%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE089+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n031.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 05:34:30 EDT 2023 % Result : Theorem 10.51s 2.19s % Output : Proof 16.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : KLE089+1 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n031.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 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 11:50:56 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 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.51/1.06 Prover 1: Preprocessing ... % 2.51/1.06 Prover 4: Preprocessing ... % 2.51/1.10 Prover 3: Preprocessing ... % 2.51/1.10 Prover 2: Preprocessing ... % 2.51/1.10 Prover 0: Preprocessing ... % 2.51/1.10 Prover 6: Preprocessing ... % 2.51/1.10 Prover 5: Preprocessing ... % 5.01/1.42 Prover 1: Constructing countermodel ... % 5.01/1.43 Prover 6: Constructing countermodel ... % 5.01/1.43 Prover 3: Constructing countermodel ... % 5.01/1.45 Prover 5: Proving ... % 5.34/1.49 Prover 0: Proving ... % 5.34/1.53 Prover 4: Constructing countermodel ... % 5.94/1.56 Prover 2: Proving ... % 6.69/1.65 Prover 3: gave up % 6.69/1.65 Prover 6: gave up % 6.83/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.83/1.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.83/1.68 Prover 8: Preprocessing ... % 6.83/1.69 Prover 1: gave up % 6.83/1.71 Prover 7: Preprocessing ... % 6.83/1.71 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 7.27/1.73 Prover 9: Preprocessing ... % 7.58/1.77 Prover 8: Warning: ignoring some quantifiers % 7.58/1.80 Prover 8: Constructing countermodel ... % 7.58/1.83 Prover 7: Constructing countermodel ... % 8.49/1.88 Prover 9: Constructing countermodel ... % 8.49/1.97 Prover 8: gave up % 8.49/1.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.49/1.99 Prover 10: Preprocessing ... % 10.13/2.12 Prover 10: Constructing countermodel ... % 10.51/2.18 Prover 9: proved (470ms) % 10.51/2.18 % 10.51/2.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.51/2.19 % 10.51/2.19 Prover 0: stopped % 10.51/2.21 Prover 5: stopped % 10.51/2.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.51/2.22 Prover 2: stopped % 10.51/2.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.51/2.23 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.51/2.23 Prover 11: Preprocessing ... % 10.51/2.23 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 10.51/2.23 Prover 13: Preprocessing ... % 10.51/2.24 Prover 10: gave up % 10.51/2.24 Prover 19: Preprocessing ... % 11.19/2.25 Prover 16: Preprocessing ... % 11.49/2.31 Prover 13: Warning: ignoring some quantifiers % 11.49/2.31 Prover 19: Warning: ignoring some quantifiers % 11.49/2.31 Prover 13: Constructing countermodel ... % 11.49/2.32 Prover 19: Constructing countermodel ... % 11.86/2.34 Prover 11: Constructing countermodel ... % 11.94/2.35 Prover 16: Warning: ignoring some quantifiers % 11.94/2.35 Prover 16: Constructing countermodel ... % 12.44/2.41 Prover 13: gave up % 12.44/2.41 Prover 19: gave up % 15.55/2.87 Prover 4: Found proof (size 54) % 15.55/2.87 Prover 4: proved (2229ms) % 15.55/2.87 Prover 16: stopped % 15.55/2.87 Prover 7: stopped % 15.55/2.87 Prover 11: stopped % 15.55/2.87 % 15.55/2.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.55/2.87 % 15.55/2.88 % SZS output start Proof for theBenchmark % 15.55/2.88 Assumptions after simplification: % 15.55/2.88 --------------------------------- % 15.55/2.88 % 15.55/2.88 (additive_associativity) % 15.55/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.55/2.91 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 15.55/2.91 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 & % 15.55/2.91 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 15.55/2.91 : ! [v4: $i] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ % 15.55/2.91 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 & % 15.55/2.91 addition(v2, v1) = v5 & $i(v5) & $i(v4))) % 15.55/2.91 % 15.55/2.91 (additive_commutativity) % 15.55/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~ % 15.55/2.91 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 15.55/2.91 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 15.55/2.91 (addition(v1, v0) = v2 & $i(v2))) % 15.55/2.91 % 15.55/2.91 (additive_idempotence) % 15.55/2.91 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0)) % 15.55/2.91 % 15.55/2.91 (additive_identity) % 15.55/2.91 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) % 15.55/2.91 | ~ $i(v0)) % 15.55/2.91 % 15.55/2.91 (domain1) % 15.55/2.91 $i(zero) & ! [v0: $i] : ! [v1: $i] : ( ~ (antidomain(v0) = v1) | ~ $i(v0) | % 15.55/2.91 multiplication(v1, v0) = zero) % 15.55/2.91 % 15.55/2.91 (domain2) % 15.55/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.55/2.92 (antidomain(v2) = v3) | ~ (antidomain(v1) = v2) | ~ (multiplication(v0, % 15.55/2.92 v3) = v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: % 15.55/2.92 $i] : (antidomain(v5) = v6 & antidomain(v4) = v7 & multiplication(v0, v1) % 15.55/2.92 = v5 & addition(v6, v7) = v7 & $i(v7) & $i(v6) & $i(v5))) & ! [v0: $i] : % 15.55/2.92 ! [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v0, v1) = v2) | ~ $i(v1) | ~ % 15.55/2.92 $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 15.55/2.92 : (antidomain(v6) = v7 & antidomain(v4) = v5 & antidomain(v2) = v3 & % 15.55/2.92 antidomain(v1) = v4 & multiplication(v0, v5) = v6 & addition(v3, v7) = v7 % 15.55/2.92 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3))) % 15.55/2.92 % 15.55/2.92 (domain4) % 15.55/2.92 ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 15.55/2.92 (antidomain(v2) = v1 & antidomain(v0) = v2 & $i(v2) & $i(v1))) & ! [v0: $i] % 15.55/2.92 : ! [v1: $i] : ( ~ (antidomain(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 15.55/2.92 (domain(v0) = v2 & antidomain(v1) = v2 & $i(v2))) % 15.55/2.92 % 15.55/2.92 (goals) % 15.55/2.92 $i(zero) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 15.55/2.92 : ( ~ (v4 = zero) & domain(v0) = v2 & antidomain(v1) = v3 & multiplication(v2, % 15.55/2.92 v1) = v4 & addition(v2, v3) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 15.55/2.92 $i(v0)) % 15.55/2.92 % 15.55/2.92 (left_distributivity) % 15.55/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.55/2.92 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | % 15.55/2.92 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 15.55/2.92 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) & % 15.55/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.55/2.92 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~ % 15.55/2.92 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) = % 15.55/2.92 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5) % 15.55/2.92 & $i(v4))) % 15.55/2.92 % 15.55/2.92 (function-axioms) % 15.55/2.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.55/2.92 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 15.55/2.92 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.55/2.92 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0: % 15.55/2.92 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3, % 15.55/2.92 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.55/2.92 [v2: $i] : (v1 = v0 | ~ (codomain(v2) = v1) | ~ (codomain(v2) = v0)) & ! % 15.55/2.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (coantidomain(v2) = v1) | % 15.55/2.92 ~ (coantidomain(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 15.55/2.92 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) & ! [v0: $i] : ! [v1: % 15.55/2.92 $i] : ! [v2: $i] : (v1 = v0 | ~ (antidomain(v2) = v1) | ~ (antidomain(v2) % 15.55/2.92 = v0)) % 15.55/2.92 % 15.55/2.92 Further assumptions not needed in the proof: % 15.55/2.92 -------------------------------------------- % 15.55/2.92 codomain1, codomain2, codomain3, codomain4, domain3, left_annihilation, % 15.55/2.92 multiplicative_associativity, multiplicative_left_identity, % 15.55/2.92 multiplicative_right_identity, order, right_annihilation, right_distributivity % 15.55/2.92 % 15.55/2.92 Those formulas are unsatisfiable: % 15.55/2.92 --------------------------------- % 15.55/2.92 % 15.55/2.92 Begin of proof % 15.55/2.93 | % 16.06/2.93 | ALPHA: (additive_commutativity) implies: % 16.06/2.93 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | % 16.06/2.93 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) % 16.06/2.93 | % 16.06/2.93 | ALPHA: (additive_associativity) implies: % 16.06/2.93 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 16.06/2.93 | ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ $i(v2) | % 16.06/2.93 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 & % 16.06/2.93 | addition(v2, v1) = v5 & $i(v5) & $i(v4))) % 16.06/2.93 | % 16.06/2.93 | ALPHA: (additive_identity) implies: % 16.06/2.93 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) | % 16.06/2.93 | ~ $i(v0)) % 16.06/2.93 | % 16.06/2.93 | ALPHA: (left_distributivity) implies: % 16.06/2.93 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 16.06/2.93 | ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ % 16.06/2.93 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 16.06/2.93 | (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & % 16.06/2.93 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 16.06/2.93 | % 16.06/2.93 | ALPHA: (domain1) implies: % 16.06/2.93 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (antidomain(v0) = v1) | ~ $i(v0) | % 16.06/2.93 | multiplication(v1, v0) = zero) % 16.06/2.93 | % 16.06/2.93 | ALPHA: (domain2) implies: % 16.06/2.93 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v0, v1) = % 16.06/2.93 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 16.06/2.93 | $i] : ? [v6: $i] : ? [v7: $i] : (antidomain(v6) = v7 & % 16.06/2.93 | antidomain(v4) = v5 & antidomain(v2) = v3 & antidomain(v1) = v4 & % 16.06/2.93 | multiplication(v0, v5) = v6 & addition(v3, v7) = v7 & $i(v7) & % 16.06/2.93 | $i(v6) & $i(v5) & $i(v4) & $i(v3))) % 16.06/2.93 | % 16.06/2.93 | ALPHA: (domain4) implies: % 16.06/2.93 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | ? [v2: % 16.06/2.93 | $i] : (antidomain(v2) = v1 & antidomain(v0) = v2 & $i(v2) & % 16.06/2.93 | $i(v1))) % 16.06/2.93 | % 16.06/2.93 | ALPHA: (goals) implies: % 16.06/2.93 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( % 16.06/2.93 | ~ (v4 = zero) & domain(v0) = v2 & antidomain(v1) = v3 & % 16.06/2.93 | multiplication(v2, v1) = v4 & addition(v2, v3) = v3 & $i(v4) & $i(v3) % 16.06/2.93 | & $i(v2) & $i(v1) & $i(v0)) % 16.06/2.93 | % 16.06/2.93 | ALPHA: (function-axioms) implies: % 16.06/2.94 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (antidomain(v2) % 16.06/2.94 | = v1) | ~ (antidomain(v2) = v0)) % 16.06/2.94 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.06/2.94 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 16.06/2.94 | % 16.06/2.94 | DELTA: instantiating (8) with fresh symbols all_24_0, all_24_1, all_24_2, % 16.06/2.94 | all_24_3, all_24_4 gives: % 16.06/2.94 | (11) ~ (all_24_0 = zero) & domain(all_24_4) = all_24_2 & % 16.06/2.94 | antidomain(all_24_3) = all_24_1 & multiplication(all_24_2, all_24_3) = % 16.06/2.94 | all_24_0 & addition(all_24_2, all_24_1) = all_24_1 & $i(all_24_0) & % 16.06/2.94 | $i(all_24_1) & $i(all_24_2) & $i(all_24_3) & $i(all_24_4) % 16.06/2.94 | % 16.06/2.94 | ALPHA: (11) implies: % 16.06/2.94 | (12) ~ (all_24_0 = zero) % 16.06/2.94 | (13) $i(all_24_4) % 16.06/2.94 | (14) $i(all_24_3) % 16.06/2.94 | (15) $i(all_24_2) % 16.06/2.94 | (16) $i(all_24_1) % 16.06/2.94 | (17) addition(all_24_2, all_24_1) = all_24_1 % 16.06/2.94 | (18) multiplication(all_24_2, all_24_3) = all_24_0 % 16.06/2.94 | (19) antidomain(all_24_3) = all_24_1 % 16.06/2.94 | (20) domain(all_24_4) = all_24_2 % 16.06/2.94 | % 16.06/2.94 | GROUND_INST: instantiating (2) with all_24_1, all_24_2, all_24_2, all_24_1, % 16.06/2.94 | all_24_1, simplifying with (15), (16), (17) gives: % 16.06/2.94 | (21) ? [v0: $i] : (addition(v0, all_24_1) = all_24_1 & addition(all_24_2, % 16.06/2.94 | all_24_2) = v0 & $i(v0)) % 16.06/2.94 | % 16.06/2.94 | GROUND_INST: instantiating (1) with all_24_1, all_24_2, all_24_1, simplifying % 16.06/2.94 | with (15), (16), (17) gives: % 16.06/2.94 | (22) addition(all_24_1, all_24_2) = all_24_1 % 16.06/2.94 | % 16.06/2.94 | GROUND_INST: instantiating (6) with all_24_2, all_24_3, all_24_0, simplifying % 16.06/2.94 | with (14), (15), (18) gives: % 16.06/2.94 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 16.06/2.94 | (antidomain(v3) = v4 & antidomain(v1) = v2 & antidomain(all_24_0) = v0 % 16.06/2.94 | & antidomain(all_24_3) = v1 & multiplication(all_24_2, v2) = v3 & % 16.06/2.94 | addition(v0, v4) = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.06/2.94 | % 16.06/2.94 | GROUND_INST: instantiating (5) with all_24_3, all_24_1, simplifying with (14), % 16.06/2.94 | (19) gives: % 16.06/2.94 | (24) multiplication(all_24_1, all_24_3) = zero % 16.06/2.94 | % 16.06/2.94 | GROUND_INST: instantiating (7) with all_24_4, all_24_2, simplifying with (13), % 16.06/2.94 | (20) gives: % 16.06/2.94 | (25) ? [v0: $i] : (antidomain(v0) = all_24_2 & antidomain(all_24_4) = v0 & % 16.06/2.94 | $i(v0) & $i(all_24_2)) % 16.06/2.94 | % 16.06/2.94 | DELTA: instantiating (21) with fresh symbol all_36_0 gives: % 16.06/2.94 | (26) addition(all_36_0, all_24_1) = all_24_1 & addition(all_24_2, all_24_2) % 16.06/2.94 | = all_36_0 & $i(all_36_0) % 16.06/2.94 | % 16.06/2.94 | ALPHA: (26) implies: % 16.06/2.94 | (27) $i(all_36_0) % 16.06/2.94 | (28) addition(all_24_2, all_24_2) = all_36_0 % 16.06/2.94 | (29) addition(all_36_0, all_24_1) = all_24_1 % 16.06/2.94 | % 16.06/2.94 | DELTA: instantiating (25) with fresh symbol all_38_0 gives: % 16.06/2.94 | (30) antidomain(all_38_0) = all_24_2 & antidomain(all_24_4) = all_38_0 & % 16.06/2.94 | $i(all_38_0) & $i(all_24_2) % 16.06/2.94 | % 16.06/2.94 | DELTA: instantiating (23) with fresh symbols all_40_0, all_40_1, all_40_2, % 16.06/2.94 | all_40_3, all_40_4 gives: % 16.06/2.94 | (31) antidomain(all_40_1) = all_40_0 & antidomain(all_40_3) = all_40_2 & % 16.06/2.94 | antidomain(all_24_0) = all_40_4 & antidomain(all_24_3) = all_40_3 & % 16.06/2.94 | multiplication(all_24_2, all_40_2) = all_40_1 & addition(all_40_4, % 16.06/2.94 | all_40_0) = all_40_0 & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) & % 16.06/2.94 | $i(all_40_3) & $i(all_40_4) % 16.06/2.94 | % 16.06/2.94 | ALPHA: (31) implies: % 16.06/2.95 | (32) $i(all_40_3) % 16.06/2.95 | (33) antidomain(all_24_3) = all_40_3 % 16.06/2.95 | % 16.06/2.95 | GROUND_INST: instantiating (9) with all_24_1, all_40_3, all_24_3, simplifying % 16.06/2.95 | with (19), (33) gives: % 16.06/2.95 | (34) all_40_3 = all_24_1 % 16.06/2.95 | % 16.06/2.95 | GROUND_INST: instantiating (additive_idempotence) with all_24_2, all_36_0, % 16.06/2.95 | simplifying with (15), (28) gives: % 16.06/2.95 | (35) all_36_0 = all_24_2 % 16.06/2.95 | % 16.06/2.95 | GROUND_INST: instantiating (4) with all_24_2, all_24_1, all_24_3, all_24_1, % 16.06/2.95 | zero, simplifying with (14), (15), (16), (17), (24) gives: % 16.06/2.95 | (36) ? [v0: $i] : ? [v1: $i] : (multiplication(all_24_1, all_24_3) = v1 & % 16.06/2.95 | multiplication(all_24_2, all_24_3) = v0 & addition(v0, v1) = zero & % 16.06/2.95 | $i(v1) & $i(v0) & $i(zero)) % 16.06/2.95 | % 16.06/2.95 | GROUND_INST: instantiating (4) with all_36_0, all_24_1, all_24_3, all_24_1, % 16.06/2.95 | zero, simplifying with (14), (16), (24), (27), (29) gives: % 16.06/2.95 | (37) ? [v0: $i] : ? [v1: $i] : (multiplication(all_36_0, all_24_3) = v0 & % 16.06/2.95 | multiplication(all_24_1, all_24_3) = v1 & addition(v0, v1) = zero & % 16.06/2.95 | $i(v1) & $i(v0) & $i(zero)) % 16.06/2.95 | % 16.06/2.95 | GROUND_INST: instantiating (4) with all_24_1, all_24_2, all_24_3, all_24_1, % 16.06/2.95 | zero, simplifying with (14), (15), (16), (22), (24) gives: % 16.06/2.95 | (38) ? [v0: $i] : ? [v1: $i] : (multiplication(all_24_1, all_24_3) = v0 & % 16.06/2.95 | multiplication(all_24_2, all_24_3) = v1 & addition(v0, v1) = zero & % 16.06/2.95 | $i(v1) & $i(v0) & $i(zero)) % 16.06/2.95 | % 16.06/2.95 | DELTA: instantiating (38) with fresh symbols all_110_0, all_110_1 gives: % 16.06/2.95 | (39) multiplication(all_24_1, all_24_3) = all_110_1 & % 16.06/2.95 | multiplication(all_24_2, all_24_3) = all_110_0 & addition(all_110_1, % 16.06/2.95 | all_110_0) = zero & $i(all_110_0) & $i(all_110_1) & $i(zero) % 16.06/2.95 | % 16.06/2.95 | ALPHA: (39) implies: % 16.06/2.95 | (40) $i(all_110_0) % 16.06/2.95 | (41) multiplication(all_24_2, all_24_3) = all_110_0 % 16.06/2.95 | (42) multiplication(all_24_1, all_24_3) = all_110_1 % 16.06/2.95 | % 16.06/2.95 | DELTA: instantiating (37) with fresh symbols all_112_0, all_112_1 gives: % 16.06/2.95 | (43) multiplication(all_36_0, all_24_3) = all_112_1 & % 16.06/2.95 | multiplication(all_24_1, all_24_3) = all_112_0 & addition(all_112_1, % 16.06/2.95 | all_112_0) = zero & $i(all_112_0) & $i(all_112_1) & $i(zero) % 16.06/2.95 | % 16.06/2.95 | ALPHA: (43) implies: % 16.06/2.95 | (44) addition(all_112_1, all_112_0) = zero % 16.06/2.95 | (45) multiplication(all_24_1, all_24_3) = all_112_0 % 16.06/2.95 | (46) multiplication(all_36_0, all_24_3) = all_112_1 % 16.06/2.95 | % 16.06/2.95 | DELTA: instantiating (36) with fresh symbols all_114_0, all_114_1 gives: % 16.06/2.95 | (47) multiplication(all_24_1, all_24_3) = all_114_0 & % 16.06/2.95 | multiplication(all_24_2, all_24_3) = all_114_1 & addition(all_114_1, % 16.06/2.95 | all_114_0) = zero & $i(all_114_0) & $i(all_114_1) & $i(zero) % 16.06/2.95 | % 16.06/2.95 | ALPHA: (47) implies: % 16.06/2.95 | (48) multiplication(all_24_2, all_24_3) = all_114_1 % 16.06/2.95 | (49) multiplication(all_24_1, all_24_3) = all_114_0 % 16.06/2.95 | % 16.06/2.95 | REDUCE: (35), (46) imply: % 16.06/2.95 | (50) multiplication(all_24_2, all_24_3) = all_112_1 % 16.06/2.95 | % 16.06/2.95 | GROUND_INST: instantiating (10) with all_110_0, all_112_1, all_24_3, all_24_2, % 16.06/2.95 | simplifying with (41), (50) gives: % 16.06/2.95 | (51) all_112_1 = all_110_0 % 16.06/2.95 | % 16.06/2.95 | GROUND_INST: instantiating (10) with all_24_0, all_114_1, all_24_3, all_24_2, % 16.06/2.95 | simplifying with (18), (48) gives: % 16.06/2.95 | (52) all_114_1 = all_24_0 % 16.06/2.95 | % 16.06/2.95 | GROUND_INST: instantiating (10) with all_112_1, all_114_1, all_24_3, all_24_2, % 16.06/2.95 | simplifying with (48), (50) gives: % 16.06/2.95 | (53) all_114_1 = all_112_1 % 16.06/2.95 | % 16.06/2.95 | GROUND_INST: instantiating (10) with zero, all_112_0, all_24_3, all_24_1, % 16.06/2.95 | simplifying with (24), (45) gives: % 16.06/2.95 | (54) all_112_0 = zero % 16.06/2.95 | % 16.06/2.96 | GROUND_INST: instantiating (10) with all_112_0, all_114_0, all_24_3, all_24_1, % 16.06/2.96 | simplifying with (45), (49) gives: % 16.06/2.96 | (55) all_114_0 = all_112_0 % 16.06/2.96 | % 16.06/2.96 | GROUND_INST: instantiating (10) with all_110_1, all_114_0, all_24_3, all_24_1, % 16.06/2.96 | simplifying with (42), (49) gives: % 16.06/2.96 | (56) all_114_0 = all_110_1 % 16.06/2.96 | % 16.06/2.96 | COMBINE_EQS: (55), (56) imply: % 16.06/2.96 | (57) all_112_0 = all_110_1 % 16.06/2.96 | % 16.06/2.96 | SIMP: (57) implies: % 16.06/2.96 | (58) all_112_0 = all_110_1 % 16.06/2.96 | % 16.06/2.96 | COMBINE_EQS: (52), (53) imply: % 16.06/2.96 | (59) all_112_1 = all_24_0 % 16.06/2.96 | % 16.06/2.96 | SIMP: (59) implies: % 16.06/2.96 | (60) all_112_1 = all_24_0 % 16.06/2.96 | % 16.06/2.96 | COMBINE_EQS: (54), (58) imply: % 16.06/2.96 | (61) all_110_1 = zero % 16.06/2.96 | % 16.06/2.96 | COMBINE_EQS: (51), (60) imply: % 16.06/2.96 | (62) all_110_0 = all_24_0 % 16.06/2.96 | % 16.06/2.96 | SIMP: (62) implies: % 16.06/2.96 | (63) all_110_0 = all_24_0 % 16.06/2.96 | % 16.06/2.96 | REDUCE: (44), (54), (60) imply: % 16.06/2.96 | (64) addition(all_24_0, zero) = zero % 16.06/2.96 | % 16.06/2.96 | REDUCE: (40), (63) imply: % 16.06/2.96 | (65) $i(all_24_0) % 16.06/2.96 | % 16.06/2.96 | GROUND_INST: instantiating (3) with all_24_0, zero, simplifying with (64), % 16.06/2.96 | (65) gives: % 16.06/2.96 | (66) all_24_0 = zero % 16.06/2.96 | % 16.06/2.96 | REDUCE: (12), (66) imply: % 16.06/2.96 | (67) $false % 16.06/2.96 | % 16.06/2.96 | CLOSE: (67) is inconsistent. % 16.06/2.96 | % 16.06/2.96 End of proof % 16.06/2.96 % SZS output end Proof for theBenchmark % 16.06/2.96 % 16.06/2.96 2352ms %------------------------------------------------------------------------------