%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM844+1 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n014.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 11:50:21 EDT 2023 % Result : Theorem 13.25s 2.63s % Output : Proof 17.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM844+1 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n014.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Fri Aug 25 13:21:18 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.63 % 0.19/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.63 (2023-06-19) % 0.19/0.63 % 0.19/0.63 (c) Philipp Rümmer, 2009-2023 % 0.19/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.63 Amanda Stjerna. % 0.19/0.63 Free software under BSD-3-Clause. % 0.19/0.63 % 0.19/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.63 % 0.19/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.65 Running up to 7 provers in parallel. % 0.19/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.20/1.30 Prover 4: Preprocessing ... % 3.75/1.30 Prover 1: Preprocessing ... % 3.75/1.36 Prover 6: Preprocessing ... % 3.75/1.36 Prover 3: Preprocessing ... % 3.75/1.36 Prover 0: Preprocessing ... % 3.75/1.36 Prover 2: Preprocessing ... % 3.75/1.36 Prover 5: Preprocessing ... % 9.54/2.21 Prover 1: Warning: ignoring some quantifiers % 9.54/2.29 Prover 1: Constructing countermodel ... % 9.54/2.30 Prover 6: Proving ... % 9.54/2.31 Prover 5: Proving ... % 9.54/2.34 Prover 3: Warning: ignoring some quantifiers % 10.16/2.36 Prover 3: Constructing countermodel ... % 10.16/2.37 Prover 2: Proving ... % 10.16/2.44 Prover 0: Proving ... % 10.16/2.45 Prover 4: Warning: ignoring some quantifiers % 12.06/2.48 Prover 4: Constructing countermodel ... % 12.66/2.62 Prover 3: proved (1959ms) % 12.66/2.62 % 13.25/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.25/2.63 % 13.25/2.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.25/2.66 Prover 0: stopped % 13.25/2.66 Prover 6: stopped % 13.25/2.66 Prover 5: stopped % 13.25/2.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.25/2.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.25/2.66 Prover 2: stopped % 13.25/2.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.25/2.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.51/2.74 Prover 11: Preprocessing ... % 14.16/2.77 Prover 10: Preprocessing ... % 14.16/2.78 Prover 8: Preprocessing ... % 14.16/2.78 Prover 13: Preprocessing ... % 14.16/2.79 Prover 7: Preprocessing ... % 14.72/3.03 Prover 10: Warning: ignoring some quantifiers % 14.72/3.08 Prover 7: Warning: ignoring some quantifiers % 14.72/3.08 Prover 10: Constructing countermodel ... % 14.72/3.09 Prover 1: Found proof (size 98) % 14.72/3.09 Prover 1: proved (2430ms) % 14.72/3.10 Prover 4: stopped % 15.45/3.10 Prover 10: stopped % 15.45/3.11 Prover 7: Constructing countermodel ... % 15.45/3.11 Prover 13: Warning: ignoring some quantifiers % 15.45/3.12 Prover 8: Warning: ignoring some quantifiers % 15.45/3.12 Prover 7: stopped % 15.45/3.13 Prover 13: Constructing countermodel ... % 15.45/3.14 Prover 13: stopped % 15.45/3.15 Prover 8: Constructing countermodel ... % 15.45/3.15 Prover 11: Warning: ignoring some quantifiers % 16.94/3.16 Prover 8: stopped % 16.94/3.17 Prover 11: Constructing countermodel ... % 16.94/3.19 Prover 11: stopped % 16.94/3.19 % 16.94/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.94/3.19 % 17.29/3.24 % SZS output start Proof for theBenchmark % 17.29/3.25 Assumptions after simplification: % 17.29/3.25 --------------------------------- % 17.29/3.25 % 17.29/3.25 (ass(cond(61, 0), 0)) % 17.50/3.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1) % 17.50/3.29 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2))) % 17.50/3.29 % 17.50/3.29 (holds(264, 412, 0)) % 17.50/3.29 $i(v1) & $i(vd411) & ? [v0: $i] : (vmul(v0, v1) = v0 & vsucc(vd411) = v0 & % 17.50/3.29 $i(v0)) % 17.50/3.29 % 17.50/3.29 (holds(264, 412, 1)) % 17.50/3.30 $i(v1) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : (vmul(vd411, v1) = v1 & % 17.50/3.30 vsucc(v1) = v0 & vsucc(vd411) = v0 & $i(v1) & $i(v0)) % 17.50/3.30 % 17.50/3.30 (holds(264, 412, 2)) % 17.50/3.30 $i(v1) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : (vmul(vd411, v1) = v0 & % 17.50/3.30 vsucc(v0) = v1 & vplus(v0, v1) = v1 & $i(v1) & $i(v0)) % 17.50/3.30 % 17.50/3.30 (holds(265, 414, 0)) % 17.50/3.30 $i(vd413) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vmul(v0, % 17.50/3.30 vd413) = v1 & vmul(vd411, vd413) = v2 & vsucc(vd411) = v0 & vplus(v2, % 17.50/3.30 vd413) = v1 & $i(v2) & $i(v1) & $i(v0)) % 17.50/3.30 % 17.50/3.30 (holds(266, 415, 0)) % 17.50/3.30 $i(vd413) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 17.50/3.30 : (vmul(v0, v1) = v2 & vmul(v0, vd413) = v3 & vsucc(vd413) = v1 & vsucc(vd411) % 17.50/3.30 = v0 & vplus(v3, v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.50/3.30 % 17.50/3.30 (holds(266, 415, 1)) % 17.50/3.31 $i(vd413) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 17.50/3.31 : ? [v4: $i] : (vmul(v0, vd413) = v1 & vmul(vd411, vd413) = v3 & vsucc(vd411) % 17.50/3.31 = v0 & vplus(v4, v0) = v2 & vplus(v3, vd413) = v4 & vplus(v1, v0) = v2 & % 17.50/3.31 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.50/3.31 % 17.50/3.31 (holds(266, 415, 2)) % 17.50/3.31 $i(vd413) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 17.50/3.31 : ? [v4: $i] : (vmul(vd411, vd413) = v0 & vsucc(vd411) = v2 & vplus(v1, v2) = % 17.50/3.31 v3 & vplus(v0, v4) = v3 & vplus(v0, vd413) = v1 & vplus(vd413, v2) = v4 & % 17.50/3.31 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.50/3.31 % 17.50/3.31 (holds(266, 415, 3)) % 17.50/3.31 $i(vd413) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 17.50/3.31 : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v3) & vmul(vd411, vd413) = v0 & % 17.50/3.31 vsucc(vd411) = v1 & vplus(v1, vd413) = v4 & vplus(v0, v4) = v5 & vplus(v0, % 17.50/3.31 v2) = v3 & vplus(vd413, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 17.50/3.31 $i(v1) & $i(v0)) % 17.50/3.32 % 17.50/3.32 (function-axioms) % 17.50/3.32 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 17.50/3.32 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 17.50/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.50/3.32 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: % 17.50/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.50/3.32 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 17.50/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.50/3.32 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : ! % 17.50/3.32 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ % 17.50/3.32 (vmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 17.50/3.32 : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i] % 17.50/3.32 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ % 17.50/3.32 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 17.50/3.32 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 17.50/3.32 % 17.50/3.32 Further assumptions not needed in the proof: % 17.50/3.32 -------------------------------------------- % 17.50/3.33 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158, % 17.50/3.33 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), % 17.50/3.33 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223, % 17.50/3.33 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), % 17.50/3.33 ass(cond(253, 0), 0), ass(cond(33, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), % 17.50/3.33 0), ass(cond(6, 0), 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), % 17.50/3.33 ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0), % 17.50/3.33 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), 0), % 17.50/3.33 ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1), ass(cond(goal(193), 0), % 17.50/3.33 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0), 1), % 17.50/3.33 ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88), 0), % 17.50/3.33 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), % 17.50/3.33 0), 3), def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 12), % 17.50/3.33 1), def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1), % 17.50/3.33 qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3), % 17.50/3.33 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), % 17.50/3.33 qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), % 17.50/3.33 holds(definiens(249), 398, 0))), qu(restrictor(axiom(1)), % 17.50/3.33 holds(scope(axiom(1)), 2, 0)) % 17.50/3.33 % 17.50/3.33 Those formulas are unsatisfiable: % 17.50/3.33 --------------------------------- % 17.50/3.33 % 17.50/3.33 Begin of proof % 17.50/3.33 | % 17.50/3.33 | ALPHA: (holds(266, 415, 2)) implies: % 17.50/3.33 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.50/3.33 | (vmul(vd411, vd413) = v0 & vsucc(vd411) = v2 & vplus(v1, v2) = v3 & % 17.50/3.33 | vplus(v0, v4) = v3 & vplus(v0, vd413) = v1 & vplus(vd413, v2) = v4 & % 17.50/3.33 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.50/3.34 | % 17.50/3.34 | ALPHA: (holds(266, 415, 1)) implies: % 17.50/3.34 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.50/3.34 | (vmul(v0, vd413) = v1 & vmul(vd411, vd413) = v3 & vsucc(vd411) = v0 & % 17.50/3.34 | vplus(v4, v0) = v2 & vplus(v3, vd413) = v4 & vplus(v1, v0) = v2 & % 17.50/3.34 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.50/3.34 | % 17.50/3.34 | ALPHA: (holds(266, 415, 0)) implies: % 17.85/3.34 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vmul(v0, v1) = % 17.85/3.34 | v2 & vmul(v0, vd413) = v3 & vsucc(vd413) = v1 & vsucc(vd411) = v0 & % 17.85/3.34 | vplus(v3, v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.85/3.34 | % 17.85/3.34 | ALPHA: (holds(265, 414, 0)) implies: % 17.85/3.34 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vmul(v0, vd413) = v1 & % 17.85/3.34 | vmul(vd411, vd413) = v2 & vsucc(vd411) = v0 & vplus(v2, vd413) = v1 & % 17.85/3.34 | $i(v2) & $i(v1) & $i(v0)) % 17.85/3.34 | % 17.85/3.34 | ALPHA: (holds(264, 412, 2)) implies: % 17.85/3.34 | (5) ? [v0: $i] : ? [v1: $i] : (vmul(vd411, v1) = v0 & vsucc(v0) = v1 & % 17.85/3.34 | vplus(v0, v1) = v1 & $i(v1) & $i(v0)) % 17.85/3.34 | % 17.85/3.34 | ALPHA: (holds(264, 412, 1)) implies: % 17.85/3.35 | (6) ? [v0: $i] : ? [v1: $i] : (vmul(vd411, v1) = v1 & vsucc(v1) = v0 & % 17.85/3.35 | vsucc(vd411) = v0 & $i(v1) & $i(v0)) % 17.85/3.35 | % 17.85/3.35 | ALPHA: (holds(264, 412, 0)) implies: % 17.85/3.35 | (7) ? [v0: $i] : (vmul(v0, v1) = v0 & vsucc(vd411) = v0 & $i(v0)) % 17.85/3.35 | % 17.85/3.35 | ALPHA: (holds(266, 415, 3)) implies: % 17.85/3.35 | (8) $i(vd413) % 17.85/3.35 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.85/3.35 | ? [v5: $i] : ( ~ (v5 = v3) & vmul(vd411, vd413) = v0 & vsucc(vd411) = % 17.85/3.35 | v1 & vplus(v1, vd413) = v4 & vplus(v0, v4) = v5 & vplus(v0, v2) = v3 % 17.85/3.35 | & vplus(vd413, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 17.85/3.35 | & $i(v0)) % 17.85/3.35 | % 17.85/3.35 | ALPHA: (function-axioms) implies: % 17.85/3.35 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = % 17.85/3.35 | v1) | ~ (vsucc(v2) = v0)) % 17.85/3.35 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.85/3.35 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 17.85/3.36 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.85/3.36 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 17.85/3.36 | % 17.85/3.36 | DELTA: instantiating (7) with fresh symbol all_46_0 gives: % 17.85/3.36 | (13) vmul(all_46_0, v1) = all_46_0 & vsucc(vd411) = all_46_0 & $i(all_46_0) % 17.85/3.36 | % 17.85/3.36 | ALPHA: (13) implies: % 17.85/3.36 | (14) vsucc(vd411) = all_46_0 % 17.85/3.36 | % 17.85/3.36 | DELTA: instantiating (6) with fresh symbols all_50_0, all_50_1 gives: % 17.85/3.36 | (15) vmul(vd411, v1) = all_50_0 & vsucc(all_50_0) = all_50_1 & vsucc(vd411) % 17.85/3.36 | = all_50_1 & $i(all_50_0) & $i(all_50_1) % 17.85/3.36 | % 17.85/3.36 | ALPHA: (15) implies: % 17.85/3.36 | (16) vsucc(vd411) = all_50_1 % 17.85/3.36 | (17) vsucc(all_50_0) = all_50_1 % 17.85/3.36 | (18) vmul(vd411, v1) = all_50_0 % 17.85/3.36 | % 17.85/3.36 | DELTA: instantiating (5) with fresh symbols all_54_0, all_54_1 gives: % 17.85/3.36 | (19) vmul(vd411, v1) = all_54_1 & vsucc(all_54_1) = all_54_0 & % 17.85/3.36 | vplus(all_54_1, v1) = all_54_0 & $i(all_54_0) & $i(all_54_1) % 17.85/3.36 | % 17.85/3.36 | ALPHA: (19) implies: % 17.85/3.36 | (20) $i(all_54_0) % 17.85/3.36 | (21) vsucc(all_54_1) = all_54_0 % 17.85/3.36 | (22) vmul(vd411, v1) = all_54_1 % 17.85/3.36 | % 17.85/3.36 | DELTA: instantiating (4) with fresh symbols all_57_0, all_57_1, all_57_2 % 17.85/3.36 | gives: % 17.85/3.36 | (23) vmul(all_57_2, vd413) = all_57_1 & vmul(vd411, vd413) = all_57_0 & % 17.85/3.36 | vsucc(vd411) = all_57_2 & vplus(all_57_0, vd413) = all_57_1 & % 17.85/3.36 | $i(all_57_0) & $i(all_57_1) & $i(all_57_2) % 17.85/3.36 | % 17.85/3.37 | ALPHA: (23) implies: % 17.85/3.37 | (24) vplus(all_57_0, vd413) = all_57_1 % 17.85/3.37 | (25) vsucc(vd411) = all_57_2 % 17.85/3.37 | (26) vmul(vd411, vd413) = all_57_0 % 17.85/3.37 | (27) vmul(all_57_2, vd413) = all_57_1 % 17.85/3.37 | % 17.85/3.37 | DELTA: instantiating (3) with fresh symbols all_61_0, all_61_1, all_61_2, % 17.85/3.37 | all_61_3 gives: % 17.85/3.37 | (28) vmul(all_61_3, all_61_2) = all_61_1 & vmul(all_61_3, vd413) = all_61_0 % 17.85/3.37 | & vsucc(vd413) = all_61_2 & vsucc(vd411) = all_61_3 & vplus(all_61_0, % 17.85/3.37 | all_61_3) = all_61_1 & $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & % 17.85/3.37 | $i(all_61_3) % 17.85/3.37 | % 17.85/3.37 | ALPHA: (28) implies: % 17.85/3.37 | (29) vplus(all_61_0, all_61_3) = all_61_1 % 17.85/3.37 | (30) vsucc(vd411) = all_61_3 % 17.85/3.37 | (31) vmul(all_61_3, vd413) = all_61_0 % 17.85/3.37 | % 17.85/3.37 | DELTA: instantiating (2) with fresh symbols all_63_0, all_63_1, all_63_2, % 17.85/3.37 | all_63_3, all_63_4 gives: % 17.99/3.37 | (32) vmul(all_63_4, vd413) = all_63_3 & vmul(vd411, vd413) = all_63_1 & % 17.99/3.37 | vsucc(vd411) = all_63_4 & vplus(all_63_0, all_63_4) = all_63_2 & % 17.99/3.37 | vplus(all_63_1, vd413) = all_63_0 & vplus(all_63_3, all_63_4) = % 17.99/3.37 | all_63_2 & $i(all_63_0) & $i(all_63_1) & $i(all_63_2) & $i(all_63_3) & % 17.99/3.37 | $i(all_63_4) % 17.99/3.37 | % 17.99/3.37 | ALPHA: (32) implies: % 17.99/3.37 | (33) $i(all_63_1) % 17.99/3.37 | (34) vsucc(vd411) = all_63_4 % 17.99/3.37 | (35) vmul(vd411, vd413) = all_63_1 % 17.99/3.37 | (36) vmul(all_63_4, vd413) = all_63_3 % 17.99/3.37 | % 17.99/3.37 | DELTA: instantiating (1) with fresh symbols all_65_0, all_65_1, all_65_2, % 17.99/3.37 | all_65_3, all_65_4 gives: % 17.99/3.37 | (37) vmul(vd411, vd413) = all_65_4 & vsucc(vd411) = all_65_2 & % 17.99/3.37 | vplus(all_65_3, all_65_2) = all_65_1 & vplus(all_65_4, all_65_0) = % 17.99/3.37 | all_65_1 & vplus(all_65_4, vd413) = all_65_3 & vplus(vd413, all_65_2) % 17.99/3.37 | = all_65_0 & $i(all_65_0) & $i(all_65_1) & $i(all_65_2) & $i(all_65_3) % 17.99/3.37 | & $i(all_65_4) % 17.99/3.37 | % 17.99/3.37 | ALPHA: (37) implies: % 17.99/3.37 | (38) vplus(vd413, all_65_2) = all_65_0 % 17.99/3.37 | (39) vplus(all_65_4, vd413) = all_65_3 % 17.99/3.38 | (40) vplus(all_65_4, all_65_0) = all_65_1 % 17.99/3.38 | (41) vplus(all_65_3, all_65_2) = all_65_1 % 17.99/3.38 | (42) vsucc(vd411) = all_65_2 % 17.99/3.38 | (43) vmul(vd411, vd413) = all_65_4 % 17.99/3.38 | % 17.99/3.38 | DELTA: instantiating (9) with fresh symbols all_67_0, all_67_1, all_67_2, % 17.99/3.38 | all_67_3, all_67_4, all_67_5 gives: % 17.99/3.38 | (44) ~ (all_67_0 = all_67_2) & vmul(vd411, vd413) = all_67_5 & % 17.99/3.38 | vsucc(vd411) = all_67_4 & vplus(all_67_4, vd413) = all_67_1 & % 17.99/3.38 | vplus(all_67_5, all_67_1) = all_67_0 & vplus(all_67_5, all_67_3) = % 17.99/3.38 | all_67_2 & vplus(vd413, all_67_4) = all_67_3 & $i(all_67_0) & % 17.99/3.38 | $i(all_67_1) & $i(all_67_2) & $i(all_67_3) & $i(all_67_4) & % 17.99/3.38 | $i(all_67_5) % 17.99/3.38 | % 17.99/3.38 | ALPHA: (44) implies: % 17.99/3.38 | (45) ~ (all_67_0 = all_67_2) % 17.99/3.38 | (46) vplus(vd413, all_67_4) = all_67_3 % 17.99/3.38 | (47) vplus(all_67_5, all_67_3) = all_67_2 % 17.99/3.38 | (48) vplus(all_67_5, all_67_1) = all_67_0 % 17.99/3.38 | (49) vplus(all_67_4, vd413) = all_67_1 % 17.99/3.38 | (50) vsucc(vd411) = all_67_4 % 17.99/3.38 | (51) vmul(vd411, vd413) = all_67_5 % 17.99/3.38 | % 17.99/3.38 | GROUND_INST: instantiating (10) with all_57_2, all_61_3, vd411, simplifying % 17.99/3.38 | with (25), (30) gives: % 17.99/3.38 | (52) all_61_3 = all_57_2 % 17.99/3.38 | % 17.99/3.38 | GROUND_INST: instantiating (10) with all_46_0, all_61_3, vd411, simplifying % 17.99/3.38 | with (14), (30) gives: % 17.99/3.38 | (53) all_61_3 = all_46_0 % 17.99/3.38 | % 17.99/3.38 | GROUND_INST: instantiating (10) with all_61_3, all_63_4, vd411, simplifying % 17.99/3.38 | with (30), (34) gives: % 17.99/3.38 | (54) all_63_4 = all_61_3 % 17.99/3.38 | % 17.99/3.38 | GROUND_INST: instantiating (10) with all_63_4, all_65_2, vd411, simplifying % 17.99/3.38 | with (34), (42) gives: % 17.99/3.38 | (55) all_65_2 = all_63_4 % 17.99/3.38 | % 17.99/3.38 | GROUND_INST: instantiating (10) with all_65_2, all_67_4, vd411, simplifying % 17.99/3.38 | with (42), (50) gives: % 17.99/3.38 | (56) all_67_4 = all_65_2 % 17.99/3.38 | % 17.99/3.38 | GROUND_INST: instantiating (10) with all_50_1, all_67_4, vd411, simplifying % 17.99/3.38 | with (16), (50) gives: % 17.99/3.38 | (57) all_67_4 = all_50_1 % 17.99/3.38 | % 17.99/3.39 | GROUND_INST: instantiating (12) with all_63_1, all_65_4, vd413, vd411, % 17.99/3.39 | simplifying with (35), (43) gives: % 17.99/3.39 | (58) all_65_4 = all_63_1 % 17.99/3.39 | % 17.99/3.39 | GROUND_INST: instantiating (12) with all_65_4, all_67_5, vd413, vd411, % 17.99/3.39 | simplifying with (43), (51) gives: % 17.99/3.39 | (59) all_67_5 = all_65_4 % 17.99/3.39 | % 17.99/3.39 | GROUND_INST: instantiating (12) with all_57_0, all_67_5, vd413, vd411, % 17.99/3.39 | simplifying with (26), (51) gives: % 17.99/3.39 | (60) all_67_5 = all_57_0 % 17.99/3.39 | % 17.99/3.39 | GROUND_INST: instantiating (12) with all_50_0, all_54_1, v1, vd411, % 17.99/3.39 | simplifying with (18), (22) gives: % 17.99/3.39 | (61) all_54_1 = all_50_0 % 17.99/3.39 | % 17.99/3.39 | COMBINE_EQS: (56), (57) imply: % 17.99/3.39 | (62) all_65_2 = all_50_1 % 17.99/3.39 | % 17.99/3.39 | SIMP: (62) implies: % 17.99/3.39 | (63) all_65_2 = all_50_1 % 17.99/3.39 | % 17.99/3.39 | COMBINE_EQS: (59), (60) imply: % 17.99/3.39 | (64) all_65_4 = all_57_0 % 17.99/3.39 | % 17.99/3.39 | SIMP: (64) implies: % 17.99/3.39 | (65) all_65_4 = all_57_0 % 17.99/3.39 | % 17.99/3.39 | COMBINE_EQS: (55), (63) imply: % 17.99/3.39 | (66) all_63_4 = all_50_1 % 17.99/3.39 | % 17.99/3.39 | SIMP: (66) implies: % 17.99/3.39 | (67) all_63_4 = all_50_1 % 17.99/3.39 | % 17.99/3.39 | COMBINE_EQS: (58), (65) imply: % 17.99/3.39 | (68) all_63_1 = all_57_0 % 17.99/3.39 | % 17.99/3.39 | SIMP: (68) implies: % 17.99/3.39 | (69) all_63_1 = all_57_0 % 17.99/3.39 | % 17.99/3.39 | COMBINE_EQS: (54), (67) imply: % 17.99/3.39 | (70) all_61_3 = all_50_1 % 17.99/3.39 | % 17.99/3.39 | SIMP: (70) implies: % 17.99/3.39 | (71) all_61_3 = all_50_1 % 17.99/3.39 | % 17.99/3.39 | COMBINE_EQS: (52), (53) imply: % 17.99/3.39 | (72) all_57_2 = all_46_0 % 17.99/3.39 | % 17.99/3.39 | COMBINE_EQS: (52), (71) imply: % 17.99/3.39 | (73) all_57_2 = all_50_1 % 17.99/3.39 | % 17.99/3.39 | COMBINE_EQS: (72), (73) imply: % 17.99/3.39 | (74) all_50_1 = all_46_0 % 17.99/3.39 | % 17.99/3.39 | COMBINE_EQS: (67), (74) imply: % 17.99/3.39 | (75) all_63_4 = all_46_0 % 17.99/3.39 | % 17.99/3.39 | COMBINE_EQS: (63), (74) imply: % 17.99/3.39 | (76) all_65_2 = all_46_0 % 17.99/3.39 | % 17.99/3.39 | COMBINE_EQS: (57), (74) imply: % 17.99/3.39 | (77) all_67_4 = all_46_0 % 17.99/3.39 | % 17.99/3.39 | REDUCE: (36), (75) imply: % 17.99/3.39 | (78) vmul(all_46_0, vd413) = all_63_3 % 17.99/3.39 | % 17.99/3.39 | REDUCE: (31), (53) imply: % 17.99/3.39 | (79) vmul(all_46_0, vd413) = all_61_0 % 17.99/3.39 | % 17.99/3.39 | REDUCE: (27), (72) imply: % 17.99/3.39 | (80) vmul(all_46_0, vd413) = all_57_1 % 17.99/3.39 | % 17.99/3.39 | REDUCE: (21), (61) imply: % 17.99/3.39 | (81) vsucc(all_50_0) = all_54_0 % 17.99/3.39 | % 17.99/3.39 | REDUCE: (17), (74) imply: % 17.99/3.39 | (82) vsucc(all_50_0) = all_46_0 % 17.99/3.39 | % 17.99/3.40 | REDUCE: (49), (77) imply: % 17.99/3.40 | (83) vplus(all_46_0, vd413) = all_67_1 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (48), (60) imply: % 17.99/3.40 | (84) vplus(all_57_0, all_67_1) = all_67_0 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (47), (60) imply: % 17.99/3.40 | (85) vplus(all_57_0, all_67_3) = all_67_2 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (41), (76) imply: % 17.99/3.40 | (86) vplus(all_65_3, all_46_0) = all_65_1 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (40), (65) imply: % 17.99/3.40 | (87) vplus(all_57_0, all_65_0) = all_65_1 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (39), (65) imply: % 17.99/3.40 | (88) vplus(all_57_0, vd413) = all_65_3 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (29), (53) imply: % 17.99/3.40 | (89) vplus(all_61_0, all_46_0) = all_61_1 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (46), (77) imply: % 17.99/3.40 | (90) vplus(vd413, all_46_0) = all_67_3 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (38), (76) imply: % 17.99/3.40 | (91) vplus(vd413, all_46_0) = all_65_0 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (33), (69) imply: % 17.99/3.40 | (92) $i(all_57_0) % 17.99/3.40 | % 17.99/3.40 | GROUND_INST: instantiating (11) with all_65_0, all_67_3, all_46_0, vd413, % 17.99/3.40 | simplifying with (90), (91) gives: % 17.99/3.40 | (93) all_67_3 = all_65_0 % 17.99/3.40 | % 17.99/3.40 | GROUND_INST: instantiating (11) with all_57_1, all_65_3, vd413, all_57_0, % 17.99/3.40 | simplifying with (24), (88) gives: % 17.99/3.40 | (94) all_65_3 = all_57_1 % 17.99/3.40 | % 17.99/3.40 | GROUND_INST: instantiating (10) with all_46_0, all_54_0, all_50_0, simplifying % 17.99/3.40 | with (81), (82) gives: % 17.99/3.40 | (95) all_54_0 = all_46_0 % 17.99/3.40 | % 17.99/3.40 | GROUND_INST: instantiating (12) with all_61_0, all_63_3, vd413, all_46_0, % 17.99/3.40 | simplifying with (78), (79) gives: % 17.99/3.40 | (96) all_63_3 = all_61_0 % 17.99/3.40 | % 17.99/3.40 | GROUND_INST: instantiating (12) with all_57_1, all_63_3, vd413, all_46_0, % 17.99/3.40 | simplifying with (78), (80) gives: % 17.99/3.40 | (97) all_63_3 = all_57_1 % 17.99/3.40 | % 17.99/3.40 | COMBINE_EQS: (96), (97) imply: % 17.99/3.40 | (98) all_61_0 = all_57_1 % 17.99/3.40 | % 17.99/3.40 | SIMP: (98) implies: % 17.99/3.40 | (99) all_61_0 = all_57_1 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (86), (94) imply: % 17.99/3.40 | (100) vplus(all_57_1, all_46_0) = all_65_1 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (89), (99) imply: % 17.99/3.40 | (101) vplus(all_57_1, all_46_0) = all_61_1 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (85), (93) imply: % 17.99/3.40 | (102) vplus(all_57_0, all_65_0) = all_67_2 % 17.99/3.40 | % 17.99/3.40 | REDUCE: (20), (95) imply: % 17.99/3.41 | (103) $i(all_46_0) % 17.99/3.41 | % 17.99/3.41 | GROUND_INST: instantiating (11) with all_61_1, all_65_1, all_46_0, all_57_1, % 17.99/3.41 | simplifying with (100), (101) gives: % 17.99/3.41 | (104) all_65_1 = all_61_1 % 17.99/3.41 | % 17.99/3.41 | GROUND_INST: instantiating (11) with all_65_1, all_67_2, all_65_0, all_57_0, % 17.99/3.41 | simplifying with (87), (102) gives: % 17.99/3.41 | (105) all_67_2 = all_65_1 % 17.99/3.41 | % 17.99/3.41 | COMBINE_EQS: (104), (105) imply: % 17.99/3.41 | (106) all_67_2 = all_61_1 % 17.99/3.41 | % 17.99/3.41 | REDUCE: (45), (106) imply: % 17.99/3.41 | (107) ~ (all_67_0 = all_61_1) % 17.99/3.41 | % 17.99/3.41 | REDUCE: (87), (104) imply: % 17.99/3.41 | (108) vplus(all_57_0, all_65_0) = all_61_1 % 17.99/3.41 | % 17.99/3.41 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd413, all_46_0, % 17.99/3.41 | all_65_0, simplifying with (8), (91), (103) gives: % 17.99/3.41 | (109) vplus(all_46_0, vd413) = all_65_0 & $i(all_65_0) % 17.99/3.41 | % 17.99/3.41 | ALPHA: (109) implies: % 17.99/3.41 | (110) $i(all_65_0) % 17.99/3.41 | (111) vplus(all_46_0, vd413) = all_65_0 % 17.99/3.41 | % 17.99/3.41 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_46_0, vd413, % 17.99/3.41 | all_67_1, simplifying with (8), (83), (103) gives: % 17.99/3.41 | (112) vplus(vd413, all_46_0) = all_67_1 & $i(all_67_1) % 17.99/3.41 | % 17.99/3.41 | ALPHA: (112) implies: % 17.99/3.41 | (113) $i(all_67_1) % 17.99/3.41 | % 17.99/3.41 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_57_0, all_65_0, % 17.99/3.41 | all_61_1, simplifying with (92), (108), (110) gives: % 17.99/3.41 | (114) vplus(all_65_0, all_57_0) = all_61_1 & $i(all_61_1) % 17.99/3.41 | % 17.99/3.41 | ALPHA: (114) implies: % 17.99/3.41 | (115) vplus(all_65_0, all_57_0) = all_61_1 % 17.99/3.41 | % 17.99/3.41 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_57_0, all_67_1, % 17.99/3.41 | all_67_0, simplifying with (84), (92), (113) gives: % 17.99/3.41 | (116) vplus(all_67_1, all_57_0) = all_67_0 & $i(all_67_0) % 17.99/3.41 | % 17.99/3.41 | ALPHA: (116) implies: % 17.99/3.41 | (117) vplus(all_67_1, all_57_0) = all_67_0 % 17.99/3.41 | % 17.99/3.41 | GROUND_INST: instantiating (11) with all_67_1, all_65_0, vd413, all_46_0, % 17.99/3.41 | simplifying with (83), (111) gives: % 17.99/3.41 | (118) all_67_1 = all_65_0 % 17.99/3.41 | % 17.99/3.41 | REDUCE: (117), (118) imply: % 17.99/3.41 | (119) vplus(all_65_0, all_57_0) = all_67_0 % 17.99/3.41 | % 17.99/3.42 | GROUND_INST: instantiating (11) with all_61_1, all_67_0, all_57_0, all_65_0, % 17.99/3.42 | simplifying with (115), (119) gives: % 17.99/3.42 | (120) all_67_0 = all_61_1 % 17.99/3.42 | % 17.99/3.42 | REDUCE: (107), (120) imply: % 17.99/3.42 | (121) $false % 17.99/3.42 | % 17.99/3.42 | CLOSE: (121) is inconsistent. % 17.99/3.42 | % 17.99/3.42 End of proof % 17.99/3.42 % SZS output end Proof for theBenchmark % 17.99/3.42 % 17.99/3.42 2784ms %------------------------------------------------------------------------------