%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET703+4 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 : 300s % DateTime : Thu Aug 31 15:26:03 EDT 2023 % Result : Theorem 8.04s 1.79s % Output : Proof 8.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET703+4 : TPTP v8.1.2. Released v2.2.0. % 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n009.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sat Aug 26 15:37:50 EDT 2023 % 0.13/0.34 % CPUTime : % 0.54/0.59 ________ _____ % 0.54/0.59 ___ __ \_________(_)________________________________ % 0.54/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.54/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.54/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.54/0.59 % 0.54/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.54/0.59 (2023-06-19) % 0.54/0.59 % 0.54/0.59 (c) Philipp Rümmer, 2009-2023 % 0.54/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.54/0.59 Amanda Stjerna. % 0.54/0.59 Free software under BSD-3-Clause. % 0.54/0.59 % 0.54/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.54/0.59 % 0.54/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.54/0.60 Running up to 7 provers in parallel. % 0.54/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.54/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.54/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.54/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.54/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.54/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.54/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.58/1.05 Prover 4: Preprocessing ... % 2.58/1.05 Prover 1: Preprocessing ... % 2.88/1.09 Prover 5: Preprocessing ... % 2.88/1.09 Prover 0: Preprocessing ... % 2.88/1.09 Prover 2: Preprocessing ... % 2.88/1.09 Prover 3: Preprocessing ... % 2.88/1.09 Prover 6: Preprocessing ... % 4.92/1.43 Prover 6: Proving ... % 4.92/1.44 Prover 1: Constructing countermodel ... % 5.55/1.45 Prover 3: Constructing countermodel ... % 5.55/1.45 Prover 5: Proving ... % 5.79/1.48 Prover 2: Proving ... % 5.79/1.49 Prover 4: Constructing countermodel ... % 5.79/1.51 Prover 0: Proving ... % 7.91/1.77 Prover 1: Found proof (size 63) % 7.91/1.77 Prover 1: proved (1157ms) % 7.91/1.77 Prover 4: stopped % 7.91/1.77 Prover 3: stopped % 7.91/1.77 Prover 5: stopped % 7.91/1.77 Prover 0: stopped % 7.91/1.77 Prover 2: stopped % 8.04/1.79 Prover 6: proved (1172ms) % 8.04/1.79 % 8.04/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.04/1.79 % 8.04/1.80 % SZS output start Proof for theBenchmark % 8.04/1.80 Assumptions after simplification: % 8.04/1.80 --------------------------------- % 8.04/1.80 % 8.04/1.80 (equal_set) % 8.22/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 8.22/1.83 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 8.22/1.83 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 8.22/1.83 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 8.22/1.83 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 8.22/1.83 % 8.22/1.83 (singleton) % 8.22/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | % 8.22/1.83 ~ (member(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 8.22/1.83 $i] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0) | ~ % 8.22/1.83 $i(v1) | ~ $i(v0)) % 8.22/1.83 % 8.22/1.83 (subset) % 8.30/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 8.30/1.84 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 8.30/1.84 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 8.30/1.84 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 8.30/1.84 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 8.30/1.84 % 8.30/1.84 (thI41) % 8.30/1.84 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.30/1.84 $i] : ? [v6: int] : ( ~ (v6 = 0) & unordered_pair(v0, v1) = v5 & % 8.30/1.84 singleton(v1) = v3 & singleton(v0) = v2 & union(v2, v3) = v4 & equal_set(v4, % 8.30/1.84 v5) = v6 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.30/1.84 % 8.30/1.84 (union) % 8.30/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.30/1.84 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 8.30/1.84 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 8.30/1.84 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 8.30/1.84 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 8.30/1.84 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 8.30/1.84 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 8.30/1.84 % 8.30/1.84 (unordered_pair) % 8.30/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.30/1.84 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | % 8.30/1.85 ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0))) & ! [v0: $i] : ! % 8.30/1.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = v0 | ~ % 8.30/1.85 (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ % 8.30/1.85 $i(v1) | ~ $i(v0)) % 8.30/1.85 % 8.30/1.85 Further assumptions not needed in the proof: % 8.30/1.85 -------------------------------------------- % 8.30/1.85 difference, empty_set, intersection, power_set, product, sum % 8.30/1.85 % 8.30/1.85 Those formulas are unsatisfiable: % 8.30/1.85 --------------------------------- % 8.30/1.85 % 8.30/1.85 Begin of proof % 8.30/1.85 | % 8.30/1.85 | ALPHA: (subset) implies: % 8.30/1.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.30/1.85 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.30/1.85 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 8.30/1.85 | % 8.30/1.85 | ALPHA: (equal_set) implies: % 8.30/1.85 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 8.30/1.85 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 8.30/1.85 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 8.30/1.85 | 0)))) % 8.30/1.85 | % 8.30/1.85 | ALPHA: (union) implies: % 8.30/1.85 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 8.30/1.85 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 8.30/1.85 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 8.30/1.85 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 8.30/1.85 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 8.30/1.85 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 8.30/1.85 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 8.30/1.86 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 8.30/1.86 | v5)) % 8.30/1.86 | % 8.30/1.86 | ALPHA: (singleton) implies: % 8.30/1.86 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1) % 8.30/1.86 | = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 8.30/1.86 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) % 8.30/1.86 | = v1) | ~ (member(v0, v1) = v2) | ~ $i(v0)) % 8.30/1.86 | % 8.30/1.86 | ALPHA: (unordered_pair) implies: % 8.30/1.86 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = % 8.30/1.86 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ % 8.30/1.86 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 8.30/1.86 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 8.30/1.86 | (v4 = 0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 8.30/1.86 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0))) % 8.30/1.86 | % 8.30/1.86 | DELTA: instantiating (thI41) with fresh symbols all_15_0, all_15_1, all_15_2, % 8.30/1.86 | all_15_3, all_15_4, all_15_5, all_15_6 gives: % 8.30/1.86 | (9) ~ (all_15_0 = 0) & unordered_pair(all_15_6, all_15_5) = all_15_1 & % 8.30/1.86 | singleton(all_15_5) = all_15_3 & singleton(all_15_6) = all_15_4 & % 8.30/1.86 | union(all_15_4, all_15_3) = all_15_2 & equal_set(all_15_2, all_15_1) = % 8.30/1.86 | all_15_0 & $i(all_15_1) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) & % 8.30/1.86 | $i(all_15_5) & $i(all_15_6) % 8.30/1.86 | % 8.30/1.86 | ALPHA: (9) implies: % 8.30/1.86 | (10) ~ (all_15_0 = 0) % 8.30/1.86 | (11) $i(all_15_6) % 8.30/1.86 | (12) $i(all_15_5) % 8.30/1.86 | (13) $i(all_15_4) % 8.30/1.86 | (14) $i(all_15_3) % 8.30/1.86 | (15) $i(all_15_2) % 8.30/1.86 | (16) $i(all_15_1) % 8.30/1.86 | (17) equal_set(all_15_2, all_15_1) = all_15_0 % 8.30/1.86 | (18) union(all_15_4, all_15_3) = all_15_2 % 8.30/1.86 | (19) singleton(all_15_6) = all_15_4 % 8.30/1.86 | (20) singleton(all_15_5) = all_15_3 % 8.30/1.86 | (21) unordered_pair(all_15_6, all_15_5) = all_15_1 % 8.30/1.86 | % 8.30/1.86 | GROUND_INST: instantiating (2) with all_15_2, all_15_1, all_15_0, simplifying % 8.30/1.86 | with (15), (16), (17) gives: % 8.30/1.87 | (22) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 8.30/1.87 | all_15_2) = v1 & subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) | % 8.30/1.87 | ~ (v0 = 0))) % 8.30/1.87 | % 8.30/1.87 | BETA: splitting (22) gives: % 8.30/1.87 | % 8.30/1.87 | Case 1: % 8.30/1.87 | | % 8.30/1.87 | | (23) all_15_0 = 0 % 8.30/1.87 | | % 8.30/1.87 | | REDUCE: (10), (23) imply: % 8.30/1.87 | | (24) $false % 8.30/1.87 | | % 8.30/1.87 | | CLOSE: (24) is inconsistent. % 8.30/1.87 | | % 8.30/1.87 | Case 2: % 8.30/1.87 | | % 8.30/1.87 | | (25) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_2) = v1 & % 8.30/1.87 | | subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.30/1.87 | | % 8.30/1.87 | | DELTA: instantiating (25) with fresh symbols all_24_0, all_24_1 gives: % 8.30/1.87 | | (26) subset(all_15_1, all_15_2) = all_24_0 & subset(all_15_2, all_15_1) = % 8.30/1.87 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0)) % 8.30/1.87 | | % 8.30/1.87 | | ALPHA: (26) implies: % 8.30/1.87 | | (27) subset(all_15_2, all_15_1) = all_24_1 % 8.30/1.87 | | (28) subset(all_15_1, all_15_2) = all_24_0 % 8.30/1.87 | | (29) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 8.30/1.87 | | % 8.30/1.87 | | GROUND_INST: instantiating (1) with all_15_2, all_15_1, all_24_1, % 8.30/1.87 | | simplifying with (15), (16), (27) gives: % 8.30/1.87 | | (30) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.30/1.87 | | member(v0, all_15_1) = v1 & member(v0, all_15_2) = 0 & $i(v0)) % 8.30/1.87 | | % 8.30/1.87 | | GROUND_INST: instantiating (1) with all_15_1, all_15_2, all_24_0, % 8.30/1.87 | | simplifying with (15), (16), (28) gives: % 8.30/1.87 | | (31) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.30/1.87 | | member(v0, all_15_1) = 0 & member(v0, all_15_2) = v1 & $i(v0)) % 8.30/1.87 | | % 8.30/1.87 | | BETA: splitting (29) gives: % 8.30/1.87 | | % 8.30/1.87 | | Case 1: % 8.30/1.87 | | | % 8.30/1.87 | | | (32) ~ (all_24_0 = 0) % 8.30/1.87 | | | % 8.30/1.87 | | | BETA: splitting (31) gives: % 8.30/1.87 | | | % 8.30/1.87 | | | Case 1: % 8.30/1.87 | | | | % 8.30/1.87 | | | | (33) all_24_0 = 0 % 8.30/1.87 | | | | % 8.30/1.87 | | | | REDUCE: (32), (33) imply: % 8.30/1.87 | | | | (34) $false % 8.30/1.87 | | | | % 8.30/1.87 | | | | CLOSE: (34) is inconsistent. % 8.30/1.87 | | | | % 8.30/1.87 | | | Case 2: % 8.30/1.87 | | | | % 8.30/1.87 | | | | (35) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 8.30/1.87 | | | | = 0 & member(v0, all_15_2) = v1 & $i(v0)) % 8.30/1.87 | | | | % 8.30/1.87 | | | | DELTA: instantiating (35) with fresh symbols all_37_0, all_37_1 gives: % 8.30/1.87 | | | | (36) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 & % 8.30/1.87 | | | | member(all_37_1, all_15_2) = all_37_0 & $i(all_37_1) % 8.30/1.87 | | | | % 8.30/1.87 | | | | ALPHA: (36) implies: % 8.30/1.87 | | | | (37) ~ (all_37_0 = 0) % 8.30/1.87 | | | | (38) $i(all_37_1) % 8.30/1.87 | | | | (39) member(all_37_1, all_15_2) = all_37_0 % 8.30/1.87 | | | | (40) member(all_37_1, all_15_1) = 0 % 8.30/1.87 | | | | % 8.30/1.87 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_4, all_15_3, % 8.30/1.87 | | | | all_15_2, all_37_0, simplifying with (13), (14), (18), % 8.30/1.87 | | | | (38), (39) gives: % 8.30/1.87 | | | | (41) all_37_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 8.30/1.87 | | | | (v0 = 0) & member(all_37_1, all_15_3) = v1 & member(all_37_1, % 8.30/1.87 | | | | all_15_4) = v0) % 8.30/1.87 | | | | % 8.30/1.88 | | | | GROUND_INST: instantiating (7) with all_37_1, all_15_6, all_15_5, % 8.30/1.88 | | | | all_15_1, simplifying with (11), (12), (21), (38), (40) % 8.30/1.88 | | | | gives: % 8.30/1.88 | | | | (42) all_37_1 = all_15_5 | all_37_1 = all_15_6 % 8.30/1.88 | | | | % 8.30/1.88 | | | | BETA: splitting (41) gives: % 8.30/1.88 | | | | % 8.30/1.88 | | | | Case 1: % 8.30/1.88 | | | | | % 8.30/1.88 | | | | | (43) all_37_0 = 0 % 8.30/1.88 | | | | | % 8.30/1.88 | | | | | REDUCE: (37), (43) imply: % 8.30/1.88 | | | | | (44) $false % 8.30/1.88 | | | | | % 8.30/1.88 | | | | | CLOSE: (44) is inconsistent. % 8.30/1.88 | | | | | % 8.30/1.88 | | | | Case 2: % 8.30/1.88 | | | | | % 8.30/1.88 | | | | | (45) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 8.30/1.88 | | | | | member(all_37_1, all_15_3) = v1 & member(all_37_1, all_15_4) % 8.30/1.88 | | | | | = v0) % 8.30/1.88 | | | | | % 8.30/1.88 | | | | | DELTA: instantiating (45) with fresh symbols all_52_0, all_52_1 gives: % 8.30/1.88 | | | | | (46) ~ (all_52_0 = 0) & ~ (all_52_1 = 0) & member(all_37_1, % 8.30/1.88 | | | | | all_15_3) = all_52_0 & member(all_37_1, all_15_4) = all_52_1 % 8.30/1.88 | | | | | % 8.30/1.88 | | | | | ALPHA: (46) implies: % 8.30/1.88 | | | | | (47) ~ (all_52_1 = 0) % 8.30/1.88 | | | | | (48) ~ (all_52_0 = 0) % 8.30/1.88 | | | | | (49) member(all_37_1, all_15_4) = all_52_1 % 8.30/1.88 | | | | | (50) member(all_37_1, all_15_3) = all_52_0 % 8.30/1.88 | | | | | % 8.30/1.88 | | | | | BETA: splitting (42) gives: % 8.30/1.88 | | | | | % 8.30/1.88 | | | | | Case 1: % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | | (51) all_37_1 = all_15_5 % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | | REDUCE: (50), (51) imply: % 8.30/1.88 | | | | | | (52) member(all_15_5, all_15_3) = all_52_0 % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | | GROUND_INST: instantiating (6) with all_15_5, all_15_3, all_52_0, % 8.30/1.88 | | | | | | simplifying with (12), (20), (52) gives: % 8.30/1.88 | | | | | | (53) all_52_0 = 0 % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | | REDUCE: (48), (53) imply: % 8.30/1.88 | | | | | | (54) $false % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | | CLOSE: (54) is inconsistent. % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | Case 2: % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | | (55) all_37_1 = all_15_6 % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | | REDUCE: (49), (55) imply: % 8.30/1.88 | | | | | | (56) member(all_15_6, all_15_4) = all_52_1 % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | | GROUND_INST: instantiating (6) with all_15_6, all_15_4, all_52_1, % 8.30/1.88 | | | | | | simplifying with (11), (19), (56) gives: % 8.30/1.88 | | | | | | (57) all_52_1 = 0 % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | | REDUCE: (47), (57) imply: % 8.30/1.88 | | | | | | (58) $false % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | | CLOSE: (58) is inconsistent. % 8.30/1.88 | | | | | | % 8.30/1.88 | | | | | End of split % 8.30/1.88 | | | | | % 8.30/1.88 | | | | End of split % 8.30/1.88 | | | | % 8.30/1.88 | | | End of split % 8.30/1.88 | | | % 8.30/1.88 | | Case 2: % 8.30/1.88 | | | % 8.30/1.88 | | | (59) ~ (all_24_1 = 0) % 8.30/1.88 | | | % 8.30/1.88 | | | BETA: splitting (30) gives: % 8.30/1.88 | | | % 8.30/1.88 | | | Case 1: % 8.30/1.88 | | | | % 8.30/1.88 | | | | (60) all_24_1 = 0 % 8.30/1.88 | | | | % 8.30/1.88 | | | | REDUCE: (59), (60) imply: % 8.30/1.88 | | | | (61) $false % 8.30/1.88 | | | | % 8.30/1.88 | | | | CLOSE: (61) is inconsistent. % 8.30/1.88 | | | | % 8.30/1.88 | | | Case 2: % 8.30/1.88 | | | | % 8.30/1.88 | | | | (62) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 8.30/1.88 | | | | = v1 & member(v0, all_15_2) = 0 & $i(v0)) % 8.30/1.88 | | | | % 8.30/1.88 | | | | DELTA: instantiating (62) with fresh symbols all_37_0, all_37_1 gives: % 8.30/1.88 | | | | (63) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 & % 8.30/1.88 | | | | member(all_37_1, all_15_2) = 0 & $i(all_37_1) % 8.30/1.88 | | | | % 8.30/1.88 | | | | ALPHA: (63) implies: % 8.30/1.88 | | | | (64) ~ (all_37_0 = 0) % 8.30/1.88 | | | | (65) $i(all_37_1) % 8.30/1.88 | | | | (66) member(all_37_1, all_15_2) = 0 % 8.30/1.88 | | | | (67) member(all_37_1, all_15_1) = all_37_0 % 8.30/1.88 | | | | % 8.30/1.88 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_4, all_15_3, % 8.30/1.88 | | | | all_15_2, simplifying with (13), (14), (18), (65), (66) % 8.30/1.88 | | | | gives: % 8.30/1.89 | | | | (68) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_3) = v1 & % 8.30/1.89 | | | | member(all_37_1, all_15_4) = v0 & (v1 = 0 | v0 = 0)) % 8.30/1.89 | | | | % 8.30/1.89 | | | | GROUND_INST: instantiating (8) with all_37_1, all_15_6, all_15_5, % 8.30/1.89 | | | | all_15_1, all_37_0, simplifying with (11), (12), (21), % 8.30/1.89 | | | | (65), (67) gives: % 8.30/1.89 | | | | (69) all_37_0 = 0 | ( ~ (all_37_1 = all_15_5) & ~ (all_37_1 = % 8.30/1.89 | | | | all_15_6)) % 8.30/1.89 | | | | % 8.30/1.89 | | | | DELTA: instantiating (68) with fresh symbols all_45_0, all_45_1 gives: % 8.30/1.89 | | | | (70) member(all_37_1, all_15_3) = all_45_0 & member(all_37_1, % 8.30/1.89 | | | | all_15_4) = all_45_1 & (all_45_0 = 0 | all_45_1 = 0) % 8.30/1.89 | | | | % 8.30/1.89 | | | | ALPHA: (70) implies: % 8.30/1.89 | | | | (71) member(all_37_1, all_15_4) = all_45_1 % 8.30/1.89 | | | | (72) member(all_37_1, all_15_3) = all_45_0 % 8.30/1.89 | | | | (73) all_45_0 = 0 | all_45_1 = 0 % 8.30/1.89 | | | | % 8.30/1.89 | | | | BETA: splitting (69) gives: % 8.30/1.89 | | | | % 8.30/1.89 | | | | Case 1: % 8.30/1.89 | | | | | % 8.30/1.89 | | | | | (74) all_37_0 = 0 % 8.30/1.89 | | | | | % 8.30/1.89 | | | | | REDUCE: (64), (74) imply: % 8.30/1.89 | | | | | (75) $false % 8.30/1.89 | | | | | % 8.30/1.89 | | | | | CLOSE: (75) is inconsistent. % 8.30/1.89 | | | | | % 8.30/1.89 | | | | Case 2: % 8.30/1.89 | | | | | % 8.30/1.89 | | | | | (76) ~ (all_37_1 = all_15_5) & ~ (all_37_1 = all_15_6) % 8.30/1.89 | | | | | % 8.30/1.89 | | | | | ALPHA: (76) implies: % 8.30/1.89 | | | | | (77) ~ (all_37_1 = all_15_6) % 8.30/1.89 | | | | | (78) ~ (all_37_1 = all_15_5) % 8.30/1.89 | | | | | % 8.30/1.89 | | | | | BETA: splitting (73) gives: % 8.30/1.89 | | | | | % 8.30/1.89 | | | | | Case 1: % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | | (79) all_45_0 = 0 % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | | REDUCE: (72), (79) imply: % 8.30/1.89 | | | | | | (80) member(all_37_1, all_15_3) = 0 % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_5, all_15_3, % 8.30/1.89 | | | | | | simplifying with (12), (20), (65), (80) gives: % 8.30/1.89 | | | | | | (81) all_37_1 = all_15_5 % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | | REDUCE: (78), (81) imply: % 8.30/1.89 | | | | | | (82) $false % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | | CLOSE: (82) is inconsistent. % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | Case 2: % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | | (83) all_45_1 = 0 % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | | REDUCE: (71), (83) imply: % 8.30/1.89 | | | | | | (84) member(all_37_1, all_15_4) = 0 % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_6, all_15_4, % 8.30/1.89 | | | | | | simplifying with (11), (19), (65), (84) gives: % 8.30/1.89 | | | | | | (85) all_37_1 = all_15_6 % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | | REDUCE: (77), (85) imply: % 8.30/1.89 | | | | | | (86) $false % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | | CLOSE: (86) is inconsistent. % 8.30/1.89 | | | | | | % 8.30/1.89 | | | | | End of split % 8.30/1.89 | | | | | % 8.30/1.89 | | | | End of split % 8.30/1.89 | | | | % 8.30/1.89 | | | End of split % 8.30/1.89 | | | % 8.30/1.89 | | End of split % 8.30/1.89 | | % 8.30/1.89 | End of split % 8.30/1.89 | % 8.30/1.89 End of proof % 8.30/1.89 % SZS output end Proof for theBenchmark % 8.30/1.89 % 8.30/1.89 1300ms %------------------------------------------------------------------------------