%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM852+2 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.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 11:50:25 EDT 2023 % Result : Theorem 6.27s 1.60s % Output : Proof 8.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : NUM852+2 : TPTP v8.1.2. Released v4.1.0. % 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n011.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Aug 25 10:29:38 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.59 ________ _____ % 0.18/0.59 ___ __ \_________(_)________________________________ % 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.59 % 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.59 (2023-06-19) % 0.18/0.59 % 0.18/0.59 (c) Philipp Rümmer, 2009-2023 % 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.59 Amanda Stjerna. % 0.18/0.59 Free software under BSD-3-Clause. % 0.18/0.59 % 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.59 % 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.60 Running up to 7 provers in parallel. % 0.18/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.52/1.03 Prover 1: Preprocessing ... % 2.52/1.03 Prover 4: Preprocessing ... % 2.85/1.07 Prover 0: Preprocessing ... % 2.85/1.07 Prover 5: Preprocessing ... % 2.85/1.08 Prover 6: Preprocessing ... % 2.85/1.08 Prover 3: Preprocessing ... % 2.85/1.08 Prover 2: Preprocessing ... % 5.20/1.41 Prover 6: Proving ... % 5.20/1.41 Prover 5: Proving ... % 5.20/1.41 Prover 3: Constructing countermodel ... % 5.20/1.42 Prover 1: Constructing countermodel ... % 5.20/1.42 Prover 4: Constructing countermodel ... % 5.81/1.47 Prover 2: Proving ... % 5.81/1.47 Prover 0: Proving ... % 6.27/1.54 Prover 3: gave up % 6.27/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.27/1.58 Prover 7: Preprocessing ... % 6.27/1.60 Prover 0: proved (996ms) % 6.27/1.60 Prover 5: proved (993ms) % 6.27/1.60 % 6.27/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.27/1.61 % 6.27/1.61 % 6.27/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.27/1.61 % 6.27/1.61 Prover 2: stopped % 6.27/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.27/1.61 Prover 6: stopped % 6.27/1.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.27/1.61 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.27/1.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.86/1.63 Prover 1: gave up % 6.86/1.63 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.86/1.65 Prover 8: Preprocessing ... % 6.86/1.65 Prover 10: Preprocessing ... % 6.86/1.66 Prover 11: Preprocessing ... % 6.86/1.66 Prover 13: Preprocessing ... % 6.86/1.66 Prover 16: Preprocessing ... % 6.86/1.67 Prover 7: Warning: ignoring some quantifiers % 7.38/1.69 Prover 7: Constructing countermodel ... % 7.38/1.75 Prover 10: Warning: ignoring some quantifiers % 7.38/1.75 Prover 13: Warning: ignoring some quantifiers % 7.38/1.76 Prover 10: Constructing countermodel ... % 7.38/1.76 Prover 16: Warning: ignoring some quantifiers % 7.38/1.76 Prover 16: Constructing countermodel ... % 7.38/1.76 Prover 13: Constructing countermodel ... % 7.98/1.77 Prover 8: Warning: ignoring some quantifiers % 8.07/1.78 Prover 4: Found proof (size 59) % 8.07/1.78 Prover 4: proved (1172ms) % 8.07/1.78 Prover 7: stopped % 8.07/1.78 Prover 16: stopped % 8.07/1.78 Prover 8: Constructing countermodel ... % 8.07/1.78 Prover 13: stopped % 8.07/1.79 Prover 10: stopped % 8.07/1.79 Prover 8: stopped % 8.07/1.80 Prover 11: Constructing countermodel ... % 8.07/1.81 Prover 11: stopped % 8.07/1.81 % 8.07/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.07/1.81 % 8.07/1.82 % SZS output start Proof for theBenchmark % 8.07/1.82 Assumptions after simplification: % 8.07/1.82 --------------------------------- % 8.07/1.82 % 8.07/1.82 (ass(cond(302, 0), 0)) % 8.07/1.86 $i(vd469) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) = % 8.07/1.86 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : % 8.07/1.86 ? [v6: $i] : ? [v7: any] : (vplus(v4, v5) = v6 & vmul(v2, vd469) = v5 & % 8.07/1.86 vmul(v1, vd469) = v4 & greater(v6, v4) = v7 & greater(v0, v1) = v3 & % 8.07/1.86 $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v7 = 0))) & ! [v0: $i] : ! % 8.07/1.86 [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : % 8.07/1.86 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (vskolem9(v0, v1) = v3 & vplus(v2, % 8.07/1.86 v4) = v5 & vmul(v3, vd469) = v4 & vmul(v1, vd469) = v2 & greater(v5, v2) % 8.07/1.86 = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 8.07/1.86 % 8.07/1.86 (ass(cond(302, 0), 1)) % 8.07/1.86 $i(vd469) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) = % 8.07/1.86 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : % 8.07/1.86 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vplus(v6, v7) = v8 & vplus(v1, v2) % 8.07/1.86 = v4 & vmul(v4, vd469) = v5 & vmul(v2, vd469) = v7 & vmul(v1, vd469) = v6 % 8.07/1.86 & greater(v0, v1) = v3 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~ % 8.07/1.86 (v3 = 0) | v8 = v5))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) % 8.07/1.86 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 8.07/1.86 ? [v5: $i] : ? [v6: $i] : (vskolem9(v0, v1) = v2 & vplus(v5, v6) = v4 & % 8.07/1.86 vplus(v1, v2) = v3 & vmul(v3, vd469) = v4 & vmul(v2, vd469) = v6 & % 8.07/1.86 vmul(v1, vd469) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 8.07/1.86 % 8.07/1.86 (ass(cond(302, 0), 2)) % 8.07/1.87 $i(vd469) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) = % 8.07/1.87 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : % 8.07/1.87 ? [v6: $i] : (vplus(v1, v2) = v5 & vmul(v5, vd469) = v6 & vmul(v0, vd469) = % 8.07/1.87 v4 & greater(v0, v1) = v3 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = % 8.07/1.87 v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ % 8.07/1.87 $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (vskolem9(v0, % 8.07/1.87 v1) = v3 & vplus(v1, v3) = v4 & vmul(v4, vd469) = v2 & vmul(v0, vd469) = % 8.07/1.87 v2 & $i(v4) & $i(v3) & $i(v2))) % 8.07/1.87 % 8.07/1.87 (ass(cond(302, 0), 3)) % 8.07/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) = v2) | ~ % 8.07/1.87 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (vplus(v1, v2) = v4 & % 8.07/1.87 greater(v0, v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0))) & ! [v0: $i] : % 8.07/1.87 ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : % 8.07/1.87 (vskolem9(v0, v1) = v2 & vplus(v1, v2) = v0 & $i(v2))) % 8.07/1.87 % 8.07/1.87 (holds(conseq_conjunct1(conseq(304)), 483, 0)) % 8.07/1.87 greater(vd481, vd480) = 0 & $i(vd480) & $i(vd481) % 8.07/1.87 % 8.07/1.87 (holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)) % 8.45/1.87 $i(vd480) & $i(vd469) & $i(vd481) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : % 8.45/1.87 ( ~ (v2 = 0) & vmul(vd480, vd469) = v1 & vmul(vd481, vd469) = v0 & greater(v0, % 8.45/1.87 v1) = v2 & $i(v1) & $i(v0)) % 8.45/1.87 % 8.45/1.87 (function-axioms) % 8.45/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.45/1.88 (vskolem9(v3, v2) = v1) | ~ (vskolem9(v3, v2) = v0)) & ! [v0: $i] : ! % 8.45/1.88 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ % 8.45/1.88 (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.45/1.88 $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) & ! [v0: % 8.45/1.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 8.45/1.88 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 8.45/1.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 8.45/1.88 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: % 8.45/1.88 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ % 8.45/1.88 (vsucc(v2) = v0)) % 8.45/1.88 % 8.45/1.88 Further assumptions not needed in the proof: % 8.45/1.88 -------------------------------------------- % 8.45/1.88 ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(261, 0), 0), ass(cond(270, % 8.45/1.88 0), 0), ass(cond(281, 0), 0), ass(cond(290, 0), 0), ass(cond(303, 0), 0), % 8.45/1.88 ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0), % 8.45/1.88 2), ass(cond(goal(130), 0), 3), def(cond(conseq(axiom(3)), 11), 1), % 8.45/1.88 def(cond(conseq(axiom(3)), 12), 1), holds(antec(304), 482, 0) % 8.45/1.88 % 8.45/1.88 Those formulas are unsatisfiable: % 8.45/1.88 --------------------------------- % 8.45/1.88 % 8.45/1.88 Begin of proof % 8.45/1.88 | % 8.45/1.88 | ALPHA: (holds(conseq_conjunct1(conseq(304)), 483, 0)) implies: % 8.45/1.88 | (1) greater(vd481, vd480) = 0 % 8.45/1.88 | % 8.45/1.88 | ALPHA: (ass(cond(302, 0), 0)) implies: % 8.45/1.88 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ % 8.45/1.88 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 8.45/1.88 | (vskolem9(v0, v1) = v3 & vplus(v2, v4) = v5 & vmul(v3, vd469) = v4 & % 8.45/1.88 | vmul(v1, vd469) = v2 & greater(v5, v2) = 0 & $i(v5) & $i(v4) & % 8.45/1.88 | $i(v3) & $i(v2))) % 8.45/1.88 | % 8.45/1.88 | ALPHA: (ass(cond(302, 0), 1)) implies: % 8.45/1.88 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ % 8.45/1.88 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 8.45/1.88 | [v6: $i] : (vskolem9(v0, v1) = v2 & vplus(v5, v6) = v4 & vplus(v1, % 8.45/1.89 | v2) = v3 & vmul(v3, vd469) = v4 & vmul(v2, vd469) = v6 & vmul(v1, % 8.45/1.89 | vd469) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 8.45/1.89 | % 8.45/1.89 | ALPHA: (ass(cond(302, 0), 2)) implies: % 8.45/1.89 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ % 8.45/1.89 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (vskolem9(v0, v1) % 8.45/1.89 | = v3 & vplus(v1, v3) = v4 & vmul(v4, vd469) = v2 & vmul(v0, vd469) % 8.45/1.89 | = v2 & $i(v4) & $i(v3) & $i(v2))) % 8.45/1.89 | % 8.45/1.89 | ALPHA: (ass(cond(302, 0), 3)) implies: % 8.45/1.89 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ % 8.45/1.89 | $i(v0) | ? [v2: $i] : (vskolem9(v0, v1) = v2 & vplus(v1, v2) = v0 & % 8.45/1.89 | $i(v2))) % 8.45/1.89 | % 8.45/1.89 | ALPHA: (holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)) % 8.45/1.89 | implies: % 8.45/1.89 | (6) $i(vd481) % 8.45/1.89 | (7) $i(vd480) % 8.45/1.89 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & vmul(vd480, % 8.45/1.89 | vd469) = v1 & vmul(vd481, vd469) = v0 & greater(v0, v1) = v2 & % 8.45/1.89 | $i(v1) & $i(v0)) % 8.45/1.89 | % 8.45/1.89 | ALPHA: (function-axioms) implies: % 8.45/1.89 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.45/1.89 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 8.45/1.89 | v2) = v0)) % 8.45/1.89 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.45/1.89 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 8.65/1.89 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.65/1.89 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 8.65/1.89 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.65/1.89 | (vskolem9(v3, v2) = v1) | ~ (vskolem9(v3, v2) = v0)) % 8.65/1.89 | % 8.65/1.89 | DELTA: instantiating (8) with fresh symbols all_20_0, all_20_1, all_20_2 % 8.65/1.89 | gives: % 8.65/1.89 | (13) ~ (all_20_0 = 0) & vmul(vd480, vd469) = all_20_1 & vmul(vd481, vd469) % 8.65/1.89 | = all_20_2 & greater(all_20_2, all_20_1) = all_20_0 & $i(all_20_1) & % 8.65/1.89 | $i(all_20_2) % 8.65/1.89 | % 8.65/1.89 | ALPHA: (13) implies: % 8.65/1.89 | (14) ~ (all_20_0 = 0) % 8.65/1.89 | (15) greater(all_20_2, all_20_1) = all_20_0 % 8.65/1.89 | (16) vmul(vd481, vd469) = all_20_2 % 8.65/1.89 | (17) vmul(vd480, vd469) = all_20_1 % 8.65/1.89 | % 8.65/1.90 | GROUND_INST: instantiating (3) with vd481, vd480, simplifying with (1), (6), % 8.65/1.90 | (7) gives: % 8.65/1.90 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 8.65/1.90 | (vskolem9(vd481, vd480) = v0 & vplus(v3, v4) = v2 & vplus(vd480, v0) = % 8.65/1.90 | v1 & vmul(v1, vd469) = v2 & vmul(v0, vd469) = v4 & vmul(vd480, % 8.65/1.90 | vd469) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.65/1.90 | % 8.65/1.90 | GROUND_INST: instantiating (2) with vd481, vd480, simplifying with (1), (6), % 8.65/1.90 | (7) gives: % 8.65/1.90 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 8.65/1.90 | (vskolem9(vd481, vd480) = v1 & vplus(v0, v2) = v3 & vmul(v1, vd469) = % 8.65/1.90 | v2 & vmul(vd480, vd469) = v0 & greater(v3, v0) = 0 & $i(v3) & $i(v2) % 8.65/1.90 | & $i(v1) & $i(v0)) % 8.65/1.90 | % 8.65/1.90 | GROUND_INST: instantiating (4) with vd481, vd480, simplifying with (1), (6), % 8.65/1.90 | (7) gives: % 8.65/1.90 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vskolem9(vd481, vd480) = v1 % 8.65/1.90 | & vplus(vd480, v1) = v2 & vmul(v2, vd469) = v0 & vmul(vd481, vd469) % 8.65/1.90 | = v0 & $i(v2) & $i(v1) & $i(v0)) % 8.65/1.90 | % 8.65/1.90 | GROUND_INST: instantiating (5) with vd481, vd480, simplifying with (1), (6), % 8.65/1.90 | (7) gives: % 8.65/1.90 | (21) ? [v0: $i] : (vskolem9(vd481, vd480) = v0 & vplus(vd480, v0) = vd481 % 8.65/1.90 | & $i(v0)) % 8.65/1.90 | % 8.65/1.90 | DELTA: instantiating (21) with fresh symbol all_34_0 gives: % 8.65/1.90 | (22) vskolem9(vd481, vd480) = all_34_0 & vplus(vd480, all_34_0) = vd481 & % 8.65/1.90 | $i(all_34_0) % 8.65/1.90 | % 8.65/1.90 | ALPHA: (22) implies: % 8.65/1.90 | (23) vplus(vd480, all_34_0) = vd481 % 8.65/1.90 | (24) vskolem9(vd481, vd480) = all_34_0 % 8.65/1.90 | % 8.65/1.90 | DELTA: instantiating (20) with fresh symbols all_40_0, all_40_1, all_40_2 % 8.65/1.90 | gives: % 8.65/1.90 | (25) vskolem9(vd481, vd480) = all_40_1 & vplus(vd480, all_40_1) = all_40_0 % 8.65/1.90 | & vmul(all_40_0, vd469) = all_40_2 & vmul(vd481, vd469) = all_40_2 & % 8.65/1.90 | $i(all_40_0) & $i(all_40_1) & $i(all_40_2) % 8.65/1.90 | % 8.65/1.90 | ALPHA: (25) implies: % 8.65/1.90 | (26) vmul(vd481, vd469) = all_40_2 % 8.65/1.90 | (27) vmul(all_40_0, vd469) = all_40_2 % 8.65/1.90 | (28) vplus(vd480, all_40_1) = all_40_0 % 8.65/1.90 | (29) vskolem9(vd481, vd480) = all_40_1 % 8.65/1.90 | % 8.65/1.90 | DELTA: instantiating (19) with fresh symbols all_42_0, all_42_1, all_42_2, % 8.65/1.90 | all_42_3 gives: % 8.65/1.90 | (30) vskolem9(vd481, vd480) = all_42_2 & vplus(all_42_3, all_42_1) = % 8.65/1.90 | all_42_0 & vmul(all_42_2, vd469) = all_42_1 & vmul(vd480, vd469) = % 8.65/1.90 | all_42_3 & greater(all_42_0, all_42_3) = 0 & $i(all_42_0) & % 8.65/1.90 | $i(all_42_1) & $i(all_42_2) & $i(all_42_3) % 8.65/1.90 | % 8.65/1.90 | ALPHA: (30) implies: % 8.65/1.90 | (31) greater(all_42_0, all_42_3) = 0 % 8.65/1.90 | (32) vmul(vd480, vd469) = all_42_3 % 8.65/1.90 | (33) vmul(all_42_2, vd469) = all_42_1 % 8.65/1.90 | (34) vplus(all_42_3, all_42_1) = all_42_0 % 8.65/1.91 | (35) vskolem9(vd481, vd480) = all_42_2 % 8.65/1.91 | % 8.65/1.91 | DELTA: instantiating (18) with fresh symbols all_44_0, all_44_1, all_44_2, % 8.65/1.91 | all_44_3, all_44_4 gives: % 8.65/1.91 | (36) vskolem9(vd481, vd480) = all_44_4 & vplus(all_44_1, all_44_0) = % 8.65/1.91 | all_44_2 & vplus(vd480, all_44_4) = all_44_3 & vmul(all_44_3, vd469) = % 8.65/1.91 | all_44_2 & vmul(all_44_4, vd469) = all_44_0 & vmul(vd480, vd469) = % 8.65/1.91 | all_44_1 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) & $i(all_44_3) & % 8.65/1.91 | $i(all_44_4) % 8.65/1.91 | % 8.65/1.91 | ALPHA: (36) implies: % 8.65/1.91 | (37) vmul(vd480, vd469) = all_44_1 % 8.65/1.91 | (38) vmul(all_44_4, vd469) = all_44_0 % 8.65/1.91 | (39) vmul(all_44_3, vd469) = all_44_2 % 8.65/1.91 | (40) vplus(vd480, all_44_4) = all_44_3 % 8.65/1.91 | (41) vplus(all_44_1, all_44_0) = all_44_2 % 8.65/1.91 | (42) vskolem9(vd481, vd480) = all_44_4 % 8.65/1.91 | % 8.65/1.91 | GROUND_INST: instantiating (10) with all_20_2, all_40_2, vd469, vd481, % 8.65/1.91 | simplifying with (16), (26) gives: % 8.65/1.91 | (43) all_40_2 = all_20_2 % 8.65/1.91 | % 8.65/1.91 | GROUND_INST: instantiating (10) with all_20_1, all_44_1, vd469, vd480, % 8.65/1.91 | simplifying with (17), (37) gives: % 8.65/1.91 | (44) all_44_1 = all_20_1 % 8.65/1.91 | % 8.65/1.91 | GROUND_INST: instantiating (10) with all_42_3, all_44_1, vd469, vd480, % 8.65/1.91 | simplifying with (32), (37) gives: % 8.65/1.91 | (45) all_44_1 = all_42_3 % 8.65/1.91 | % 8.65/1.91 | GROUND_INST: instantiating (12) with all_34_0, all_42_2, vd480, vd481, % 8.65/1.91 | simplifying with (24), (35) gives: % 8.65/1.91 | (46) all_42_2 = all_34_0 % 8.65/1.91 | % 8.65/1.91 | GROUND_INST: instantiating (12) with all_42_2, all_44_4, vd480, vd481, % 8.65/1.91 | simplifying with (35), (42) gives: % 8.65/1.91 | (47) all_44_4 = all_42_2 % 8.65/1.91 | % 8.65/1.91 | GROUND_INST: instantiating (12) with all_40_1, all_44_4, vd480, vd481, % 8.65/1.91 | simplifying with (29), (42) gives: % 8.65/1.91 | (48) all_44_4 = all_40_1 % 8.65/1.91 | % 8.65/1.91 | COMBINE_EQS: (44), (45) imply: % 8.65/1.91 | (49) all_42_3 = all_20_1 % 8.65/1.91 | % 8.65/1.91 | COMBINE_EQS: (47), (48) imply: % 8.65/1.91 | (50) all_42_2 = all_40_1 % 8.65/1.91 | % 8.65/1.91 | SIMP: (50) implies: % 8.65/1.91 | (51) all_42_2 = all_40_1 % 8.65/1.91 | % 8.65/1.91 | COMBINE_EQS: (46), (51) imply: % 8.65/1.91 | (52) all_40_1 = all_34_0 % 8.65/1.91 | % 8.65/1.91 | SIMP: (52) implies: % 8.65/1.91 | (53) all_40_1 = all_34_0 % 8.65/1.91 | % 8.65/1.91 | COMBINE_EQS: (48), (53) imply: % 8.65/1.91 | (54) all_44_4 = all_34_0 % 8.65/1.91 | % 8.65/1.91 | REDUCE: (41), (44) imply: % 8.65/1.91 | (55) vplus(all_20_1, all_44_0) = all_44_2 % 8.65/1.91 | % 8.65/1.91 | REDUCE: (34), (49) imply: % 8.65/1.91 | (56) vplus(all_20_1, all_42_1) = all_42_0 % 8.65/1.91 | % 8.65/1.91 | REDUCE: (40), (54) imply: % 8.65/1.91 | (57) vplus(vd480, all_34_0) = all_44_3 % 8.65/1.91 | % 8.65/1.91 | REDUCE: (28), (53) imply: % 8.65/1.91 | (58) vplus(vd480, all_34_0) = all_40_0 % 8.65/1.91 | % 8.65/1.91 | REDUCE: (38), (54) imply: % 8.65/1.91 | (59) vmul(all_34_0, vd469) = all_44_0 % 8.65/1.91 | % 8.65/1.91 | REDUCE: (33), (46) imply: % 8.65/1.91 | (60) vmul(all_34_0, vd469) = all_42_1 % 8.65/1.91 | % 8.65/1.91 | REDUCE: (27), (43) imply: % 8.65/1.91 | (61) vmul(all_40_0, vd469) = all_20_2 % 8.65/1.91 | % 8.65/1.91 | REDUCE: (31), (49) imply: % 8.65/1.91 | (62) greater(all_42_0, all_20_1) = 0 % 8.65/1.91 | % 8.65/1.91 | GROUND_INST: instantiating (10) with all_42_1, all_44_0, vd469, all_34_0, % 8.65/1.91 | simplifying with (59), (60) gives: % 8.65/1.91 | (63) all_44_0 = all_42_1 % 8.65/1.91 | % 8.65/1.91 | GROUND_INST: instantiating (11) with vd481, all_44_3, all_34_0, vd480, % 8.65/1.91 | simplifying with (23), (57) gives: % 8.65/1.92 | (64) all_44_3 = vd481 % 8.65/1.92 | % 8.65/1.92 | GROUND_INST: instantiating (11) with all_40_0, all_44_3, all_34_0, vd480, % 8.65/1.92 | simplifying with (57), (58) gives: % 8.65/1.92 | (65) all_44_3 = all_40_0 % 8.65/1.92 | % 8.65/1.92 | COMBINE_EQS: (64), (65) imply: % 8.65/1.92 | (66) all_40_0 = vd481 % 8.65/1.92 | % 8.65/1.92 | SIMP: (66) implies: % 8.65/1.92 | (67) all_40_0 = vd481 % 8.65/1.92 | % 8.65/1.92 | REDUCE: (55), (63) imply: % 8.65/1.92 | (68) vplus(all_20_1, all_42_1) = all_44_2 % 8.65/1.92 | % 8.65/1.92 | REDUCE: (39), (64) imply: % 8.65/1.92 | (69) vmul(vd481, vd469) = all_44_2 % 8.65/1.92 | % 8.65/1.92 | GROUND_INST: instantiating (10) with all_20_2, all_44_2, vd469, vd481, % 8.65/1.92 | simplifying with (16), (69) gives: % 8.65/1.92 | (70) all_44_2 = all_20_2 % 8.65/1.92 | % 8.65/1.92 | GROUND_INST: instantiating (11) with all_42_0, all_44_2, all_42_1, all_20_1, % 8.65/1.92 | simplifying with (56), (68) gives: % 8.65/1.92 | (71) all_44_2 = all_42_0 % 8.65/1.92 | % 8.65/1.92 | COMBINE_EQS: (70), (71) imply: % 8.65/1.92 | (72) all_42_0 = all_20_2 % 8.65/1.92 | % 8.65/1.92 | SIMP: (72) implies: % 8.65/1.92 | (73) all_42_0 = all_20_2 % 8.65/1.92 | % 8.65/1.92 | REDUCE: (62), (73) imply: % 8.65/1.92 | (74) greater(all_20_2, all_20_1) = 0 % 8.65/1.92 | % 8.65/1.92 | GROUND_INST: instantiating (9) with all_20_0, 0, all_20_1, all_20_2, % 8.65/1.92 | simplifying with (15), (74) gives: % 8.65/1.92 | (75) all_20_0 = 0 % 8.65/1.92 | % 8.65/1.92 | REDUCE: (14), (75) imply: % 8.65/1.92 | (76) $false % 8.65/1.92 | % 8.65/1.92 | CLOSE: (76) is inconsistent. % 8.65/1.92 | % 8.65/1.92 End of proof % 8.65/1.92 % SZS output end Proof for theBenchmark % 8.65/1.92 % 8.65/1.92 1332ms %------------------------------------------------------------------------------