%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM849+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 : n017.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 11:50:24 EDT 2023 % Result : Theorem 6.32s 1.53s % Output : Proof 8.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM849+2 : TPTP v8.1.2. Released v4.1.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n017.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 16:56:25 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.44/1.00 Prover 4: Preprocessing ... % 2.44/1.00 Prover 1: Preprocessing ... % 2.44/1.05 Prover 6: Preprocessing ... % 2.44/1.05 Prover 5: Preprocessing ... % 2.44/1.05 Prover 3: Preprocessing ... % 2.44/1.05 Prover 0: Preprocessing ... % 2.44/1.05 Prover 2: Preprocessing ... % 4.05/1.28 Prover 1: Warning: ignoring some quantifiers % 4.66/1.30 Prover 3: Warning: ignoring some quantifiers % 4.66/1.32 Prover 1: Constructing countermodel ... % 4.66/1.32 Prover 3: Constructing countermodel ... % 4.66/1.34 Prover 6: Proving ... % 4.66/1.40 Prover 4: Constructing countermodel ... % 5.82/1.46 Prover 5: Proving ... % 5.82/1.46 Prover 0: Proving ... % 6.32/1.52 Prover 3: proved (897ms) % 6.32/1.53 % 6.32/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.32/1.53 % 6.32/1.53 Prover 2: Proving ... % 6.32/1.53 Prover 5: stopped % 6.32/1.53 Prover 0: stopped % 6.32/1.53 Prover 6: stopped % 6.32/1.53 Prover 2: stopped % 6.32/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.32/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.32/1.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.32/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.32/1.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.46/1.57 Prover 7: Preprocessing ... % 6.46/1.58 Prover 11: Preprocessing ... % 6.46/1.58 Prover 8: Preprocessing ... % 6.46/1.58 Prover 10: Preprocessing ... % 6.46/1.59 Prover 13: Preprocessing ... % 7.46/1.68 Prover 8: Warning: ignoring some quantifiers % 7.46/1.69 Prover 8: Constructing countermodel ... % 7.46/1.70 Prover 10: Constructing countermodel ... % 7.46/1.71 Prover 13: Warning: ignoring some quantifiers % 7.46/1.72 Prover 13: Constructing countermodel ... % 7.46/1.75 Prover 7: Constructing countermodel ... % 8.00/1.76 Prover 11: Constructing countermodel ... % 8.15/1.77 Prover 1: Found proof (size 60) % 8.15/1.77 Prover 1: proved (1163ms) % 8.15/1.78 Prover 4: stopped % 8.15/1.78 Prover 8: stopped % 8.15/1.78 Prover 13: stopped % 8.15/1.78 Prover 10: stopped % 8.15/1.78 Prover 11: stopped % 8.15/1.78 Prover 7: stopped % 8.15/1.78 % 8.15/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.15/1.78 % 8.15/1.79 % SZS output start Proof for theBenchmark % 8.15/1.80 Assumptions after simplification: % 8.15/1.80 --------------------------------- % 8.15/1.80 % 8.15/1.80 (ass(cond(270, 0), 0)) % 8.38/1.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) % 8.38/1.82 | ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2))) % 8.38/1.83 % 8.38/1.83 (ass(cond(281, 0), 0)) % 8.38/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 8.38/1.83 $i] : ( ~ (vplus(v3, v4) = v5) | ~ (vmul(v0, v2) = v4) | ~ (vmul(v0, v1) = % 8.38/1.83 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (vplus(v1, v2) = % 8.38/1.83 v6 & vmul(v0, v6) = v5 & $i(v6) & $i(v5))) % 8.38/1.83 % 8.38/1.83 (ass(cond(conseq(292), 1), 0)) % 8.38/1.83 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! % 8.38/1.83 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 8.38/1.83 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 8.38/1.83 [v9: $i] : (vplus(v3, vd449) = v5 & vsucc(v1) = v7 & vmul(vd449, v7) = v8 % 8.38/1.83 & vmul(vd449, v1) = v3 & vmul(vd448, v8) = v9 & vmul(vd448, v5) = v6 & % 8.38/1.83 vmul(vd448, v3) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 8.38/1.83 $i(v4) & $i(v3) & ( ~ (v4 = v2) | v9 = v6)))) % 8.38/1.83 % 8.38/1.83 (ass(cond(conseq(292), 1), 1)) % 8.38/1.84 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! % 8.38/1.84 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 8.38/1.84 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v4, v0) = % 8.38/1.84 v5 & vplus(v3, vd449) = v6 & vmul(vd449, v1) = v3 & vmul(vd448, v6) = v7 % 8.38/1.84 & vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( % 8.38/1.84 ~ (v4 = v2) | v7 = v5)))) % 8.38/1.84 % 8.38/1.84 (ass(cond(conseq(292), 1), 2)) % 8.38/1.84 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! % 8.38/1.84 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 8.38/1.84 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v4, v0) = v6 & vplus(v2, % 8.38/1.84 v0) = v5 & vmul(vd449, v1) = v3 & vmul(vd448, v3) = v4 & $i(v6) & % 8.38/1.84 $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v6 = v5)))) % 8.38/1.84 % 8.38/1.84 (ass(cond(conseq(292), 1), 3)) % 8.52/1.84 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! % 8.52/1.84 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 8.52/1.84 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v2, v0) = % 8.52/1.84 v7 & vsucc(v1) = v5 & vmul(v0, v5) = v6 & vmul(vd449, v1) = v3 & % 8.52/1.84 vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ % 8.52/1.84 (v4 = v2) | v7 = v6)))) % 8.52/1.84 % 8.52/1.84 (holds(293, 450, 1)) % 8.52/1.84 $i(v1) & $i(vd449) & $i(vd448) & ? [v0: $i] : ? [v1: $i] : (vmul(vd449, v1) % 8.52/1.84 = v1 & vmul(vd448, v1) = v0 & vmul(vd448, vd449) = v0 & $i(v1) & $i(v0)) % 8.52/1.84 % 8.52/1.84 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) % 8.52/1.85 $i(v1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.52/1.85 (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 8.52/1.85 $i] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4 & $i(v4) & $i(v3))) & ? % 8.52/1.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (vmul(v1, v1) = v2) | ~ % 8.52/1.85 $i(v1) | ~ $i(v0)) % 8.52/1.85 % 8.52/1.85 (qu(ind(296), imp(296))) % 8.52/1.85 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ? % 8.52/1.85 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 8.52/1.85 $i] : ? [v7: $i] : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 & % 8.52/1.85 vmul(v0, v1) = v2 & vmul(vd449, v4) = v6 & vmul(vd449, v1) = v3 & % 8.52/1.85 vmul(vd448, v6) = v7 & vmul(vd448, v3) = v2 & $i(v7) & $i(v6) & $i(v5) & % 8.52/1.85 $i(v4) & $i(v3) & $i(v2) & $i(v1))) % 8.52/1.85 % 8.52/1.85 (function-axioms) % 8.52/1.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.52/1.85 (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 8.52/1.85 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, % 8.52/1.85 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 8.52/1.85 (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 8.52/1.85 % 8.52/1.85 Further assumptions not needed in the proof: % 8.52/1.85 -------------------------------------------- % 8.52/1.85 ass(cond(261, 0), 0), ass(cond(61, 0), 0), qu(cond(conseq(axiom(3)), 3), % 8.52/1.85 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))) % 8.52/1.85 % 8.52/1.85 Those formulas are unsatisfiable: % 8.52/1.85 --------------------------------- % 8.52/1.85 % 8.52/1.85 Begin of proof % 8.52/1.85 | % 8.52/1.85 | ALPHA: (ass(cond(conseq(292), 1), 0)) implies: % 8.52/1.86 | (1) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 8.52/1.86 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 8.52/1.86 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 8.52/1.86 | [v9: $i] : (vplus(v3, vd449) = v5 & vsucc(v1) = v7 & vmul(vd449, % 8.52/1.86 | v7) = v8 & vmul(vd449, v1) = v3 & vmul(vd448, v8) = v9 & % 8.52/1.86 | vmul(vd448, v5) = v6 & vmul(vd448, v3) = v4 & $i(v9) & $i(v8) & % 8.52/1.86 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v9 = % 8.52/1.86 | v6)))) % 8.52/1.86 | % 8.52/1.86 | ALPHA: (ass(cond(conseq(292), 1), 1)) implies: % 8.52/1.86 | (2) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 8.52/1.86 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 8.52/1.86 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v4, v0) = % 8.52/1.86 | v5 & vplus(v3, vd449) = v6 & vmul(vd449, v1) = v3 & vmul(vd448, % 8.52/1.86 | v6) = v7 & vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & % 8.52/1.86 | $i(v4) & $i(v3) & ( ~ (v4 = v2) | v7 = v5)))) % 8.52/1.86 | % 8.52/1.86 | ALPHA: (ass(cond(conseq(292), 1), 2)) implies: % 8.52/1.86 | (3) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 8.52/1.86 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 8.52/1.86 | $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v4, v0) = v6 & vplus(v2, % 8.52/1.86 | v0) = v5 & vmul(vd449, v1) = v3 & vmul(vd448, v3) = v4 & $i(v6) % 8.52/1.86 | & $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v6 = v5)))) % 8.52/1.86 | % 8.52/1.86 | ALPHA: (ass(cond(conseq(292), 1), 3)) implies: % 8.52/1.86 | (4) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 8.52/1.86 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 8.52/1.86 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v2, v0) = % 8.52/1.86 | v7 & vsucc(v1) = v5 & vmul(v0, v5) = v6 & vmul(vd449, v1) = v3 & % 8.52/1.86 | vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 8.52/1.86 | & ( ~ (v4 = v2) | v7 = v6)))) % 8.52/1.86 | % 8.52/1.86 | ALPHA: (holds(293, 450, 1)) implies: % 8.52/1.86 | (5) ? [v0: $i] : ? [v1: $i] : (vmul(vd449, v1) = v1 & vmul(vd448, v1) = % 8.52/1.86 | v0 & vmul(vd448, vd449) = v0 & $i(v1) & $i(v0)) % 8.52/1.86 | % 8.52/1.86 | ALPHA: (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), % 8.52/1.86 | holds(definiens(249), 398, 0)))) implies: % 8.52/1.86 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v1) % 8.52/1.86 | = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 8.52/1.86 | $i] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4 & $i(v4) & $i(v3))) % 8.52/1.86 | % 8.52/1.86 | ALPHA: (qu(ind(296), imp(296))) implies: % 8.52/1.86 | (7) $i(vd448) % 8.52/1.86 | (8) $i(vd449) % 8.52/1.87 | (9) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ? [v1: $i] : ? [v2: % 8.52/1.87 | $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? % 8.52/1.87 | [v7: $i] : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 & % 8.52/1.87 | vmul(v0, v1) = v2 & vmul(vd449, v4) = v6 & vmul(vd449, v1) = v3 & % 8.52/1.87 | vmul(vd448, v6) = v7 & vmul(vd448, v3) = v2 & $i(v7) & $i(v6) & % 8.52/1.87 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1))) % 8.52/1.87 | % 8.52/1.87 | ALPHA: (function-axioms) implies: % 8.52/1.87 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.52/1.87 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 8.52/1.87 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.52/1.87 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 8.52/1.87 | % 8.52/1.87 | DELTA: instantiating (5) with fresh symbols all_14_0, all_14_1 gives: % 8.52/1.87 | (12) vmul(vd449, v1) = all_14_0 & vmul(vd448, all_14_0) = all_14_1 & % 8.52/1.87 | vmul(vd448, vd449) = all_14_1 & $i(all_14_0) & $i(all_14_1) % 8.52/1.87 | % 8.52/1.87 | ALPHA: (12) implies: % 8.52/1.87 | (13) $i(all_14_0) % 8.52/1.87 | (14) vmul(vd448, vd449) = all_14_1 % 8.52/1.87 | (15) vmul(vd448, all_14_0) = all_14_1 % 8.52/1.87 | % 8.52/1.87 | DELTA: instantiating (3) with fresh symbol all_16_0 gives: % 8.52/1.87 | (16) vmul(vd448, vd449) = all_16_0 & $i(all_16_0) & ! [v0: $i] : ! [v1: % 8.52/1.87 | $i] : ( ~ (vmul(all_16_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 8.52/1.87 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (vplus(v3, all_16_0) = v5 & % 8.52/1.87 | vplus(v1, all_16_0) = v4 & vmul(vd449, v0) = v2 & vmul(vd448, v2) % 8.52/1.87 | = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v5 = % 8.52/1.87 | v4))) % 8.52/1.87 | % 8.52/1.87 | ALPHA: (16) implies: % 8.52/1.87 | (17) vmul(vd448, vd449) = all_16_0 % 8.52/1.87 | % 8.52/1.87 | DELTA: instantiating (2) with fresh symbol all_19_0 gives: % 8.52/1.87 | (18) vmul(vd448, vd449) = all_19_0 & $i(all_19_0) & ! [v0: $i] : ! [v1: % 8.52/1.87 | $i] : ( ~ (vmul(all_19_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 8.52/1.87 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v3, % 8.52/1.87 | all_19_0) = v4 & vplus(v2, vd449) = v5 & vmul(vd449, v0) = v2 & % 8.52/1.87 | vmul(vd448, v5) = v6 & vmul(vd448, v2) = v3 & $i(v6) & $i(v5) & % 8.52/1.87 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v6 = v4))) % 8.52/1.87 | % 8.52/1.87 | ALPHA: (18) implies: % 8.52/1.87 | (19) vmul(vd448, vd449) = all_19_0 % 8.52/1.87 | % 8.52/1.87 | DELTA: instantiating (4) with fresh symbol all_22_0 gives: % 8.52/1.87 | (20) vmul(vd448, vd449) = all_22_0 & $i(all_22_0) & ! [v0: $i] : ! [v1: % 8.52/1.87 | $i] : ( ~ (vmul(all_22_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 8.52/1.87 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v1, % 8.52/1.87 | all_22_0) = v6 & vsucc(v0) = v4 & vmul(all_22_0, v4) = v5 & % 8.52/1.87 | vmul(vd449, v0) = v2 & vmul(vd448, v2) = v3 & $i(v6) & $i(v5) & % 8.52/1.87 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v6 = v5))) % 8.52/1.87 | % 8.52/1.87 | ALPHA: (20) implies: % 8.52/1.87 | (21) vmul(vd448, vd449) = all_22_0 % 8.52/1.87 | % 8.52/1.87 | DELTA: instantiating (9) with fresh symbol all_25_0 gives: % 8.52/1.88 | (22) vmul(vd448, vd449) = all_25_0 & $i(all_25_0) & ? [v0: $i] : ? [v1: % 8.52/1.88 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 8.52/1.88 | [v6: $i] : ( ~ (v6 = v4) & vsucc(v0) = v3 & vmul(all_25_0, v3) = v4 & % 8.52/1.88 | vmul(all_25_0, v0) = v1 & vmul(vd449, v3) = v5 & vmul(vd449, v0) = % 8.52/1.88 | v2 & vmul(vd448, v5) = v6 & vmul(vd448, v2) = v1 & $i(v6) & $i(v5) & % 8.52/1.88 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.52/1.88 | % 8.52/1.88 | ALPHA: (22) implies: % 8.52/1.88 | (23) vmul(vd448, vd449) = all_25_0 % 8.52/1.88 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 8.52/1.88 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & vsucc(v0) = v3 & % 8.52/1.88 | vmul(all_25_0, v3) = v4 & vmul(all_25_0, v0) = v1 & vmul(vd449, v3) % 8.52/1.88 | = v5 & vmul(vd449, v0) = v2 & vmul(vd448, v5) = v6 & vmul(vd448, v2) % 8.52/1.88 | = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.52/1.88 | % 8.52/1.88 | DELTA: instantiating (1) with fresh symbol all_27_0 gives: % 8.52/1.88 | (25) vmul(vd448, vd449) = all_27_0 & $i(all_27_0) & ! [v0: $i] : ! [v1: % 8.52/1.88 | $i] : ( ~ (vmul(all_27_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 8.52/1.88 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 8.52/1.88 | ? [v8: $i] : (vplus(v2, vd449) = v4 & vsucc(v0) = v6 & vmul(vd449, % 8.52/1.88 | v6) = v7 & vmul(vd449, v0) = v2 & vmul(vd448, v7) = v8 & % 8.52/1.88 | vmul(vd448, v4) = v5 & vmul(vd448, v2) = v3 & $i(v8) & $i(v7) & % 8.52/1.88 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v8 = % 8.52/1.88 | v5))) % 8.52/1.88 | % 8.52/1.88 | ALPHA: (25) implies: % 8.52/1.88 | (26) vmul(vd448, vd449) = all_27_0 % 8.52/1.88 | % 8.52/1.88 | DELTA: instantiating (24) with fresh symbols all_30_0, all_30_1, all_30_2, % 8.52/1.88 | all_30_3, all_30_4, all_30_5, all_30_6 gives: % 8.52/1.88 | (27) ~ (all_30_0 = all_30_2) & vsucc(all_30_6) = all_30_3 & vmul(all_25_0, % 8.52/1.88 | all_30_3) = all_30_2 & vmul(all_25_0, all_30_6) = all_30_5 & % 8.52/1.88 | vmul(vd449, all_30_3) = all_30_1 & vmul(vd449, all_30_6) = all_30_4 & % 8.52/1.88 | vmul(vd448, all_30_1) = all_30_0 & vmul(vd448, all_30_4) = all_30_5 & % 8.52/1.88 | $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & $i(all_30_3) & % 8.52/1.88 | $i(all_30_4) & $i(all_30_5) & $i(all_30_6) % 8.52/1.88 | % 8.52/1.88 | ALPHA: (27) implies: % 8.52/1.88 | (28) ~ (all_30_0 = all_30_2) % 8.52/1.88 | (29) $i(all_30_6) % 8.52/1.88 | (30) vmul(vd448, all_30_4) = all_30_5 % 8.52/1.88 | (31) vmul(vd448, all_30_1) = all_30_0 % 8.52/1.88 | (32) vmul(vd449, all_30_6) = all_30_4 % 8.52/1.88 | (33) vmul(vd449, all_30_3) = all_30_1 % 8.52/1.88 | (34) vmul(all_25_0, all_30_6) = all_30_5 % 8.52/1.88 | (35) vmul(all_25_0, all_30_3) = all_30_2 % 8.52/1.88 | (36) vsucc(all_30_6) = all_30_3 % 8.52/1.88 | % 8.52/1.88 | GROUND_INST: instantiating (10) with all_16_0, all_22_0, vd449, vd448, % 8.52/1.88 | simplifying with (17), (21) gives: % 8.52/1.88 | (37) all_22_0 = all_16_0 % 8.52/1.88 | % 8.52/1.88 | GROUND_INST: instantiating (10) with all_22_0, all_25_0, vd449, vd448, % 8.52/1.88 | simplifying with (21), (23) gives: % 8.52/1.88 | (38) all_25_0 = all_22_0 % 8.52/1.88 | % 8.52/1.88 | GROUND_INST: instantiating (10) with all_19_0, all_25_0, vd449, vd448, % 8.52/1.88 | simplifying with (19), (23) gives: % 8.52/1.88 | (39) all_25_0 = all_19_0 % 8.52/1.89 | % 8.52/1.89 | GROUND_INST: instantiating (10) with all_22_0, all_27_0, vd449, vd448, % 8.52/1.89 | simplifying with (21), (26) gives: % 8.52/1.89 | (40) all_27_0 = all_22_0 % 8.52/1.89 | % 8.52/1.89 | GROUND_INST: instantiating (10) with all_14_1, all_27_0, vd449, vd448, % 8.52/1.89 | simplifying with (14), (26) gives: % 8.52/1.89 | (41) all_27_0 = all_14_1 % 8.52/1.89 | % 8.52/1.89 | COMBINE_EQS: (40), (41) imply: % 8.52/1.89 | (42) all_22_0 = all_14_1 % 8.52/1.89 | % 8.52/1.89 | SIMP: (42) implies: % 8.52/1.89 | (43) all_22_0 = all_14_1 % 8.52/1.89 | % 8.52/1.89 | COMBINE_EQS: (38), (39) imply: % 8.52/1.89 | (44) all_22_0 = all_19_0 % 8.52/1.89 | % 8.52/1.89 | SIMP: (44) implies: % 8.52/1.89 | (45) all_22_0 = all_19_0 % 8.52/1.89 | % 8.52/1.89 | COMBINE_EQS: (37), (45) imply: % 8.52/1.89 | (46) all_19_0 = all_16_0 % 8.52/1.89 | % 8.52/1.89 | COMBINE_EQS: (43), (45) imply: % 8.52/1.89 | (47) all_19_0 = all_14_1 % 8.52/1.89 | % 8.52/1.89 | COMBINE_EQS: (46), (47) imply: % 8.52/1.89 | (48) all_16_0 = all_14_1 % 8.52/1.89 | % 8.52/1.89 | COMBINE_EQS: (39), (47) imply: % 8.52/1.89 | (49) all_25_0 = all_14_1 % 8.52/1.89 | % 8.52/1.89 | REDUCE: (35), (49) imply: % 8.52/1.89 | (50) vmul(all_14_1, all_30_3) = all_30_2 % 8.52/1.89 | % 8.52/1.89 | REDUCE: (34), (49) imply: % 8.52/1.89 | (51) vmul(all_14_1, all_30_6) = all_30_5 % 8.52/1.89 | % 8.52/1.89 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd448, all_14_0, % 8.52/1.89 | all_14_1, simplifying with (7), (13), (15) gives: % 8.52/1.89 | (52) vmul(all_14_0, vd448) = all_14_1 & $i(all_14_1) % 8.52/1.89 | % 8.52/1.89 | ALPHA: (52) implies: % 8.52/1.89 | (53) $i(all_14_1) % 8.52/1.89 | % 8.52/1.89 | GROUND_INST: instantiating (6) with all_14_1, all_30_6, all_30_3, all_30_2, % 8.52/1.89 | simplifying with (29), (36), (50), (53) gives: % 8.52/1.89 | (54) ? [v0: $i] : (vplus(v0, all_14_1) = all_30_2 & vmul(all_14_1, % 8.52/1.89 | all_30_6) = v0 & $i(v0) & $i(all_30_2)) % 8.52/1.89 | % 8.52/1.89 | GROUND_INST: instantiating (6) with vd449, all_30_6, all_30_3, all_30_1, % 8.52/1.89 | simplifying with (8), (29), (33), (36) gives: % 8.52/1.89 | (55) ? [v0: $i] : (vplus(v0, vd449) = all_30_1 & vmul(vd449, all_30_6) = % 8.52/1.89 | v0 & $i(v0) & $i(all_30_1)) % 8.52/1.89 | % 8.52/1.89 | DELTA: instantiating (55) with fresh symbol all_42_0 gives: % 8.52/1.89 | (56) vplus(all_42_0, vd449) = all_30_1 & vmul(vd449, all_30_6) = all_42_0 & % 8.52/1.89 | $i(all_42_0) & $i(all_30_1) % 8.52/1.89 | % 8.52/1.89 | ALPHA: (56) implies: % 8.52/1.89 | (57) $i(all_42_0) % 8.52/1.89 | (58) vmul(vd449, all_30_6) = all_42_0 % 8.52/1.89 | (59) vplus(all_42_0, vd449) = all_30_1 % 8.52/1.89 | % 8.52/1.89 | DELTA: instantiating (54) with fresh symbol all_44_0 gives: % 8.52/1.89 | (60) vplus(all_44_0, all_14_1) = all_30_2 & vmul(all_14_1, all_30_6) = % 8.52/1.89 | all_44_0 & $i(all_44_0) & $i(all_30_2) % 8.52/1.89 | % 8.52/1.89 | ALPHA: (60) implies: % 8.52/1.89 | (61) vmul(all_14_1, all_30_6) = all_44_0 % 8.52/1.89 | (62) vplus(all_44_0, all_14_1) = all_30_2 % 8.52/1.89 | % 8.52/1.89 | GROUND_INST: instantiating (10) with all_30_4, all_42_0, all_30_6, vd449, % 8.52/1.89 | simplifying with (32), (58) gives: % 8.52/1.89 | (63) all_42_0 = all_30_4 % 8.52/1.89 | % 8.52/1.89 | GROUND_INST: instantiating (10) with all_30_5, all_44_0, all_30_6, all_14_1, % 8.52/1.89 | simplifying with (51), (61) gives: % 8.52/1.89 | (64) all_44_0 = all_30_5 % 8.52/1.89 | % 8.52/1.90 | REDUCE: (62), (64) imply: % 8.52/1.90 | (65) vplus(all_30_5, all_14_1) = all_30_2 % 8.52/1.90 | % 8.52/1.90 | REDUCE: (59), (63) imply: % 8.52/1.90 | (66) vplus(all_30_4, vd449) = all_30_1 % 8.52/1.90 | % 8.52/1.90 | REDUCE: (57), (63) imply: % 8.52/1.90 | (67) $i(all_30_4) % 8.52/1.90 | % 8.52/1.90 | GROUND_INST: instantiating (ass(cond(281, 0), 0)) with vd448, all_30_4, vd449, % 8.52/1.90 | all_30_5, all_14_1, all_30_2, simplifying with (7), (8), (14), % 8.52/1.90 | (30), (65), (67) gives: % 8.52/1.90 | (68) ? [v0: $i] : (vplus(all_30_4, vd449) = v0 & vmul(vd448, v0) = % 8.52/1.90 | all_30_2 & $i(v0) & $i(all_30_2)) % 8.52/1.90 | % 8.52/1.90 | DELTA: instantiating (68) with fresh symbol all_58_0 gives: % 8.52/1.90 | (69) vplus(all_30_4, vd449) = all_58_0 & vmul(vd448, all_58_0) = all_30_2 & % 8.52/1.90 | $i(all_58_0) & $i(all_30_2) % 8.52/1.90 | % 8.52/1.90 | ALPHA: (69) implies: % 8.52/1.90 | (70) vmul(vd448, all_58_0) = all_30_2 % 8.52/1.90 | (71) vplus(all_30_4, vd449) = all_58_0 % 8.52/1.90 | % 8.52/1.90 | GROUND_INST: instantiating (11) with all_30_1, all_58_0, vd449, all_30_4, % 8.52/1.90 | simplifying with (66), (71) gives: % 8.52/1.90 | (72) all_58_0 = all_30_1 % 8.52/1.90 | % 8.52/1.90 | REDUCE: (70), (72) imply: % 8.52/1.90 | (73) vmul(vd448, all_30_1) = all_30_2 % 8.52/1.90 | % 8.52/1.90 | GROUND_INST: instantiating (10) with all_30_0, all_30_2, all_30_1, vd448, % 8.52/1.90 | simplifying with (31), (73) gives: % 8.52/1.90 | (74) all_30_0 = all_30_2 % 8.52/1.90 | % 8.52/1.90 | REDUCE: (28), (74) imply: % 8.52/1.90 | (75) $false % 8.52/1.90 | % 8.52/1.90 | CLOSE: (75) is inconsistent. % 8.52/1.90 | % 8.52/1.90 End of proof % 8.52/1.90 % SZS output end Proof for theBenchmark % 8.52/1.90 % 8.52/1.90 1307ms %------------------------------------------------------------------------------