%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM847+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 : n021.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 11:50:22 EDT 2023 % Result : Theorem 9.89s 2.11s % Output : Proof 12.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM847+1 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n021.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 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 08:13:56 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.10/1.14 Prover 4: Preprocessing ... % 3.10/1.14 Prover 1: Preprocessing ... % 3.48/1.18 Prover 0: Preprocessing ... % 3.48/1.18 Prover 5: Preprocessing ... % 3.48/1.18 Prover 2: Preprocessing ... % 3.48/1.18 Prover 3: Preprocessing ... % 3.48/1.18 Prover 6: Preprocessing ... % 8.04/1.83 Prover 1: Warning: ignoring some quantifiers % 8.04/1.83 Prover 3: Warning: ignoring some quantifiers % 8.50/1.86 Prover 3: Constructing countermodel ... % 8.60/1.88 Prover 6: Proving ... % 8.60/1.88 Prover 4: Warning: ignoring some quantifiers % 8.60/1.89 Prover 5: Proving ... % 8.60/1.89 Prover 1: Constructing countermodel ... % 8.98/1.94 Prover 4: Constructing countermodel ... % 9.25/1.98 Prover 2: Proving ... % 9.25/2.00 Prover 0: Proving ... % 9.89/2.11 Prover 3: proved (1482ms) % 9.89/2.11 % 9.89/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.89/2.11 % 9.89/2.11 Prover 6: stopped % 9.89/2.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.89/2.12 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.89/2.13 Prover 5: stopped % 9.89/2.14 Prover 2: stopped % 9.89/2.15 Prover 0: stopped % 9.89/2.15 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.89/2.15 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.89/2.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.89/2.21 Prover 7: Preprocessing ... % 9.89/2.21 Prover 8: Preprocessing ... % 10.59/2.23 Prover 13: Preprocessing ... % 10.59/2.24 Prover 11: Preprocessing ... % 10.59/2.25 Prover 10: Preprocessing ... % 11.79/2.34 Prover 1: Found proof (size 80) % 11.79/2.34 Prover 1: proved (1715ms) % 11.79/2.34 Prover 4: stopped % 11.79/2.35 Prover 11: stopped % 11.79/2.37 Prover 10: Warning: ignoring some quantifiers % 11.79/2.38 Prover 7: Warning: ignoring some quantifiers % 11.79/2.38 Prover 10: Constructing countermodel ... % 11.79/2.39 Prover 7: Constructing countermodel ... % 11.79/2.39 Prover 10: stopped % 11.79/2.40 Prover 13: Warning: ignoring some quantifiers % 11.79/2.40 Prover 8: Warning: ignoring some quantifiers % 11.79/2.40 Prover 7: stopped % 12.52/2.42 Prover 13: Constructing countermodel ... % 12.52/2.42 Prover 8: Constructing countermodel ... % 12.52/2.43 Prover 13: stopped % 12.52/2.43 Prover 8: stopped % 12.52/2.43 % 12.52/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.52/2.43 % 12.52/2.45 % SZS output start Proof for theBenchmark % 12.52/2.46 Assumptions after simplification: % 12.52/2.46 --------------------------------- % 12.52/2.46 % 12.52/2.46 (ass(cond(33, 0), 0)) % 12.52/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 12.52/2.49 (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 12.52/2.49 $i(v0) | ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) & % 12.52/2.49 $i(v4))) % 12.52/2.49 % 12.52/2.49 (holds(284, 438, 1)) % 12.52/2.49 $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.52/2.49 (vsucc(vd437) = v0 & vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 & % 12.52/2.49 vplus(v2, vd436) = v1 & $i(v2) & $i(v1) & $i(v0)) % 12.52/2.49 % 12.52/2.49 (holds(284, 438, 2)) % 12.52/2.49 $i(v1) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.52/2.49 (vmul(vd436, v1) = v2 & vmul(vd436, vd437) = v0 & vplus(v0, v2) = v1 & % 12.52/2.49 vplus(v0, vd436) = v1 & $i(v2) & $i(v1) & $i(v0)) % 12.52/2.49 % 12.52/2.49 (holds(285, 440, 0)) % 12.95/2.49 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.95/2.49 ? [v3: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436, % 12.95/2.49 vd437) = v2 & vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) & % 12.95/2.49 $i(v2) & $i(v1) & $i(v0)) % 12.95/2.49 % 12.95/2.49 (holds(286, 441, 0)) % 12.95/2.50 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.95/2.50 ? [v3: $i] : ? [v4: $i] : (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436, % 12.95/2.50 v4) = v2 & vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437, % 12.95/2.50 vd439) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.95/2.50 % 12.95/2.50 (holds(286, 441, 1)) % 12.95/2.50 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.95/2.50 ? [v3: $i] : (vsucc(v0) = v1 & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 & % 12.95/2.50 vplus(v3, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1) % 12.95/2.50 & $i(v0)) % 12.95/2.50 % 12.95/2.50 (holds(286, 441, 2)) % 12.95/2.50 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.95/2.50 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, % 12.95/2.50 vd439) = v4 & vmul(vd436, vd437) = v3 & vplus(v5, vd436) = v2 & vplus(v3, % 12.95/2.50 v4) = v5 & vplus(v1, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v5) & % 12.95/2.50 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.95/2.50 % 12.95/2.50 (holds(286, 441, 3)) % 12.95/2.50 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.95/2.50 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v3) & vmul(vd436, vd439) = % 12.95/2.50 v1 & vmul(vd436, vd437) = v0 & vplus(v2, vd436) = v3 & vplus(v1, vd436) = v4 % 12.95/2.50 & vplus(v0, v4) = v5 & vplus(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & % 12.95/2.50 $i(v2) & $i(v1) & $i(v0)) % 12.95/2.50 % 12.95/2.50 (function-axioms) % 12.95/2.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.95/2.51 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 12.95/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.95/2.51 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: % 12.95/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.95/2.51 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 12.95/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.95/2.51 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : ! % 12.95/2.51 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ % 12.95/2.51 (vmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 12.95/2.51 : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i] % 12.95/2.51 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ % 12.95/2.51 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 12.95/2.51 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 12.95/2.51 % 12.95/2.51 Further assumptions not needed in the proof: % 12.95/2.51 -------------------------------------------- % 12.95/2.51 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158, % 12.95/2.51 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), % 12.95/2.51 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223, % 12.95/2.51 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), % 12.95/2.51 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(270, 0), 0), ass(cond(43, % 12.95/2.51 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0), 0), % 12.95/2.51 ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 0), % 12.95/2.51 ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), % 12.95/2.51 3), ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0), 0), % 12.95/2.51 ass(cond(goal(193), 0), 1), ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), % 12.95/2.51 0), ass(cond(goal(202), 0), 1), ass(cond(goal(202), 0), 2), % 12.95/2.51 ass(cond(goal(216), 0), 0), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0), % 12.95/2.51 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), 0), 3), % 12.95/2.51 def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 12), 1), % 12.95/2.51 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1), % 12.95/2.51 holds(284, 438, 0), qu(antec(axiom(3)), imp(antec(axiom(3)))), % 12.95/2.51 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), % 12.95/2.51 holds(definiens(29), 44, 0))), qu(cond(conseq(axiom(3)), 32), % 12.95/2.51 and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), % 12.95/2.51 qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)) % 12.95/2.51 % 12.95/2.51 Those formulas are unsatisfiable: % 12.95/2.51 --------------------------------- % 12.95/2.51 % 12.95/2.51 Begin of proof % 12.95/2.51 | % 12.95/2.51 | ALPHA: (holds(286, 441, 2)) implies: % 12.95/2.51 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.95/2.51 | ? [v5: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v4 & % 12.95/2.51 | vmul(vd436, vd437) = v3 & vplus(v5, vd436) = v2 & vplus(v3, v4) = v5 % 12.95/2.51 | & vplus(v1, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v5) & $i(v4) % 12.95/2.51 | & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.95/2.51 | % 12.95/2.51 | ALPHA: (holds(286, 441, 1)) implies: % 12.95/2.51 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vsucc(v0) = v1 % 12.95/2.51 | & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 & vplus(v3, vd436) = v2 % 12.95/2.51 | & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.95/2.51 | % 12.95/2.51 | ALPHA: (holds(286, 441, 0)) implies: % 12.95/2.52 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.95/2.52 | (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436, v4) = v2 & % 12.95/2.52 | vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437, vd439) = % 12.95/2.52 | v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.95/2.52 | % 12.95/2.52 | ALPHA: (holds(285, 440, 0)) implies: % 12.95/2.52 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vmul(vd436, % 12.95/2.52 | v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436, vd437) = v2 & % 12.95/2.52 | vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & % 12.95/2.52 | $i(v1) & $i(v0)) % 12.95/2.52 | % 12.95/2.52 | ALPHA: (holds(284, 438, 2)) implies: % 12.95/2.52 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vmul(vd436, v1) = v2 & % 12.95/2.52 | vmul(vd436, vd437) = v0 & vplus(v0, v2) = v1 & vplus(v0, vd436) = v1 % 12.95/2.52 | & $i(v2) & $i(v1) & $i(v0)) % 12.95/2.52 | % 12.95/2.52 | ALPHA: (holds(284, 438, 1)) implies: % 12.95/2.52 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vsucc(vd437) = v0 & % 12.95/2.52 | vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 & vplus(v2, vd436) = % 12.95/2.52 | v1 & $i(v2) & $i(v1) & $i(v0)) % 12.95/2.52 | % 12.95/2.52 | ALPHA: (holds(286, 441, 3)) implies: % 12.95/2.52 | (7) $i(vd436) % 12.95/2.52 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.95/2.52 | ? [v5: $i] : ( ~ (v5 = v3) & vmul(vd436, vd439) = v1 & vmul(vd436, % 12.95/2.52 | vd437) = v0 & vplus(v2, vd436) = v3 & vplus(v1, vd436) = v4 & % 12.95/2.52 | vplus(v0, v4) = v5 & vplus(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & % 12.95/2.52 | $i(v2) & $i(v1) & $i(v0)) % 12.95/2.52 | % 12.95/2.52 | ALPHA: (function-axioms) implies: % 12.95/2.52 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.95/2.52 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 12.95/2.52 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.95/2.52 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 12.95/2.52 | % 12.95/2.52 | DELTA: instantiating (6) with fresh symbols all_53_0, all_53_1, all_53_2 % 12.95/2.52 | gives: % 12.95/2.52 | (11) vsucc(vd437) = all_53_2 & vmul(vd436, all_53_2) = all_53_1 & % 12.95/2.52 | vmul(vd436, vd437) = all_53_0 & vplus(all_53_0, vd436) = all_53_1 & % 12.95/2.52 | $i(all_53_0) & $i(all_53_1) & $i(all_53_2) % 12.95/2.52 | % 12.95/2.52 | ALPHA: (11) implies: % 12.95/2.52 | (12) vmul(vd436, vd437) = all_53_0 % 12.95/2.52 | % 12.95/2.52 | DELTA: instantiating (5) with fresh symbols all_55_0, all_55_1, all_55_2 % 12.95/2.52 | gives: % 12.95/2.52 | (13) vmul(vd436, v1) = all_55_0 & vmul(vd436, vd437) = all_55_2 & % 12.95/2.52 | vplus(all_55_2, all_55_0) = all_55_1 & vplus(all_55_2, vd436) = % 12.95/2.52 | all_55_1 & $i(all_55_0) & $i(all_55_1) & $i(all_55_2) % 12.95/2.52 | % 12.95/2.52 | ALPHA: (13) implies: % 12.95/2.52 | (14) $i(all_55_2) % 12.95/2.52 | (15) vmul(vd436, vd437) = all_55_2 % 12.95/2.52 | % 12.95/2.52 | DELTA: instantiating (4) with fresh symbols all_61_0, all_61_1, all_61_2, % 12.95/2.52 | all_61_3 gives: % 12.95/2.53 | (16) vmul(vd436, all_61_3) = all_61_2 & vmul(vd436, vd439) = all_61_0 & % 12.95/2.53 | vmul(vd436, vd437) = all_61_1 & vplus(all_61_1, all_61_0) = all_61_2 & % 12.95/2.53 | vplus(vd437, vd439) = all_61_3 & $i(all_61_0) & $i(all_61_1) & % 12.95/2.53 | $i(all_61_2) & $i(all_61_3) % 12.95/2.53 | % 12.95/2.53 | ALPHA: (16) implies: % 12.95/2.53 | (17) vplus(vd437, vd439) = all_61_3 % 12.95/2.53 | (18) vplus(all_61_1, all_61_0) = all_61_2 % 12.95/2.53 | (19) vmul(vd436, vd437) = all_61_1 % 12.95/2.53 | (20) vmul(vd436, vd439) = all_61_0 % 12.95/2.53 | (21) vmul(vd436, all_61_3) = all_61_2 % 12.95/2.53 | % 12.95/2.53 | DELTA: instantiating (2) with fresh symbols all_63_0, all_63_1, all_63_2, % 12.95/2.53 | all_63_3 gives: % 12.95/2.53 | (22) vsucc(all_63_3) = all_63_2 & vmul(vd436, all_63_2) = all_63_1 & % 12.95/2.53 | vmul(vd436, all_63_3) = all_63_0 & vplus(all_63_0, vd436) = all_63_1 & % 12.95/2.53 | vplus(vd437, vd439) = all_63_3 & $i(all_63_0) & $i(all_63_1) & % 12.95/2.53 | $i(all_63_2) & $i(all_63_3) % 12.95/2.53 | % 12.95/2.53 | ALPHA: (22) implies: % 12.95/2.53 | (23) vplus(vd437, vd439) = all_63_3 % 12.95/2.53 | (24) vplus(all_63_0, vd436) = all_63_1 % 12.95/2.53 | (25) vmul(vd436, all_63_3) = all_63_0 % 12.95/2.53 | % 12.95/2.53 | DELTA: instantiating (3) with fresh symbols all_65_0, all_65_1, all_65_2, % 12.95/2.53 | all_65_3, all_65_4 gives: % 12.95/2.53 | (26) vsucc(all_65_1) = all_65_0 & vsucc(vd439) = all_65_4 & vmul(vd436, % 12.95/2.53 | all_65_0) = all_65_2 & vmul(vd436, all_65_3) = all_65_2 & % 12.95/2.53 | vplus(vd437, all_65_4) = all_65_3 & vplus(vd437, vd439) = all_65_1 & % 12.95/2.53 | $i(all_65_0) & $i(all_65_1) & $i(all_65_2) & $i(all_65_3) & % 12.95/2.53 | $i(all_65_4) % 12.95/2.53 | % 12.95/2.53 | ALPHA: (26) implies: % 12.95/2.53 | (27) vplus(vd437, vd439) = all_65_1 % 12.95/2.53 | % 12.95/2.53 | DELTA: instantiating (8) with fresh symbols all_67_0, all_67_1, all_67_2, % 12.95/2.53 | all_67_3, all_67_4, all_67_5 gives: % 12.95/2.53 | (28) ~ (all_67_0 = all_67_2) & vmul(vd436, vd439) = all_67_4 & vmul(vd436, % 12.95/2.53 | vd437) = all_67_5 & vplus(all_67_3, vd436) = all_67_2 & % 12.95/2.53 | vplus(all_67_4, vd436) = all_67_1 & vplus(all_67_5, all_67_1) = % 12.95/2.53 | all_67_0 & vplus(all_67_5, all_67_4) = all_67_3 & $i(all_67_0) & % 12.95/2.53 | $i(all_67_1) & $i(all_67_2) & $i(all_67_3) & $i(all_67_4) & % 12.95/2.53 | $i(all_67_5) % 12.95/2.53 | % 12.95/2.53 | ALPHA: (28) implies: % 12.95/2.53 | (29) ~ (all_67_0 = all_67_2) % 12.95/2.53 | (30) $i(all_67_4) % 12.95/2.53 | (31) vplus(all_67_5, all_67_4) = all_67_3 % 12.95/2.53 | (32) vplus(all_67_5, all_67_1) = all_67_0 % 12.95/2.53 | (33) vplus(all_67_4, vd436) = all_67_1 % 12.95/2.53 | (34) vplus(all_67_3, vd436) = all_67_2 % 12.95/2.53 | (35) vmul(vd436, vd437) = all_67_5 % 12.95/2.53 | (36) vmul(vd436, vd439) = all_67_4 % 12.95/2.53 | % 12.95/2.53 | DELTA: instantiating (1) with fresh symbols all_69_0, all_69_1, all_69_2, % 12.95/2.53 | all_69_3, all_69_4, all_69_5 gives: % 12.95/2.53 | (37) vmul(vd436, all_69_5) = all_69_4 & vmul(vd436, vd439) = all_69_1 & % 12.95/2.53 | vmul(vd436, vd437) = all_69_2 & vplus(all_69_0, vd436) = all_69_3 & % 12.95/2.53 | vplus(all_69_2, all_69_1) = all_69_0 & vplus(all_69_4, vd436) = % 12.95/2.53 | all_69_3 & vplus(vd437, vd439) = all_69_5 & $i(all_69_0) & % 12.95/2.53 | $i(all_69_1) & $i(all_69_2) & $i(all_69_3) & $i(all_69_4) & % 12.95/2.53 | $i(all_69_5) % 12.95/2.53 | % 12.95/2.53 | ALPHA: (37) implies: % 12.95/2.53 | (38) vplus(vd437, vd439) = all_69_5 % 12.95/2.53 | (39) vplus(all_69_4, vd436) = all_69_3 % 12.95/2.53 | (40) vplus(all_69_2, all_69_1) = all_69_0 % 12.95/2.53 | (41) vmul(vd436, vd437) = all_69_2 % 12.95/2.53 | (42) vmul(vd436, vd439) = all_69_1 % 12.95/2.53 | (43) vmul(vd436, all_69_5) = all_69_4 % 12.95/2.53 | % 12.95/2.53 | GROUND_INST: instantiating (9) with all_61_3, all_65_1, vd439, vd437, % 12.95/2.53 | simplifying with (17), (27) gives: % 12.95/2.53 | (44) all_65_1 = all_61_3 % 12.95/2.53 | % 12.95/2.53 | GROUND_INST: instantiating (9) with all_65_1, all_69_5, vd439, vd437, % 12.95/2.53 | simplifying with (27), (38) gives: % 12.95/2.54 | (45) all_69_5 = all_65_1 % 12.95/2.54 | % 12.95/2.54 | GROUND_INST: instantiating (9) with all_63_3, all_69_5, vd439, vd437, % 12.95/2.54 | simplifying with (23), (38) gives: % 12.95/2.54 | (46) all_69_5 = all_63_3 % 12.95/2.54 | % 12.95/2.54 | GROUND_INST: instantiating (10) with all_53_0, all_61_1, vd437, vd436, % 12.95/2.54 | simplifying with (12), (19) gives: % 12.95/2.54 | (47) all_61_1 = all_53_0 % 12.95/2.54 | % 12.95/2.54 | GROUND_INST: instantiating (10) with all_61_1, all_67_5, vd437, vd436, % 12.95/2.54 | simplifying with (19), (35) gives: % 12.95/2.54 | (48) all_67_5 = all_61_1 % 12.95/2.54 | % 12.95/2.54 | GROUND_INST: instantiating (10) with all_67_5, all_69_2, vd437, vd436, % 12.95/2.54 | simplifying with (35), (41) gives: % 12.95/2.54 | (49) all_69_2 = all_67_5 % 12.95/2.54 | % 12.95/2.54 | GROUND_INST: instantiating (10) with all_55_2, all_69_2, vd437, vd436, % 12.95/2.54 | simplifying with (15), (41) gives: % 12.95/2.54 | (50) all_69_2 = all_55_2 % 12.95/2.54 | % 12.95/2.54 | GROUND_INST: instantiating (10) with all_67_4, all_69_1, vd439, vd436, % 12.95/2.54 | simplifying with (36), (42) gives: % 12.95/2.54 | (51) all_69_1 = all_67_4 % 12.95/2.54 | % 12.95/2.54 | GROUND_INST: instantiating (10) with all_61_0, all_69_1, vd439, vd436, % 12.95/2.54 | simplifying with (20), (42) gives: % 12.95/2.54 | (52) all_69_1 = all_61_0 % 12.95/2.54 | % 12.95/2.54 | COMBINE_EQS: (51), (52) imply: % 12.95/2.54 | (53) all_67_4 = all_61_0 % 12.95/2.54 | % 12.95/2.54 | COMBINE_EQS: (49), (50) imply: % 12.95/2.54 | (54) all_67_5 = all_55_2 % 12.95/2.54 | % 12.95/2.54 | SIMP: (54) implies: % 12.95/2.54 | (55) all_67_5 = all_55_2 % 12.95/2.54 | % 12.95/2.54 | COMBINE_EQS: (45), (46) imply: % 12.95/2.54 | (56) all_65_1 = all_63_3 % 12.95/2.54 | % 12.95/2.54 | SIMP: (56) implies: % 12.95/2.54 | (57) all_65_1 = all_63_3 % 12.95/2.54 | % 12.95/2.54 | COMBINE_EQS: (48), (55) imply: % 12.95/2.54 | (58) all_61_1 = all_55_2 % 12.95/2.54 | % 12.95/2.54 | SIMP: (58) implies: % 12.95/2.54 | (59) all_61_1 = all_55_2 % 12.95/2.54 | % 12.95/2.54 | COMBINE_EQS: (44), (57) imply: % 12.95/2.54 | (60) all_63_3 = all_61_3 % 12.95/2.54 | % 12.95/2.54 | COMBINE_EQS: (47), (59) imply: % 12.95/2.54 | (61) all_55_2 = all_53_0 % 12.95/2.54 | % 12.95/2.54 | COMBINE_EQS: (55), (61) imply: % 12.95/2.54 | (62) all_67_5 = all_53_0 % 12.95/2.54 | % 12.95/2.54 | COMBINE_EQS: (46), (60) imply: % 12.95/2.54 | (63) all_69_5 = all_61_3 % 12.95/2.54 | % 12.95/2.54 | COMBINE_EQS: (50), (61) imply: % 12.95/2.54 | (64) all_69_2 = all_53_0 % 12.95/2.54 | % 12.95/2.54 | REDUCE: (43), (63) imply: % 12.95/2.54 | (65) vmul(vd436, all_61_3) = all_69_4 % 12.95/2.54 | % 12.95/2.54 | REDUCE: (25), (60) imply: % 12.95/2.54 | (66) vmul(vd436, all_61_3) = all_63_0 % 12.95/2.54 | % 12.95/2.54 | REDUCE: (40), (52), (64) imply: % 12.95/2.54 | (67) vplus(all_53_0, all_61_0) = all_69_0 % 12.95/2.54 | % 12.95/2.54 | REDUCE: (33), (53) imply: % 12.95/2.54 | (68) vplus(all_61_0, vd436) = all_67_1 % 12.95/2.54 | % 12.95/2.54 | REDUCE: (32), (62) imply: % 12.95/2.54 | (69) vplus(all_53_0, all_67_1) = all_67_0 % 12.95/2.54 | % 12.95/2.54 | REDUCE: (31), (53), (62) imply: % 12.95/2.54 | (70) vplus(all_53_0, all_61_0) = all_67_3 % 12.95/2.54 | % 12.95/2.54 | REDUCE: (18), (47) imply: % 12.95/2.54 | (71) vplus(all_53_0, all_61_0) = all_61_2 % 12.95/2.54 | % 12.95/2.54 | REDUCE: (30), (53) imply: % 12.95/2.54 | (72) $i(all_61_0) % 12.95/2.54 | % 12.95/2.54 | REDUCE: (14), (61) imply: % 12.95/2.54 | (73) $i(all_53_0) % 12.95/2.54 | % 12.95/2.54 | GROUND_INST: instantiating (9) with all_67_3, all_69_0, all_61_0, all_53_0, % 12.95/2.54 | simplifying with (67), (70) gives: % 12.95/2.54 | (74) all_69_0 = all_67_3 % 12.95/2.54 | % 12.95/2.54 | GROUND_INST: instantiating (9) with all_61_2, all_69_0, all_61_0, all_53_0, % 12.95/2.54 | simplifying with (67), (71) gives: % 12.95/2.54 | (75) all_69_0 = all_61_2 % 12.95/2.54 | % 12.95/2.54 | GROUND_INST: instantiating (10) with all_61_2, all_69_4, all_61_3, vd436, % 12.95/2.54 | simplifying with (21), (65) gives: % 12.95/2.54 | (76) all_69_4 = all_61_2 % 12.95/2.54 | % 12.95/2.54 | GROUND_INST: instantiating (10) with all_63_0, all_69_4, all_61_3, vd436, % 12.95/2.54 | simplifying with (65), (66) gives: % 12.95/2.54 | (77) all_69_4 = all_63_0 % 12.95/2.55 | % 12.95/2.55 | COMBINE_EQS: (74), (75) imply: % 12.95/2.55 | (78) all_67_3 = all_61_2 % 12.95/2.55 | % 12.95/2.55 | SIMP: (78) implies: % 12.95/2.55 | (79) all_67_3 = all_61_2 % 12.95/2.55 | % 12.95/2.55 | COMBINE_EQS: (76), (77) imply: % 12.95/2.55 | (80) all_63_0 = all_61_2 % 12.95/2.55 | % 12.95/2.55 | REDUCE: (39), (76) imply: % 12.95/2.55 | (81) vplus(all_61_2, vd436) = all_69_3 % 12.95/2.55 | % 12.95/2.55 | REDUCE: (34), (79) imply: % 12.95/2.55 | (82) vplus(all_61_2, vd436) = all_67_2 % 12.95/2.55 | % 12.95/2.55 | REDUCE: (24), (80) imply: % 12.95/2.55 | (83) vplus(all_61_2, vd436) = all_63_1 % 12.95/2.55 | % 12.95/2.55 | GROUND_INST: instantiating (9) with all_67_2, all_69_3, vd436, all_61_2, % 12.95/2.55 | simplifying with (81), (82) gives: % 12.95/2.55 | (84) all_69_3 = all_67_2 % 12.95/2.55 | % 12.95/2.55 | GROUND_INST: instantiating (9) with all_63_1, all_69_3, vd436, all_61_2, % 12.95/2.55 | simplifying with (81), (83) gives: % 12.95/2.55 | (85) all_69_3 = all_63_1 % 12.95/2.55 | % 12.95/2.55 | COMBINE_EQS: (84), (85) imply: % 12.95/2.55 | (86) all_67_2 = all_63_1 % 12.95/2.55 | % 12.95/2.55 | SIMP: (86) implies: % 12.95/2.55 | (87) all_67_2 = all_63_1 % 12.95/2.55 | % 12.95/2.55 | REDUCE: (29), (87) imply: % 12.95/2.55 | (88) ~ (all_67_0 = all_63_1) % 12.95/2.55 | % 12.95/2.55 | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_53_0, all_61_0, % 12.95/2.55 | vd436, all_61_2, all_63_1, simplifying with (7), (71), (72), % 12.95/2.55 | (73), (83) gives: % 12.95/2.55 | (89) ? [v0: $i] : (vplus(all_61_0, vd436) = v0 & vplus(all_53_0, v0) = % 12.95/2.55 | all_63_1 & $i(v0) & $i(all_63_1)) % 12.95/2.55 | % 12.95/2.55 | DELTA: instantiating (89) with fresh symbol all_91_0 gives: % 12.95/2.55 | (90) vplus(all_61_0, vd436) = all_91_0 & vplus(all_53_0, all_91_0) = % 12.95/2.55 | all_63_1 & $i(all_91_0) & $i(all_63_1) % 12.95/2.55 | % 12.95/2.55 | ALPHA: (90) implies: % 12.95/2.55 | (91) vplus(all_53_0, all_91_0) = all_63_1 % 12.95/2.55 | (92) vplus(all_61_0, vd436) = all_91_0 % 12.95/2.55 | % 12.95/2.55 | GROUND_INST: instantiating (9) with all_67_1, all_91_0, vd436, all_61_0, % 12.95/2.55 | simplifying with (68), (92) gives: % 12.95/2.55 | (93) all_91_0 = all_67_1 % 12.95/2.55 | % 12.95/2.55 | REDUCE: (91), (93) imply: % 12.95/2.55 | (94) vplus(all_53_0, all_67_1) = all_63_1 % 12.95/2.55 | % 12.95/2.55 | GROUND_INST: instantiating (9) with all_67_0, all_63_1, all_67_1, all_53_0, % 12.95/2.55 | simplifying with (69), (94) gives: % 12.95/2.55 | (95) all_67_0 = all_63_1 % 12.95/2.55 | % 12.95/2.55 | REDUCE: (88), (95) imply: % 12.95/2.55 | (96) $false % 12.95/2.55 | % 12.95/2.55 | CLOSE: (96) is inconsistent. % 12.95/2.55 | % 12.95/2.55 End of proof % 12.95/2.55 % SZS output end Proof for theBenchmark % 12.95/2.55 % 12.95/2.55 1952ms %------------------------------------------------------------------------------