%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM849+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 : n003.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 11:50:23 EDT 2023 % Result : Theorem 11.77s 2.29s % Output : Proof 14.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM849+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 : n003.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 14:12:38 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 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 % 4.44/1.27 Prover 4: Preprocessing ... % 4.44/1.28 Prover 1: Preprocessing ... % 4.44/1.31 Prover 5: Preprocessing ... % 4.44/1.31 Prover 3: Preprocessing ... % 4.44/1.31 Prover 6: Preprocessing ... % 4.44/1.31 Prover 0: Preprocessing ... % 4.44/1.31 Prover 2: Preprocessing ... % 8.93/1.89 Prover 1: Warning: ignoring some quantifiers % 9.64/1.96 Prover 1: Constructing countermodel ... % 9.64/1.99 Prover 3: Warning: ignoring some quantifiers % 9.83/2.01 Prover 6: Proving ... % 9.83/2.01 Prover 5: Proving ... % 9.83/2.01 Prover 3: Constructing countermodel ... % 9.83/2.02 Prover 4: Warning: ignoring some quantifiers % 9.83/2.13 Prover 4: Constructing countermodel ... % 10.85/2.17 Prover 2: Proving ... % 10.85/2.18 Prover 0: Proving ... % 11.77/2.28 Prover 3: proved (1666ms) % 11.77/2.29 % 11.77/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.77/2.29 % 11.77/2.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.77/2.29 Prover 2: stopped % 11.77/2.29 Prover 0: stopped % 11.77/2.29 Prover 5: stopped % 11.77/2.29 Prover 6: stopped % 11.77/2.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.77/2.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.77/2.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.77/2.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.34/2.37 Prover 10: Preprocessing ... % 12.55/2.38 Prover 8: Preprocessing ... % 12.55/2.40 Prover 7: Preprocessing ... % 12.55/2.41 Prover 11: Preprocessing ... % 12.55/2.42 Prover 13: Preprocessing ... % 13.02/2.46 Prover 1: Found proof (size 77) % 13.02/2.46 Prover 1: proved (1846ms) % 13.02/2.46 Prover 10: stopped % 13.02/2.46 Prover 4: stopped % 13.02/2.48 Prover 7: stopped % 13.02/2.49 Prover 11: stopped % 13.02/2.50 Prover 13: stopped % 13.50/2.54 Prover 8: Warning: ignoring some quantifiers % 13.50/2.56 Prover 8: Constructing countermodel ... % 13.77/2.57 Prover 8: stopped % 13.77/2.57 % 13.77/2.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.77/2.57 % 13.77/2.59 % SZS output start Proof for theBenchmark % 13.77/2.60 Assumptions after simplification: % 13.77/2.60 --------------------------------- % 13.77/2.60 % 13.77/2.60 (ass(cond(253, 0), 0)) % 13.77/2.64 $i(v1) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (vmul(v1, v0) = v1) | ~ % 13.77/2.64 $i(v0)) % 13.77/2.64 % 13.77/2.64 (ass(cond(270, 0), 0)) % 13.77/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) % 13.77/2.64 | ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2))) % 13.77/2.64 % 13.77/2.64 (ass(cond(281, 0), 0)) % 13.77/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.77/2.64 $i] : ( ~ (vplus(v3, v4) = v5) | ~ (vmul(v0, v2) = v4) | ~ (vmul(v0, v1) = % 13.77/2.64 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (vplus(v1, v2) = % 13.77/2.64 v6 & vmul(v0, v6) = v5 & $i(v6) & $i(v5))) % 13.77/2.64 % 13.77/2.64 (ass(cond(conseq(292), 1), 0)) % 13.77/2.64 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! % 13.77/2.64 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 13.77/2.64 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 13.77/2.64 [v9: $i] : (vplus(v3, vd449) = v5 & vsucc(v1) = v7 & vmul(vd449, v7) = v8 % 13.77/2.64 & vmul(vd449, v1) = v3 & vmul(vd448, v8) = v9 & vmul(vd448, v5) = v6 & % 13.77/2.64 vmul(vd448, v3) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 13.77/2.64 $i(v4) & $i(v3) & ( ~ (v4 = v2) | v9 = v6)))) % 13.77/2.64 % 13.77/2.64 (ass(cond(conseq(292), 1), 1)) % 13.77/2.65 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! % 13.77/2.65 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 13.77/2.65 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v4, v0) = % 13.77/2.65 v5 & vplus(v3, vd449) = v6 & vmul(vd449, v1) = v3 & vmul(vd448, v6) = v7 % 13.77/2.65 & vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( % 13.77/2.65 ~ (v4 = v2) | v7 = v5)))) % 13.77/2.65 % 13.77/2.65 (ass(cond(conseq(292), 1), 2)) % 13.77/2.65 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! % 13.77/2.65 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 13.77/2.65 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v4, v0) = v6 & vplus(v2, % 13.77/2.65 v0) = v5 & vmul(vd449, v1) = v3 & vmul(vd448, v3) = v4 & $i(v6) & % 13.77/2.65 $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v6 = v5)))) % 13.77/2.65 % 13.77/2.65 (ass(cond(conseq(292), 1), 3)) % 14.16/2.65 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! % 14.16/2.65 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 14.16/2.65 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v2, v0) = % 14.16/2.65 v7 & vsucc(v1) = v5 & vmul(v0, v5) = v6 & vmul(vd449, v1) = v3 & % 14.16/2.65 vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ % 14.16/2.65 (v4 = v2) | v7 = v6)))) % 14.16/2.65 % 14.16/2.65 (holds(293, 450, 0)) % 14.16/2.65 $i(v1) & $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(v0, v1) = v0 & % 14.16/2.65 vmul(vd448, vd449) = v0 & $i(v0)) % 14.16/2.65 % 14.16/2.65 (holds(293, 450, 1)) % 14.16/2.65 $i(v1) & $i(vd449) & $i(vd448) & ? [v0: $i] : ? [v1: $i] : (vmul(vd449, v1) % 14.16/2.65 = v1 & vmul(vd448, v1) = v0 & vmul(vd448, vd449) = v0 & $i(v1) & $i(v0)) % 14.16/2.65 % 14.16/2.65 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) % 14.16/2.66 $i(v1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.16/2.66 (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 14.16/2.66 $i] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4 & $i(v4) & $i(v3))) & ? % 14.16/2.66 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (vmul(v1, v1) = v2) | ~ % 14.16/2.66 $i(v1) | ~ $i(v0)) % 14.16/2.66 % 14.16/2.66 (qu(ind(296), imp(296))) % 14.16/2.66 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ? % 14.16/2.66 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 14.16/2.66 $i] : ? [v7: $i] : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 & % 14.16/2.66 vmul(v0, v1) = v2 & vmul(vd449, v4) = v6 & vmul(vd449, v1) = v3 & % 14.16/2.66 vmul(vd448, v6) = v7 & vmul(vd448, v3) = v2 & $i(v7) & $i(v6) & $i(v5) & % 14.16/2.66 $i(v4) & $i(v3) & $i(v2) & $i(v1))) % 14.16/2.66 % 14.16/2.66 (qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))) % 14.16/2.66 $i(v1) & ! [v0: $i] : ( ~ (vsucc(v0) = v1) | ~ $i(v0)) % 14.16/2.66 % 14.16/2.66 (function-axioms) % 14.16/2.66 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.16/2.66 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 14.16/2.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.16/2.66 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: % 14.16/2.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.16/2.66 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 14.16/2.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.16/2.66 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : ! % 14.16/2.66 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ % 14.16/2.66 (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 14.16/2.66 $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) & ! [v0: % 14.16/2.66 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ % 14.16/2.66 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 14.16/2.66 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 14.16/2.66 % 14.16/2.66 Further assumptions not needed in the proof: % 14.16/2.66 -------------------------------------------- % 14.16/2.66 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158, % 14.16/2.66 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), % 14.16/2.66 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223, % 14.16/2.66 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), % 14.16/2.66 ass(cond(261, 0), 0), ass(cond(33, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), % 14.16/2.66 0), ass(cond(6, 0), 0), ass(cond(61, 0), 0), ass(cond(73, 0), 0), ass(cond(81, % 14.16/2.66 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), % 14.16/2.66 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), % 14.16/2.66 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1), % 14.16/2.66 ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0), % 14.16/2.66 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88), % 14.16/2.66 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2), % 14.16/2.66 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1), % 14.16/2.66 def(cond(conseq(axiom(3)), 12), 1), def(cond(conseq(axiom(3)), 16), 1), % 14.16/2.66 def(cond(conseq(axiom(3)), 17), 1), qu(antec(axiom(3)), imp(antec(axiom(3)))), % 14.16/2.66 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), % 14.16/2.66 holds(definiens(29), 44, 0))) % 14.16/2.66 % 14.16/2.66 Those formulas are unsatisfiable: % 14.16/2.66 --------------------------------- % 14.16/2.66 % 14.16/2.66 Begin of proof % 14.16/2.66 | % 14.16/2.66 | ALPHA: (ass(cond(conseq(292), 1), 0)) implies: % 14.16/2.67 | (1) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 14.16/2.67 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 14.16/2.67 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 14.16/2.67 | [v9: $i] : (vplus(v3, vd449) = v5 & vsucc(v1) = v7 & vmul(vd449, % 14.16/2.67 | v7) = v8 & vmul(vd449, v1) = v3 & vmul(vd448, v8) = v9 & % 14.16/2.67 | vmul(vd448, v5) = v6 & vmul(vd448, v3) = v4 & $i(v9) & $i(v8) & % 14.16/2.67 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v9 = % 14.16/2.67 | v6)))) % 14.16/2.67 | % 14.16/2.67 | ALPHA: (ass(cond(conseq(292), 1), 1)) implies: % 14.16/2.67 | (2) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 14.16/2.67 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 14.16/2.67 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v4, v0) = % 14.16/2.67 | v5 & vplus(v3, vd449) = v6 & vmul(vd449, v1) = v3 & vmul(vd448, % 14.16/2.67 | v6) = v7 & vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & % 14.16/2.67 | $i(v4) & $i(v3) & ( ~ (v4 = v2) | v7 = v5)))) % 14.16/2.67 | % 14.16/2.67 | ALPHA: (ass(cond(conseq(292), 1), 2)) implies: % 14.16/2.67 | (3) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 14.16/2.67 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 14.16/2.67 | $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v4, v0) = v6 & vplus(v2, % 14.16/2.67 | v0) = v5 & vmul(vd449, v1) = v3 & vmul(vd448, v3) = v4 & $i(v6) % 14.16/2.67 | & $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v6 = v5)))) % 14.16/2.67 | % 14.16/2.67 | ALPHA: (ass(cond(conseq(292), 1), 3)) implies: % 14.16/2.67 | (4) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 14.16/2.67 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 14.16/2.67 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v2, v0) = % 14.16/2.67 | v7 & vsucc(v1) = v5 & vmul(v0, v5) = v6 & vmul(vd449, v1) = v3 & % 14.16/2.67 | vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 14.16/2.67 | & ( ~ (v4 = v2) | v7 = v6)))) % 14.16/2.67 | % 14.16/2.67 | ALPHA: (holds(293, 450, 1)) implies: % 14.16/2.67 | (5) ? [v0: $i] : ? [v1: $i] : (vmul(vd449, v1) = v1 & vmul(vd448, v1) = % 14.16/2.67 | v0 & vmul(vd448, vd449) = v0 & $i(v1) & $i(v0)) % 14.16/2.67 | % 14.16/2.67 | ALPHA: (holds(293, 450, 0)) implies: % 14.16/2.67 | (6) ? [v0: $i] : (vmul(v0, v1) = v0 & vmul(vd448, vd449) = v0 & $i(v0)) % 14.16/2.67 | % 14.16/2.67 | ALPHA: (ass(cond(253, 0), 0)) implies: % 14.16/2.67 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (vmul(v1, v0) = v1) | ~ % 14.16/2.67 | $i(v0)) % 14.16/2.67 | % 14.16/2.67 | ALPHA: (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), % 14.16/2.67 | holds(definiens(249), 398, 0)))) implies: % 14.16/2.67 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v1) % 14.16/2.67 | = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 14.16/2.67 | $i] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4 & $i(v4) & $i(v3))) % 14.16/2.67 | % 14.16/2.67 | ALPHA: (qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))) implies: % 14.16/2.67 | (9) $i(v1) % 14.16/2.67 | % 14.16/2.67 | ALPHA: (qu(ind(296), imp(296))) implies: % 14.16/2.68 | (10) $i(vd448) % 14.16/2.68 | (11) $i(vd449) % 14.16/2.68 | (12) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ? [v1: $i] : ? % 14.16/2.68 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 14.16/2.68 | ? [v7: $i] : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 & % 14.16/2.68 | vmul(v0, v1) = v2 & vmul(vd449, v4) = v6 & vmul(vd449, v1) = v3 & % 14.16/2.68 | vmul(vd448, v6) = v7 & vmul(vd448, v3) = v2 & $i(v7) & $i(v6) & % 14.16/2.68 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1))) % 14.16/2.68 | % 14.16/2.68 | ALPHA: (function-axioms) implies: % 14.16/2.68 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.16/2.68 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 14.16/2.68 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.16/2.68 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 14.16/2.68 | % 14.16/2.68 | DELTA: instantiating (6) with fresh symbol all_47_0 gives: % 14.16/2.68 | (15) vmul(all_47_0, v1) = all_47_0 & vmul(vd448, vd449) = all_47_0 & % 14.16/2.68 | $i(all_47_0) % 14.16/2.68 | % 14.16/2.68 | ALPHA: (15) implies: % 14.16/2.68 | (16) vmul(vd448, vd449) = all_47_0 % 14.16/2.68 | % 14.16/2.68 | DELTA: instantiating (5) with fresh symbols all_53_0, all_53_1 gives: % 14.16/2.68 | (17) vmul(vd449, v1) = all_53_0 & vmul(vd448, all_53_0) = all_53_1 & % 14.16/2.68 | vmul(vd448, vd449) = all_53_1 & $i(all_53_0) & $i(all_53_1) % 14.16/2.68 | % 14.16/2.68 | ALPHA: (17) implies: % 14.16/2.68 | (18) $i(all_53_0) % 14.16/2.68 | (19) vmul(vd448, vd449) = all_53_1 % 14.16/2.68 | (20) vmul(vd448, all_53_0) = all_53_1 % 14.16/2.68 | (21) vmul(vd449, v1) = all_53_0 % 14.16/2.68 | % 14.16/2.68 | DELTA: instantiating (3) with fresh symbol all_60_0 gives: % 14.16/2.68 | (22) vmul(vd448, vd449) = all_60_0 & $i(all_60_0) & ! [v0: $i] : ! [v1: % 14.16/2.68 | $i] : ( ~ (vmul(all_60_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 14.16/2.68 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (vplus(v3, all_60_0) = v5 & % 14.16/2.68 | vplus(v1, all_60_0) = v4 & vmul(vd449, v0) = v2 & vmul(vd448, v2) % 14.16/2.68 | = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v5 = % 14.16/2.68 | v4))) % 14.16/2.68 | % 14.16/2.68 | ALPHA: (22) implies: % 14.16/2.68 | (23) vmul(vd448, vd449) = all_60_0 % 14.16/2.68 | % 14.16/2.68 | DELTA: instantiating (2) with fresh symbol all_63_0 gives: % 14.16/2.68 | (24) vmul(vd448, vd449) = all_63_0 & $i(all_63_0) & ! [v0: $i] : ! [v1: % 14.16/2.68 | $i] : ( ~ (vmul(all_63_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 14.16/2.68 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v3, % 14.16/2.68 | all_63_0) = v4 & vplus(v2, vd449) = v5 & vmul(vd449, v0) = v2 & % 14.16/2.68 | vmul(vd448, v5) = v6 & vmul(vd448, v2) = v3 & $i(v6) & $i(v5) & % 14.16/2.68 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v6 = v4))) % 14.16/2.68 | % 14.16/2.68 | ALPHA: (24) implies: % 14.16/2.68 | (25) vmul(vd448, vd449) = all_63_0 % 14.16/2.68 | % 14.16/2.68 | DELTA: instantiating (4) with fresh symbol all_66_0 gives: % 14.16/2.69 | (26) vmul(vd448, vd449) = all_66_0 & $i(all_66_0) & ! [v0: $i] : ! [v1: % 14.16/2.69 | $i] : ( ~ (vmul(all_66_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 14.16/2.69 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v1, % 14.16/2.69 | all_66_0) = v6 & vsucc(v0) = v4 & vmul(all_66_0, v4) = v5 & % 14.16/2.69 | vmul(vd449, v0) = v2 & vmul(vd448, v2) = v3 & $i(v6) & $i(v5) & % 14.16/2.69 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v6 = v5))) % 14.16/2.69 | % 14.16/2.69 | ALPHA: (26) implies: % 14.16/2.69 | (27) vmul(vd448, vd449) = all_66_0 % 14.16/2.69 | % 14.16/2.69 | DELTA: instantiating (12) with fresh symbol all_69_0 gives: % 14.16/2.69 | (28) vmul(vd448, vd449) = all_69_0 & $i(all_69_0) & ? [v0: $i] : ? [v1: % 14.16/2.69 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 14.16/2.69 | [v6: $i] : ( ~ (v6 = v4) & vsucc(v0) = v3 & vmul(all_69_0, v3) = v4 & % 14.16/2.69 | vmul(all_69_0, v0) = v1 & vmul(vd449, v3) = v5 & vmul(vd449, v0) = % 14.16/2.69 | v2 & vmul(vd448, v5) = v6 & vmul(vd448, v2) = v1 & $i(v6) & $i(v5) & % 14.16/2.69 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.16/2.69 | % 14.16/2.69 | ALPHA: (28) implies: % 14.16/2.69 | (29) vmul(vd448, vd449) = all_69_0 % 14.16/2.69 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 14.16/2.69 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & vsucc(v0) = v3 & % 14.16/2.69 | vmul(all_69_0, v3) = v4 & vmul(all_69_0, v0) = v1 & vmul(vd449, v3) % 14.16/2.69 | = v5 & vmul(vd449, v0) = v2 & vmul(vd448, v5) = v6 & vmul(vd448, v2) % 14.16/2.69 | = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.16/2.69 | % 14.16/2.69 | DELTA: instantiating (1) with fresh symbol all_71_0 gives: % 14.16/2.69 | (31) vmul(vd448, vd449) = all_71_0 & $i(all_71_0) & ! [v0: $i] : ! [v1: % 14.16/2.69 | $i] : ( ~ (vmul(all_71_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 14.16/2.69 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 14.16/2.69 | ? [v8: $i] : (vplus(v2, vd449) = v4 & vsucc(v0) = v6 & vmul(vd449, % 14.16/2.69 | v6) = v7 & vmul(vd449, v0) = v2 & vmul(vd448, v7) = v8 & % 14.16/2.69 | vmul(vd448, v4) = v5 & vmul(vd448, v2) = v3 & $i(v8) & $i(v7) & % 14.16/2.69 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v8 = % 14.16/2.69 | v5))) % 14.16/2.69 | % 14.16/2.69 | ALPHA: (31) implies: % 14.16/2.69 | (32) vmul(vd448, vd449) = all_71_0 % 14.16/2.69 | % 14.16/2.69 | DELTA: instantiating (30) with fresh symbols all_74_0, all_74_1, all_74_2, % 14.16/2.69 | all_74_3, all_74_4, all_74_5, all_74_6 gives: % 14.16/2.69 | (33) ~ (all_74_0 = all_74_2) & vsucc(all_74_6) = all_74_3 & vmul(all_69_0, % 14.16/2.69 | all_74_3) = all_74_2 & vmul(all_69_0, all_74_6) = all_74_5 & % 14.16/2.69 | vmul(vd449, all_74_3) = all_74_1 & vmul(vd449, all_74_6) = all_74_4 & % 14.16/2.69 | vmul(vd448, all_74_1) = all_74_0 & vmul(vd448, all_74_4) = all_74_5 & % 14.16/2.69 | $i(all_74_0) & $i(all_74_1) & $i(all_74_2) & $i(all_74_3) & % 14.16/2.69 | $i(all_74_4) & $i(all_74_5) & $i(all_74_6) % 14.16/2.69 | % 14.16/2.69 | ALPHA: (33) implies: % 14.16/2.69 | (34) ~ (all_74_0 = all_74_2) % 14.16/2.69 | (35) $i(all_74_6) % 14.16/2.69 | (36) vmul(vd448, all_74_4) = all_74_5 % 14.16/2.69 | (37) vmul(vd448, all_74_1) = all_74_0 % 14.16/2.69 | (38) vmul(vd449, all_74_6) = all_74_4 % 14.16/2.69 | (39) vmul(vd449, all_74_3) = all_74_1 % 14.16/2.69 | (40) vmul(all_69_0, all_74_6) = all_74_5 % 14.16/2.69 | (41) vmul(all_69_0, all_74_3) = all_74_2 % 14.16/2.69 | (42) vsucc(all_74_6) = all_74_3 % 14.16/2.69 | % 14.16/2.70 | GROUND_INST: instantiating (13) with all_60_0, all_63_0, vd449, vd448, % 14.16/2.70 | simplifying with (23), (25) gives: % 14.16/2.70 | (43) all_63_0 = all_60_0 % 14.16/2.70 | % 14.16/2.70 | GROUND_INST: instantiating (13) with all_53_1, all_63_0, vd449, vd448, % 14.16/2.70 | simplifying with (19), (25) gives: % 14.16/2.70 | (44) all_63_0 = all_53_1 % 14.16/2.70 | % 14.16/2.70 | GROUND_INST: instantiating (13) with all_63_0, all_66_0, vd449, vd448, % 14.16/2.70 | simplifying with (25), (27) gives: % 14.16/2.70 | (45) all_66_0 = all_63_0 % 14.16/2.70 | % 14.16/2.70 | GROUND_INST: instantiating (13) with all_66_0, all_69_0, vd449, vd448, % 14.16/2.70 | simplifying with (27), (29) gives: % 14.16/2.70 | (46) all_69_0 = all_66_0 % 14.16/2.70 | % 14.16/2.70 | GROUND_INST: instantiating (13) with all_69_0, all_71_0, vd449, vd448, % 14.16/2.70 | simplifying with (29), (32) gives: % 14.16/2.70 | (47) all_71_0 = all_69_0 % 14.16/2.70 | % 14.16/2.70 | GROUND_INST: instantiating (13) with all_47_0, all_71_0, vd449, vd448, % 14.16/2.70 | simplifying with (16), (32) gives: % 14.16/2.70 | (48) all_71_0 = all_47_0 % 14.16/2.70 | % 14.16/2.70 | COMBINE_EQS: (47), (48) imply: % 14.16/2.70 | (49) all_69_0 = all_47_0 % 14.16/2.70 | % 14.16/2.70 | SIMP: (49) implies: % 14.16/2.70 | (50) all_69_0 = all_47_0 % 14.16/2.70 | % 14.16/2.70 | COMBINE_EQS: (46), (50) imply: % 14.16/2.70 | (51) all_66_0 = all_47_0 % 14.16/2.70 | % 14.16/2.70 | SIMP: (51) implies: % 14.16/2.70 | (52) all_66_0 = all_47_0 % 14.16/2.70 | % 14.16/2.70 | COMBINE_EQS: (45), (52) imply: % 14.16/2.70 | (53) all_63_0 = all_47_0 % 14.16/2.70 | % 14.16/2.70 | SIMP: (53) implies: % 14.16/2.70 | (54) all_63_0 = all_47_0 % 14.16/2.70 | % 14.16/2.70 | COMBINE_EQS: (43), (44) imply: % 14.16/2.70 | (55) all_60_0 = all_53_1 % 14.16/2.70 | % 14.16/2.70 | COMBINE_EQS: (43), (54) imply: % 14.16/2.70 | (56) all_60_0 = all_47_0 % 14.16/2.70 | % 14.16/2.70 | COMBINE_EQS: (55), (56) imply: % 14.16/2.70 | (57) all_53_1 = all_47_0 % 14.16/2.70 | % 14.16/2.70 | SIMP: (57) implies: % 14.16/2.70 | (58) all_53_1 = all_47_0 % 14.16/2.70 | % 14.16/2.70 | REDUCE: (41), (50) imply: % 14.16/2.70 | (59) vmul(all_47_0, all_74_3) = all_74_2 % 14.16/2.70 | % 14.16/2.70 | REDUCE: (40), (50) imply: % 14.16/2.70 | (60) vmul(all_47_0, all_74_6) = all_74_5 % 14.16/2.70 | % 14.16/2.70 | REDUCE: (20), (58) imply: % 14.16/2.70 | (61) vmul(vd448, all_53_0) = all_47_0 % 14.16/2.70 | % 14.16/2.70 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd448, all_53_0, % 14.16/2.70 | all_47_0, simplifying with (10), (18), (61) gives: % 14.16/2.70 | (62) vmul(all_53_0, vd448) = all_47_0 & $i(all_47_0) % 14.16/2.70 | % 14.16/2.70 | ALPHA: (62) implies: % 14.16/2.70 | (63) $i(all_47_0) % 14.16/2.70 | % 14.16/2.70 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd449, v1, all_53_0, % 14.16/2.70 | simplifying with (9), (11), (21) gives: % 14.16/2.70 | (64) vmul(v1, vd449) = all_53_0 & $i(all_53_0) % 14.16/2.70 | % 14.16/2.70 | ALPHA: (64) implies: % 14.16/2.70 | (65) vmul(v1, vd449) = all_53_0 % 14.16/2.70 | % 14.16/2.70 | GROUND_INST: instantiating (8) with all_47_0, all_74_6, all_74_3, all_74_2, % 14.16/2.70 | simplifying with (35), (42), (59), (63) gives: % 14.16/2.70 | (66) ? [v0: $i] : (vplus(v0, all_47_0) = all_74_2 & vmul(all_47_0, % 14.16/2.70 | all_74_6) = v0 & $i(v0) & $i(all_74_2)) % 14.16/2.70 | % 14.16/2.70 | GROUND_INST: instantiating (8) with vd449, all_74_6, all_74_3, all_74_1, % 14.16/2.70 | simplifying with (11), (35), (39), (42) gives: % 14.16/2.70 | (67) ? [v0: $i] : (vplus(v0, vd449) = all_74_1 & vmul(vd449, all_74_6) = % 14.16/2.70 | v0 & $i(v0) & $i(all_74_1)) % 14.16/2.70 | % 14.16/2.70 | DELTA: instantiating (67) with fresh symbol all_86_0 gives: % 14.16/2.71 | (68) vplus(all_86_0, vd449) = all_74_1 & vmul(vd449, all_74_6) = all_86_0 & % 14.16/2.71 | $i(all_86_0) & $i(all_74_1) % 14.16/2.71 | % 14.16/2.71 | ALPHA: (68) implies: % 14.16/2.71 | (69) $i(all_86_0) % 14.16/2.71 | (70) vmul(vd449, all_74_6) = all_86_0 % 14.16/2.71 | (71) vplus(all_86_0, vd449) = all_74_1 % 14.16/2.71 | % 14.16/2.71 | DELTA: instantiating (66) with fresh symbol all_88_0 gives: % 14.16/2.71 | (72) vplus(all_88_0, all_47_0) = all_74_2 & vmul(all_47_0, all_74_6) = % 14.16/2.71 | all_88_0 & $i(all_88_0) & $i(all_74_2) % 14.16/2.71 | % 14.16/2.71 | ALPHA: (72) implies: % 14.16/2.71 | (73) vmul(all_47_0, all_74_6) = all_88_0 % 14.16/2.71 | (74) vplus(all_88_0, all_47_0) = all_74_2 % 14.16/2.71 | % 14.16/2.71 | GROUND_INST: instantiating (13) with all_74_4, all_86_0, all_74_6, vd449, % 14.16/2.71 | simplifying with (38), (70) gives: % 14.16/2.71 | (75) all_86_0 = all_74_4 % 14.16/2.71 | % 14.16/2.71 | GROUND_INST: instantiating (13) with all_74_5, all_88_0, all_74_6, all_47_0, % 14.16/2.71 | simplifying with (60), (73) gives: % 14.16/2.71 | (76) all_88_0 = all_74_5 % 14.16/2.71 | % 14.16/2.71 | REDUCE: (74), (76) imply: % 14.16/2.71 | (77) vplus(all_74_5, all_47_0) = all_74_2 % 14.16/2.71 | % 14.16/2.71 | REDUCE: (71), (75) imply: % 14.16/2.71 | (78) vplus(all_74_4, vd449) = all_74_1 % 14.16/2.71 | % 14.16/2.71 | REDUCE: (69), (75) imply: % 14.16/2.71 | (79) $i(all_74_4) % 14.16/2.71 | % 14.16/2.71 | GROUND_INST: instantiating (7) with vd449, all_53_0, simplifying with (11), % 14.16/2.71 | (65) gives: % 14.16/2.71 | (80) all_53_0 = vd449 % 14.16/2.71 | % 14.16/2.71 | GROUND_INST: instantiating (ass(cond(281, 0), 0)) with vd448, all_74_4, % 14.16/2.71 | all_53_0, all_74_5, all_47_0, all_74_2, simplifying with (10), % 14.16/2.71 | (18), (36), (61), (77), (79) gives: % 14.16/2.71 | (81) ? [v0: $i] : (vplus(all_74_4, all_53_0) = v0 & vmul(vd448, v0) = % 14.16/2.71 | all_74_2 & $i(v0) & $i(all_74_2)) % 14.16/2.71 | % 14.16/2.71 | GROUND_INST: instantiating (ass(cond(281, 0), 0)) with vd448, all_74_4, vd449, % 14.16/2.71 | all_74_5, all_47_0, all_74_2, simplifying with (10), (11), (16), % 14.16/2.71 | (36), (77), (79) gives: % 14.16/2.71 | (82) ? [v0: $i] : (vplus(all_74_4, vd449) = v0 & vmul(vd448, v0) = % 14.16/2.71 | all_74_2 & $i(v0) & $i(all_74_2)) % 14.16/2.71 | % 14.16/2.71 | DELTA: instantiating (82) with fresh symbol all_102_0 gives: % 14.16/2.71 | (83) vplus(all_74_4, vd449) = all_102_0 & vmul(vd448, all_102_0) = all_74_2 % 14.16/2.71 | & $i(all_102_0) & $i(all_74_2) % 14.16/2.71 | % 14.16/2.71 | ALPHA: (83) implies: % 14.16/2.71 | (84) vmul(vd448, all_102_0) = all_74_2 % 14.16/2.71 | (85) vplus(all_74_4, vd449) = all_102_0 % 14.16/2.71 | % 14.16/2.71 | DELTA: instantiating (81) with fresh symbol all_104_0 gives: % 14.16/2.71 | (86) vplus(all_74_4, all_53_0) = all_104_0 & vmul(vd448, all_104_0) = % 14.16/2.71 | all_74_2 & $i(all_104_0) & $i(all_74_2) % 14.16/2.71 | % 14.16/2.71 | ALPHA: (86) implies: % 14.16/2.71 | (87) vplus(all_74_4, all_53_0) = all_104_0 % 14.16/2.71 | % 14.16/2.71 | REDUCE: (80), (87) imply: % 14.16/2.71 | (88) vplus(all_74_4, vd449) = all_104_0 % 14.16/2.71 | % 14.16/2.71 | GROUND_INST: instantiating (14) with all_74_1, all_104_0, vd449, all_74_4, % 14.16/2.71 | simplifying with (78), (88) gives: % 14.16/2.71 | (89) all_104_0 = all_74_1 % 14.16/2.71 | % 14.16/2.71 | GROUND_INST: instantiating (14) with all_102_0, all_104_0, vd449, all_74_4, % 14.16/2.71 | simplifying with (85), (88) gives: % 14.16/2.71 | (90) all_104_0 = all_102_0 % 14.16/2.72 | % 14.16/2.72 | COMBINE_EQS: (89), (90) imply: % 14.16/2.72 | (91) all_102_0 = all_74_1 % 14.16/2.72 | % 14.16/2.72 | REDUCE: (84), (91) imply: % 14.16/2.72 | (92) vmul(vd448, all_74_1) = all_74_2 % 14.16/2.72 | % 14.16/2.72 | GROUND_INST: instantiating (13) with all_74_0, all_74_2, all_74_1, vd448, % 14.16/2.72 | simplifying with (37), (92) gives: % 14.16/2.72 | (93) all_74_0 = all_74_2 % 14.16/2.72 | % 14.16/2.72 | REDUCE: (34), (93) imply: % 14.16/2.72 | (94) $false % 14.16/2.72 | % 14.16/2.72 | CLOSE: (94) is inconsistent. % 14.16/2.72 | % 14.16/2.72 End of proof % 14.16/2.72 % SZS output end Proof for theBenchmark % 14.16/2.72 % 14.16/2.72 2119ms %------------------------------------------------------------------------------