%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM845+2 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n020.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 9.22s 2.02s % Output : Proof 12.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM845+2 : 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 : n020.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 14:41:00 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.72/1.08 Prover 4: Preprocessing ... % 2.72/1.09 Prover 1: Preprocessing ... % 3.10/1.13 Prover 2: Preprocessing ... % 3.10/1.13 Prover 5: Preprocessing ... % 3.10/1.14 Prover 6: Preprocessing ... % 3.10/1.14 Prover 0: Preprocessing ... % 3.10/1.14 Prover 3: Preprocessing ... % 4.79/1.48 Prover 1: Warning: ignoring some quantifiers % 4.79/1.50 Prover 3: Warning: ignoring some quantifiers % 5.43/1.52 Prover 3: Constructing countermodel ... % 5.43/1.52 Prover 6: Proving ... % 5.43/1.52 Prover 1: Constructing countermodel ... % 6.63/1.62 Prover 4: Constructing countermodel ... % 6.89/1.68 Prover 0: Proving ... % 6.89/1.70 Prover 5: Proving ... % 6.89/1.70 Prover 2: Proving ... % 9.22/2.02 Prover 3: proved (1381ms) % 9.22/2.02 % 9.22/2.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.22/2.02 % 9.22/2.04 Prover 0: stopped % 9.22/2.04 Prover 6: stopped % 9.22/2.05 Prover 5: stopped % 9.22/2.08 Prover 2: stopped % 9.22/2.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.22/2.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.22/2.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.22/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.22/2.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.22/2.11 Prover 7: Preprocessing ... % 9.22/2.12 Prover 10: Preprocessing ... % 9.22/2.13 Prover 8: Preprocessing ... % 9.22/2.13 Prover 11: Preprocessing ... % 10.09/2.15 Prover 13: Preprocessing ... % 10.89/2.21 Prover 8: Warning: ignoring some quantifiers % 10.89/2.22 Prover 10: Constructing countermodel ... % 10.89/2.23 Prover 8: Constructing countermodel ... % 11.40/2.27 Prover 7: Constructing countermodel ... % 11.40/2.27 Prover 13: Warning: ignoring some quantifiers % 11.40/2.27 Prover 13: Constructing countermodel ... % 11.40/2.29 Prover 1: Found proof (size 130) % 11.40/2.29 Prover 1: proved (1661ms) % 11.40/2.30 Prover 13: stopped % 11.40/2.30 Prover 7: stopped % 11.40/2.30 Prover 10: stopped % 11.40/2.30 Prover 8: stopped % 11.40/2.30 Prover 4: stopped % 11.67/2.30 Prover 11: Constructing countermodel ... % 11.67/2.31 Prover 11: stopped % 11.67/2.31 % 11.67/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.67/2.31 % 11.67/2.33 % SZS output start Proof for theBenchmark % 11.67/2.33 Assumptions after simplification: % 11.67/2.33 --------------------------------- % 11.67/2.33 % 11.67/2.33 (ass(cond(33, 0), 0)) % 11.84/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 11.84/2.36 (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 11.84/2.36 $i(v0) | ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) & % 11.84/2.36 $i(v4))) % 11.84/2.36 % 11.84/2.36 (ass(cond(61, 0), 0)) % 11.84/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1) % 11.84/2.36 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2))) % 11.84/2.36 % 11.84/2.36 (ass(cond(conseq(263), 1), 0)) % 11.84/2.36 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 11.84/2.36 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v4) | ~ % 11.84/2.36 (vmul(vd411, v1) = v2) | ~ (vplus(v3, v4) = v5) | ~ (vplus(v2, vd411) = % 11.84/2.36 v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 11.84/2.36 : (vmul(v0, v1) = v6 & vmul(vd411, v4) = v8 & vplus(v8, v4) = v9 & % 11.84/2.36 vplus(v2, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 = v6) | % 11.84/2.36 v9 = v5)))) % 11.84/2.36 % 11.84/2.36 (ass(cond(conseq(263), 1), 1)) % 11.84/2.37 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 11.84/2.37 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v3) | ~ % 11.84/2.37 (vmul(vd411, v1) = v2) | ~ (vplus(v4, v3) = v5) | ~ (vplus(v2, vd411) = % 11.84/2.37 v4) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 11.84/2.37 : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 & vplus(v2, v1) = v7 & % 11.84/2.37 vplus(vd411, v3) = v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 = % 11.84/2.37 v6) | v9 = v5)))) % 11.84/2.37 % 11.84/2.37 (ass(cond(conseq(263), 1), 2)) % 11.84/2.37 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 11.84/2.37 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~ % 11.84/2.37 (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411, v1) = % 11.84/2.37 v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 11.84/2.37 : ? [v10: $i] : (vsucc(v1) = v8 & vmul(v0, v1) = v6 & vplus(v2, v9) = v10 % 11.84/2.37 & vplus(v2, v1) = v7 & vplus(vd411, v8) = v9 & $i(v10) & $i(v9) & $i(v8) % 11.84/2.37 & $i(v7) & $i(v6) & ( ~ (v7 = v6) | v10 = v5)))) % 11.84/2.37 % 11.84/2.37 (ass(cond(conseq(263), 1), 3)) % 11.84/2.37 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 11.84/2.37 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~ % 11.84/2.37 (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411, v1) = % 11.84/2.37 v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 11.84/2.37 : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 & vplus(v2, v1) = v7 & vplus(v0, % 11.84/2.37 v1) = v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 = v6) | v9 = % 11.84/2.37 v5)))) % 11.84/2.37 % 11.84/2.37 (ass(cond(conseq(263), 1), 4)) % 11.84/2.37 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 11.84/2.37 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~ % 11.84/2.37 (vplus(v2, v3) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v1) | ? [v5: $i] : % 11.84/2.37 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vmul(v0, v1) = v5 & vplus(v2, % 11.84/2.37 v7) = v8 & vplus(v2, v1) = v6 & vplus(v1, v0) = v7 & $i(v8) & $i(v7) & % 11.84/2.38 $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4)))) % 11.84/2.38 % 11.84/2.38 (ass(cond(conseq(263), 1), 5)) % 11.84/2.38 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 11.84/2.38 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~ % 11.84/2.38 (vplus(v2, v3) = v4) | ~ (vplus(v1, v0) = v3) | ~ $i(v1) | ? [v5: $i] : % 11.84/2.38 ? [v6: $i] : ? [v7: $i] : (vmul(v0, v1) = v5 & vplus(v6, v0) = v7 & % 11.84/2.38 vplus(v2, v1) = v6 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) | v7 = % 11.84/2.38 v4)))) % 11.84/2.38 % 11.84/2.38 (ass(cond(conseq(263), 1), 6)) % 11.84/2.38 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 11.84/2.38 $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? % 11.84/2.38 [v5: $i] : ? [v6: $i] : (vmul(vd411, v1) = v3 & vplus(v4, v0) = v6 & % 11.84/2.38 vplus(v3, v1) = v4 & vplus(v2, v0) = v5 & $i(v6) & $i(v5) & $i(v4) & % 11.84/2.38 $i(v3) & ( ~ (v4 = v2) | v6 = v5)))) % 11.84/2.38 % 11.84/2.38 (ass(cond(conseq(263), 1), 7)) % 11.84/2.38 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 11.84/2.38 $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? % 11.84/2.38 [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vsucc(v1) = v5 & vmul(v0, v5) = v6 % 11.84/2.38 & vmul(vd411, v1) = v3 & vplus(v3, v1) = v4 & vplus(v2, v0) = v7 & % 11.84/2.38 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v7 = v6)))) % 11.84/2.38 % 11.84/2.38 (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))) % 11.84/2.38 $i(v1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 11.84/2.38 (vsucc(v1) = v2) | ~ (vplus(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 11.84/2.38 $i] : (vsucc(v4) = v3 & vplus(v0, v1) = v4 & $i(v4) & $i(v3))) & ? [v0: % 11.84/2.38 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v1, v1) = v2) | ~ $i(v1) | ~ % 11.84/2.38 $i(v0) | (vsucc(v1) = v2 & $i(v2))) % 11.84/2.38 % 11.84/2.38 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) % 11.84/2.39 $i(v1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 11.84/2.39 (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 11.84/2.39 $i] : (vmul(v0, v1) = v4 & vplus(v4, v0) = v3 & $i(v4) & $i(v3))) & ? % 11.84/2.39 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (vmul(v1, v1) = v2) | ~ % 11.84/2.39 $i(v1) | ~ $i(v0)) % 11.84/2.39 % 11.84/2.39 (qu(ind(267), imp(267))) % 11.84/2.39 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ? [v1: $i] : ? [v2: % 11.84/2.39 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 11.84/2.39 : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 & vmul(v0, v1) = v2 & % 11.84/2.39 vmul(vd411, v4) = v6 & vmul(vd411, v1) = v3 & vplus(v6, v4) = v7 & % 11.84/2.39 vplus(v3, v1) = v2 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 11.84/2.39 $i(v1))) % 11.84/2.39 % 11.84/2.39 (function-axioms) % 11.84/2.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.84/2.39 (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 11.84/2.39 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, % 11.84/2.39 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 11.84/2.39 (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 11.84/2.39 % 11.84/2.39 Further assumptions not needed in the proof: % 11.84/2.39 -------------------------------------------- % 11.84/2.39 ass(cond(43, 0), 0), holds(264, 412, 2) % 11.84/2.39 % 11.84/2.39 Those formulas are unsatisfiable: % 11.84/2.39 --------------------------------- % 11.84/2.39 % 11.84/2.39 Begin of proof % 11.84/2.39 | % 11.84/2.39 | ALPHA: (ass(cond(conseq(263), 1), 0)) implies: % 11.84/2.39 | (1) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 11.84/2.39 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v4) | ~ % 11.84/2.39 | (vmul(vd411, v1) = v2) | ~ (vplus(v3, v4) = v5) | ~ (vplus(v2, % 11.84/2.39 | vd411) = v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: % 11.84/2.39 | $i] : ? [v9: $i] : (vmul(v0, v1) = v6 & vmul(vd411, v4) = v8 & % 11.84/2.39 | vplus(v8, v4) = v9 & vplus(v2, v1) = v7 & $i(v9) & $i(v8) & % 11.84/2.40 | $i(v7) & $i(v6) & ( ~ (v7 = v6) | v9 = v5)))) % 11.84/2.40 | % 11.84/2.40 | ALPHA: (ass(cond(conseq(263), 1), 1)) implies: % 11.84/2.40 | (2) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 11.84/2.40 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v3) | ~ % 11.84/2.40 | (vmul(vd411, v1) = v2) | ~ (vplus(v4, v3) = v5) | ~ (vplus(v2, % 11.84/2.40 | vd411) = v4) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: % 11.84/2.40 | $i] : ? [v9: $i] : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 & % 11.84/2.40 | vplus(v2, v1) = v7 & vplus(vd411, v3) = v8 & $i(v9) & $i(v8) & % 11.84/2.40 | $i(v7) & $i(v6) & ( ~ (v7 = v6) | v9 = v5)))) % 11.84/2.40 | % 11.84/2.40 | ALPHA: (ass(cond(conseq(263), 1), 2)) implies: % 11.84/2.40 | (3) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 11.84/2.40 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~ % 11.84/2.40 | (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411, % 11.84/2.40 | v1) = v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 11.84/2.40 | : ? [v9: $i] : ? [v10: $i] : (vsucc(v1) = v8 & vmul(v0, v1) = v6 % 11.84/2.40 | & vplus(v2, v9) = v10 & vplus(v2, v1) = v7 & vplus(vd411, v8) = % 11.84/2.40 | v9 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 = v6) % 11.84/2.40 | | v10 = v5)))) % 11.84/2.40 | % 11.84/2.40 | ALPHA: (ass(cond(conseq(263), 1), 3)) implies: % 11.84/2.40 | (4) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 11.84/2.40 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~ % 11.84/2.40 | (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411, % 11.84/2.40 | v1) = v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 11.84/2.40 | : ? [v9: $i] : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 & vplus(v2, % 11.84/2.40 | v1) = v7 & vplus(v0, v1) = v8 & $i(v9) & $i(v8) & $i(v7) & % 11.84/2.40 | $i(v6) & ( ~ (v7 = v6) | v9 = v5)))) % 11.84/2.40 | % 11.84/2.40 | ALPHA: (ass(cond(conseq(263), 1), 4)) implies: % 11.84/2.40 | (5) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 11.84/2.40 | ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~ % 11.84/2.40 | (vplus(v2, v3) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v1) | ? % 11.84/2.40 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vmul(v0, v1) % 11.84/2.40 | = v5 & vplus(v2, v7) = v8 & vplus(v2, v1) = v6 & vplus(v1, v0) = % 11.84/2.40 | v7 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = % 11.84/2.40 | v4)))) % 11.84/2.40 | % 11.84/2.40 | ALPHA: (ass(cond(conseq(263), 1), 5)) implies: % 11.84/2.41 | (6) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 11.84/2.41 | ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~ % 11.84/2.41 | (vplus(v2, v3) = v4) | ~ (vplus(v1, v0) = v3) | ~ $i(v1) | ? % 11.84/2.41 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vmul(v0, v1) = v5 & % 11.84/2.41 | vplus(v6, v0) = v7 & vplus(v2, v1) = v6 & $i(v7) & $i(v6) & % 11.84/2.41 | $i(v5) & ( ~ (v6 = v5) | v7 = v4)))) % 11.84/2.41 | % 11.84/2.41 | ALPHA: (ass(cond(conseq(263), 1), 6)) implies: % 11.84/2.41 | (7) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 11.84/2.41 | ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? % 11.84/2.41 | [v5: $i] : ? [v6: $i] : (vmul(vd411, v1) = v3 & vplus(v4, v0) = v6 % 11.84/2.41 | & vplus(v3, v1) = v4 & vplus(v2, v0) = v5 & $i(v6) & $i(v5) & % 11.84/2.41 | $i(v4) & $i(v3) & ( ~ (v4 = v2) | v6 = v5)))) % 11.84/2.41 | % 11.84/2.41 | ALPHA: (ass(cond(conseq(263), 1), 7)) implies: % 11.84/2.41 | (8) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 11.84/2.41 | ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? % 11.84/2.41 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vsucc(v1) = v5 & vmul(v0, % 11.84/2.41 | v5) = v6 & vmul(vd411, v1) = v3 & vplus(v3, v1) = v4 & % 11.84/2.41 | vplus(v2, v0) = v7 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 11.84/2.41 | ( ~ (v4 = v2) | v7 = v6)))) % 11.84/2.41 | % 11.84/2.41 | ALPHA: (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), % 11.84/2.41 | holds(definiens(249), 398, 0)))) implies: % 11.84/2.41 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v1) % 11.84/2.41 | = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 11.84/2.41 | $i] : (vmul(v0, v1) = v4 & vplus(v4, v0) = v3 & $i(v4) & $i(v3))) % 11.84/2.41 | % 11.84/2.41 | ALPHA: (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), % 11.84/2.41 | holds(definiens(29), 44, 0)))) implies: % 11.84/2.41 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v1) % 11.84/2.41 | = v2) | ~ (vplus(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 11.84/2.41 | $i] : (vsucc(v4) = v3 & vplus(v0, v1) = v4 & $i(v4) & $i(v3))) % 11.84/2.41 | % 11.84/2.41 | ALPHA: (qu(ind(267), imp(267))) implies: % 11.84/2.41 | (11) $i(vd411) % 11.84/2.42 | (12) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ? [v1: $i] : ? [v2: $i] % 11.84/2.42 | : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 11.84/2.42 | $i] : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 & % 11.84/2.42 | vmul(v0, v1) = v2 & vmul(vd411, v4) = v6 & vmul(vd411, v1) = v3 & % 11.84/2.42 | vplus(v6, v4) = v7 & vplus(v3, v1) = v2 & $i(v7) & $i(v6) & $i(v5) % 11.84/2.42 | & $i(v4) & $i(v3) & $i(v2) & $i(v1))) % 11.84/2.42 | % 11.84/2.42 | ALPHA: (function-axioms) implies: % 11.84/2.42 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = % 11.84/2.42 | v1) | ~ (vsucc(v2) = v0)) % 11.84/2.42 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.84/2.42 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 11.84/2.42 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.84/2.42 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 11.84/2.42 | % 11.84/2.42 | DELTA: instantiating (7) with fresh symbol all_15_0 gives: % 11.84/2.42 | (16) vsucc(vd411) = all_15_0 & $i(all_15_0) & ! [v0: $i] : ! [v1: $i] : ( % 11.84/2.42 | ~ (vmul(all_15_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] % 11.84/2.42 | : ? [v4: $i] : ? [v5: $i] : (vmul(vd411, v0) = v2 & vplus(v3, % 11.84/2.42 | all_15_0) = v5 & vplus(v2, v0) = v3 & vplus(v1, all_15_0) = v4 & % 11.84/2.42 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v5 = v4))) % 11.84/2.42 | % 11.84/2.42 | ALPHA: (16) implies: % 11.84/2.42 | (17) vsucc(vd411) = all_15_0 % 11.84/2.42 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ (vmul(all_15_0, v0) = v1) | ~ $i(v0) % 11.84/2.42 | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 11.84/2.42 | (vmul(vd411, v0) = v2 & vplus(v3, all_15_0) = v5 & vplus(v2, v0) = % 11.84/2.42 | v3 & vplus(v1, all_15_0) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 11.84/2.42 | & ( ~ (v3 = v1) | v5 = v4))) % 11.84/2.42 | % 11.84/2.42 | DELTA: instantiating (6) with fresh symbol all_18_0 gives: % 11.84/2.42 | (19) vsucc(vd411) = all_18_0 & $i(all_18_0) & ! [v0: $i] : ! [v1: $i] : % 11.84/2.42 | ! [v2: $i] : ! [v3: $i] : ( ~ (vmul(vd411, v0) = v1) | ~ (vplus(v1, % 11.84/2.42 | v2) = v3) | ~ (vplus(v0, all_18_0) = v2) | ~ $i(v0) | ? [v4: % 11.84/2.42 | $i] : ? [v5: $i] : ? [v6: $i] : (vmul(all_18_0, v0) = v4 & % 11.84/2.42 | vplus(v5, all_18_0) = v6 & vplus(v1, v0) = v5 & $i(v6) & $i(v5) & % 11.84/2.42 | $i(v4) & ( ~ (v5 = v4) | v6 = v3))) % 11.84/2.42 | % 11.84/2.42 | ALPHA: (19) implies: % 11.84/2.42 | (20) $i(all_18_0) % 11.84/2.42 | (21) vsucc(vd411) = all_18_0 % 11.84/2.42 | % 11.84/2.42 | DELTA: instantiating (8) with fresh symbol all_21_0 gives: % 11.84/2.43 | (22) vsucc(vd411) = all_21_0 & $i(all_21_0) & ! [v0: $i] : ! [v1: $i] : ( % 11.84/2.43 | ~ (vmul(all_21_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] % 11.84/2.43 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vsucc(v0) = v4 & % 11.84/2.43 | vmul(all_21_0, v4) = v5 & vmul(vd411, v0) = v2 & vplus(v2, v0) = % 11.84/2.43 | v3 & vplus(v1, all_21_0) = v6 & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 11.84/2.43 | & $i(v2) & ( ~ (v3 = v1) | v6 = v5))) % 11.84/2.43 | % 11.84/2.43 | ALPHA: (22) implies: % 11.84/2.43 | (23) vsucc(vd411) = all_21_0 % 11.84/2.43 | % 11.84/2.43 | DELTA: instantiating (5) with fresh symbol all_24_0 gives: % 11.84/2.43 | (24) vsucc(vd411) = all_24_0 & $i(all_24_0) & ! [v0: $i] : ! [v1: $i] : % 11.84/2.43 | ! [v2: $i] : ! [v3: $i] : ( ~ (vmul(vd411, v0) = v1) | ~ (vplus(v1, % 11.84/2.43 | v2) = v3) | ~ (vplus(all_24_0, v0) = v2) | ~ $i(v0) | ? [v4: % 11.84/2.43 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vmul(all_24_0, % 11.84/2.43 | v0) = v4 & vplus(v1, v6) = v7 & vplus(v1, v0) = v5 & vplus(v0, % 11.84/2.43 | all_24_0) = v6 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~ (v5 = % 11.84/2.43 | v4) | v7 = v3))) % 11.84/2.43 | % 11.84/2.43 | ALPHA: (24) implies: % 11.84/2.43 | (25) vsucc(vd411) = all_24_0 % 11.84/2.43 | % 11.84/2.43 | DELTA: instantiating (12) with fresh symbol all_27_0 gives: % 11.84/2.43 | (26) vsucc(vd411) = all_27_0 & $i(all_27_0) & ? [v0: $i] : ? [v1: $i] : % 11.84/2.43 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( % 11.84/2.43 | ~ (v6 = v4) & vsucc(v0) = v3 & vmul(all_27_0, v3) = v4 & % 11.84/2.43 | vmul(all_27_0, v0) = v1 & vmul(vd411, v3) = v5 & vmul(vd411, v0) = % 11.84/2.43 | v2 & vplus(v5, v3) = v6 & vplus(v2, v0) = v1 & $i(v6) & $i(v5) & % 11.84/2.43 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 11.84/2.43 | % 11.84/2.43 | ALPHA: (26) implies: % 11.84/2.43 | (27) vsucc(vd411) = all_27_0 % 12.29/2.43 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.29/2.43 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & vsucc(v0) = v3 & % 12.29/2.43 | vmul(all_27_0, v3) = v4 & vmul(all_27_0, v0) = v1 & vmul(vd411, v3) % 12.29/2.43 | = v5 & vmul(vd411, v0) = v2 & vplus(v5, v3) = v6 & vplus(v2, v0) = % 12.29/2.43 | v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.29/2.43 | % 12.29/2.43 | DELTA: instantiating (1) with fresh symbol all_29_0 gives: % 12.29/2.44 | (29) vsucc(vd411) = all_29_0 & $i(all_29_0) & ! [v0: $i] : ! [v1: $i] : % 12.29/2.44 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v0) = v3) | ~ % 12.29/2.44 | (vmul(vd411, v0) = v1) | ~ (vplus(v2, v3) = v4) | ~ (vplus(v1, % 12.29/2.44 | vd411) = v2) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: % 12.29/2.44 | $i] : ? [v8: $i] : (vmul(all_29_0, v0) = v5 & vmul(vd411, v3) = % 12.29/2.44 | v7 & vplus(v7, v3) = v8 & vplus(v1, v0) = v6 & $i(v8) & $i(v7) & % 12.29/2.44 | $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4))) % 12.29/2.44 | % 12.29/2.44 | ALPHA: (29) implies: % 12.29/2.44 | (30) vsucc(vd411) = all_29_0 % 12.29/2.44 | % 12.29/2.44 | DELTA: instantiating (2) with fresh symbol all_32_0 gives: % 12.29/2.44 | (31) vsucc(vd411) = all_32_0 & $i(all_32_0) & ! [v0: $i] : ! [v1: $i] : % 12.29/2.44 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v0) = v2) | ~ % 12.29/2.44 | (vmul(vd411, v0) = v1) | ~ (vplus(v3, v2) = v4) | ~ (vplus(v1, % 12.29/2.44 | vd411) = v3) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: % 12.29/2.44 | $i] : ? [v8: $i] : (vmul(all_32_0, v0) = v5 & vplus(v1, v7) = v8 % 12.29/2.44 | & vplus(v1, v0) = v6 & vplus(vd411, v2) = v7 & $i(v8) & $i(v7) & % 12.29/2.44 | $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4))) % 12.29/2.44 | % 12.29/2.44 | ALPHA: (31) implies: % 12.29/2.44 | (32) vsucc(vd411) = all_32_0 % 12.29/2.44 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 12.29/2.44 | ( ~ (vsucc(v0) = v2) | ~ (vmul(vd411, v0) = v1) | ~ (vplus(v3, v2) = % 12.29/2.44 | v4) | ~ (vplus(v1, vd411) = v3) | ~ $i(v0) | ? [v5: $i] : ? % 12.29/2.44 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vmul(all_32_0, v0) = v5 & % 12.29/2.44 | vplus(v1, v7) = v8 & vplus(v1, v0) = v6 & vplus(vd411, v2) = v7 & % 12.29/2.44 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4))) % 12.29/2.44 | % 12.29/2.44 | DELTA: instantiating (4) with fresh symbol all_35_0 gives: % 12.29/2.44 | (34) vsucc(vd411) = all_35_0 & $i(all_35_0) & ! [v0: $i] : ! [v1: $i] : % 12.29/2.44 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v2) = v3) | ~ % 12.29/2.44 | (vmul(vd411, v0) = v1) | ~ (vplus(v1, v3) = v4) | ~ (vplus(vd411, % 12.29/2.44 | v0) = v2) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 12.29/2.44 | : ? [v8: $i] : (vmul(all_35_0, v0) = v5 & vplus(v1, v7) = v8 & % 12.29/2.44 | vplus(v1, v0) = v6 & vplus(all_35_0, v0) = v7 & $i(v8) & $i(v7) & % 12.29/2.44 | $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4))) % 12.29/2.44 | % 12.29/2.44 | ALPHA: (34) implies: % 12.29/2.44 | (35) vsucc(vd411) = all_35_0 % 12.29/2.44 | % 12.29/2.44 | DELTA: instantiating (3) with fresh symbol all_38_0 gives: % 12.29/2.44 | (36) vsucc(vd411) = all_38_0 & $i(all_38_0) & ! [v0: $i] : ! [v1: $i] : % 12.29/2.44 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v2) = v3) | ~ % 12.29/2.44 | (vmul(vd411, v0) = v1) | ~ (vplus(v1, v3) = v4) | ~ (vplus(vd411, % 12.29/2.44 | v0) = v2) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 12.29/2.44 | : ? [v8: $i] : ? [v9: $i] : (vsucc(v0) = v7 & vmul(all_38_0, v0) = % 12.29/2.44 | v5 & vplus(v1, v8) = v9 & vplus(v1, v0) = v6 & vplus(vd411, v7) = % 12.29/2.44 | v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) | % 12.29/2.44 | v9 = v4))) % 12.29/2.44 | % 12.29/2.44 | ALPHA: (36) implies: % 12.29/2.45 | (37) vsucc(vd411) = all_38_0 % 12.29/2.45 | % 12.29/2.45 | DELTA: instantiating (28) with fresh symbols all_41_0, all_41_1, all_41_2, % 12.29/2.45 | all_41_3, all_41_4, all_41_5, all_41_6 gives: % 12.29/2.45 | (38) ~ (all_41_0 = all_41_2) & vsucc(all_41_6) = all_41_3 & vmul(all_27_0, % 12.29/2.45 | all_41_3) = all_41_2 & vmul(all_27_0, all_41_6) = all_41_5 & % 12.29/2.45 | vmul(vd411, all_41_3) = all_41_1 & vmul(vd411, all_41_6) = all_41_4 & % 12.29/2.45 | vplus(all_41_1, all_41_3) = all_41_0 & vplus(all_41_4, all_41_6) = % 12.29/2.45 | all_41_5 & $i(all_41_0) & $i(all_41_1) & $i(all_41_2) & $i(all_41_3) & % 12.29/2.45 | $i(all_41_4) & $i(all_41_5) & $i(all_41_6) % 12.29/2.45 | % 12.29/2.45 | ALPHA: (38) implies: % 12.29/2.45 | (39) ~ (all_41_0 = all_41_2) % 12.29/2.45 | (40) $i(all_41_6) % 12.29/2.45 | (41) $i(all_41_3) % 12.29/2.45 | (42) $i(all_41_1) % 12.29/2.45 | (43) vplus(all_41_4, all_41_6) = all_41_5 % 12.29/2.45 | (44) vplus(all_41_1, all_41_3) = all_41_0 % 12.29/2.45 | (45) vmul(vd411, all_41_6) = all_41_4 % 12.29/2.45 | (46) vmul(vd411, all_41_3) = all_41_1 % 12.29/2.45 | (47) vmul(all_27_0, all_41_6) = all_41_5 % 12.29/2.45 | (48) vmul(all_27_0, all_41_3) = all_41_2 % 12.29/2.45 | (49) vsucc(all_41_6) = all_41_3 % 12.29/2.45 | % 12.29/2.45 | GROUND_INST: instantiating (13) with all_21_0, all_27_0, vd411, simplifying % 12.29/2.45 | with (23), (27) gives: % 12.29/2.45 | (50) all_27_0 = all_21_0 % 12.29/2.45 | % 12.29/2.45 | GROUND_INST: instantiating (13) with all_27_0, all_29_0, vd411, simplifying % 12.29/2.45 | with (27), (30) gives: % 12.29/2.45 | (51) all_29_0 = all_27_0 % 12.29/2.45 | % 12.29/2.45 | GROUND_INST: instantiating (13) with all_24_0, all_32_0, vd411, simplifying % 12.29/2.45 | with (25), (32) gives: % 12.29/2.45 | (52) all_32_0 = all_24_0 % 12.29/2.45 | % 12.29/2.45 | GROUND_INST: instantiating (13) with all_21_0, all_32_0, vd411, simplifying % 12.29/2.45 | with (23), (32) gives: % 12.29/2.45 | (53) all_32_0 = all_21_0 % 12.29/2.45 | % 12.29/2.45 | GROUND_INST: instantiating (13) with all_29_0, all_35_0, vd411, simplifying % 12.29/2.45 | with (30), (35) gives: % 12.29/2.45 | (54) all_35_0 = all_29_0 % 12.29/2.45 | % 12.29/2.45 | GROUND_INST: instantiating (13) with all_18_0, all_35_0, vd411, simplifying % 12.29/2.45 | with (21), (35) gives: % 12.29/2.45 | (55) all_35_0 = all_18_0 % 12.29/2.45 | % 12.29/2.45 | GROUND_INST: instantiating (13) with all_32_0, all_38_0, vd411, simplifying % 12.29/2.45 | with (32), (37) gives: % 12.29/2.45 | (56) all_38_0 = all_32_0 % 12.29/2.45 | % 12.29/2.45 | GROUND_INST: instantiating (13) with all_15_0, all_38_0, vd411, simplifying % 12.29/2.45 | with (17), (37) gives: % 12.29/2.45 | (57) all_38_0 = all_15_0 % 12.29/2.45 | % 12.29/2.45 | COMBINE_EQS: (56), (57) imply: % 12.29/2.45 | (58) all_32_0 = all_15_0 % 12.29/2.45 | % 12.29/2.45 | SIMP: (58) implies: % 12.29/2.45 | (59) all_32_0 = all_15_0 % 12.29/2.45 | % 12.29/2.45 | COMBINE_EQS: (54), (55) imply: % 12.29/2.45 | (60) all_29_0 = all_18_0 % 12.29/2.45 | % 12.29/2.45 | SIMP: (60) implies: % 12.29/2.45 | (61) all_29_0 = all_18_0 % 12.29/2.45 | % 12.29/2.45 | COMBINE_EQS: (52), (59) imply: % 12.29/2.45 | (62) all_24_0 = all_15_0 % 12.29/2.45 | % 12.29/2.45 | COMBINE_EQS: (52), (53) imply: % 12.29/2.45 | (63) all_24_0 = all_21_0 % 12.29/2.45 | % 12.29/2.45 | COMBINE_EQS: (51), (61) imply: % 12.29/2.45 | (64) all_27_0 = all_18_0 % 12.29/2.45 | % 12.29/2.45 | SIMP: (64) implies: % 12.29/2.45 | (65) all_27_0 = all_18_0 % 12.29/2.45 | % 12.29/2.45 | COMBINE_EQS: (50), (65) imply: % 12.29/2.46 | (66) all_21_0 = all_18_0 % 12.29/2.46 | % 12.29/2.46 | SIMP: (66) implies: % 12.29/2.46 | (67) all_21_0 = all_18_0 % 12.29/2.46 | % 12.29/2.46 | COMBINE_EQS: (62), (63) imply: % 12.29/2.46 | (68) all_21_0 = all_15_0 % 12.29/2.46 | % 12.29/2.46 | SIMP: (68) implies: % 12.29/2.46 | (69) all_21_0 = all_15_0 % 12.29/2.46 | % 12.29/2.46 | COMBINE_EQS: (67), (69) imply: % 12.29/2.46 | (70) all_18_0 = all_15_0 % 12.29/2.46 | % 12.29/2.46 | COMBINE_EQS: (65), (70) imply: % 12.29/2.46 | (71) all_27_0 = all_15_0 % 12.29/2.46 | % 12.29/2.46 | REDUCE: (48), (71) imply: % 12.29/2.46 | (72) vmul(all_15_0, all_41_3) = all_41_2 % 12.29/2.46 | % 12.29/2.46 | REDUCE: (47), (71) imply: % 12.29/2.46 | (73) vmul(all_15_0, all_41_6) = all_41_5 % 12.29/2.46 | % 12.29/2.46 | REDUCE: (20), (70) imply: % 12.29/2.46 | (74) $i(all_15_0) % 12.29/2.46 | % 12.29/2.46 | GROUND_INST: instantiating (18) with all_41_6, all_41_5, simplifying with % 12.29/2.46 | (40), (73) gives: % 12.29/2.46 | (75) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vmul(vd411, % 12.29/2.46 | all_41_6) = v0 & vplus(v1, all_15_0) = v3 & vplus(v0, all_41_6) = % 12.29/2.46 | v1 & vplus(all_41_5, all_15_0) = v2 & $i(v3) & $i(v2) & $i(v1) & % 12.29/2.46 | $i(v0) & ( ~ (v1 = all_41_5) | v3 = v2)) % 12.29/2.46 | % 12.29/2.46 | GROUND_INST: instantiating (18) with all_41_3, all_41_2, simplifying with % 12.29/2.46 | (41), (72) gives: % 12.29/2.46 | (76) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vmul(vd411, % 12.29/2.46 | all_41_3) = v0 & vplus(v1, all_15_0) = v3 & vplus(v0, all_41_3) = % 12.29/2.46 | v1 & vplus(all_41_2, all_15_0) = v2 & $i(v3) & $i(v2) & $i(v1) & % 12.29/2.46 | $i(v0) & ( ~ (v1 = all_41_2) | v3 = v2)) % 12.29/2.46 | % 12.29/2.46 | GROUND_INST: instantiating (9) with all_15_0, all_41_6, all_41_3, all_41_2, % 12.29/2.46 | simplifying with (40), (49), (72), (74) gives: % 12.29/2.46 | (77) ? [v0: $i] : (vmul(all_15_0, all_41_6) = v0 & vplus(v0, all_15_0) = % 12.29/2.46 | all_41_2 & $i(v0) & $i(all_41_2)) % 12.29/2.46 | % 12.29/2.46 | GROUND_INST: instantiating (9) with vd411, all_41_6, all_41_3, all_41_1, % 12.29/2.46 | simplifying with (11), (40), (46), (49) gives: % 12.29/2.46 | (78) ? [v0: $i] : (vmul(vd411, all_41_6) = v0 & vplus(v0, vd411) = % 12.29/2.46 | all_41_1 & $i(v0) & $i(all_41_1)) % 12.29/2.46 | % 12.29/2.47 | GROUND_INST: instantiating (10) with all_41_1, all_41_6, all_41_3, all_41_0, % 12.29/2.47 | simplifying with (40), (42), (44), (49) gives: % 12.29/2.47 | (79) ? [v0: $i] : (vsucc(v0) = all_41_0 & vplus(all_41_1, all_41_6) = v0 & % 12.29/2.47 | $i(v0) & $i(all_41_0)) % 12.29/2.47 | % 12.29/2.47 | DELTA: instantiating (78) with fresh symbol all_53_0 gives: % 12.29/2.47 | (80) vmul(vd411, all_41_6) = all_53_0 & vplus(all_53_0, vd411) = all_41_1 & % 12.29/2.47 | $i(all_53_0) & $i(all_41_1) % 12.29/2.47 | % 12.29/2.47 | ALPHA: (80) implies: % 12.29/2.47 | (81) $i(all_53_0) % 12.29/2.47 | (82) vplus(all_53_0, vd411) = all_41_1 % 12.29/2.47 | (83) vmul(vd411, all_41_6) = all_53_0 % 12.29/2.47 | % 12.29/2.47 | DELTA: instantiating (77) with fresh symbol all_55_0 gives: % 12.29/2.47 | (84) vmul(all_15_0, all_41_6) = all_55_0 & vplus(all_55_0, all_15_0) = % 12.29/2.47 | all_41_2 & $i(all_55_0) & $i(all_41_2) % 12.29/2.47 | % 12.29/2.47 | ALPHA: (84) implies: % 12.29/2.47 | (85) vplus(all_55_0, all_15_0) = all_41_2 % 12.29/2.47 | (86) vmul(all_15_0, all_41_6) = all_55_0 % 12.29/2.47 | % 12.29/2.47 | DELTA: instantiating (79) with fresh symbol all_57_0 gives: % 12.29/2.47 | (87) vsucc(all_57_0) = all_41_0 & vplus(all_41_1, all_41_6) = all_57_0 & % 12.29/2.47 | $i(all_57_0) & $i(all_41_0) % 12.29/2.47 | % 12.29/2.47 | ALPHA: (87) implies: % 12.29/2.47 | (88) vplus(all_41_1, all_41_6) = all_57_0 % 12.29/2.47 | (89) vsucc(all_57_0) = all_41_0 % 12.29/2.47 | % 12.29/2.47 | DELTA: instantiating (76) with fresh symbols all_59_0, all_59_1, all_59_2, % 12.29/2.47 | all_59_3 gives: % 12.29/2.47 | (90) vmul(vd411, all_41_3) = all_59_3 & vplus(all_59_2, all_15_0) = % 12.29/2.47 | all_59_0 & vplus(all_59_3, all_41_3) = all_59_2 & vplus(all_41_2, % 12.29/2.47 | all_15_0) = all_59_1 & $i(all_59_0) & $i(all_59_1) & $i(all_59_2) & % 12.29/2.47 | $i(all_59_3) & ( ~ (all_59_2 = all_41_2) | all_59_0 = all_59_1) % 12.29/2.47 | % 12.29/2.47 | ALPHA: (90) implies: % 12.29/2.47 | (91) vplus(all_59_3, all_41_3) = all_59_2 % 12.29/2.47 | (92) vmul(vd411, all_41_3) = all_59_3 % 12.29/2.47 | % 12.29/2.47 | DELTA: instantiating (75) with fresh symbols all_61_0, all_61_1, all_61_2, % 12.29/2.47 | all_61_3 gives: % 12.29/2.47 | (93) vmul(vd411, all_41_6) = all_61_3 & vplus(all_61_2, all_15_0) = % 12.29/2.47 | all_61_0 & vplus(all_61_3, all_41_6) = all_61_2 & vplus(all_41_5, % 12.29/2.47 | all_15_0) = all_61_1 & $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & % 12.29/2.47 | $i(all_61_3) & ( ~ (all_61_2 = all_41_5) | all_61_0 = all_61_1) % 12.29/2.47 | % 12.29/2.47 | ALPHA: (93) implies: % 12.29/2.47 | (94) $i(all_61_2) % 12.29/2.47 | (95) vplus(all_41_5, all_15_0) = all_61_1 % 12.29/2.47 | (96) vplus(all_61_3, all_41_6) = all_61_2 % 12.29/2.47 | (97) vplus(all_61_2, all_15_0) = all_61_0 % 12.29/2.47 | (98) vmul(vd411, all_41_6) = all_61_3 % 12.29/2.47 | (99) ~ (all_61_2 = all_41_5) | all_61_0 = all_61_1 % 12.29/2.47 | % 12.29/2.47 | GROUND_INST: instantiating (15) with all_41_4, all_61_3, all_41_6, vd411, % 12.29/2.47 | simplifying with (45), (98) gives: % 12.29/2.47 | (100) all_61_3 = all_41_4 % 12.29/2.47 | % 12.29/2.47 | GROUND_INST: instantiating (15) with all_53_0, all_61_3, all_41_6, vd411, % 12.29/2.47 | simplifying with (83), (98) gives: % 12.29/2.47 | (101) all_61_3 = all_53_0 % 12.29/2.47 | % 12.29/2.47 | GROUND_INST: instantiating (15) with all_41_1, all_59_3, all_41_3, vd411, % 12.29/2.47 | simplifying with (46), (92) gives: % 12.29/2.47 | (102) all_59_3 = all_41_1 % 12.29/2.47 | % 12.29/2.47 | GROUND_INST: instantiating (15) with all_41_5, all_55_0, all_41_6, all_15_0, % 12.29/2.47 | simplifying with (73), (86) gives: % 12.29/2.47 | (103) all_55_0 = all_41_5 % 12.29/2.47 | % 12.29/2.47 | COMBINE_EQS: (100), (101) imply: % 12.29/2.48 | (104) all_53_0 = all_41_4 % 12.29/2.48 | % 12.29/2.48 | REDUCE: (96), (100) imply: % 12.29/2.48 | (105) vplus(all_41_4, all_41_6) = all_61_2 % 12.29/2.48 | % 12.29/2.48 | REDUCE: (91), (102) imply: % 12.29/2.48 | (106) vplus(all_41_1, all_41_3) = all_59_2 % 12.29/2.48 | % 12.29/2.48 | REDUCE: (85), (103) imply: % 12.29/2.48 | (107) vplus(all_41_5, all_15_0) = all_41_2 % 12.29/2.48 | % 12.29/2.48 | REDUCE: (82), (104) imply: % 12.29/2.48 | (108) vplus(all_41_4, vd411) = all_41_1 % 12.29/2.48 | % 12.29/2.48 | REDUCE: (81), (104) imply: % 12.29/2.48 | (109) $i(all_41_4) % 12.29/2.48 | % 12.29/2.48 | GROUND_INST: instantiating (14) with all_61_1, all_41_2, all_15_0, all_41_5, % 12.29/2.48 | simplifying with (95), (107) gives: % 12.29/2.48 | (110) all_61_1 = all_41_2 % 12.29/2.48 | % 12.29/2.48 | GROUND_INST: instantiating (14) with all_41_5, all_61_2, all_41_6, all_41_4, % 12.29/2.48 | simplifying with (43), (105) gives: % 12.29/2.48 | (111) all_61_2 = all_41_5 % 12.29/2.48 | % 12.29/2.48 | GROUND_INST: instantiating (14) with all_41_0, all_59_2, all_41_3, all_41_1, % 12.29/2.48 | simplifying with (44), (106) gives: % 12.29/2.48 | (112) all_59_2 = all_41_0 % 12.29/2.48 | % 12.29/2.48 | REDUCE: (97), (111) imply: % 12.29/2.48 | (113) vplus(all_41_5, all_15_0) = all_61_0 % 12.29/2.48 | % 12.29/2.48 | REDUCE: (94), (111) imply: % 12.29/2.48 | (114) $i(all_41_5) % 12.29/2.48 | % 12.29/2.48 | BETA: splitting (99) gives: % 12.29/2.48 | % 12.29/2.48 | Case 1: % 12.29/2.48 | | % 12.29/2.48 | | (115) ~ (all_61_2 = all_41_5) % 12.29/2.48 | | % 12.29/2.48 | | REDUCE: (111), (115) imply: % 12.29/2.48 | | (116) $false % 12.29/2.48 | | % 12.29/2.48 | | CLOSE: (116) is inconsistent. % 12.29/2.48 | | % 12.29/2.48 | Case 2: % 12.29/2.48 | | % 12.29/2.48 | | (117) all_61_0 = all_61_1 % 12.29/2.48 | | % 12.29/2.48 | | COMBINE_EQS: (110), (117) imply: % 12.29/2.48 | | (118) all_61_0 = all_41_2 % 12.29/2.48 | | % 12.29/2.48 | | GROUND_INST: instantiating (10) with all_41_5, vd411, all_15_0, all_41_2, % 12.29/2.48 | | simplifying with (11), (17), (107), (114) gives: % 12.29/2.48 | | (119) ? [v0: $i] : (vsucc(v0) = all_41_2 & vplus(all_41_5, vd411) = v0 & % 12.29/2.48 | | $i(v0) & $i(all_41_2)) % 12.29/2.48 | | % 12.29/2.48 | | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_41_4, all_41_6, % 12.29/2.48 | | all_15_0, all_41_5, all_41_2, simplifying with (40), (43), % 12.29/2.48 | | (74), (107), (109) gives: % 12.29/2.48 | | (120) ? [v0: $i] : (vplus(all_41_4, v0) = all_41_2 & vplus(all_41_6, % 12.29/2.48 | | all_15_0) = v0 & $i(v0) & $i(all_41_2)) % 12.29/2.48 | | % 12.29/2.48 | | GROUND_INST: instantiating (33) with all_41_6, all_41_4, all_41_3, all_41_1, % 12.29/2.48 | | all_41_0, simplifying with (40), (44), (45), (49), (108) gives: % 12.29/2.48 | | (121) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 12.29/2.48 | | (vmul(all_32_0, all_41_6) = v0 & vplus(all_41_4, v2) = v3 & % 12.29/2.48 | | vplus(all_41_4, all_41_6) = v1 & vplus(vd411, all_41_3) = v2 & % 12.29/2.48 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v1 = v0) | v3 = % 12.29/2.48 | | all_41_0)) % 12.29/2.48 | | % 12.29/2.49 | | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_41_4, vd411, % 12.29/2.49 | | all_41_6, all_41_1, all_57_0, simplifying with (11), (40), % 12.29/2.49 | | (88), (108), (109) gives: % 12.29/2.49 | | (122) ? [v0: $i] : (vplus(all_41_4, v0) = all_57_0 & vplus(vd411, % 12.29/2.49 | | all_41_6) = v0 & $i(v0) & $i(all_57_0)) % 12.29/2.49 | | % 12.29/2.49 | | DELTA: instantiating (119) with fresh symbol all_87_0 gives: % 12.29/2.49 | | (123) vsucc(all_87_0) = all_41_2 & vplus(all_41_5, vd411) = all_87_0 & % 12.29/2.49 | | $i(all_87_0) & $i(all_41_2) % 12.29/2.49 | | % 12.29/2.49 | | ALPHA: (123) implies: % 12.29/2.49 | | (124) vplus(all_41_5, vd411) = all_87_0 % 12.29/2.49 | | (125) vsucc(all_87_0) = all_41_2 % 12.29/2.49 | | % 12.29/2.49 | | DELTA: instantiating (120) with fresh symbol all_91_0 gives: % 12.29/2.49 | | (126) vplus(all_41_4, all_91_0) = all_41_2 & vplus(all_41_6, all_15_0) = % 12.29/2.49 | | all_91_0 & $i(all_91_0) & $i(all_41_2) % 12.29/2.49 | | % 12.29/2.49 | | ALPHA: (126) implies: % 12.29/2.49 | | (127) vplus(all_41_6, all_15_0) = all_91_0 % 12.29/2.49 | | % 12.29/2.49 | | DELTA: instantiating (122) with fresh symbol all_99_0 gives: % 12.29/2.49 | | (128) vplus(all_41_4, all_99_0) = all_57_0 & vplus(vd411, all_41_6) = % 12.29/2.49 | | all_99_0 & $i(all_99_0) & $i(all_57_0) % 12.29/2.49 | | % 12.29/2.49 | | ALPHA: (128) implies: % 12.29/2.49 | | (129) vplus(vd411, all_41_6) = all_99_0 % 12.29/2.49 | | (130) vplus(all_41_4, all_99_0) = all_57_0 % 12.29/2.49 | | % 12.29/2.49 | | DELTA: instantiating (121) with fresh symbols all_101_0, all_101_1, % 12.29/2.49 | | all_101_2, all_101_3 gives: % 12.29/2.49 | | (131) vmul(all_32_0, all_41_6) = all_101_3 & vplus(all_41_4, all_101_1) = % 12.29/2.49 | | all_101_0 & vplus(all_41_4, all_41_6) = all_101_2 & vplus(vd411, % 12.29/2.49 | | all_41_3) = all_101_1 & $i(all_101_0) & $i(all_101_1) & % 12.29/2.49 | | $i(all_101_2) & $i(all_101_3) & ( ~ (all_101_2 = all_101_3) | % 12.29/2.49 | | all_101_0 = all_41_0) % 12.29/2.49 | | % 12.29/2.49 | | ALPHA: (131) implies: % 12.29/2.49 | | (132) vplus(all_41_4, all_41_6) = all_101_2 % 12.29/2.49 | | % 12.29/2.49 | | GROUND_INST: instantiating (14) with all_41_5, all_101_2, all_41_6, % 12.29/2.49 | | all_41_4, simplifying with (43), (132) gives: % 12.29/2.49 | | (133) all_101_2 = all_41_5 % 12.29/2.49 | | % 12.29/2.49 | | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd411, all_41_6, % 12.29/2.49 | | all_99_0, simplifying with (11), (40), (129) gives: % 12.29/2.49 | | (134) vplus(all_41_6, vd411) = all_99_0 & $i(all_99_0) % 12.29/2.49 | | % 12.29/2.49 | | ALPHA: (134) implies: % 12.29/2.49 | | (135) vplus(all_41_6, vd411) = all_99_0 % 12.29/2.49 | | % 12.29/2.49 | | GROUND_INST: instantiating (10) with all_41_6, vd411, all_15_0, all_91_0, % 12.29/2.49 | | simplifying with (11), (17), (40), (127) gives: % 12.29/2.49 | | (136) ? [v0: $i] : (vsucc(v0) = all_91_0 & vplus(all_41_6, vd411) = v0 & % 12.29/2.49 | | $i(v0) & $i(all_91_0)) % 12.29/2.49 | | % 12.29/2.49 | | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_41_4, all_41_6, % 12.29/2.49 | | vd411, all_41_5, all_87_0, simplifying with (11), (40), (43), % 12.29/2.49 | | (109), (124) gives: % 12.29/2.49 | | (137) ? [v0: $i] : (vplus(all_41_4, v0) = all_87_0 & vplus(all_41_6, % 12.29/2.49 | | vd411) = v0 & $i(v0) & $i(all_87_0)) % 12.29/2.49 | | % 12.29/2.49 | | DELTA: instantiating (136) with fresh symbol all_153_0 gives: % 12.29/2.49 | | (138) vsucc(all_153_0) = all_91_0 & vplus(all_41_6, vd411) = all_153_0 & % 12.29/2.49 | | $i(all_153_0) & $i(all_91_0) % 12.29/2.49 | | % 12.29/2.49 | | ALPHA: (138) implies: % 12.29/2.49 | | (139) vplus(all_41_6, vd411) = all_153_0 % 12.29/2.49 | | % 12.29/2.49 | | DELTA: instantiating (137) with fresh symbol all_167_0 gives: % 12.29/2.49 | | (140) vplus(all_41_4, all_167_0) = all_87_0 & vplus(all_41_6, vd411) = % 12.29/2.49 | | all_167_0 & $i(all_167_0) & $i(all_87_0) % 12.29/2.49 | | % 12.29/2.49 | | ALPHA: (140) implies: % 12.29/2.49 | | (141) vplus(all_41_6, vd411) = all_167_0 % 12.29/2.49 | | (142) vplus(all_41_4, all_167_0) = all_87_0 % 12.29/2.49 | | % 12.29/2.49 | | GROUND_INST: instantiating (14) with all_153_0, all_167_0, vd411, all_41_6, % 12.29/2.49 | | simplifying with (139), (141) gives: % 12.29/2.49 | | (143) all_167_0 = all_153_0 % 12.29/2.49 | | % 12.29/2.49 | | GROUND_INST: instantiating (14) with all_99_0, all_167_0, vd411, all_41_6, % 12.59/2.49 | | simplifying with (135), (141) gives: % 12.59/2.50 | | (144) all_167_0 = all_99_0 % 12.59/2.50 | | % 12.59/2.50 | | COMBINE_EQS: (143), (144) imply: % 12.59/2.50 | | (145) all_153_0 = all_99_0 % 12.59/2.50 | | % 12.59/2.50 | | REDUCE: (142), (144) imply: % 12.59/2.50 | | (146) vplus(all_41_4, all_99_0) = all_87_0 % 12.59/2.50 | | % 12.59/2.50 | | GROUND_INST: instantiating (14) with all_57_0, all_87_0, all_99_0, all_41_4, % 12.59/2.50 | | simplifying with (130), (146) gives: % 12.59/2.50 | | (147) all_87_0 = all_57_0 % 12.59/2.50 | | % 12.59/2.50 | | REDUCE: (125), (147) imply: % 12.59/2.50 | | (148) vsucc(all_57_0) = all_41_2 % 12.59/2.50 | | % 12.59/2.50 | | GROUND_INST: instantiating (13) with all_41_0, all_41_2, all_57_0, % 12.59/2.50 | | simplifying with (89), (148) gives: % 12.59/2.50 | | (149) all_41_0 = all_41_2 % 12.59/2.50 | | % 12.59/2.50 | | REDUCE: (39), (149) imply: % 12.59/2.50 | | (150) $false % 12.59/2.50 | | % 12.59/2.50 | | CLOSE: (150) is inconsistent. % 12.59/2.50 | | % 12.59/2.50 | End of split % 12.59/2.50 | % 12.59/2.50 End of proof % 12.59/2.50 % SZS output end Proof for theBenchmark % 12.59/2.50 % 12.59/2.50 1883ms %------------------------------------------------------------------------------