%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM846+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 : n004.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 8.69s 1.99s % Output : Proof 12.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM846+1 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n004.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 13:29:38 EDT 2023 % 0.12/0.34 % 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 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 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 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 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 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 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 % 3.46/1.19 Prover 1: Preprocessing ... % 3.46/1.19 Prover 4: Preprocessing ... % 3.78/1.24 Prover 5: Preprocessing ... % 3.78/1.24 Prover 2: Preprocessing ... % 3.78/1.24 Prover 6: Preprocessing ... % 3.78/1.24 Prover 0: Preprocessing ... % 3.78/1.25 Prover 3: Preprocessing ... % 7.77/1.80 Prover 1: Warning: ignoring some quantifiers % 7.77/1.86 Prover 1: Constructing countermodel ... % 7.77/1.87 Prover 3: Warning: ignoring some quantifiers % 7.77/1.87 Prover 6: Proving ... % 8.42/1.88 Prover 5: Proving ... % 8.49/1.89 Prover 3: Constructing countermodel ... % 8.69/1.93 Prover 4: Warning: ignoring some quantifiers % 8.69/1.97 Prover 2: Proving ... % 8.69/1.99 Prover 4: Constructing countermodel ... % 8.69/1.99 Prover 6: proved (1361ms) % 8.69/1.99 Prover 5: proved (1362ms) % 8.69/1.99 % 8.69/1.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.69/1.99 % 8.69/2.00 % 8.69/2.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.69/2.00 % 8.69/2.00 Prover 3: proved (1366ms) % 8.69/2.00 % 9.31/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.31/2.01 % 9.31/2.01 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.31/2.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.31/2.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.31/2.02 Prover 2: stopped % 9.31/2.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.31/2.03 Prover 0: Proving ... % 9.31/2.03 Prover 0: stopped % 9.31/2.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.84/2.11 Prover 7: Preprocessing ... % 9.84/2.12 Prover 8: Preprocessing ... % 9.84/2.12 Prover 10: Preprocessing ... % 9.84/2.14 Prover 11: Preprocessing ... % 9.84/2.14 Prover 13: Preprocessing ... % 11.21/2.29 Prover 10: Warning: ignoring some quantifiers % 11.39/2.31 Prover 4: Found proof (size 53) % 11.39/2.31 Prover 4: proved (1688ms) % 11.39/2.32 Prover 1: stopped % 11.55/2.32 Prover 10: Constructing countermodel ... % 11.55/2.33 Prover 13: Warning: ignoring some quantifiers % 11.55/2.33 Prover 7: Warning: ignoring some quantifiers % 11.55/2.34 Prover 10: stopped % 11.55/2.36 Prover 13: Constructing countermodel ... % 11.55/2.36 Prover 7: Constructing countermodel ... % 11.55/2.36 Prover 8: Warning: ignoring some quantifiers % 11.55/2.37 Prover 13: stopped % 11.55/2.37 Prover 7: stopped % 11.55/2.38 Prover 8: Constructing countermodel ... % 11.55/2.39 Prover 8: stopped % 11.55/2.41 Prover 11: Warning: ignoring some quantifiers % 12.19/2.43 Prover 11: Constructing countermodel ... % 12.19/2.44 Prover 11: stopped % 12.19/2.44 % 12.19/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.19/2.44 % 12.19/2.46 % SZS output start Proof for theBenchmark % 12.19/2.47 Assumptions after simplification: % 12.19/2.47 --------------------------------- % 12.19/2.47 % 12.19/2.47 (holds(284, 438, 1)) % 12.55/2.50 $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.55/2.50 (vsucc(vd437) = v0 & vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 & % 12.55/2.50 vplus(v2, vd436) = v1 & $i(v2) & $i(v1) & $i(v0)) % 12.55/2.50 % 12.55/2.50 (holds(284, 438, 2)) % 12.55/2.50 $i(v1) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.55/2.50 (vmul(vd436, v1) = v2 & vmul(vd436, vd437) = v0 & vplus(v0, v2) = v1 & % 12.55/2.50 vplus(v0, vd436) = v1 & $i(v2) & $i(v1) & $i(v0)) % 12.55/2.50 % 12.55/2.50 (holds(285, 440, 0)) % 12.55/2.50 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.55/2.50 ? [v3: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436, % 12.55/2.50 vd437) = v2 & vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) & % 12.55/2.51 $i(v2) & $i(v1) & $i(v0)) % 12.55/2.51 % 12.55/2.51 (holds(286, 441, 0)) % 12.55/2.51 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.55/2.51 ? [v3: $i] : ? [v4: $i] : (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436, % 12.55/2.51 v4) = v2 & vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437, % 12.55/2.51 vd439) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.55/2.51 % 12.55/2.51 (holds(286, 441, 1)) % 12.55/2.51 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.55/2.51 ? [v3: $i] : (vsucc(v0) = v1 & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 & % 12.55/2.51 vplus(v3, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1) % 12.55/2.51 & $i(v0)) % 12.55/2.51 % 12.55/2.51 (holds(286, 441, 2)) % 12.55/2.51 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.55/2.51 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v2) & % 12.55/2.51 vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v4 & vmul(vd436, vd437) = v3 & % 12.55/2.51 vplus(v5, vd436) = v6 & vplus(v3, v4) = v5 & vplus(v1, vd436) = v2 & % 12.55/2.51 vplus(vd437, vd439) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 12.55/2.51 $i(v1) & $i(v0)) % 12.55/2.51 % 12.55/2.51 (function-axioms) % 12.55/2.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.55/2.52 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 12.55/2.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.55/2.52 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: % 12.55/2.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.55/2.52 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 12.55/2.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.55/2.52 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: $i] : % 12.55/2.52 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | % 12.55/2.52 ~ (vmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 12.55/2.52 $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! % 12.55/2.52 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ % 12.55/2.52 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 12.55/2.52 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 12.55/2.52 % 12.55/2.52 Further assumptions not needed in the proof: % 12.55/2.52 -------------------------------------------- % 12.55/2.52 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158, % 12.55/2.52 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), % 12.55/2.52 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223, % 12.55/2.52 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), % 12.55/2.52 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(270, 0), 0), ass(cond(33, % 12.55/2.52 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), % 12.55/2.52 ass(cond(61, 0), 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), % 12.55/2.52 ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0), % 12.55/2.52 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), 0), % 12.55/2.52 ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1), ass(cond(goal(193), 0), % 12.55/2.52 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0), 1), % 12.55/2.52 ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88), 0), % 12.55/2.52 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), % 12.55/2.52 0), 3), def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 12), % 12.55/2.52 1), def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1), % 12.55/2.52 holds(284, 438, 0), qu(antec(axiom(3)), imp(antec(axiom(3)))), % 12.55/2.52 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), % 12.55/2.52 holds(definiens(29), 44, 0))), qu(cond(conseq(axiom(3)), 32), % 12.55/2.52 and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), % 12.55/2.52 qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)) % 12.55/2.52 % 12.55/2.52 Those formulas are unsatisfiable: % 12.55/2.52 --------------------------------- % 12.55/2.52 % 12.55/2.52 Begin of proof % 12.55/2.52 | % 12.55/2.52 | ALPHA: (holds(286, 441, 1)) implies: % 12.55/2.53 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vsucc(v0) = v1 % 12.55/2.53 | & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 & vplus(v3, vd436) = v2 % 12.55/2.53 | & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.55/2.53 | % 12.55/2.53 | ALPHA: (holds(286, 441, 0)) implies: % 12.55/2.53 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.55/2.53 | (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436, v4) = v2 & % 12.55/2.53 | vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437, vd439) = % 12.55/2.53 | v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.55/2.53 | % 12.55/2.53 | ALPHA: (holds(285, 440, 0)) implies: % 12.55/2.53 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vmul(vd436, % 12.55/2.53 | v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436, vd437) = v2 & % 12.55/2.53 | vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & % 12.55/2.53 | $i(v1) & $i(v0)) % 12.55/2.53 | % 12.55/2.53 | ALPHA: (holds(284, 438, 2)) implies: % 12.55/2.53 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vmul(vd436, v1) = v2 & % 12.55/2.53 | vmul(vd436, vd437) = v0 & vplus(v0, v2) = v1 & vplus(v0, vd436) = v1 % 12.55/2.53 | & $i(v2) & $i(v1) & $i(v0)) % 12.55/2.53 | % 12.55/2.53 | ALPHA: (holds(284, 438, 1)) implies: % 12.55/2.53 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vsucc(vd437) = v0 & % 12.55/2.53 | vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 & vplus(v2, vd436) = % 12.55/2.53 | v1 & $i(v2) & $i(v1) & $i(v0)) % 12.55/2.53 | % 12.55/2.53 | ALPHA: (holds(286, 441, 2)) implies: % 12.55/2.53 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.55/2.53 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v2) & vmul(vd436, v0) = v1 & % 12.55/2.53 | vmul(vd436, vd439) = v4 & vmul(vd436, vd437) = v3 & vplus(v5, vd436) % 12.55/2.53 | = v6 & vplus(v3, v4) = v5 & vplus(v1, vd436) = v2 & vplus(vd437, % 12.55/2.53 | vd439) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 12.55/2.53 | $i(v0)) % 12.55/2.53 | % 12.55/2.53 | ALPHA: (function-axioms) implies: % 12.55/2.54 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.55/2.54 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 12.55/2.54 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.55/2.54 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 12.55/2.54 | % 12.55/2.54 | DELTA: instantiating (5) with fresh symbols all_51_0, all_51_1, all_51_2 % 12.55/2.54 | gives: % 12.55/2.54 | (9) vsucc(vd437) = all_51_2 & vmul(vd436, all_51_2) = all_51_1 & % 12.55/2.54 | vmul(vd436, vd437) = all_51_0 & vplus(all_51_0, vd436) = all_51_1 & % 12.55/2.54 | $i(all_51_0) & $i(all_51_1) & $i(all_51_2) % 12.55/2.54 | % 12.55/2.54 | ALPHA: (9) implies: % 12.55/2.54 | (10) vmul(vd436, vd437) = all_51_0 % 12.55/2.54 | % 12.55/2.54 | DELTA: instantiating (4) with fresh symbols all_53_0, all_53_1, all_53_2 % 12.55/2.54 | gives: % 12.55/2.54 | (11) vmul(vd436, v1) = all_53_0 & vmul(vd436, vd437) = all_53_2 & % 12.55/2.54 | vplus(all_53_2, all_53_0) = all_53_1 & vplus(all_53_2, vd436) = % 12.55/2.54 | all_53_1 & $i(all_53_0) & $i(all_53_1) & $i(all_53_2) % 12.55/2.54 | % 12.55/2.54 | ALPHA: (11) implies: % 12.55/2.54 | (12) vmul(vd436, vd437) = all_53_2 % 12.55/2.54 | % 12.55/2.54 | DELTA: instantiating (1) with fresh symbols all_58_0, all_58_1, all_58_2, % 12.55/2.54 | all_58_3 gives: % 12.55/2.54 | (13) vsucc(all_58_3) = all_58_2 & vmul(vd436, all_58_2) = all_58_1 & % 12.55/2.54 | vmul(vd436, all_58_3) = all_58_0 & vplus(all_58_0, vd436) = all_58_1 & % 12.55/2.54 | vplus(vd437, vd439) = all_58_3 & $i(all_58_0) & $i(all_58_1) & % 12.55/2.54 | $i(all_58_2) & $i(all_58_3) % 12.55/2.54 | % 12.55/2.54 | ALPHA: (13) implies: % 12.55/2.54 | (14) vplus(vd437, vd439) = all_58_3 % 12.55/2.54 | (15) vplus(all_58_0, vd436) = all_58_1 % 12.55/2.54 | (16) vmul(vd436, all_58_3) = all_58_0 % 12.55/2.54 | % 12.55/2.54 | DELTA: instantiating (3) with fresh symbols all_60_0, all_60_1, all_60_2, % 12.55/2.54 | all_60_3 gives: % 12.55/2.54 | (17) vmul(vd436, all_60_3) = all_60_2 & vmul(vd436, vd439) = all_60_0 & % 12.55/2.54 | vmul(vd436, vd437) = all_60_1 & vplus(all_60_1, all_60_0) = all_60_2 & % 12.55/2.54 | vplus(vd437, vd439) = all_60_3 & $i(all_60_0) & $i(all_60_1) & % 12.55/2.54 | $i(all_60_2) & $i(all_60_3) % 12.55/2.54 | % 12.55/2.54 | ALPHA: (17) implies: % 12.55/2.54 | (18) vplus(vd437, vd439) = all_60_3 % 12.55/2.54 | (19) vplus(all_60_1, all_60_0) = all_60_2 % 12.55/2.54 | (20) vmul(vd436, vd437) = all_60_1 % 12.55/2.54 | (21) vmul(vd436, vd439) = all_60_0 % 12.55/2.54 | (22) vmul(vd436, all_60_3) = all_60_2 % 12.55/2.54 | % 12.55/2.54 | DELTA: instantiating (2) with fresh symbols all_62_0, all_62_1, all_62_2, % 12.55/2.54 | all_62_3, all_62_4 gives: % 12.55/2.54 | (23) vsucc(all_62_1) = all_62_0 & vsucc(vd439) = all_62_4 & vmul(vd436, % 12.55/2.54 | all_62_0) = all_62_2 & vmul(vd436, all_62_3) = all_62_2 & % 12.55/2.54 | vplus(vd437, all_62_4) = all_62_3 & vplus(vd437, vd439) = all_62_1 & % 12.55/2.54 | $i(all_62_0) & $i(all_62_1) & $i(all_62_2) & $i(all_62_3) & % 12.55/2.54 | $i(all_62_4) % 12.55/2.54 | % 12.55/2.54 | ALPHA: (23) implies: % 12.55/2.54 | (24) vplus(vd437, vd439) = all_62_1 % 12.55/2.54 | % 12.55/2.54 | DELTA: instantiating (6) with fresh symbols all_64_0, all_64_1, all_64_2, % 12.55/2.54 | all_64_3, all_64_4, all_64_5, all_64_6 gives: % 12.55/2.55 | (25) ~ (all_64_0 = all_64_4) & vmul(vd436, all_64_6) = all_64_5 & % 12.55/2.55 | vmul(vd436, vd439) = all_64_2 & vmul(vd436, vd437) = all_64_3 & % 12.55/2.55 | vplus(all_64_1, vd436) = all_64_0 & vplus(all_64_3, all_64_2) = % 12.55/2.55 | all_64_1 & vplus(all_64_5, vd436) = all_64_4 & vplus(vd437, vd439) = % 12.55/2.55 | all_64_6 & $i(all_64_0) & $i(all_64_1) & $i(all_64_2) & $i(all_64_3) & % 12.55/2.55 | $i(all_64_4) & $i(all_64_5) & $i(all_64_6) % 12.55/2.55 | % 12.55/2.55 | ALPHA: (25) implies: % 12.55/2.55 | (26) ~ (all_64_0 = all_64_4) % 12.55/2.55 | (27) vplus(vd437, vd439) = all_64_6 % 12.55/2.55 | (28) vplus(all_64_5, vd436) = all_64_4 % 12.55/2.55 | (29) vplus(all_64_3, all_64_2) = all_64_1 % 12.55/2.55 | (30) vplus(all_64_1, vd436) = all_64_0 % 12.55/2.55 | (31) vmul(vd436, vd437) = all_64_3 % 12.55/2.55 | (32) vmul(vd436, vd439) = all_64_2 % 12.55/2.55 | (33) vmul(vd436, all_64_6) = all_64_5 % 12.55/2.55 | % 12.55/2.55 | GROUND_INST: instantiating (7) with all_62_1, all_64_6, vd439, vd437, % 12.55/2.55 | simplifying with (24), (27) gives: % 12.55/2.55 | (34) all_64_6 = all_62_1 % 12.55/2.55 | % 12.55/2.55 | GROUND_INST: instantiating (7) with all_60_3, all_64_6, vd439, vd437, % 12.55/2.55 | simplifying with (18), (27) gives: % 12.55/2.55 | (35) all_64_6 = all_60_3 % 12.55/2.55 | % 12.55/2.55 | GROUND_INST: instantiating (7) with all_58_3, all_64_6, vd439, vd437, % 12.55/2.55 | simplifying with (14), (27) gives: % 12.55/2.55 | (36) all_64_6 = all_58_3 % 12.55/2.55 | % 12.55/2.55 | GROUND_INST: instantiating (8) with all_53_2, all_60_1, vd437, vd436, % 12.55/2.55 | simplifying with (12), (20) gives: % 12.55/2.55 | (37) all_60_1 = all_53_2 % 12.55/2.55 | % 12.55/2.55 | GROUND_INST: instantiating (8) with all_60_1, all_64_3, vd437, vd436, % 12.55/2.55 | simplifying with (20), (31) gives: % 12.55/2.55 | (38) all_64_3 = all_60_1 % 12.55/2.55 | % 12.55/2.55 | GROUND_INST: instantiating (8) with all_51_0, all_64_3, vd437, vd436, % 12.55/2.55 | simplifying with (10), (31) gives: % 12.55/2.55 | (39) all_64_3 = all_51_0 % 12.55/2.55 | % 12.55/2.55 | GROUND_INST: instantiating (8) with all_60_0, all_64_2, vd439, vd436, % 12.55/2.55 | simplifying with (21), (32) gives: % 12.55/2.55 | (40) all_64_2 = all_60_0 % 12.55/2.55 | % 12.55/2.55 | COMBINE_EQS: (38), (39) imply: % 12.55/2.55 | (41) all_60_1 = all_51_0 % 12.55/2.55 | % 12.55/2.55 | SIMP: (41) implies: % 12.55/2.55 | (42) all_60_1 = all_51_0 % 12.55/2.55 | % 12.55/2.55 | COMBINE_EQS: (34), (36) imply: % 12.55/2.55 | (43) all_62_1 = all_58_3 % 12.55/2.55 | % 12.55/2.55 | COMBINE_EQS: (34), (35) imply: % 12.55/2.55 | (44) all_62_1 = all_60_3 % 12.55/2.55 | % 12.55/2.55 | COMBINE_EQS: (43), (44) imply: % 12.55/2.55 | (45) all_60_3 = all_58_3 % 12.55/2.55 | % 12.55/2.55 | COMBINE_EQS: (37), (42) imply: % 12.55/2.55 | (46) all_53_2 = all_51_0 % 12.55/2.55 | % 12.55/2.55 | REDUCE: (33), (36) imply: % 12.55/2.55 | (47) vmul(vd436, all_58_3) = all_64_5 % 12.55/2.55 | % 12.55/2.55 | REDUCE: (22), (45) imply: % 12.55/2.55 | (48) vmul(vd436, all_58_3) = all_60_2 % 12.55/2.55 | % 12.55/2.55 | REDUCE: (29), (39), (40) imply: % 12.55/2.56 | (49) vplus(all_51_0, all_60_0) = all_64_1 % 12.55/2.56 | % 12.55/2.56 | REDUCE: (19), (42) imply: % 12.55/2.56 | (50) vplus(all_51_0, all_60_0) = all_60_2 % 12.55/2.56 | % 12.55/2.56 | GROUND_INST: instantiating (7) with all_60_2, all_64_1, all_60_0, all_51_0, % 12.55/2.56 | simplifying with (49), (50) gives: % 12.55/2.56 | (51) all_64_1 = all_60_2 % 12.55/2.56 | % 12.55/2.56 | GROUND_INST: instantiating (8) with all_58_0, all_64_5, all_58_3, vd436, % 12.55/2.56 | simplifying with (16), (47) gives: % 12.55/2.56 | (52) all_64_5 = all_58_0 % 12.55/2.56 | % 12.55/2.56 | GROUND_INST: instantiating (8) with all_60_2, all_64_5, all_58_3, vd436, % 12.55/2.56 | simplifying with (47), (48) gives: % 12.55/2.56 | (53) all_64_5 = all_60_2 % 12.55/2.56 | % 12.55/2.56 | COMBINE_EQS: (52), (53) imply: % 12.55/2.56 | (54) all_60_2 = all_58_0 % 12.55/2.56 | % 12.55/2.56 | COMBINE_EQS: (51), (54) imply: % 12.55/2.56 | (55) all_64_1 = all_58_0 % 12.55/2.56 | % 12.55/2.56 | REDUCE: (30), (55) imply: % 12.55/2.56 | (56) vplus(all_58_0, vd436) = all_64_0 % 12.55/2.56 | % 12.55/2.56 | REDUCE: (28), (52) imply: % 12.55/2.56 | (57) vplus(all_58_0, vd436) = all_64_4 % 12.55/2.56 | % 12.55/2.56 | GROUND_INST: instantiating (7) with all_58_1, all_64_0, vd436, all_58_0, % 12.55/2.56 | simplifying with (15), (56) gives: % 12.55/2.56 | (58) all_64_0 = all_58_1 % 12.55/2.56 | % 12.55/2.56 | GROUND_INST: instantiating (7) with all_64_4, all_64_0, vd436, all_58_0, % 12.55/2.56 | simplifying with (56), (57) gives: % 12.55/2.56 | (59) all_64_0 = all_64_4 % 12.55/2.56 | % 12.55/2.56 | COMBINE_EQS: (58), (59) imply: % 12.55/2.56 | (60) all_64_4 = all_58_1 % 12.55/2.56 | % 12.55/2.56 | SIMP: (60) implies: % 12.55/2.56 | (61) all_64_4 = all_58_1 % 12.55/2.56 | % 12.55/2.56 | REDUCE: (26), (58), (61) imply: % 12.55/2.56 | (62) $false % 12.55/2.56 | % 12.55/2.56 | CLOSE: (62) is inconsistent. % 12.55/2.56 | % 12.55/2.56 End of proof % 12.55/2.56 % SZS output end Proof for theBenchmark % 12.55/2.56 % 12.55/2.56 1955ms %------------------------------------------------------------------------------