%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN943+1 : TPTP v8.1.2. Released v3.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n020.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 : Fri Sep 1 03:29:18 EDT 2023 % Result : Theorem 3.73s 1.35s % Output : Proof 5.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SYN943+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n020.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 16:52:29 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.85/0.98 Prover 1: Preprocessing ... % 1.85/0.98 Prover 4: Preprocessing ... % 2.38/1.03 Prover 2: Preprocessing ... % 2.38/1.03 Prover 5: Preprocessing ... % 2.38/1.03 Prover 3: Preprocessing ... % 2.38/1.03 Prover 6: Preprocessing ... % 2.38/1.03 Prover 0: Preprocessing ... % 3.22/1.17 Prover 2: Proving ... % 3.31/1.17 Prover 5: Proving ... % 3.31/1.18 Prover 6: Proving ... % 3.31/1.18 Prover 3: Warning: ignoring some quantifiers % 3.31/1.18 Prover 3: Constructing countermodel ... % 3.31/1.19 Prover 1: Warning: ignoring some quantifiers % 3.31/1.20 Prover 1: Constructing countermodel ... % 3.58/1.22 Prover 4: Constructing countermodel ... % 3.58/1.24 Prover 0: Proving ... % 3.73/1.34 Prover 2: proved (701ms) % 3.73/1.35 % 3.73/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.73/1.35 % 3.73/1.36 Prover 0: stopped % 3.73/1.37 Prover 3: stopped % 3.73/1.37 Prover 5: stopped % 3.73/1.37 Prover 6: stopped % 3.73/1.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.73/1.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.73/1.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.73/1.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.73/1.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.73/1.37 Prover 1: gave up % 3.73/1.38 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 3.73/1.39 Prover 7: Preprocessing ... % 3.73/1.39 Prover 11: Preprocessing ... % 3.73/1.39 Prover 8: Preprocessing ... % 3.73/1.40 Prover 10: Preprocessing ... % 3.73/1.41 Prover 13: Preprocessing ... % 3.73/1.41 Prover 7: Constructing countermodel ... % 3.73/1.41 Prover 10: Constructing countermodel ... % 3.73/1.42 Prover 16: Preprocessing ... % 3.73/1.42 Prover 7: gave up % 3.73/1.42 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 3.73/1.43 Prover 10: gave up % 4.73/1.44 Prover 19: Preprocessing ... % 4.73/1.44 Prover 13: Constructing countermodel ... % 4.73/1.45 Prover 8: Warning: ignoring some quantifiers % 4.73/1.46 Prover 8: Constructing countermodel ... % 4.73/1.46 Prover 16: Constructing countermodel ... % 4.73/1.49 Prover 4: Found proof (size 37) % 4.73/1.49 Prover 4: proved (846ms) % 4.73/1.49 Prover 16: stopped % 4.73/1.49 Prover 13: stopped % 4.73/1.49 Prover 8: stopped % 5.32/1.51 Prover 11: Constructing countermodel ... % 5.32/1.51 Prover 11: stopped % 5.32/1.51 Prover 19: Warning: ignoring some quantifiers % 5.32/1.52 Prover 19: Constructing countermodel ... % 5.32/1.52 Prover 19: stopped % 5.32/1.52 % 5.32/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.32/1.52 % 5.32/1.53 % SZS output start Proof for theBenchmark % 5.32/1.53 Assumptions after simplification: % 5.32/1.53 --------------------------------- % 5.32/1.53 % 5.32/1.53 (prove_this) % 5.71/1.58 ? [v0: $i] : (p(v0) = 0 & e(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 5.71/1.58 [v3: int] : (v3 = 0 | ~ (c(v2) = v3) | ~ (f(v1) = v2) | ~ $i(v1) | ? % 5.71/1.58 [v4: any] : ? [v5: any] : (g(v1) = v5 & e(v1) = v4 & ( ~ (v4 = 0) | v5 = % 5.71/1.58 0))) & ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (f(v1) % 5.71/1.58 = v2) | ~ (s(v1, v2) = v3) | ~ $i(v1) | ? [v4: any] : ? [v5: any] : % 5.71/1.58 (g(v1) = v5 & e(v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v1: $i] : ! % 5.71/1.58 [v2: int] : (v2 = 0 | ~ (p(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = % 5.71/1.58 0) & s(v0, v1) = v3)) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 5.71/1.58 (g(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 5.71/1.58 (c(v4) = v5 & e(v1) = v3 & f(v1) = v4 & $i(v4) & ( ~ (v3 = 0) | v5 = 0))) % 5.71/1.58 & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (g(v1) = v2) | ~ $i(v1) | ? % 5.71/1.58 [v3: any] : ? [v4: $i] : ? [v5: any] : (e(v1) = v3 & f(v1) = v4 & s(v1, % 5.71/1.58 v4) = v5 & $i(v4) & ( ~ (v3 = 0) | v5 = 0))) & ! [v1: $i] : ( ~ % 5.71/1.58 (p(v1) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & c(v1) = v2)) & ! % 5.71/1.58 [v1: $i] : ( ~ (p(v1) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & g(v1) % 5.71/1.58 = v2)) & ! [v1: $i] : ( ~ (c(v1) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ % 5.71/1.58 (v2 = 0) & p(v1) = v2)) & ! [v1: $i] : ( ~ (g(v1) = 0) | ~ $i(v1) | ? % 5.71/1.58 [v2: int] : ( ~ (v2 = 0) & p(v1) = v2)) & ! [v1: $i] : ( ~ (e(v1) = 0) | % 5.71/1.58 ~ $i(v1) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : (c(v3) = v4 & g(v1) % 5.71/1.58 = v2 & f(v1) = v3 & $i(v3) & (v4 = 0 | v2 = 0))) & ! [v1: $i] : ( ~ % 5.71/1.58 (e(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 5.71/1.58 (g(v1) = v2 & f(v1) = v3 & s(v1, v3) = v4 & $i(v3) & (v4 = 0 | v2 = 0))) & % 5.71/1.58 ! [v1: $i] : ( ~ (s(v0, v1) = 0) | ~ $i(v1) | p(v1) = 0)) % 5.71/1.58 % 5.71/1.58 (function-axioms) % 5.71/1.59 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.71/1.59 [v3: $i] : (v1 = v0 | ~ (s(v3, v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0: % 5.71/1.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 5.71/1.59 ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 5.71/1.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = % 5.71/1.59 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 5.71/1.59 $i] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) & ! [v0: % 5.71/1.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 5.71/1.59 ~ (e(v2) = v1) | ~ (e(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 5.71/1.59 : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) % 5.71/1.59 % 5.71/1.59 Those formulas are unsatisfiable: % 5.71/1.59 --------------------------------- % 5.71/1.59 % 5.71/1.59 Begin of proof % 5.71/1.59 | % 5.71/1.59 | ALPHA: (function-axioms) implies: % 5.71/1.59 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (f(v2) = v1) | % 5.71/1.59 | ~ (f(v2) = v0)) % 5.71/1.59 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.71/1.59 | (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) % 5.71/1.59 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.71/1.59 | (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 5.71/1.59 | % 5.71/1.59 | DELTA: instantiating (prove_this) with fresh symbol all_3_0 gives: % 5.86/1.60 | (4) p(all_3_0) = 0 & e(all_3_0) = 0 & $i(all_3_0) & ! [v0: $i] : ! [v1: % 5.86/1.60 | $i] : ! [v2: int] : (v2 = 0 | ~ (c(v1) = v2) | ~ (f(v0) = v1) | ~ % 5.86/1.60 | $i(v0) | ? [v3: any] : ? [v4: any] : (g(v0) = v4 & e(v0) = v3 & ( ~ % 5.86/1.60 | (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 5.86/1.60 | (v2 = 0 | ~ (f(v0) = v1) | ~ (s(v0, v1) = v2) | ~ $i(v0) | ? [v3: % 5.86/1.60 | any] : ? [v4: any] : (g(v0) = v4 & e(v0) = v3 & ( ~ (v3 = 0) | v4 % 5.86/1.60 | = 0))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | % 5.86/1.60 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & s(all_3_0, v0) = v2)) & ! % 5.86/1.60 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (g(v0) = v1) | ~ $i(v0) | ? % 5.86/1.60 | [v2: any] : ? [v3: $i] : ? [v4: any] : (c(v3) = v4 & e(v0) = v2 & % 5.86/1.60 | f(v0) = v3 & $i(v3) & ( ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ! % 5.86/1.60 | [v1: int] : (v1 = 0 | ~ (g(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 5.86/1.60 | [v3: $i] : ? [v4: any] : (e(v0) = v2 & f(v0) = v3 & s(v0, v3) = v4 & % 5.86/1.60 | $i(v3) & ( ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ( ~ (p(v0) = 0) | % 5.86/1.60 | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & c(v0) = v1)) & ! [v0: $i] % 5.86/1.60 | : ( ~ (p(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & g(v0) = % 5.86/1.60 | v1)) & ! [v0: $i] : ( ~ (c(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( % 5.86/1.60 | ~ (v1 = 0) & p(v0) = v1)) & ! [v0: $i] : ( ~ (g(v0) = 0) | ~ % 5.86/1.60 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & p(v0) = v1)) & ! [v0: $i] : ( % 5.86/1.60 | ~ (e(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any] % 5.86/1.60 | : (c(v2) = v3 & g(v0) = v1 & f(v0) = v2 & $i(v2) & (v3 = 0 | v1 = % 5.86/1.60 | 0))) & ! [v0: $i] : ( ~ (e(v0) = 0) | ~ $i(v0) | ? [v1: any] : % 5.86/1.60 | ? [v2: $i] : ? [v3: any] : (g(v0) = v1 & f(v0) = v2 & s(v0, v2) = % 5.86/1.60 | v3 & $i(v2) & (v3 = 0 | v1 = 0))) & ! [v0: $i] : ( ~ (s(all_3_0, % 5.86/1.60 | v0) = 0) | ~ $i(v0) | p(v0) = 0) % 5.86/1.60 | % 5.86/1.60 | ALPHA: (4) implies: % 5.86/1.60 | (5) $i(all_3_0) % 5.86/1.60 | (6) e(all_3_0) = 0 % 5.86/1.60 | (7) p(all_3_0) = 0 % 5.86/1.60 | (8) ! [v0: $i] : ( ~ (s(all_3_0, v0) = 0) | ~ $i(v0) | p(v0) = 0) % 5.86/1.61 | (9) ! [v0: $i] : ( ~ (e(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 5.86/1.61 | : ? [v3: any] : (g(v0) = v1 & f(v0) = v2 & s(v0, v2) = v3 & $i(v2) & % 5.86/1.61 | (v3 = 0 | v1 = 0))) % 5.86/1.61 | (10) ! [v0: $i] : ( ~ (e(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 5.86/1.61 | : ? [v3: any] : (c(v2) = v3 & g(v0) = v1 & f(v0) = v2 & $i(v2) & % 5.86/1.61 | (v3 = 0 | v1 = 0))) % 5.86/1.61 | (11) ! [v0: $i] : ( ~ (c(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 5.86/1.61 | 0) & p(v0) = v1)) % 5.86/1.61 | (12) ! [v0: $i] : ( ~ (p(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 5.86/1.61 | 0) & g(v0) = v1)) % 5.86/1.61 | % 5.86/1.61 | GROUND_INST: instantiating (10) with all_3_0, simplifying with (5), (6) gives: % 5.86/1.61 | (13) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (c(v1) = v2 & g(all_3_0) = % 5.86/1.61 | v0 & f(all_3_0) = v1 & $i(v1) & (v2 = 0 | v0 = 0)) % 5.86/1.61 | % 5.86/1.61 | GROUND_INST: instantiating (9) with all_3_0, simplifying with (5), (6) gives: % 5.86/1.61 | (14) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (g(all_3_0) = v0 & % 5.86/1.61 | f(all_3_0) = v1 & s(all_3_0, v1) = v2 & $i(v1) & (v2 = 0 | v0 = 0)) % 5.86/1.61 | % 5.86/1.61 | GROUND_INST: instantiating (12) with all_3_0, simplifying with (5), (7) gives: % 5.86/1.61 | (15) ? [v0: int] : ( ~ (v0 = 0) & g(all_3_0) = v0) % 5.86/1.61 | % 5.86/1.61 | DELTA: instantiating (15) with fresh symbol all_11_0 gives: % 5.86/1.61 | (16) ~ (all_11_0 = 0) & g(all_3_0) = all_11_0 % 5.86/1.61 | % 5.86/1.61 | ALPHA: (16) implies: % 5.86/1.61 | (17) ~ (all_11_0 = 0) % 5.86/1.61 | (18) g(all_3_0) = all_11_0 % 5.86/1.61 | % 5.86/1.61 | DELTA: instantiating (14) with fresh symbols all_15_0, all_15_1, all_15_2 % 5.86/1.61 | gives: % 5.86/1.61 | (19) g(all_3_0) = all_15_2 & f(all_3_0) = all_15_1 & s(all_3_0, all_15_1) = % 5.86/1.61 | all_15_0 & $i(all_15_1) & (all_15_0 = 0 | all_15_2 = 0) % 5.86/1.61 | % 5.86/1.61 | ALPHA: (19) implies: % 5.86/1.61 | (20) s(all_3_0, all_15_1) = all_15_0 % 5.86/1.61 | (21) f(all_3_0) = all_15_1 % 5.86/1.61 | (22) g(all_3_0) = all_15_2 % 5.86/1.61 | (23) all_15_0 = 0 | all_15_2 = 0 % 5.86/1.61 | % 5.86/1.61 | DELTA: instantiating (13) with fresh symbols all_17_0, all_17_1, all_17_2 % 5.86/1.61 | gives: % 5.86/1.61 | (24) c(all_17_1) = all_17_0 & g(all_3_0) = all_17_2 & f(all_3_0) = all_17_1 % 5.86/1.61 | & $i(all_17_1) & (all_17_0 = 0 | all_17_2 = 0) % 5.86/1.61 | % 5.86/1.61 | ALPHA: (24) implies: % 5.86/1.61 | (25) $i(all_17_1) % 5.86/1.61 | (26) f(all_3_0) = all_17_1 % 5.86/1.61 | (27) g(all_3_0) = all_17_2 % 5.86/1.61 | (28) c(all_17_1) = all_17_0 % 5.86/1.62 | (29) all_17_0 = 0 | all_17_2 = 0 % 5.86/1.62 | % 5.86/1.62 | GROUND_INST: instantiating (1) with all_15_1, all_17_1, all_3_0, simplifying % 5.86/1.62 | with (21), (26) gives: % 5.86/1.62 | (30) all_17_1 = all_15_1 % 5.86/1.62 | % 5.86/1.62 | GROUND_INST: instantiating (2) with all_15_2, all_17_2, all_3_0, simplifying % 5.86/1.62 | with (22), (27) gives: % 5.86/1.62 | (31) all_17_2 = all_15_2 % 5.86/1.62 | % 5.86/1.62 | GROUND_INST: instantiating (2) with all_11_0, all_17_2, all_3_0, simplifying % 5.86/1.62 | with (18), (27) gives: % 5.86/1.62 | (32) all_17_2 = all_11_0 % 5.86/1.62 | % 5.86/1.62 | COMBINE_EQS: (31), (32) imply: % 5.86/1.62 | (33) all_15_2 = all_11_0 % 5.86/1.62 | % 5.86/1.62 | REDUCE: (28), (30) imply: % 5.86/1.62 | (34) c(all_15_1) = all_17_0 % 5.86/1.62 | % 5.86/1.62 | REDUCE: (25), (30) imply: % 5.86/1.62 | (35) $i(all_15_1) % 5.86/1.62 | % 5.86/1.62 | BETA: splitting (29) gives: % 5.86/1.62 | % 5.86/1.62 | Case 1: % 5.86/1.62 | | % 5.86/1.62 | | (36) all_17_0 = 0 % 5.86/1.62 | | % 5.86/1.62 | | REDUCE: (34), (36) imply: % 5.86/1.62 | | (37) c(all_15_1) = 0 % 5.86/1.62 | | % 5.86/1.62 | | BETA: splitting (23) gives: % 5.86/1.62 | | % 5.86/1.62 | | Case 1: % 5.86/1.62 | | | % 5.86/1.62 | | | (38) all_15_0 = 0 % 5.86/1.62 | | | % 5.86/1.62 | | | REDUCE: (20), (38) imply: % 5.86/1.62 | | | (39) s(all_3_0, all_15_1) = 0 % 5.86/1.62 | | | % 5.86/1.62 | | | GROUND_INST: instantiating (8) with all_15_1, simplifying with (35), (39) % 5.86/1.62 | | | gives: % 5.86/1.62 | | | (40) p(all_15_1) = 0 % 5.86/1.62 | | | % 5.86/1.62 | | | GROUND_INST: instantiating (11) with all_15_1, simplifying with (35), (37) % 5.86/1.62 | | | gives: % 5.86/1.62 | | | (41) ? [v0: int] : ( ~ (v0 = 0) & p(all_15_1) = v0) % 5.86/1.62 | | | % 5.86/1.62 | | | DELTA: instantiating (41) with fresh symbol all_37_0 gives: % 5.86/1.62 | | | (42) ~ (all_37_0 = 0) & p(all_15_1) = all_37_0 % 5.86/1.62 | | | % 5.86/1.62 | | | ALPHA: (42) implies: % 5.86/1.62 | | | (43) ~ (all_37_0 = 0) % 5.86/1.62 | | | (44) p(all_15_1) = all_37_0 % 5.86/1.62 | | | % 5.86/1.62 | | | GROUND_INST: instantiating (3) with 0, all_37_0, all_15_1, simplifying % 5.86/1.62 | | | with (40), (44) gives: % 5.86/1.62 | | | (45) all_37_0 = 0 % 5.86/1.62 | | | % 5.86/1.62 | | | REDUCE: (43), (45) imply: % 5.86/1.62 | | | (46) $false % 5.86/1.62 | | | % 5.86/1.62 | | | CLOSE: (46) is inconsistent. % 5.86/1.62 | | | % 5.86/1.62 | | Case 2: % 5.86/1.62 | | | % 5.86/1.62 | | | (47) all_15_2 = 0 % 5.86/1.62 | | | % 5.86/1.62 | | | COMBINE_EQS: (33), (47) imply: % 5.86/1.62 | | | (48) all_11_0 = 0 % 5.86/1.62 | | | % 5.86/1.62 | | | REDUCE: (17), (48) imply: % 5.86/1.62 | | | (49) $false % 5.86/1.62 | | | % 5.86/1.62 | | | CLOSE: (49) is inconsistent. % 5.86/1.62 | | | % 5.86/1.62 | | End of split % 5.86/1.62 | | % 5.86/1.62 | Case 2: % 5.86/1.62 | | % 5.86/1.62 | | (50) all_17_2 = 0 % 5.86/1.62 | | % 5.86/1.62 | | COMBINE_EQS: (32), (50) imply: % 5.86/1.63 | | (51) all_11_0 = 0 % 5.86/1.63 | | % 5.86/1.63 | | SIMP: (51) implies: % 5.86/1.63 | | (52) all_11_0 = 0 % 5.86/1.63 | | % 5.86/1.63 | | REDUCE: (17), (52) imply: % 5.86/1.63 | | (53) $false % 5.86/1.63 | | % 5.86/1.63 | | CLOSE: (53) is inconsistent. % 5.86/1.63 | | % 5.86/1.63 | End of split % 5.86/1.63 | % 5.86/1.63 End of proof % 5.86/1.63 % SZS output end Proof for theBenchmark % 5.86/1.63 % 5.86/1.63 1009ms %------------------------------------------------------------------------------