TSTP Solution File: LCL154-1 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : LCL154-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n021.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 12:42:44 EDT 2022
% Result : Unsatisfiable 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL154-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 12:08:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 7694: Facts:
% 0.12/0.34 7694: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
% 0.12/0.34 7694: Id : 3, {_}:
% 0.12/0.34 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
% 0.12/0.34 =>=
% 0.12/0.34 truth
% 0.12/0.34 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
% 0.12/0.34 7694: Id : 4, {_}:
% 0.12/0.34 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
% 0.12/0.34 [9, 8] by wajsberg_3 ?8 ?9
% 0.12/0.34 7694: Id : 5, {_}:
% 0.12/0.34 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
% 0.12/0.34 [12, 11] by wajsberg_4 ?11 ?12
% 0.12/0.34 7694: Id : 6, {_}:
% 0.12/0.34 or ?14 ?15 =<= implies (not ?14) ?15
% 0.12/0.34 [15, 14] by or_definition ?14 ?15
% 0.12/0.34 7694: Id : 7, {_}:
% 0.12/0.34 or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
% 0.12/0.34 [19, 18, 17] by or_associativity ?17 ?18 ?19
% 0.12/0.34 7694: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
% 0.12/0.34 7694: Id : 9, {_}:
% 0.12/0.34 and ?24 ?25 =<= not (or (not ?24) (not ?25))
% 0.12/0.34 [25, 24] by and_definition ?24 ?25
% 0.12/0.34 7694: Id : 10, {_}:
% 0.12/0.34 and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
% 0.12/0.34 [29, 28, 27] by and_associativity ?27 ?28 ?29
% 0.12/0.34 7694: Id : 11, {_}:
% 0.12/0.34 and ?31 ?32 =?= and ?32 ?31
% 0.12/0.34 [32, 31] by and_commutativity ?31 ?32
% 0.12/0.34 7694: Id : 12, {_}:
% 0.12/0.34 xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
% 0.12/0.34 [35, 34] by xor_definition ?34 ?35
% 0.12/0.34 7694: Id : 13, {_}:
% 0.12/0.34 xor ?37 ?38 =?= xor ?38 ?37
% 0.12/0.34 [38, 37] by xor_commutativity ?37 ?38
% 0.12/0.34 7694: Id : 14, {_}:
% 0.12/0.34 and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
% 0.12/0.34 [41, 40] by and_star_definition ?40 ?41
% 0.12/0.34 7694: Id : 15, {_}:
% 0.12/0.34 and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
% 0.12/0.34 [45, 44, 43] by and_star_associativity ?43 ?44 ?45
% 0.12/0.34 7694: Id : 16, {_}:
% 0.12/0.34 and_star ?47 ?48 =?= and_star ?48 ?47
% 0.12/0.34 [48, 47] by and_star_commutativity ?47 ?48
% 0.12/0.34 7694: Id : 17, {_}: not truth =>= falsehood [] by false_definition
% 0.12/0.34 7694: Goal:
% 0.12/0.34 7694: Id : 1, {_}: xor x falsehood =>= x [] by prove_alternative_wajsberg_axiom
% 0.19/0.53 Statistics :
% 0.19/0.53 Max weight : 27
% 0.19/0.53 Found proof, 0.194807s
% 0.19/0.53 % SZS status Unsatisfiable for theBenchmark.p
% 0.19/0.53 % SZS output start CNFRefutation for theBenchmark.p
% 0.19/0.53 Id : 3, {_}: implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) =>= truth [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
% 0.19/0.53 Id : 17, {_}: not truth =>= falsehood [] by false_definition
% 0.19/0.53 Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
% 0.19/0.53 Id : 20, {_}: implies (implies ?55 ?56) (implies (implies ?56 ?57) (implies ?55 ?57)) =>= truth [57, 56, 55] by wajsberg_2 ?55 ?56 ?57
% 0.19/0.53 Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
% 0.19/0.53 Id : 6, {_}: or ?14 ?15 =<= implies (not ?14) ?15 [15, 14] by or_definition ?14 ?15
% 0.19/0.53 Id : 5, {_}: implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by wajsberg_4 ?11 ?12
% 0.19/0.53 Id : 4, {_}: implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 [9, 8] by wajsberg_3 ?8 ?9
% 0.19/0.53 Id : 9, {_}: and ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by and_definition ?24 ?25
% 0.19/0.53 Id : 14, {_}: and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) [41, 40] by and_star_definition ?40 ?41
% 0.19/0.53 Id : 12, {_}: xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by xor_definition ?34 ?35
% 0.19/0.53 Id : 173, {_}: and_star ?40 ?41 =<= and ?40 ?41 [41, 40] by Demod 14 with 9 at 3
% 0.19/0.53 Id : 181, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by Demod 12 with 173 at 1,3
% 0.19/0.53 Id : 182, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 181 with 173 at 2,3
% 0.19/0.53 Id : 176, {_}: and_star ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by Demod 9 with 173 at 2
% 0.19/0.53 Id : 70, {_}: implies (or ?11 (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by Demod 5 with 6 at 1,2
% 0.19/0.53 Id : 410, {_}: implies (implies ?1001 truth) (implies ?1002 (implies ?1001 ?1002)) =>= truth [1002, 1001] by Super 20 with 2 at 1,2,2
% 0.19/0.53 Id : 411, {_}: implies (implies truth truth) (implies ?1004 ?1004) =>= truth [1004] by Super 410 with 2 at 2,2,2
% 0.19/0.53 Id : 446, {_}: implies truth (implies ?1004 ?1004) =>= truth [1004] by Demod 411 with 2 at 1,2
% 0.19/0.53 Id : 447, {_}: implies ?1004 ?1004 =>= truth [1004] by Demod 446 with 2 at 2
% 0.19/0.53 Id : 470, {_}: or ?1085 (not ?1085) =>= truth [1085] by Super 6 with 447 at 3
% 0.19/0.53 Id : 526, {_}: or (not ?1140) ?1140 =>= truth [1140] by Super 8 with 470 at 3
% 0.19/0.53 Id : 728, {_}: implies truth (implies ?1343 (not (not ?1343))) =>= truth [1343] by Super 70 with 526 at 1,2
% 0.19/0.53 Id : 744, {_}: implies ?1343 (not (not ?1343)) =>= truth [1343] by Demod 728 with 2 at 2
% 0.19/0.53 Id : 1141, {_}: implies (implies (not (not ?1789)) ?1789) ?1789 =>= implies truth (not (not ?1789)) [1789] by Super 4 with 744 at 1,3
% 0.19/0.53 Id : 1190, {_}: implies (or (not ?1789) ?1789) ?1789 =>= implies truth (not (not ?1789)) [1789] by Demod 1141 with 6 at 1,2
% 0.19/0.53 Id : 1191, {_}: implies (or (not ?1789) ?1789) ?1789 =>= not (not ?1789) [1789] by Demod 1190 with 2 at 3
% 0.19/0.53 Id : 1192, {_}: implies truth ?1789 =>= not (not ?1789) [1789] by Demod 1191 with 526 at 1,2
% 0.19/0.53 Id : 1193, {_}: ?1789 =<= not (not ?1789) [1789] by Demod 1192 with 2 at 2
% 0.19/0.53 Id : 1222, {_}: and_star ?1867 (not ?1868) =<= not (or (not ?1867) ?1868) [1868, 1867] by Super 176 with 1193 at 2,1,3
% 0.19/0.53 Id : 1219, {_}: or (not ?1858) ?1859 =>= implies ?1858 ?1859 [1859, 1858] by Super 6 with 1193 at 1,3
% 0.19/0.53 Id : 2406, {_}: and_star ?1867 (not ?1868) =>= not (implies ?1867 ?1868) [1868, 1867] by Demod 1222 with 1219 at 1,3
% 0.19/0.53 Id : 2408, {_}: xor ?34 ?35 =<= or (not (implies ?34 ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 182 with 2406 at 1,3
% 0.19/0.53 Id : 2412, {_}: xor ?34 ?35 =<= implies (implies ?34 ?35) (and_star (not ?34) ?35) [35, 34] by Demod 2408 with 1219 at 3
% 0.19/0.53 Id : 2423, {_}: and_star ?3517 (not ?3518) =>= not (implies ?3517 ?3518) [3518, 3517] by Demod 1222 with 1219 at 1,3
% 0.19/0.53 Id : 2424, {_}: and_star ?3520 falsehood =<= not (implies ?3520 truth) [3520] by Super 2423 with 17 at 2,2
% 0.19/0.53 Id : 22, {_}: implies (implies (implies ?62 ?63) ?64) (implies (implies ?64 (implies (implies ?63 ?65) (implies ?62 ?65))) truth) =>= truth [65, 64, 63, 62] by Super 20 with 3 at 2,2,2
% 0.19/0.53 Id : 27, {_}: implies truth (implies (implies (implies (implies ?81 ?82) (implies ?83 ?82)) ?84) (implies (implies ?83 ?81) ?84)) =>= truth [84, 83, 82, 81] by Super 20 with 3 at 1,2
% 0.19/0.53 Id : 32, {_}: implies (implies (implies (implies ?81 ?82) (implies ?83 ?82)) ?84) (implies (implies ?83 ?81) ?84) =>= truth [84, 83, 82, 81] by Demod 27 with 2 at 2
% 0.19/0.53 Id : 1986, {_}: implies (implies (implies (implies ?2907 ?2908) (implies (implies ?2908 ?2909) (implies ?2907 ?2909))) ?2910) (implies (implies ?2910 truth) truth) =>= truth [2910, 2909, 2908, 2907] by Super 22 with 32 at 2,1,2,2
% 0.19/0.53 Id : 2084, {_}: implies (implies truth ?2910) (implies (implies ?2910 truth) truth) =>= truth [2910] by Demod 1986 with 3 at 1,1,2
% 0.19/0.53 Id : 190, {_}: implies (or ?532 falsehood) (implies truth ?532) =>= truth [532] by Super 70 with 17 at 2,1,2
% 0.19/0.53 Id : 345, {_}: implies (or ?896 falsehood) ?896 =>= truth [896] by Demod 190 with 2 at 2,2
% 0.19/0.53 Id : 347, {_}: implies (or falsehood ?901) ?901 =>= truth [901] by Super 345 with 8 at 1,2
% 0.19/0.53 Id : 522, {_}: implies truth (not falsehood) =>= truth [] by Super 347 with 470 at 1,2
% 0.19/0.53 Id : 549, {_}: not falsehood =>= truth [] by Demod 522 with 2 at 2
% 0.19/0.53 Id : 803, {_}: and_star falsehood ?1423 =<= not (or truth (not ?1423)) [1423] by Super 176 with 549 at 1,1,3
% 0.19/0.53 Id : 559, {_}: and_star falsehood ?1170 =<= not (or truth (not ?1170)) [1170] by Super 176 with 549 at 1,1,3
% 0.19/0.53 Id : 807, {_}: and_star falsehood (or truth (not ?1430)) =>= not (or truth (and_star falsehood ?1430)) [1430] by Super 803 with 559 at 2,1,3
% 0.19/0.53 Id : 1487, {_}: or ?2402 (not ?2403) =>= implies ?2403 ?2402 [2403, 2402] by Super 8 with 1219 at 3
% 0.19/0.53 Id : 1820, {_}: and_star falsehood (implies ?1430 truth) =<= not (or truth (and_star falsehood ?1430)) [1430] by Demod 807 with 1487 at 2,2
% 0.19/0.53 Id : 1829, {_}: or truth (and_star falsehood ?2735) =<= not (and_star falsehood (implies ?2735 truth)) [2735] by Super 1193 with 1820 at 1,3
% 0.19/0.53 Id : 1227, {_}: ?1879 =<= not (not ?1879) [1879] by Demod 1192 with 2 at 2
% 0.19/0.53 Id : 1231, {_}: or truth (not ?1886) =>= not (and_star falsehood ?1886) [1886] by Super 1227 with 559 at 1,3
% 0.19/0.53 Id : 1767, {_}: implies ?1886 truth =<= not (and_star falsehood ?1886) [1886] by Demod 1231 with 1487 at 2
% 0.19/0.53 Id : 1840, {_}: or truth (and_star falsehood ?2735) =<= implies (implies ?2735 truth) truth [2735] by Demod 1829 with 1767 at 3
% 0.19/0.53 Id : 1865, {_}: implies (implies truth ?2761) ?2761 =>= or truth (and_star falsehood ?2761) [2761] by Super 4 with 1840 at 3
% 0.19/0.53 Id : 1917, {_}: implies ?2761 ?2761 =?= or truth (and_star falsehood ?2761) [2761] by Demod 1865 with 2 at 1,2
% 0.19/0.53 Id : 1918, {_}: truth =<= or truth (and_star falsehood ?2761) [2761] by Demod 1917 with 447 at 2
% 0.19/0.53 Id : 1952, {_}: truth =<= implies (implies ?2735 truth) truth [2735] by Demod 1840 with 1918 at 2
% 0.19/0.53 Id : 2085, {_}: implies (implies truth ?2910) truth =>= truth [2910] by Demod 2084 with 1952 at 2,2
% 0.19/0.53 Id : 2086, {_}: implies ?2910 truth =>= truth [2910] by Demod 2085 with 2 at 1,2
% 0.19/0.53 Id : 2447, {_}: and_star ?3520 falsehood =>= not truth [3520] by Demod 2424 with 2086 at 1,3
% 0.19/0.53 Id : 2448, {_}: and_star ?3520 falsehood =>= falsehood [3520] by Demod 2447 with 17 at 3
% 0.19/0.53 Id : 2467, {_}: xor ?3564 falsehood =<= implies (implies ?3564 falsehood) falsehood [3564] by Super 2412 with 2448 at 2,3
% 0.19/0.53 Id : 562, {_}: or falsehood ?1176 =<= implies truth ?1176 [1176] by Super 6 with 549 at 1,3
% 0.19/0.53 Id : 569, {_}: or falsehood ?1176 =>= ?1176 [1176] by Demod 562 with 2 at 3
% 0.19/0.53 Id : 620, {_}: or ?1203 falsehood =>= ?1203 [1203] by Super 8 with 569 at 3
% 0.19/0.53 Id : 1481, {_}: implies ?2383 falsehood =>= not ?2383 [2383] by Super 620 with 1219 at 2
% 0.19/0.53 Id : 2475, {_}: xor ?3564 falsehood =<= not (implies ?3564 falsehood) [3564] by Demod 2467 with 1481 at 3
% 0.19/0.53 Id : 2476, {_}: xor ?3564 falsehood =>= not (not ?3564) [3564] by Demod 2475 with 1481 at 1,3
% 0.19/0.53 Id : 2477, {_}: xor ?3564 falsehood =>= ?3564 [3564] by Demod 2476 with 1193 at 3
% 0.19/0.53 Id : 2559, {_}: x === x [] by Demod 1 with 2477 at 2
% 0.19/0.53 Id : 1, {_}: xor x falsehood =>= x [] by prove_alternative_wajsberg_axiom
% 0.19/0.53 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.53 7694: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 0.199069 using nrkbo
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