%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS116+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 : n029.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 05:51:18 EDT 2023 % Result : Unsatisfiable 6.47s 1.80s % Output : Proof 10.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS116+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.34 % Computer : n029.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Mon Aug 28 02:28:56 EDT 2023 % 0.16/0.34 % 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 % 0.20/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.58 Running up to 7 provers in parallel. % 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 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 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 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 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 % 2.28/1.05 Prover 4: Preprocessing ... % 2.28/1.05 Prover 1: Preprocessing ... % 2.28/1.09 Prover 2: Preprocessing ... % 2.28/1.09 Prover 0: Preprocessing ... % 2.28/1.09 Prover 6: Preprocessing ... % 2.28/1.09 Prover 5: Preprocessing ... % 2.28/1.10 Prover 3: Preprocessing ... % 5.07/1.41 Prover 5: Proving ... % 5.07/1.43 Prover 2: Proving ... % 5.82/1.54 Prover 6: Proving ... % 5.82/1.55 Prover 3: Constructing countermodel ... % 5.82/1.58 Prover 1: Constructing countermodel ... % 6.47/1.60 Prover 4: Constructing countermodel ... % 6.47/1.66 Prover 0: Proving ... % 6.47/1.69 Prover 1: gave up % 6.47/1.69 Prover 3: gave up % 6.47/1.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.47/1.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.47/1.73 Prover 7: Preprocessing ... % 6.47/1.75 Prover 8: Preprocessing ... % 6.47/1.77 Prover 7: Warning: ignoring some quantifiers % 6.47/1.78 Prover 7: Constructing countermodel ... % 6.47/1.80 Prover 5: proved (1199ms) % 6.47/1.80 % 6.47/1.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.47/1.80 % 6.47/1.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.47/1.80 Prover 0: stopped % 6.47/1.80 Prover 2: stopped % 6.47/1.81 Prover 6: stopped % 6.47/1.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.47/1.83 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.47/1.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.82/1.85 Prover 13: Preprocessing ... % 7.82/1.85 Prover 11: Preprocessing ... % 7.82/1.86 Prover 10: Preprocessing ... % 7.82/1.87 Prover 16: Preprocessing ... % 7.82/1.89 Prover 10: Warning: ignoring some quantifiers % 7.82/1.90 Prover 10: Constructing countermodel ... % 7.82/1.91 Prover 16: Warning: ignoring some quantifiers % 7.82/1.92 Prover 16: Constructing countermodel ... % 7.82/1.92 Prover 13: Warning: ignoring some quantifiers % 7.82/1.93 Prover 13: Constructing countermodel ... % 8.83/1.94 Prover 8: Warning: ignoring some quantifiers % 8.88/1.96 Prover 8: Constructing countermodel ... % 9.36/2.01 Prover 4: Found proof (size 37) % 9.36/2.01 Prover 4: proved (1417ms) % 9.36/2.02 Prover 16: stopped % 9.36/2.02 Prover 8: stopped % 9.36/2.02 Prover 13: stopped % 9.36/2.02 Prover 10: stopped % 9.36/2.02 Prover 7: stopped % 9.65/2.06 Prover 11: Constructing countermodel ... % 9.65/2.07 Prover 11: stopped % 9.65/2.07 % 9.65/2.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.65/2.07 % 9.65/2.08 % SZS output start Proof for theBenchmark % 9.65/2.09 Assumptions after simplification: % 9.65/2.09 --------------------------------- % 9.65/2.09 % 9.65/2.09 (axiom_10) % 9.65/2.11 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (ca_Vx5(v0) = 0) | ~ % 9.65/2.12 (cc(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rr(v0, % 9.65/2.12 v1) = v3)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ca_Vx5(v0) = v1) % 9.65/2.12 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & rr(v0, v2) = 0 & % 9.65/2.12 cc(v2) = v3 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (rr(v0, v1) = 0) % 9.65/2.12 | ~ (ca_Vx5(v0) = 0) | ~ $i(v1) | ~ $i(v0) | cc(v1) = 0) % 9.65/2.12 % 9.65/2.12 (axiom_11) % 9.65/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (ca_Vx6(v0) = 0) | ~ % 9.65/2.12 (caxcomp(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 9.65/2.12 rinvS(v0, v1) = v3)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 9.65/2.12 (ca_Vx6(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 9.65/2.12 rinvS(v0, v2) = 0 & caxcomp(v2) = v3 & $i(v2))) & ! [v0: $i] : ! [v1: % 9.65/2.12 $i] : ( ~ (ca_Vx6(v0) = 0) | ~ (rinvS(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) % 9.65/2.12 | caxcomp(v1) = 0) % 9.65/2.12 % 9.65/2.12 (axiom_12) % 9.65/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (ca_Vx6(v1) = v2) | ~ % 9.65/2.13 (ca_Vx7(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 9.65/2.13 rinvP(v0, v1) = v3)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 9.65/2.13 (ca_Vx7(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 9.65/2.13 rinvP(v0, v2) = 0 & ca_Vx6(v2) = v3 & $i(v2))) & ! [v0: $i] : ! [v1: $i] % 9.65/2.13 : ( ~ (rinvP(v0, v1) = 0) | ~ (ca_Vx7(v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 9.65/2.13 ca_Vx6(v1) = 0) % 9.65/2.13 % 9.65/2.13 (axiom_13) % 9.65/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rinvP(v0, v1) = v2) | % 9.65/2.13 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rp(v1, v0) = v3)) & ! % 9.65/2.13 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ % 9.65/2.13 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rinvP(v0, v1) = v3)) & ! % 9.65/2.13 [v0: $i] : ! [v1: $i] : ( ~ (rinvP(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 9.65/2.13 rp(v1, v0) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rp(v1, v0) = 0) | ~ % 9.65/2.13 $i(v1) | ~ $i(v0) | rinvP(v0, v1) = 0) % 9.65/2.13 % 9.65/2.13 (axiom_14) % 9.65/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rr(v1, v0) = v2) | ~ % 9.65/2.14 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rinvR(v0, v1) = v3)) & ! % 9.65/2.14 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rinvR(v0, v1) = v2) | ~ % 9.65/2.14 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rr(v1, v0) = v3)) & ! % 9.65/2.14 [v0: $i] : ! [v1: $i] : ( ~ (rr(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 9.65/2.14 rinvR(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rinvR(v0, v1) = 0) | % 9.65/2.14 ~ $i(v1) | ~ $i(v0) | rr(v1, v0) = 0) % 9.65/2.14 % 9.65/2.14 (axiom_15) % 9.65/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rinvS(v0, v1) = v2) | % 9.65/2.14 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rs(v1, v0) = v3)) & ! % 9.65/2.14 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rs(v1, v0) = v2) | ~ % 9.65/2.14 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rinvS(v0, v1) = v3)) & ! % 9.65/2.14 [v0: $i] : ! [v1: $i] : ( ~ (rinvS(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 9.65/2.14 rs(v1, v0) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rs(v1, v0) = 0) | ~ % 9.65/2.14 $i(v1) | ~ $i(v0) | rinvS(v0, v1) = 0) % 9.65/2.14 % 9.65/2.14 (axiom_17) % 9.65/2.14 cUnsatisfiable(i2003_11_14_17_21_33997) = 0 & $i(i2003_11_14_17_21_33997) % 9.65/2.14 % 9.65/2.14 (axiom_2) % 9.65/2.15 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ca(v0) = v1) | ~ $i(v0) | ? [v2: % 9.65/2.15 int] : ( ~ (v2 = 0) & cUnsatisfiable(v0) = v2)) & ! [v0: $i] : ( ~ % 9.65/2.15 (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ca(v0) = 0) % 9.65/2.15 % 9.65/2.15 (axiom_3) % 9.65/2.15 ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (rs(v0, % 9.65/2.15 v1) = 0 & ca_Ax2(v1) = 0 & $i(v1))) % 9.65/2.15 % 9.65/2.15 (axiom_4) % 9.65/2.15 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ca(v0) = v1) | ~ $i(v0) | ? [v2: % 9.65/2.15 $i] : (ra_Px1(v0, v2) = 0 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 9.65/2.15 (ra_Px1(v0, v1) = 0) | ~ (ca(v0) = 0) | ~ $i(v1) | ~ $i(v0)) % 9.65/2.15 % 9.65/2.15 (axiom_5) % 9.65/2.15 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (caxcomp(v0) = v1) | % 9.65/2.15 ~ (ra_Px1(v0, v2) = 0) | ~ $i(v2) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 9.65/2.15 (caxcomp(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (ra_Px1(v0, v1) = 0 & $i(v1))) % 10.10/2.15 % 10.10/2.15 (axiom_6) % 10.10/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (cc(v0) = 0) | ~ % 10.10/2.15 (ca_Vx7(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 10.10/2.15 rinvR(v0, v1) = v3)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cc(v0) = % 10.10/2.15 v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ca_Vx7(v2) = % 10.10/2.15 v3 & rinvR(v0, v2) = 0 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.10/2.15 (cc(v0) = 0) | ~ (rinvR(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ca_Vx7(v1) = % 10.10/2.15 0) % 10.10/2.15 % 10.10/2.15 (axiom_7) % 10.10/2.17 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ (rr(v0, % 10.10/2.17 v3) = 0) | ~ (rp(v0, v2) = 0) | ~ (ca_Ax2(v0) = v1) | ~ $i(v3) | ~ % 10.10/2.17 $i(v2) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ? [v6: int] : ? [v7: % 10.10/2.17 int] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : ? % 10.10/2.17 [v12: $i] : ? [v13: int] : ? [v14: int] : ? [v15: $i] : ? [v16: int] : % 10.10/2.17 ? [v17: int] : ($i(v15) & $i(v12) & $i(v9) & $i(v4) & ((v16 = 0 & ~ (v17 = % 10.10/2.17 0) & ca_Vx3(v15) = v17 & rp(v0, v15) = 0) | (v13 = 0 & ~ (v14 = 0) % 10.10/2.17 & ca_Vx5(v12) = v14 & rp(v0, v12) = 0) | (v10 = 0 & ~ (v11 = 0) & % 10.10/2.17 rr(v0, v9) = 0 & cc(v9) = v11) | (v5 = 0 & ~ (v6 = 0) & ca_Vx4(v4) = % 10.10/2.17 v6 & rp(v0, v4) = 0) | ( ~ (v8 = 0) & cowlThing(v3) = v8) | ( ~ (v7 = % 10.10/2.17 0) & cowlThing(v2) = v7)))) & ! [v0: $i] : ! [v1: int] : ! [v2: % 10.10/2.17 $i] : ! [v3: $i] : (v1 = 0 | ~ (rr(v0, v3) = 0) | ~ (ca_Ax2(v0) = v1) | % 10.10/2.17 ~ (cowlThing(v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: $i] : ? % 10.10/2.17 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: $i] : ? % 10.10/2.17 [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : ? [v14: int] : % 10.10/2.17 ? [v15: $i] : ? [v16: int] : ? [v17: int] : ($i(v15) & $i(v12) & $i(v9) & % 10.10/2.17 $i(v4) & ((v16 = 0 & ~ (v17 = 0) & ca_Vx3(v15) = v17 & rp(v0, v15) = 0) | % 10.10/2.17 (v13 = 0 & ~ (v14 = 0) & ca_Vx5(v12) = v14 & rp(v0, v12) = 0) | (v10 = % 10.10/2.17 0 & ~ (v11 = 0) & rr(v0, v9) = 0 & cc(v9) = v11) | (v5 = 0 & ~ (v6 = % 10.10/2.17 0) & ca_Vx4(v4) = v6 & rp(v0, v4) = 0) | ( ~ (v8 = 0) & % 10.10/2.17 cowlThing(v3) = v8) | ( ~ (v7 = 0) & rp(v0, v2) = v7)))) & ! [v0: $i] % 10.10/2.17 : ! [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ (rp(v0, v2) = 0) | % 10.10/2.17 ~ (ca_Ax2(v0) = v1) | ~ (cowlThing(v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 10.10/2.17 $i(v0) | ? [v4: $i] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: % 10.10/2.17 int] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : ? [v12: $i] : ? % 10.10/2.17 [v13: int] : ? [v14: int] : ? [v15: $i] : ? [v16: int] : ? [v17: int] : % 10.10/2.17 ($i(v15) & $i(v12) & $i(v9) & $i(v4) & ((v16 = 0 & ~ (v17 = 0) & % 10.10/2.17 ca_Vx3(v15) = v17 & rp(v0, v15) = 0) | (v13 = 0 & ~ (v14 = 0) & % 10.10/2.17 ca_Vx5(v12) = v14 & rp(v0, v12) = 0) | (v10 = 0 & ~ (v11 = 0) & % 10.10/2.17 rr(v0, v9) = 0 & cc(v9) = v11) | (v5 = 0 & ~ (v6 = 0) & ca_Vx4(v4) = % 10.10/2.17 v6 & rp(v0, v4) = 0) | ( ~ (v8 = 0) & rr(v0, v3) = v8) | ( ~ (v7 = 0) % 10.10/2.17 & cowlThing(v2) = v7)))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : % 10.10/2.17 ! [v3: $i] : (v1 = 0 | ~ (ca_Ax2(v0) = v1) | ~ (cowlThing(v3) = 0) | ~ % 10.10/2.17 (cowlThing(v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: $i] : ? % 10.10/2.17 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: $i] : ? % 10.10/2.17 [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : ? [v14: int] : % 10.10/2.17 ? [v15: $i] : ? [v16: int] : ? [v17: int] : ($i(v15) & $i(v12) & $i(v9) & % 10.10/2.17 $i(v4) & ((v16 = 0 & ~ (v17 = 0) & ca_Vx3(v15) = v17 & rp(v0, v15) = 0) | % 10.10/2.17 (v13 = 0 & ~ (v14 = 0) & ca_Vx5(v12) = v14 & rp(v0, v12) = 0) | (v10 = % 10.10/2.17 0 & ~ (v11 = 0) & rr(v0, v9) = 0 & cc(v9) = v11) | (v5 = 0 & ~ (v6 = % 10.10/2.17 0) & ca_Vx4(v4) = v6 & rp(v0, v4) = 0) | ( ~ (v8 = 0) & rr(v0, v3) = % 10.10/2.17 v8) | ( ~ (v7 = 0) & rp(v0, v2) = v7)))) & ! [v0: $i] : ! [v1: $i] : % 10.10/2.17 ! [v2: int] : (v2 = 0 | ~ (ca_Vx4(v1) = v2) | ~ (ca_Ax2(v0) = 0) | ~ % 10.10/2.17 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rp(v0, v1) = v3)) & ! % 10.10/2.17 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (ca_Vx5(v1) = v2) | ~ % 10.10/2.17 (ca_Ax2(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 10.10/2.17 rp(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 10.10/2.17 ~ (ca_Vx3(v1) = v2) | ~ (ca_Ax2(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 10.10/2.17 int] : ( ~ (v3 = 0) & rp(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! % 10.10/2.17 [v2: int] : (v2 = 0 | ~ (cc(v1) = v2) | ~ (ca_Ax2(v0) = 0) | ~ $i(v1) | ~ % 10.10/2.17 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rr(v0, v1) = v3)) & ! [v0: $i] : ! % 10.10/2.17 [v1: $i] : ( ~ (rr(v0, v1) = 0) | ~ (ca_Ax2(v0) = 0) | ~ $i(v1) | ~ $i(v0) % 10.10/2.17 | cc(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rp(v0, v1) = 0) | ~ % 10.10/2.17 (ca_Ax2(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ca_Vx4(v1) = 0) & ! [v0: $i] : % 10.10/2.17 ! [v1: $i] : ( ~ (rp(v0, v1) = 0) | ~ (ca_Ax2(v0) = 0) | ~ $i(v1) | ~ % 10.10/2.17 $i(v0) | ca_Vx5(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rp(v0, v1) = 0) % 10.10/2.17 | ~ (ca_Ax2(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ca_Vx3(v1) = 0) & ! [v0: % 10.10/2.17 $i] : ( ~ (ca_Ax2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (rr(v0, v1) = 0 & % 10.10/2.17 cowlThing(v1) = 0 & $i(v1))) & ! [v0: $i] : ( ~ (ca_Ax2(v0) = 0) | ~ % 10.10/2.17 $i(v0) | ? [v1: $i] : (rp(v0, v1) = 0 & cowlThing(v1) = 0 & $i(v1))) % 10.10/2.17 % 10.10/2.17 (axiom_8) % 10.10/2.18 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (rr(v0, v2) = 0) | ~ % 10.10/2.18 (ca_Vx3(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 10.10/2.18 cowlThing(v2) = v3)) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 % 10.10/2.18 | ~ (ca_Vx3(v0) = v1) | ~ (cowlThing(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? % 10.10/2.18 [v3: int] : ( ~ (v3 = 0) & rr(v0, v2) = v3)) & ! [v0: $i] : ( ~ (ca_Vx3(v0) % 10.10/2.18 = 0) | ~ $i(v0) | ? [v1: $i] : (rr(v0, v1) = 0 & cowlThing(v1) = 0 & % 10.10/2.18 $i(v1))) % 10.10/2.18 % 10.10/2.18 Further assumptions not needed in the proof: % 10.10/2.18 -------------------------------------------- % 10.10/2.18 axiom_0, axiom_1, axiom_16, axiom_9 % 10.10/2.18 % 10.10/2.18 Those formulas are unsatisfiable: % 10.10/2.18 --------------------------------- % 10.10/2.18 % 10.10/2.18 Begin of proof % 10.10/2.18 | % 10.10/2.18 | ALPHA: (axiom_2) implies: % 10.10/2.18 | (1) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ca(v0) = 0) % 10.10/2.18 | % 10.10/2.18 | ALPHA: (axiom_4) implies: % 10.10/2.18 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (ra_Px1(v0, v1) = 0) | ~ (ca(v0) = 0) % 10.10/2.18 | | ~ $i(v1) | ~ $i(v0)) % 10.10/2.18 | % 10.10/2.18 | ALPHA: (axiom_5) implies: % 10.10/2.18 | (3) ! [v0: $i] : ( ~ (caxcomp(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 10.10/2.18 | (ra_Px1(v0, v1) = 0 & $i(v1))) % 10.10/2.18 | % 10.10/2.18 | ALPHA: (axiom_6) implies: % 10.10/2.18 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cc(v0) = 0) | ~ (rinvR(v0, v1) = 0) | % 10.10/2.18 | ~ $i(v1) | ~ $i(v0) | ca_Vx7(v1) = 0) % 10.10/2.18 | % 10.10/2.18 | ALPHA: (axiom_7) implies: % 10.10/2.18 | (5) ! [v0: $i] : ( ~ (ca_Ax2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (rp(v0, % 10.10/2.18 | v1) = 0 & cowlThing(v1) = 0 & $i(v1))) % 10.10/2.18 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (rp(v0, v1) = 0) | ~ (ca_Ax2(v0) = 0) % 10.10/2.18 | | ~ $i(v1) | ~ $i(v0) | ca_Vx3(v1) = 0) % 10.10/2.18 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (rp(v0, v1) = 0) | ~ (ca_Ax2(v0) = 0) % 10.10/2.18 | | ~ $i(v1) | ~ $i(v0) | ca_Vx5(v1) = 0) % 10.10/2.18 | % 10.10/2.18 | ALPHA: (axiom_8) implies: % 10.10/2.19 | (8) ! [v0: $i] : ( ~ (ca_Vx3(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (rr(v0, % 10.10/2.19 | v1) = 0 & cowlThing(v1) = 0 & $i(v1))) % 10.10/2.19 | % 10.10/2.19 | ALPHA: (axiom_10) implies: % 10.10/2.19 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (rr(v0, v1) = 0) | ~ (ca_Vx5(v0) = 0) % 10.10/2.19 | | ~ $i(v1) | ~ $i(v0) | cc(v1) = 0) % 10.10/2.19 | % 10.10/2.19 | ALPHA: (axiom_11) implies: % 10.10/2.19 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (ca_Vx6(v0) = 0) | ~ (rinvS(v0, v1) = % 10.10/2.19 | 0) | ~ $i(v1) | ~ $i(v0) | caxcomp(v1) = 0) % 10.10/2.19 | % 10.10/2.19 | ALPHA: (axiom_12) implies: % 10.10/2.19 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (rinvP(v0, v1) = 0) | ~ (ca_Vx7(v0) = % 10.10/2.19 | 0) | ~ $i(v1) | ~ $i(v0) | ca_Vx6(v1) = 0) % 10.10/2.19 | % 10.10/2.19 | ALPHA: (axiom_13) implies: % 10.10/2.19 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (rp(v1, v0) = 0) | ~ $i(v1) | ~ % 10.10/2.19 | $i(v0) | rinvP(v0, v1) = 0) % 10.10/2.19 | % 10.10/2.19 | ALPHA: (axiom_14) implies: % 10.27/2.19 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (rr(v1, v0) = 0) | ~ $i(v1) | ~ % 10.27/2.19 | $i(v0) | rinvR(v0, v1) = 0) % 10.27/2.19 | % 10.27/2.19 | ALPHA: (axiom_15) implies: % 10.27/2.19 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (rs(v1, v0) = 0) | ~ $i(v1) | ~ % 10.27/2.19 | $i(v0) | rinvS(v0, v1) = 0) % 10.27/2.19 | % 10.27/2.19 | ALPHA: (axiom_17) implies: % 10.27/2.19 | (15) $i(i2003_11_14_17_21_33997) % 10.27/2.19 | (16) cUnsatisfiable(i2003_11_14_17_21_33997) = 0 % 10.27/2.19 | % 10.27/2.19 | GROUND_INST: instantiating (1) with i2003_11_14_17_21_33997, simplifying with % 10.27/2.19 | (15), (16) gives: % 10.27/2.19 | (17) ca(i2003_11_14_17_21_33997) = 0 % 10.27/2.19 | % 10.27/2.19 | GROUND_INST: instantiating (axiom_3) with i2003_11_14_17_21_33997, simplifying % 10.27/2.19 | with (15), (16) gives: % 10.27/2.20 | (18) ? [v0: $i] : (rs(i2003_11_14_17_21_33997, v0) = 0 & ca_Ax2(v0) = 0 & % 10.27/2.20 | $i(v0)) % 10.27/2.20 | % 10.27/2.20 | DELTA: instantiating (18) with fresh symbol all_27_0 gives: % 10.27/2.20 | (19) rs(i2003_11_14_17_21_33997, all_27_0) = 0 & ca_Ax2(all_27_0) = 0 & % 10.27/2.20 | $i(all_27_0) % 10.27/2.20 | % 10.27/2.20 | ALPHA: (19) implies: % 10.27/2.20 | (20) $i(all_27_0) % 10.27/2.20 | (21) ca_Ax2(all_27_0) = 0 % 10.27/2.20 | (22) rs(i2003_11_14_17_21_33997, all_27_0) = 0 % 10.27/2.20 | % 10.27/2.20 | GROUND_INST: instantiating (5) with all_27_0, simplifying with (20), (21) % 10.27/2.20 | gives: % 10.27/2.20 | (23) ? [v0: $i] : (rp(all_27_0, v0) = 0 & cowlThing(v0) = 0 & $i(v0)) % 10.27/2.20 | % 10.27/2.20 | GROUND_INST: instantiating (14) with all_27_0, i2003_11_14_17_21_33997, % 10.27/2.20 | simplifying with (15), (20), (22) gives: % 10.27/2.20 | (24) rinvS(all_27_0, i2003_11_14_17_21_33997) = 0 % 10.27/2.20 | % 10.27/2.20 | DELTA: instantiating (23) with fresh symbol all_35_0 gives: % 10.27/2.20 | (25) rp(all_27_0, all_35_0) = 0 & cowlThing(all_35_0) = 0 & $i(all_35_0) % 10.27/2.20 | % 10.27/2.20 | ALPHA: (25) implies: % 10.27/2.20 | (26) $i(all_35_0) % 10.27/2.20 | (27) rp(all_27_0, all_35_0) = 0 % 10.27/2.20 | % 10.27/2.20 | GROUND_INST: instantiating (7) with all_27_0, all_35_0, simplifying with (20), % 10.27/2.20 | (21), (26), (27) gives: % 10.27/2.20 | (28) ca_Vx5(all_35_0) = 0 % 10.27/2.20 | % 10.27/2.20 | GROUND_INST: instantiating (6) with all_27_0, all_35_0, simplifying with (20), % 10.27/2.20 | (21), (26), (27) gives: % 10.27/2.20 | (29) ca_Vx3(all_35_0) = 0 % 10.27/2.20 | % 10.27/2.20 | GROUND_INST: instantiating (12) with all_35_0, all_27_0, simplifying with % 10.27/2.20 | (20), (26), (27) gives: % 10.27/2.20 | (30) rinvP(all_35_0, all_27_0) = 0 % 10.27/2.20 | % 10.27/2.20 | GROUND_INST: instantiating (8) with all_35_0, simplifying with (26), (29) % 10.27/2.20 | gives: % 10.27/2.20 | (31) ? [v0: $i] : (rr(all_35_0, v0) = 0 & cowlThing(v0) = 0 & $i(v0)) % 10.27/2.20 | % 10.27/2.20 | DELTA: instantiating (31) with fresh symbol all_53_0 gives: % 10.27/2.20 | (32) rr(all_35_0, all_53_0) = 0 & cowlThing(all_53_0) = 0 & $i(all_53_0) % 10.27/2.20 | % 10.27/2.20 | ALPHA: (32) implies: % 10.27/2.20 | (33) $i(all_53_0) % 10.27/2.20 | (34) rr(all_35_0, all_53_0) = 0 % 10.27/2.20 | % 10.27/2.20 | GROUND_INST: instantiating (9) with all_35_0, all_53_0, simplifying with (26), % 10.27/2.20 | (28), (33), (34) gives: % 10.27/2.20 | (35) cc(all_53_0) = 0 % 10.27/2.20 | % 10.27/2.20 | GROUND_INST: instantiating (13) with all_53_0, all_35_0, simplifying with % 10.27/2.20 | (26), (33), (34) gives: % 10.27/2.20 | (36) rinvR(all_53_0, all_35_0) = 0 % 10.27/2.20 | % 10.27/2.20 | GROUND_INST: instantiating (4) with all_53_0, all_35_0, simplifying with (26), % 10.27/2.20 | (33), (35), (36) gives: % 10.27/2.20 | (37) ca_Vx7(all_35_0) = 0 % 10.27/2.20 | % 10.27/2.21 | GROUND_INST: instantiating (11) with all_35_0, all_27_0, simplifying with % 10.27/2.21 | (20), (26), (30), (37) gives: % 10.27/2.21 | (38) ca_Vx6(all_27_0) = 0 % 10.27/2.21 | % 10.27/2.21 | GROUND_INST: instantiating (10) with all_27_0, i2003_11_14_17_21_33997, % 10.27/2.21 | simplifying with (15), (20), (24), (38) gives: % 10.27/2.21 | (39) caxcomp(i2003_11_14_17_21_33997) = 0 % 10.27/2.21 | % 10.27/2.21 | GROUND_INST: instantiating (3) with i2003_11_14_17_21_33997, simplifying with % 10.27/2.21 | (15), (39) gives: % 10.27/2.21 | (40) ? [v0: $i] : (ra_Px1(i2003_11_14_17_21_33997, v0) = 0 & $i(v0)) % 10.27/2.21 | % 10.27/2.21 | DELTA: instantiating (40) with fresh symbol all_89_0 gives: % 10.27/2.21 | (41) ra_Px1(i2003_11_14_17_21_33997, all_89_0) = 0 & $i(all_89_0) % 10.27/2.21 | % 10.27/2.21 | ALPHA: (41) implies: % 10.27/2.21 | (42) $i(all_89_0) % 10.27/2.21 | (43) ra_Px1(i2003_11_14_17_21_33997, all_89_0) = 0 % 10.27/2.21 | % 10.27/2.21 | GROUND_INST: instantiating (2) with i2003_11_14_17_21_33997, all_89_0, % 10.27/2.21 | simplifying with (15), (17), (42), (43) gives: % 10.27/2.21 | (44) $false % 10.27/2.21 | % 10.27/2.21 | CLOSE: (44) is inconsistent. % 10.27/2.21 | % 10.27/2.21 End of proof % 10.27/2.21 % SZS output end Proof for theBenchmark % 10.27/2.21 % 10.27/2.21 1637ms %------------------------------------------------------------------------------