/1.10 Id : 245, {_}: implies ?379 ?379 =>= truth [379] by Demod 228 with 3 at 3
% 3.16/1.10 Id : 1517, {_}: not (implies ?1658 (implies ?1659 ?1658)) =>= not (implies ?1659 truth) [1659, 1658] by Super 1515 with 245 at 2,1,3
% 3.16/1.10 Id : 220, {_}: implies ?355 truth =<= xor truth (and_star ?355 falsehood) [355] by Super 218 with 4 at 2,2,3
% 3.16/1.10 Id : 237, {_}: implies ?355 truth =?= xor truth falsehood [355] by Demod 220 with 6 at 2,3
% 3.16/1.10 Id : 238, {_}: implies ?355 truth =>= truth [355] by Demod 237 with 3 at 3
% 3.16/1.10 Id : 1557, {_}: not (implies ?1658 (implies ?1659 ?1658)) =>= not truth [1659, 1658] by Demod 1517 with 238 at 1,3
% 3.16/1.10 Id : 1558, {_}: not (implies ?1658 (implies ?1659 ?1658)) =>= falsehood [1659, 1658] by Demod 1557 with 13 at 3
% 3.16/1.10 Id : 1935, {_}: implies ?2008 (implies ?2009 ?2008) =>= not falsehood [2009, 2008] by Super 56 with 1558 at 1,3
% 3.16/1.10 Id : 262, {_}: ?400 =<= not (not ?400) [400] by Demod 55 with 2 at 3
% 3.16/1.10 Id : 263, {_}: truth =<= not falsehood [] by Super 262 with 13 at 1,3
% 3.16/1.10 Id : 1964, {_}: implies ?2008 (implies ?2009 ?2008) =>= truth [2009, 2008] by Demod 1935 with 263 at 3
% 3.16/1.10 Id : 9522, {_}: implies (implies (implies ?11388 ?11389) ?11389) ?11389 =>= implies truth (implies ?11388 ?11389) [11389, 11388] by Super 9513 with 1964 at 1,3
% 3.16/1.10 Id : 185, {_}: and_star truth ?271 =>= ?271 [271] by Super 5 with 12 at 2
% 3.16/1.10 Id : 483, {_}: implies truth ?592 =>= not (not ?592) [592] by Super 381 with 185 at 1,3
% 3.16/1.10 Id : 495, {_}: implies truth ?592 =>= ?592 [592] by Demod 483 with 56 at 3
% 3.16/1.10 Id : 9793, {_}: implies (implies (implies ?11733 ?11734) ?11734) ?11734 =>= implies ?11733 ?11734 [11734, 11733] by Demod 9522 with 495 at 3
% 3.16/1.10 Id : 980, {_}: implies (implies ?942 ?943) ?943 =?= implies (implies ?943 ?942) ?942 [943, 942] by Demod 979 with 56 at 1,1,3
% 3.16/1.10 Id : 9834, {_}: implies (implies (implies ?11872 ?11873) ?11873) ?11872 =>= implies ?11873 ?11872 [11873, 11872] by Super 9793 with 980 at 1,2
% 3.16/1.10 Id : 10055, {_}: implies ?11985 (not ?11986) =<= not (and_star ?11986 (implies (implies (not ?11986) ?11985) ?11985)) [11986, 11985] by Super 945 with 9834 at 2
% 3.16/1.10 Id : 10165, {_}: not (and_star ?11986 ?11985) =<= not (and_star ?11986 (implies (implies (not ?11986) ?11985) ?11985)) [11985, 11986] by Demod 10055 with 945 at 2
% 3.16/1.10 Id : 13519, {_}: and_star ?15384 (implies (implies (not ?15384) ?15385) ?15385) =>= not (not (and_star ?15384 ?15385)) [15385, 15384] by Super 56 with 10165 at 1,3
% 3.16/1.10 Id : 13599, {_}: and_star ?15384 (implies (implies (not ?15384) ?15385) ?15385) =>= and_star ?15384 ?15385 [15385, 15384] by Demod 13519 with 56 at 3
% 3.16/1.10 Id : 13912, {_}: and_star ?15683 (and_star ?15684 (implies ?15683 (implies (not ?15684) ?15683))) =>= and_star (implies (not ?15684) ?15683) (and_star ?15684 ?15683) [15684, 15683] by Super 3069 with 13599 at 2,3
% 3.16/1.10 Id : 14013, {_}: and_star ?15683 (and_star ?15684 truth) =<= and_star (implies (not ?15684) ?15683) (and_star ?15684 ?15683) [15684, 15683] by Demod 13912 with 1964 at 2,2,2
% 3.16/1.10 Id : 14014, {_}: and_star ?15683 (and_star ?15684 truth) =<= and_star (and_star ?15684 ?15683) (implies (not ?15684) ?15683) [15684, 15683] by Demod 14013 with 12 at 3
% 3.16/1.10 Id : 14015, {_}: and_star ?15683 ?15684 =<= and_star (and_star ?15684 ?15683) (implies (not ?15684) ?15683) [15684, 15683] by Demod 14014 with 5 at 2,2
% 3.16/1.10 Id : 14016, {_}: and_star ?15683 ?15684 =<= and_star ?15684 (and_star ?15683 (implies (not ?15684) ?15683)) [15684, 15683] by Demod 14015 with 11 at 3
% 3.16/1.10 Id : 14302, {_}: and_star ?16004 (not ?16005) =<= not (implies (and_star ?16004 (implies (not (not ?16005)) ?16004)) ?16005) [16005, 16004] by Super 937 with 14016 at 2
% 3.16/1.10 Id : 14400, {_}: not (implies ?16004 ?16005) =<= not (implies (and_star ?16004 (implies (not (not ?16005)) ?16004)) ?16005) [16005, 16004] by Demod 14302 with 1109 at 2
% 3.16/1.10 Id : 14401, {_}: not (implies ?16004 ?16005) =<= not (implies (implies (not (not ?16005)) ?16004) (implies ?16004 ?16005)) [16005, 16004] by Demod 14400 with 1411 at 1,3
% 3.16/1.10 Id : 1500, {_}: not (implies ?1209 (implies ?1208 ?1210)) =?= not (implies ?1208 (implies ?1209 ?1210)) [1210, 1208, 1209] by Demod 1246 with 1411 at 1,2
% 3.16/1.10 Id : 14402, {_}: not (implies ?16004 ?16005) =<= not (implies ?16004 (implies (implies (not (not ?16005)) ?16004) ?16005)) [16005, 16004] by Demod 14401 with 1500 at 3
% 3.16/1.10 Id : 14403, {_}: not (implies ?16004 ?16005) =<= not (implies ?16004 (implies (implies ?16005 ?16004) ?16005)) [16005, 16004] by Demod 14402 with 56 at 1,1,2,1,3
% 3.16/1.10 Id : 15197, {_}: implies ?16618 (implies (implies ?16619 ?16618) ?16619) =>= not (not (implies ?16618 ?16619)) [16619, 16618] by Super 56 with 14403 at 1,3
% 3.16/1.10 Id : 15296, {_}: implies ?16618 (implies (implies ?16619 ?16618) ?16619) =>= implies ?16618 ?16619 [16619, 16618] by Demod 15197 with 56 at 3
% 3.16/1.10 Id : 1390, {_}: not (implies ?1426 (implies ?1427 ?1428)) =<= not (implies (and_star ?1427 ?1426) ?1428) [1428, 1427, 1426] by Demod 1145 with 937 at 3
% 3.16/1.10 Id : 1398, {_}: not (implies ?1455 (implies (not ?1456) ?1457)) =<= not (implies (not (implies ?1455 ?1456)) ?1457) [1457, 1456, 1455] by Super 1390 with 937 at 1,1,3
% 3.16/1.10 Id : 2145, {_}: implies (not (implies ?2135 ?2136)) ?2137 =<= not (not (implies ?2135 (implies (not ?2136) ?2137))) [2137, 2136, 2135] by Super 56 with 1398 at 1,3
% 3.16/1.10 Id : 2201, {_}: implies (not (implies ?2135 ?2136)) ?2137 =>= implies ?2135 (implies (not ?2136) ?2137) [2137, 2136, 2135] by Demod 2145 with 56 at 3
% 3.16/1.10 Id : 2302, {_}: implies ?2326 (implies (not ?2327) (not (implies ?2326 ?2327))) =>= truth [2327, 2326] by Super 245 with 2201 at 2
% 3.16/1.10 Id : 2323, {_}: implies ?2326 (not (and_star (implies ?2326 ?2327) (not ?2327))) =>= truth [2327, 2326] by Demod 2302 with 945 at 2,2
% 3.16/1.10 Id : 2324, {_}: not (and_star (and_star (implies ?2326 ?2327) (not ?2327)) ?2326) =>= truth [2327, 2326] by Demod 2323 with 945 at 2
% 3.16/1.10 Id : 222, {_}: implies ?360 (xor truth ?361) =<= xor truth (and_star ?360 (xor (not truth) ?361)) [361, 360] by Super 218 with 43 at 2,2,3
% 3.16/1.10 Id : 240, {_}: implies ?360 (xor truth ?361) =<= xor truth (and_star ?360 (xor falsehood ?361)) [361, 360] by Demod 222 with 13 at 1,2,2,3
% 3.16/1.10 Id : 1285, {_}: implies ?360 (not ?361) =<= xor truth (and_star ?360 (xor falsehood ?361)) [361, 360] by Demod 240 with 120 at 2,2
% 3.16/1.10 Id : 1286, {_}: implies ?360 (not ?361) =<= not (and_star ?360 (xor falsehood ?361)) [361, 360] by Demod 1285 with 120 at 3
% 3.16/1.10 Id : 1287, {_}: not (and_star ?361 ?360) =<= not (and_star ?360 (xor falsehood ?361)) [360, 361] by Demod 1286 with 945 at 2
% 3.16/1.10 Id : 122, {_}: xor falsehood ?152 =>= ?152 [152] by Super 3 with 10 at 2
% 3.16/1.10 Id : 1288, {_}: not (and_star ?361 ?360) =?= not (and_star ?360 ?361) [360, 361] by Demod 1287 with 122 at 2,1,3
% 3.16/1.10 Id : 2325, {_}: not (and_star ?2326 (and_star (implies ?2326 ?2327) (not ?2327))) =>= truth [2327, 2326] by Demod 2324 with 1288 at 2
% 3.16/1.10 Id : 2326, {_}: not (and_star ?2326 (and_star (not ?2327) (implies ?2326 ?2327))) =>= truth [2327, 2326] by Demod 2325 with 12 at 2,1,2
% 3.16/1.10 Id : 2327, {_}: not (and_star ?2326 (not (implies (implies ?2326 ?2327) ?2327))) =>= truth [2327, 2326] by Demod 2326 with 937 at 2,1,2
% 3.16/1.10 Id : 2328, {_}: not (not (implies ?2326 (implies (implies ?2326 ?2327) ?2327))) =>= truth [2327, 2326] by Demod 2327 with 1109 at 1,2
% 3.16/1.10 Id : 2329, {_}: implies ?2326 (implies (implies ?2326 ?2327) ?2327) =>= truth [2327, 2326] by Demod 2328 with 56 at 2
% 3.16/1.10 Id : 15947, {_}: truth =?= truth [] by Demod 15946 with 2329 at 2
% 3.16/1.10 Id : 15946, {_}: implies b (implies (implies b a) a) =>= truth [] by Demod 15945 with 15296 at 1,2,2
% 3.16/1.10 Id : 15945, {_}: implies b (implies (implies b (implies (implies a b) a)) a) =>= truth [] by Demod 15944 with 3525 at 1,2,2
% 3.16/1.10 Id : 15944, {_}: implies b (implies (implies (implies a b) (implies b a)) a) =>= truth [] by Demod 1 with 3525 at 2
% 3.16/1.10 Id : 1, {_}: implies (implies (implies a b) (implies b a)) (implies b a) =>= truth [] by prove_wajsberg_mv_4
% 3.16/1.10 % SZS output end CNFRefutation for theBenchmark.p
% 3.16/1.11 16323: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 0.778636 using kbo
%------------------------------------------------------------------------------