TSTP Solution File: LCL163-1 by Matita---1.0
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% File : Matita---1.0
% Problem : LCL163-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n003.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 12:42:47 EDT 2022
% Result : Unsatisfiable 1.94s 0.79s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL163-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.11 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.12/0.32 % Computer : n003.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jul 4 19:21:25 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 10116: Facts:
% 0.12/0.33 10116: Id : 2, {_}: not ?2 =<= xor ?2 truth [2] by axiom_1 ?2
% 0.12/0.33 10116: Id : 3, {_}: xor ?4 falsehood =>= ?4 [4] by axiom_2 ?4
% 0.12/0.33 10116: Id : 4, {_}: xor ?6 ?6 =>= falsehood [6] by axiom_3 ?6
% 0.12/0.33 10116: Id : 5, {_}: and_star ?8 truth =>= ?8 [8] by axiom_4 ?8
% 0.12/0.33 10116: Id : 6, {_}: and_star ?10 falsehood =>= falsehood [10] by axiom_5 ?10
% 0.12/0.33 10116: Id : 7, {_}: and_star (xor truth ?12) ?12 =>= falsehood [12] by axiom_6 ?12
% 0.12/0.33 10116: Id : 8, {_}:
% 0.12/0.33 xor ?14 (xor truth ?15) =?= xor (xor ?14 truth) ?15
% 0.12/0.33 [15, 14] by axiom_7 ?14 ?15
% 0.12/0.33 10116: Id : 9, {_}:
% 0.12/0.33 and_star (xor (and_star (xor truth ?17) ?18) truth) ?18
% 0.12/0.33 =?=
% 0.12/0.33 and_star (xor (and_star (xor truth ?18) ?17) truth) ?17
% 0.12/0.33 [18, 17] by axiom_8 ?17 ?18
% 0.12/0.33 10116: Id : 10, {_}:
% 0.12/0.33 xor ?20 ?21 =?= xor ?21 ?20
% 0.12/0.33 [21, 20] by xor_commutativity ?20 ?21
% 0.12/0.33 10116: Id : 11, {_}:
% 0.12/0.33 and_star (and_star ?23 ?24) ?25 =?= and_star ?23 (and_star ?24 ?25)
% 0.12/0.33 [25, 24, 23] by and_star_associativity ?23 ?24 ?25
% 0.12/0.33 10116: Id : 12, {_}:
% 0.12/0.33 and_star ?27 ?28 =?= and_star ?28 ?27
% 0.12/0.33 [28, 27] by and_star_commutativity ?27 ?28
% 0.12/0.33 10116: Id : 13, {_}: not truth =>= falsehood [] by false_definition
% 0.12/0.33 10116: Id : 14, {_}:
% 0.12/0.33 implies ?31 ?32 =<= xor truth (and_star ?31 (xor truth ?32))
% 0.12/0.33 [32, 31] by implies_definition ?31 ?32
% 0.12/0.33 10116: Goal:
% 0.12/0.33 10116: Id : 1, {_}:
% 0.12/0.33 implies (implies x y) y =<= implies (implies y x) x
% 0.12/0.33 [] by prove_wajsberg_axiom
% 1.94/0.79 Statistics :
% 1.94/0.79 Max weight : 27
% 1.94/0.79 Found proof, 0.460747s
% 1.94/0.79 % SZS status Unsatisfiable for theBenchmark.p
% 1.94/0.79 % SZS output start CNFRefutation for theBenchmark.p
% 1.94/0.79 Id : 3, {_}: xor ?4 falsehood =>= ?4 [4] by axiom_2 ?4
% 1.94/0.79 Id : 4, {_}: xor ?6 ?6 =>= falsehood [6] by axiom_3 ?6
% 1.94/0.79 Id : 14, {_}: implies ?31 ?32 =<= xor truth (and_star ?31 (xor truth ?32)) [32, 31] by implies_definition ?31 ?32
% 1.94/0.79 Id : 8, {_}: xor ?14 (xor truth ?15) =<= xor (xor ?14 truth) ?15 [15, 14] by axiom_7 ?14 ?15
% 1.94/0.79 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
% 1.94/0.79 Id : 10, {_}: xor ?20 ?21 =?= xor ?21 ?20 [21, 20] by xor_commutativity ?20 ?21
% 1.94/0.79 Id : 2, {_}: not ?2 =<= xor ?2 truth [2] by axiom_1 ?2
% 1.94/0.79 Id : 12, {_}: and_star ?27 ?28 =?= and_star ?28 ?27 [28, 27] by and_star_commutativity ?27 ?28
% 1.94/0.79 Id : 218, {_}: implies ?350 ?351 =<= xor truth (and_star ?350 (xor truth ?351)) [351, 350] by implies_definition ?350 ?351
% 1.94/0.79 Id : 227, {_}: implies ?376 ?377 =<= xor truth (and_star (xor truth ?377) ?376) [377, 376] by Super 218 with 12 at 2,3
% 1.94/0.79 Id : 120, {_}: not ?148 =<= xor truth ?148 [148] by Super 2 with 10 at 3
% 1.94/0.79 Id : 930, {_}: implies ?376 ?377 =<= not (and_star (xor truth ?377) ?376) [377, 376] by Demod 227 with 120 at 3
% 1.94/0.79 Id : 943, {_}: implies ?906 ?907 =<= not (and_star (not ?907) ?906) [907, 906] by Demod 930 with 120 at 1,1,3
% 1.94/0.79 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
% 1.94/0.79 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
% 1.94/0.79 Id : 43, {_}: xor ?14 (xor truth ?15) =>= xor (not ?14) ?15 [15, 14] by Demod 8 with 2 at 1,3
% 1.94/0.79 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
% 1.94/0.79 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
% 1.94/0.79 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
% 1.94/0.79 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
% 1.94/0.79 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
% 1.94/0.79 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
% 1.94/0.79 Id : 377, {_}: xor ?14 (not ?15) =<= xor (not ?14) ?15 [15, 14] by Demod 43 with 120 at 2,2
% 1.94/0.79 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
% 1.94/0.79 Id : 380, {_}: implies ?31 ?32 =<= not (and_star ?31 (xor truth ?32)) [32, 31] by Demod 14 with 120 at 3
% 1.94/0.79 Id : 381, {_}: implies ?31 ?32 =<= not (and_star ?31 (not ?32)) [32, 31] by Demod 380 with 120 at 2,1,3
% 1.94/0.79 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
% 1.94/0.79 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
% 1.94/0.79 Id : 46, {_}: xor ?70 (xor truth ?71) =>= xor (not ?70) ?71 [71, 70] by Demod 8 with 2 at 1,3
% 1.94/0.79 Id : 48, {_}: xor ?75 falsehood =<= xor (not ?75) truth [75] by Super 46 with 4 at 2,2
% 1.94/0.79 Id : 55, {_}: ?75 =<= xor (not ?75) truth [75] by Demod 48 with 3 at 2
% 1.94/0.79 Id : 56, {_}: ?75 =<= not (not ?75) [75] by Demod 55 with 2 at 3
% 1.94/0.79 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
% 1.94/0.79 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
% 1.94/0.79 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
% 1.94/0.79 Id : 931, {_}: implies ?376 ?377 =<= not (and_star (not ?377) ?376) [377, 376] by Demod 930 with 120 at 1,1,3
% 1.94/0.79 Id : 979, {_}: implies (implies ?942 ?943) ?943 =?= implies (implies (not (not ?943)) ?942) ?942 [943, 942] by Demod 978 with 931 at 3
% 1.94/0.79 Id : 980, {_}: implies (implies ?942 ?943) ?943 =?= implies (implies ?943 ?942) ?942 [943, 942] by Demod 979 with 56 at 1,1,3
% 1.94/0.79 Id : 9708, {_}: implies (implies x y) y =?= implies (implies x y) y [] by Demod 1 with 980 at 3
% 1.94/0.79 Id : 1, {_}: implies (implies x y) y =<= implies (implies y x) x [] by prove_wajsberg_axiom
% 1.94/0.79 % SZS output end CNFRefutation for theBenchmark.p
% 1.94/0.79 10117: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 0.463348 using kbo
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