%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS109+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 : n015.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 05:51:17 EDT 2023 % Result : Unsatisfiable 7.42s 1.69s % Output : Proof 10.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS109+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n015.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 02:06:55 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.57 ________ _____ % 0.20/0.57 ___ __ \_________(_)________________________________ % 0.20/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.57 % 0.20/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.57 (2023-06-19) % 0.20/0.57 % 0.20/0.57 (c) Philipp Rümmer, 2009-2023 % 0.20/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.57 Amanda Stjerna. % 0.20/0.57 Free software under BSD-3-Clause. % 0.20/0.57 % 0.20/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.57 % 0.20/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.59 Running up to 7 provers in parallel. % 0.20/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.98/1.05 Prover 1: Preprocessing ... % 2.98/1.05 Prover 4: Preprocessing ... % 3.17/1.09 Prover 0: Preprocessing ... % 3.17/1.09 Prover 3: Preprocessing ... % 3.17/1.09 Prover 6: Preprocessing ... % 3.17/1.10 Prover 2: Preprocessing ... % 3.17/1.10 Prover 5: Preprocessing ... % 5.70/1.47 Prover 5: Proving ... % 5.70/1.48 Prover 2: Proving ... % 6.00/1.50 Prover 1: Constructing countermodel ... % 6.00/1.51 Prover 6: Proving ... % 6.39/1.55 Prover 3: Constructing countermodel ... % 6.52/1.56 Prover 4: Constructing countermodel ... % 6.52/1.58 Prover 0: Proving ... % 7.04/1.63 Prover 1: gave up % 7.04/1.64 Prover 3: gave up % 7.04/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.04/1.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.42/1.69 Prover 2: proved (1090ms) % 7.42/1.69 % 7.42/1.69 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.42/1.69 % 7.42/1.69 Prover 5: stopped % 7.42/1.70 Prover 0: stopped % 7.42/1.70 Prover 6: stopped % 7.42/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.42/1.70 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.42/1.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.42/1.70 Prover 8: Preprocessing ... % 7.42/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.42/1.74 Prover 7: Preprocessing ... % 8.19/1.78 Prover 13: Preprocessing ... % 8.19/1.79 Prover 16: Preprocessing ... % 8.19/1.79 Prover 10: Preprocessing ... % 8.19/1.80 Prover 11: Preprocessing ... % 8.75/1.87 Prover 7: Warning: ignoring some quantifiers % 8.75/1.88 Prover 7: Constructing countermodel ... % 8.75/1.91 Prover 16: Warning: ignoring some quantifiers % 9.24/1.92 Prover 16: Constructing countermodel ... % 9.24/1.93 Prover 13: Warning: ignoring some quantifiers % 9.24/1.94 Prover 13: Constructing countermodel ... % 9.24/1.94 Prover 10: Warning: ignoring some quantifiers % 9.24/1.94 Prover 4: Found proof (size 44) % 9.24/1.94 Prover 4: proved (1348ms) % 9.24/1.95 Prover 7: stopped % 9.24/1.95 Prover 13: stopped % 9.24/1.95 Prover 10: Constructing countermodel ... % 9.24/1.95 Prover 16: stopped % 9.24/1.96 Prover 10: stopped % 9.24/1.96 Prover 8: Warning: ignoring some quantifiers % 9.24/1.97 Prover 8: Constructing countermodel ... % 9.24/1.98 Prover 8: stopped % 9.24/2.03 Prover 11: Constructing countermodel ... % 9.24/2.04 Prover 11: stopped % 9.24/2.04 % 9.24/2.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.24/2.04 % 9.24/2.05 % SZS output start Proof for theBenchmark % 9.24/2.05 Assumptions after simplification: % 9.24/2.05 --------------------------------- % 9.24/2.05 % 9.24/2.05 (axiom_11) % 10.03/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rs(v1, v0) = v2) | ~ % 10.03/2.08 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rinvS(v0, v1) = v3)) & ! % 10.03/2.08 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rinvS(v0, v1) = v2) | ~ % 10.03/2.08 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rs(v1, v0) = v3)) & ! % 10.03/2.08 [v0: $i] : ! [v1: $i] : ( ~ (rs(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 10.03/2.08 rinvS(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rinvS(v0, v1) = 0) | % 10.03/2.08 ~ $i(v1) | ~ $i(v0) | rs(v1, v0) = 0) % 10.03/2.08 % 10.03/2.08 (axiom_13) % 10.03/2.08 cUnsatisfiable(i2003_11_14_17_21_08508) = 0 & $i(i2003_11_14_17_21_08508) % 10.03/2.08 % 10.03/2.08 (axiom_14) % 10.03/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rf(v0, v1) = v2) | ~ % 10.03/2.08 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rs(v0, v1) = v3)) & ! % 10.03/2.08 [v0: $i] : ! [v1: $i] : ( ~ (rs(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | rf(v0, % 10.03/2.08 v1) = 0) % 10.03/2.08 % 10.03/2.08 (axiom_2) % 10.03/2.09 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (rf(v0, v2) = 0) | ~ % 10.03/2.09 (cUnsatisfiable(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : (( ~ (v3 % 10.03/2.09 = 0) & cpxcomp(v0) = v3) | ( ~ (v3 = 0) & ca_Ax2(v2) = v3))) & ! [v0: % 10.03/2.09 $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (ca_Ax2(v2) = 0) | ~ % 10.03/2.09 (cUnsatisfiable(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : (( ~ (v3 % 10.03/2.09 = 0) & rf(v0, v2) = v3) | ( ~ (v3 = 0) & cpxcomp(v0) = v3))) & ! [v0: % 10.03/2.09 $i] : ! [v1: int] : (v1 = 0 | ~ (cpxcomp(v0) = v1) | ~ $i(v0) | ? [v2: % 10.03/2.09 int] : ( ~ (v2 = 0) & cUnsatisfiable(v0) = v2)) & ! [v0: $i] : ! [v1: % 10.03/2.09 $i] : ( ~ (rf(v0, v1) = 0) | ~ (cpxcomp(v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 10.03/2.09 ? [v2: int] : ((v2 = 0 & cUnsatisfiable(v0) = 0) | ( ~ (v2 = 0) & ca_Ax2(v1) % 10.03/2.09 = v2))) & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (cpxcomp(v0) = % 10.03/2.09 v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: int] % 10.03/2.09 : ($i(v3) & ((v5 = 0 & v4 = 0 & rf(v0, v3) = 0 & ca_Ax2(v3) = 0) | ( ~ (v2 = % 10.03/2.09 0) & cUnsatisfiable(v0) = v2)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.03/2.09 (cpxcomp(v0) = 0) | ~ (ca_Ax2(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 10.03/2.09 int] : ((v2 = 0 & cUnsatisfiable(v0) = 0) | ( ~ (v2 = 0) & rf(v0, v1) = % 10.03/2.09 v2))) & ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | % 10.03/2.09 cpxcomp(v0) = 0) & ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | % 10.03/2.09 ? [v1: $i] : (rf(v0, v1) = 0 & ca_Ax2(v1) = 0 & $i(v1))) % 10.03/2.09 % 10.03/2.09 (axiom_3) % 10.03/2.09 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cp(v0) = v1) | ~ $i(v0) | ? [v2: % 10.03/2.09 $i] : (ra_Px1(v0, v2) = 0 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.03/2.09 (ra_Px1(v0, v1) = 0) | ~ (cp(v0) = 0) | ~ $i(v1) | ~ $i(v0)) % 10.03/2.09 % 10.03/2.09 (axiom_4) % 10.03/2.09 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (ra_Px1(v0, v2) = 0) | % 10.03/2.09 ~ (cpxcomp(v0) = v1) | ~ $i(v2) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 10.03/2.09 (cpxcomp(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (ra_Px1(v0, v1) = 0 & $i(v1))) % 10.03/2.09 % 10.03/2.09 (axiom_5) % 10.03/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (cp(v1) = v2) | ~ % 10.03/2.10 (ca_Ax2(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 10.03/2.10 rinvS(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 % 10.03/2.10 | ~ (ca_Vx3(v1) = v2) | ~ (ca_Ax2(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 10.03/2.10 [v3: int] : ( ~ (v3 = 0) & rinvF(v0, v1) = v3)) & ! [v0: $i] : ! [v1: int] % 10.03/2.10 : (v1 = 0 | ~ (ca_Ax2(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ? % 10.03/2.10 [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ($i(v5) & $i(v2) & % 10.03/2.10 ((v6 = 0 & ~ (v7 = 0) & rinvS(v0, v5) = 0 & cp(v5) = v7) | (v3 = 0 & ~ % 10.03/2.10 (v4 = 0) & rinvF(v0, v2) = 0 & ca_Vx3(v2) = v4)))) & ! [v0: $i] : ! % 10.03/2.10 [v1: $i] : ( ~ (rinvS(v0, v1) = 0) | ~ (ca_Ax2(v0) = 0) | ~ $i(v1) | ~ % 10.03/2.10 $i(v0) | cp(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rinvF(v0, v1) = 0) | % 10.03/2.10 ~ (ca_Ax2(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ca_Vx3(v1) = 0) % 10.03/2.10 % 10.03/2.10 (axiom_6) % 10.03/2.10 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (rs(v0, v2) = 0) | ~ % 10.03/2.10 (ca_Vx3(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 10.03/2.10 cp(v2) = v3)) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ % 10.03/2.10 (cp(v2) = 0) | ~ (ca_Vx3(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : % 10.03/2.10 ( ~ (v3 = 0) & rs(v0, v2) = v3)) & ! [v0: $i] : ( ~ (ca_Vx3(v0) = 0) | ~ % 10.03/2.10 $i(v0) | ? [v1: $i] : (rs(v0, v1) = 0 & cp(v1) = 0 & $i(v1))) % 10.03/2.10 % 10.03/2.10 (axiom_7) % 10.03/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (rf(v0, v2) = 0) | ~ % 10.03/2.10 (rf(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 10.03/2.10 % 10.03/2.10 (axiom_9) % 10.03/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rinvF(v0, v1) = v2) | % 10.03/2.10 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rf(v1, v0) = v3)) & ! % 10.03/2.10 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rf(v1, v0) = v2) | ~ % 10.03/2.10 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rinvF(v0, v1) = v3)) & ! % 10.03/2.10 [v0: $i] : ! [v1: $i] : ( ~ (rinvF(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 10.03/2.10 rf(v1, v0) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rf(v1, v0) = 0) | ~ % 10.03/2.10 $i(v1) | ~ $i(v0) | rinvF(v0, v1) = 0) % 10.03/2.10 % 10.03/2.10 (function-axioms) % 10.03/2.11 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.03/2.11 [v3: $i] : (v1 = v0 | ~ (rs(v3, v2) = v1) | ~ (rs(v3, v2) = v0)) & ! [v0: % 10.03/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.03/2.11 : (v1 = v0 | ~ (rinvS(v3, v2) = v1) | ~ (rinvS(v3, v2) = v0)) & ! [v0: % 10.03/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.03/2.11 : (v1 = v0 | ~ (rinvF1(v3, v2) = v1) | ~ (rinvF1(v3, v2) = v0)) & ! [v0: % 10.03/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.03/2.11 : (v1 = v0 | ~ (rinvF(v3, v2) = v1) | ~ (rinvF(v3, v2) = v0)) & ! [v0: % 10.03/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.03/2.11 : (v1 = v0 | ~ (rf1(v3, v2) = v1) | ~ (rf1(v3, v2) = v0)) & ! [v0: % 10.03/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.03/2.11 : (v1 = v0 | ~ (rf(v3, v2) = v1) | ~ (rf(v3, v2) = v0)) & ! [v0: % 10.03/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.03/2.11 : (v1 = v0 | ~ (ra_Px1(v3, v2) = v1) | ~ (ra_Px1(v3, v2) = v0)) & ! [v0: % 10.03/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.03/2.11 ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0: % 10.03/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.03/2.11 ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0: % 10.03/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.03/2.11 ~ (cpxcomp(v2) = v1) | ~ (cpxcomp(v2) = v0)) & ! [v0: MultipleValueBool] : % 10.03/2.11 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cp(v2) = v1) | ~ % 10.03/2.11 (cp(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.03/2.11 ! [v2: $i] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & % 10.03/2.11 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 10.03/2.11 v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0: % 10.03/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.03/2.11 ~ (ca_Vx3(v2) = v1) | ~ (ca_Vx3(v2) = v0)) & ! [v0: MultipleValueBool] : % 10.03/2.11 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ca_Ax2(v2) = v1) | ~ % 10.03/2.11 (ca_Ax2(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 10.03/2.11 : ! [v2: $i] : (v1 = v0 | ~ (cUnsatisfiable(v2) = v1) | ~ % 10.03/2.11 (cUnsatisfiable(v2) = v0)) % 10.03/2.11 % 10.03/2.11 Further assumptions not needed in the proof: % 10.03/2.11 -------------------------------------------- % 10.03/2.11 axiom_0, axiom_1, axiom_10, axiom_12, axiom_15, axiom_8, % 10.03/2.11 cUnsatisfiable_substitution_1, ca_Ax2_substitution_1, ca_Vx3_substitution_1, % 10.03/2.11 cowlNothing_substitution_1, cowlThing_substitution_1, cp_substitution_1, % 10.03/2.11 cpxcomp_substitution_1, ra_Px1_substitution_1, ra_Px1_substitution_2, % 10.03/2.11 rf1_substitution_1, rf1_substitution_2, rf_substitution_1, rf_substitution_2, % 10.03/2.11 rinvF1_substitution_1, rinvF1_substitution_2, rinvF_substitution_1, % 10.03/2.11 rinvF_substitution_2, rinvS_substitution_1, rinvS_substitution_2, % 10.03/2.11 rs_substitution_1, rs_substitution_2, xsd_integer_substitution_1, % 10.03/2.11 xsd_string_substitution_1 % 10.03/2.11 % 10.03/2.11 Those formulas are unsatisfiable: % 10.03/2.11 --------------------------------- % 10.03/2.11 % 10.03/2.11 Begin of proof % 10.03/2.11 | % 10.03/2.11 | ALPHA: (axiom_2) implies: % 10.03/2.11 | (1) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 10.03/2.11 | (rf(v0, v1) = 0 & ca_Ax2(v1) = 0 & $i(v1))) % 10.03/2.11 | (2) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | cpxcomp(v0) = % 10.03/2.11 | 0) % 10.03/2.11 | (3) ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (cpxcomp(v0) = v1) | ~ % 10.03/2.11 | $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : % 10.03/2.11 | ($i(v3) & ((v5 = 0 & v4 = 0 & rf(v0, v3) = 0 & ca_Ax2(v3) = 0) | ( ~ % 10.03/2.11 | (v2 = 0) & cUnsatisfiable(v0) = v2)))) % 10.03/2.11 | % 10.03/2.11 | ALPHA: (axiom_3) implies: % 10.03/2.11 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (ra_Px1(v0, v1) = 0) | ~ (cp(v0) = 0) % 10.03/2.11 | | ~ $i(v1) | ~ $i(v0)) % 10.03/2.11 | % 10.03/2.11 | ALPHA: (axiom_4) implies: % 10.03/2.11 | (5) ! [v0: $i] : ( ~ (cpxcomp(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 10.03/2.11 | (ra_Px1(v0, v1) = 0 & $i(v1))) % 10.03/2.11 | % 10.03/2.11 | ALPHA: (axiom_5) implies: % 10.03/2.11 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (rinvF(v0, v1) = 0) | ~ (ca_Ax2(v0) = % 10.03/2.11 | 0) | ~ $i(v1) | ~ $i(v0) | ca_Vx3(v1) = 0) % 10.03/2.11 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (rinvS(v0, v1) = 0) | ~ (ca_Ax2(v0) = % 10.03/2.11 | 0) | ~ $i(v1) | ~ $i(v0) | cp(v1) = 0) % 10.03/2.11 | % 10.03/2.11 | ALPHA: (axiom_6) implies: % 10.03/2.12 | (8) ! [v0: $i] : ( ~ (ca_Vx3(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (rs(v0, % 10.03/2.12 | v1) = 0 & cp(v1) = 0 & $i(v1))) % 10.03/2.12 | % 10.03/2.12 | ALPHA: (axiom_9) implies: % 10.03/2.12 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (rf(v1, v0) = 0) | ~ $i(v1) | ~ % 10.03/2.12 | $i(v0) | rinvF(v0, v1) = 0) % 10.03/2.12 | % 10.03/2.12 | ALPHA: (axiom_11) implies: % 10.03/2.12 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (rs(v1, v0) = 0) | ~ $i(v1) | ~ % 10.03/2.12 | $i(v0) | rinvS(v0, v1) = 0) % 10.03/2.12 | % 10.03/2.12 | ALPHA: (axiom_13) implies: % 10.03/2.12 | (11) $i(i2003_11_14_17_21_08508) % 10.03/2.12 | (12) cUnsatisfiable(i2003_11_14_17_21_08508) = 0 % 10.03/2.12 | % 10.03/2.12 | ALPHA: (axiom_14) implies: % 10.03/2.12 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (rs(v0, v1) = 0) | ~ $i(v1) | ~ % 10.03/2.12 | $i(v0) | rf(v0, v1) = 0) % 10.03/2.12 | % 10.03/2.12 | ALPHA: (function-axioms) implies: % 10.03/2.12 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 10.03/2.12 | : (v1 = v0 | ~ (cUnsatisfiable(v2) = v1) | ~ (cUnsatisfiable(v2) = % 10.03/2.12 | v0)) % 10.03/2.12 | % 10.03/2.12 | GROUND_INST: instantiating (2) with i2003_11_14_17_21_08508, simplifying with % 10.03/2.12 | (11), (12) gives: % 10.03/2.12 | (15) cpxcomp(i2003_11_14_17_21_08508) = 0 % 10.03/2.12 | % 10.03/2.12 | GROUND_INST: instantiating (1) with i2003_11_14_17_21_08508, simplifying with % 10.03/2.12 | (11), (12) gives: % 10.03/2.12 | (16) ? [v0: $i] : (rf(i2003_11_14_17_21_08508, v0) = 0 & ca_Ax2(v0) = 0 & % 10.03/2.12 | $i(v0)) % 10.03/2.12 | % 10.03/2.12 | DELTA: instantiating (16) with fresh symbol all_25_0 gives: % 10.03/2.12 | (17) rf(i2003_11_14_17_21_08508, all_25_0) = 0 & ca_Ax2(all_25_0) = 0 & % 10.03/2.12 | $i(all_25_0) % 10.03/2.12 | % 10.03/2.12 | ALPHA: (17) implies: % 10.03/2.12 | (18) $i(all_25_0) % 10.03/2.12 | (19) ca_Ax2(all_25_0) = 0 % 10.03/2.12 | (20) rf(i2003_11_14_17_21_08508, all_25_0) = 0 % 10.03/2.12 | % 10.03/2.12 | GROUND_INST: instantiating (5) with i2003_11_14_17_21_08508, simplifying with % 10.03/2.12 | (11), (15) gives: % 10.03/2.12 | (21) ? [v0: $i] : (ra_Px1(i2003_11_14_17_21_08508, v0) = 0 & $i(v0)) % 10.03/2.12 | % 10.03/2.12 | GROUND_INST: instantiating (3) with i2003_11_14_17_21_08508, 0, simplifying % 10.03/2.12 | with (11), (15) gives: % 10.03/2.12 | (22) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ($i(v1) & % 10.03/2.12 | ((v3 = 0 & v2 = 0 & rf(i2003_11_14_17_21_08508, v1) = 0 & ca_Ax2(v1) % 10.03/2.12 | = 0) | ( ~ (v0 = 0) & cUnsatisfiable(i2003_11_14_17_21_08508) = % 10.03/2.12 | v0))) % 10.03/2.12 | % 10.03/2.12 | GROUND_INST: instantiating (9) with all_25_0, i2003_11_14_17_21_08508, % 10.03/2.12 | simplifying with (11), (18), (20) gives: % 10.03/2.12 | (23) rinvF(all_25_0, i2003_11_14_17_21_08508) = 0 % 10.03/2.12 | % 10.03/2.12 | DELTA: instantiating (21) with fresh symbol all_33_0 gives: % 10.03/2.12 | (24) ra_Px1(i2003_11_14_17_21_08508, all_33_0) = 0 & $i(all_33_0) % 10.03/2.12 | % 10.03/2.12 | ALPHA: (24) implies: % 10.03/2.12 | (25) $i(all_33_0) % 10.03/2.12 | (26) ra_Px1(i2003_11_14_17_21_08508, all_33_0) = 0 % 10.03/2.12 | % 10.03/2.12 | DELTA: instantiating (22) with fresh symbols all_35_0, all_35_1, all_35_2, % 10.03/2.12 | all_35_3 gives: % 10.03/2.13 | (27) $i(all_35_2) & ((all_35_0 = 0 & all_35_1 = 0 & % 10.03/2.13 | rf(i2003_11_14_17_21_08508, all_35_2) = 0 & ca_Ax2(all_35_2) = 0) % 10.03/2.13 | | ( ~ (all_35_3 = 0) & cUnsatisfiable(i2003_11_14_17_21_08508) = % 10.03/2.13 | all_35_3)) % 10.03/2.13 | % 10.03/2.13 | ALPHA: (27) implies: % 10.03/2.13 | (28) $i(all_35_2) % 10.03/2.13 | (29) (all_35_0 = 0 & all_35_1 = 0 & rf(i2003_11_14_17_21_08508, all_35_2) = % 10.03/2.13 | 0 & ca_Ax2(all_35_2) = 0) | ( ~ (all_35_3 = 0) & % 10.03/2.13 | cUnsatisfiable(i2003_11_14_17_21_08508) = all_35_3) % 10.03/2.13 | % 10.03/2.13 | BETA: splitting (29) gives: % 10.03/2.13 | % 10.03/2.13 | Case 1: % 10.03/2.13 | | % 10.03/2.13 | | (30) all_35_0 = 0 & all_35_1 = 0 & rf(i2003_11_14_17_21_08508, all_35_2) % 10.03/2.13 | | = 0 & ca_Ax2(all_35_2) = 0 % 10.03/2.13 | | % 10.03/2.13 | | ALPHA: (30) implies: % 10.03/2.13 | | (31) ca_Ax2(all_35_2) = 0 % 10.03/2.13 | | (32) rf(i2003_11_14_17_21_08508, all_35_2) = 0 % 10.03/2.13 | | % 10.03/2.13 | | GROUND_INST: instantiating (axiom_7) with i2003_11_14_17_21_08508, all_25_0, % 10.03/2.13 | | all_35_2, simplifying with (11), (18), (20), (28), (32) gives: % 10.03/2.13 | | (33) all_35_2 = all_25_0 % 10.03/2.13 | | % 10.03/2.13 | | GROUND_INST: instantiating (6) with all_25_0, i2003_11_14_17_21_08508, % 10.03/2.13 | | simplifying with (11), (18), (19), (23) gives: % 10.03/2.13 | | (34) ca_Vx3(i2003_11_14_17_21_08508) = 0 % 10.03/2.13 | | % 10.03/2.13 | | GROUND_INST: instantiating (8) with i2003_11_14_17_21_08508, simplifying % 10.03/2.13 | | with (11), (34) gives: % 10.03/2.13 | | (35) ? [v0: $i] : (rs(i2003_11_14_17_21_08508, v0) = 0 & cp(v0) = 0 & % 10.03/2.13 | | $i(v0)) % 10.03/2.13 | | % 10.03/2.13 | | DELTA: instantiating (35) with fresh symbol all_52_0 gives: % 10.03/2.13 | | (36) rs(i2003_11_14_17_21_08508, all_52_0) = 0 & cp(all_52_0) = 0 & % 10.03/2.13 | | $i(all_52_0) % 10.03/2.13 | | % 10.03/2.13 | | ALPHA: (36) implies: % 10.03/2.13 | | (37) $i(all_52_0) % 10.03/2.13 | | (38) rs(i2003_11_14_17_21_08508, all_52_0) = 0 % 10.03/2.13 | | % 10.03/2.13 | | GROUND_INST: instantiating (10) with all_52_0, i2003_11_14_17_21_08508, % 10.03/2.13 | | simplifying with (11), (37), (38) gives: % 10.03/2.13 | | (39) rinvS(all_52_0, i2003_11_14_17_21_08508) = 0 % 10.03/2.13 | | % 10.03/2.13 | | GROUND_INST: instantiating (13) with i2003_11_14_17_21_08508, all_52_0, % 10.03/2.13 | | simplifying with (11), (37), (38) gives: % 10.03/2.13 | | (40) rf(i2003_11_14_17_21_08508, all_52_0) = 0 % 10.03/2.13 | | % 10.03/2.13 | | GROUND_INST: instantiating (axiom_7) with i2003_11_14_17_21_08508, all_25_0, % 10.03/2.13 | | all_52_0, simplifying with (11), (18), (20), (37), (40) gives: % 10.03/2.13 | | (41) all_52_0 = all_25_0 % 10.03/2.13 | | % 10.03/2.13 | | REDUCE: (39), (41) imply: % 10.03/2.13 | | (42) rinvS(all_25_0, i2003_11_14_17_21_08508) = 0 % 10.03/2.13 | | % 10.03/2.13 | | GROUND_INST: instantiating (7) with all_25_0, i2003_11_14_17_21_08508, % 10.03/2.13 | | simplifying with (11), (18), (19), (42) gives: % 10.03/2.13 | | (43) cp(i2003_11_14_17_21_08508) = 0 % 10.03/2.13 | | % 10.03/2.13 | | GROUND_INST: instantiating (4) with i2003_11_14_17_21_08508, all_33_0, % 10.03/2.13 | | simplifying with (11), (25), (26), (43) gives: % 10.03/2.13 | | (44) $false % 10.03/2.13 | | % 10.03/2.13 | | CLOSE: (44) is inconsistent. % 10.03/2.13 | | % 10.03/2.14 | Case 2: % 10.03/2.14 | | % 10.03/2.14 | | (45) ~ (all_35_3 = 0) & cUnsatisfiable(i2003_11_14_17_21_08508) = % 10.03/2.14 | | all_35_3 % 10.03/2.14 | | % 10.03/2.14 | | ALPHA: (45) implies: % 10.03/2.14 | | (46) ~ (all_35_3 = 0) % 10.03/2.14 | | (47) cUnsatisfiable(i2003_11_14_17_21_08508) = all_35_3 % 10.03/2.14 | | % 10.03/2.14 | | GROUND_INST: instantiating (14) with 0, all_35_3, i2003_11_14_17_21_08508, % 10.03/2.14 | | simplifying with (12), (47) gives: % 10.03/2.14 | | (48) all_35_3 = 0 % 10.03/2.14 | | % 10.03/2.14 | | REDUCE: (46), (48) imply: % 10.03/2.14 | | (49) $false % 10.03/2.14 | | % 10.03/2.14 | | CLOSE: (49) is inconsistent. % 10.03/2.14 | | % 10.03/2.14 | End of split % 10.03/2.14 | % 10.03/2.14 End of proof % 10.03/2.14 % SZS output end Proof for theBenchmark % 10.03/2.14 % 10.03/2.14 1562ms %------------------------------------------------------------------------------