%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM845+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 : n023.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 11:50:21 EDT 2023 % Result : Theorem 13.01s 2.41s % Output : Proof 15.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : NUM845+1 : TPTP v8.1.2. Released v4.1.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n023.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 08:45:12 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.68/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.68/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.68/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.68/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.68/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.68/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.68/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.11/1.14 Prover 1: Preprocessing ... % 3.11/1.15 Prover 4: Preprocessing ... % 3.84/1.19 Prover 6: Preprocessing ... % 3.84/1.19 Prover 0: Preprocessing ... % 3.84/1.19 Prover 5: Preprocessing ... % 3.84/1.19 Prover 2: Preprocessing ... % 3.84/1.19 Prover 3: Preprocessing ... % 8.38/1.81 Prover 1: Warning: ignoring some quantifiers % 8.84/1.89 Prover 4: Warning: ignoring some quantifiers % 8.84/1.89 Prover 3: Warning: ignoring some quantifiers % 8.84/1.89 Prover 1: Constructing countermodel ... % 8.84/1.90 Prover 6: Proving ... % 8.84/1.91 Prover 3: Constructing countermodel ... % 9.43/1.92 Prover 5: Proving ... % 9.43/1.94 Prover 4: Constructing countermodel ... % 9.88/1.98 Prover 2: Proving ... % 9.88/2.00 Prover 0: Proving ... % 13.01/2.41 Prover 0: proved (1803ms) % 13.01/2.41 % 13.01/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.01/2.41 % 13.01/2.41 Prover 6: stopped % 13.01/2.41 Prover 5: stopped % 13.24/2.41 Prover 3: stopped % 13.34/2.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.34/2.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.34/2.43 Prover 2: stopped % 13.34/2.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.34/2.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.34/2.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.34/2.50 Prover 7: Preprocessing ... % 13.34/2.50 Prover 10: Preprocessing ... % 14.00/2.52 Prover 11: Preprocessing ... % 14.00/2.56 Prover 8: Preprocessing ... % 14.00/2.57 Prover 13: Preprocessing ... % 14.48/2.62 Prover 1: Found proof (size 165) % 14.48/2.62 Prover 1: proved (2008ms) % 14.48/2.62 Prover 7: stopped % 14.48/2.63 Prover 4: stopped % 14.48/2.65 Prover 11: stopped % 14.48/2.67 Prover 13: stopped % 15.14/2.68 Prover 8: Warning: ignoring some quantifiers % 15.24/2.69 Prover 10: Warning: ignoring some quantifiers % 15.24/2.69 Prover 8: Constructing countermodel ... % 15.24/2.70 Prover 10: Constructing countermodel ... % 15.24/2.70 Prover 8: stopped % 15.24/2.71 Prover 10: stopped % 15.24/2.71 % 15.24/2.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.24/2.71 % 15.47/2.76 % SZS output start Proof for theBenchmark % 15.47/2.76 Assumptions after simplification: % 15.47/2.76 --------------------------------- % 15.47/2.76 % 15.47/2.76 (ass(cond(33, 0), 0)) % 15.47/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.47/2.78 (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.47/2.78 $i(v0) | ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) & % 15.47/2.78 $i(v4))) % 15.47/2.78 % 15.47/2.78 (ass(cond(52, 0), 0)) % 15.47/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v0) = v2) | % 15.47/2.78 ~ (vplus(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (vsucc(v4) = % 15.47/2.78 v3 & vplus(v0, v1) = v4 & $i(v4) & $i(v3))) % 15.47/2.78 % 15.47/2.78 (ass(cond(6, 0), 0)) % 15.47/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~ % 15.47/2.78 (vsucc(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 15.47/2.78 % 15.47/2.78 (ass(cond(61, 0), 0)) % 15.47/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1) % 15.47/2.79 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2))) % 15.47/2.79 % 15.47/2.79 (ass(cond(conseq(263), 1), 0)) % 15.47/2.79 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 15.47/2.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v4) | ~ % 15.47/2.79 (vmul(vd411, v1) = v2) | ~ (vplus(v3, v4) = v5) | ~ (vplus(v2, vd411) = % 15.47/2.79 v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 15.47/2.79 : (vmul(v0, v1) = v6 & vmul(vd411, v4) = v8 & vplus(v8, v4) = v9 & % 15.47/2.79 vplus(v2, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 = v6) | % 15.47/2.79 v9 = v5)))) % 15.47/2.79 % 15.47/2.79 (ass(cond(conseq(263), 1), 1)) % 15.47/2.79 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 15.47/2.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v3) | ~ % 15.47/2.79 (vmul(vd411, v1) = v2) | ~ (vplus(v4, v3) = v5) | ~ (vplus(v2, vd411) = % 15.47/2.79 v4) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 15.47/2.79 : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 & vplus(v2, v1) = v7 & % 15.47/2.79 vplus(vd411, v3) = v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 = % 15.47/2.79 v6) | v9 = v5)))) % 15.47/2.79 % 15.47/2.79 (ass(cond(conseq(263), 1), 2)) % 15.47/2.79 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 15.47/2.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~ % 15.47/2.79 (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411, v1) = % 15.47/2.79 v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 15.47/2.79 : ? [v10: $i] : (vsucc(v1) = v8 & vmul(v0, v1) = v6 & vplus(v2, v9) = v10 % 15.47/2.79 & vplus(v2, v1) = v7 & vplus(vd411, v8) = v9 & $i(v10) & $i(v9) & $i(v8) % 15.47/2.79 & $i(v7) & $i(v6) & ( ~ (v7 = v6) | v10 = v5)))) % 15.47/2.79 % 15.47/2.79 (ass(cond(conseq(263), 1), 3)) % 15.47/2.79 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 15.47/2.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~ % 15.47/2.79 (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411, v1) = % 15.47/2.79 v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 15.47/2.79 : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 & vplus(v2, v1) = v7 & vplus(v0, % 15.47/2.79 v1) = v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 = v6) | v9 = % 15.47/2.80 v5)))) % 15.47/2.80 % 15.47/2.80 (ass(cond(conseq(263), 1), 4)) % 15.47/2.80 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 15.47/2.80 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~ % 15.47/2.80 (vplus(v2, v3) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v1) | ? [v5: $i] : % 15.47/2.80 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vmul(v0, v1) = v5 & vplus(v2, % 15.47/2.80 v7) = v8 & vplus(v2, v1) = v6 & vplus(v1, v0) = v7 & $i(v8) & $i(v7) & % 15.47/2.80 $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4)))) % 15.47/2.80 % 15.47/2.80 (ass(cond(conseq(263), 1), 5)) % 15.47/2.80 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 15.47/2.80 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~ % 15.47/2.80 (vplus(v2, v3) = v4) | ~ (vplus(v1, v0) = v3) | ~ $i(v1) | ? [v5: $i] : % 15.47/2.80 ? [v6: $i] : ? [v7: $i] : (vmul(v0, v1) = v5 & vplus(v6, v0) = v7 & % 15.47/2.80 vplus(v2, v1) = v6 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) | v7 = % 15.47/2.80 v4)))) % 15.47/2.80 % 15.47/2.80 (ass(cond(conseq(263), 1), 6)) % 15.47/2.80 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 15.47/2.80 $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? % 15.47/2.80 [v5: $i] : ? [v6: $i] : (vmul(vd411, v1) = v3 & vplus(v4, v0) = v6 & % 15.47/2.80 vplus(v3, v1) = v4 & vplus(v2, v0) = v5 & $i(v6) & $i(v5) & $i(v4) & % 15.47/2.80 $i(v3) & ( ~ (v4 = v2) | v6 = v5)))) % 15.47/2.80 % 15.47/2.80 (ass(cond(conseq(263), 1), 7)) % 15.47/2.80 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 15.47/2.80 $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? % 15.47/2.80 [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vsucc(v1) = v5 & vmul(v0, v5) = v6 % 15.47/2.80 & vmul(vd411, v1) = v3 & vplus(v3, v1) = v4 & vplus(v2, v0) = v7 & % 15.47/2.80 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v7 = v6)))) % 15.47/2.80 % 15.47/2.80 (holds(264, 412, 0)) % 15.47/2.80 $i(v1) & $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & vmul(v0, v1) = v0 & % 15.47/2.80 $i(v0)) % 15.47/2.80 % 15.47/2.80 (holds(264, 412, 1)) % 15.47/2.80 $i(v1) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : (vsucc(v1) = v0 & % 15.47/2.80 vsucc(vd411) = v0 & vmul(vd411, v1) = v1 & $i(v1) & $i(v0)) % 15.47/2.80 % 15.47/2.80 (holds(264, 412, 2)) % 15.47/2.80 $i(v1) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : (vsucc(v0) = v1 & vmul(vd411, % 15.47/2.80 v1) = v0 & vplus(v0, v1) = v1 & $i(v1) & $i(v0)) % 15.47/2.80 % 15.47/2.80 (qu(antec(axiom(3)), imp(antec(axiom(3))))) % 15.47/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~ % 15.47/2.80 (vsucc(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 15.47/2.80 % 15.47/2.80 (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))) % 15.47/2.80 $i(v1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.47/2.80 (vsucc(v1) = v2) | ~ (vplus(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 15.47/2.80 $i] : (vsucc(v4) = v3 & vplus(v0, v1) = v4 & $i(v4) & $i(v3))) & ? [v0: % 15.47/2.80 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v1, v1) = v2) | ~ $i(v1) | ~ % 15.47/2.80 $i(v0) | (vsucc(v1) = v2 & $i(v2))) % 15.47/2.80 % 15.47/2.80 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) % 15.47/2.81 $i(v1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.47/2.81 (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 15.47/2.81 $i] : (vmul(v0, v1) = v4 & vplus(v4, v0) = v3 & $i(v4) & $i(v3))) & ? % 15.47/2.81 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (vmul(v1, v1) = v2) | ~ % 15.47/2.81 $i(v1) | ~ $i(v0)) % 15.47/2.81 % 15.47/2.81 (qu(ind(267), imp(267))) % 15.47/2.81 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ? [v1: $i] : ? [v2: % 15.47/2.81 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 15.47/2.81 : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 & vmul(v0, v1) = v2 & % 15.47/2.81 vmul(vd411, v4) = v6 & vmul(vd411, v1) = v3 & vplus(v6, v4) = v7 & % 15.47/2.81 vplus(v3, v1) = v2 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 15.47/2.81 $i(v1))) % 15.47/2.81 % 15.47/2.81 (qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))) % 15.47/2.81 $i(v1) & ! [v0: $i] : ( ~ (vsucc(v0) = v1) | ~ $i(v0)) % 15.47/2.81 % 15.47/2.81 (function-axioms) % 15.47/2.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.47/2.81 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 15.47/2.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.47/2.81 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: % 15.47/2.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.47/2.81 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 15.47/2.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.47/2.81 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : ! % 15.47/2.81 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ % 15.47/2.81 (vmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 15.47/2.81 : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i] % 15.47/2.81 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ % 15.47/2.81 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 15.47/2.81 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 15.47/2.81 % 15.47/2.81 Further assumptions not needed in the proof: % 15.47/2.81 -------------------------------------------- % 15.47/2.81 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158, % 15.47/2.81 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), % 15.47/2.81 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223, % 15.47/2.81 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), % 15.47/2.81 ass(cond(253, 0), 0), ass(cond(43, 0), 0), ass(cond(73, 0), 0), ass(cond(81, 0), % 15.47/2.81 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), % 15.47/2.81 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), % 15.47/2.81 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1), % 15.47/2.81 ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0), % 15.47/2.81 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88), % 15.47/2.81 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2), % 15.47/2.81 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1), % 15.47/2.81 def(cond(conseq(axiom(3)), 12), 1), def(cond(conseq(axiom(3)), 16), 1), % 15.47/2.81 def(cond(conseq(axiom(3)), 17), 1) % 15.47/2.81 % 15.47/2.81 Those formulas are unsatisfiable: % 15.47/2.81 --------------------------------- % 15.47/2.81 % 15.47/2.81 Begin of proof % 15.47/2.81 | % 15.47/2.81 | ALPHA: (ass(cond(conseq(263), 1), 0)) implies: % 15.47/2.82 | (1) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 15.47/2.82 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v4) | ~ % 15.47/2.82 | (vmul(vd411, v1) = v2) | ~ (vplus(v3, v4) = v5) | ~ (vplus(v2, % 15.47/2.82 | vd411) = v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: % 15.47/2.82 | $i] : ? [v9: $i] : (vmul(v0, v1) = v6 & vmul(vd411, v4) = v8 & % 15.47/2.82 | vplus(v8, v4) = v9 & vplus(v2, v1) = v7 & $i(v9) & $i(v8) & % 15.47/2.82 | $i(v7) & $i(v6) & ( ~ (v7 = v6) | v9 = v5)))) % 15.47/2.82 | % 15.47/2.82 | ALPHA: (ass(cond(conseq(263), 1), 1)) implies: % 15.47/2.82 | (2) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 15.47/2.82 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v3) | ~ % 15.47/2.82 | (vmul(vd411, v1) = v2) | ~ (vplus(v4, v3) = v5) | ~ (vplus(v2, % 15.47/2.82 | vd411) = v4) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: % 15.47/2.82 | $i] : ? [v9: $i] : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 & % 15.47/2.82 | vplus(v2, v1) = v7 & vplus(vd411, v3) = v8 & $i(v9) & $i(v8) & % 15.47/2.82 | $i(v7) & $i(v6) & ( ~ (v7 = v6) | v9 = v5)))) % 15.47/2.82 | % 15.47/2.82 | ALPHA: (ass(cond(conseq(263), 1), 2)) implies: % 15.89/2.82 | (3) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 15.89/2.82 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~ % 15.89/2.82 | (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411, % 15.89/2.82 | v1) = v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 15.89/2.82 | : ? [v9: $i] : ? [v10: $i] : (vsucc(v1) = v8 & vmul(v0, v1) = v6 % 15.89/2.82 | & vplus(v2, v9) = v10 & vplus(v2, v1) = v7 & vplus(vd411, v8) = % 15.89/2.82 | v9 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 = v6) % 15.89/2.82 | | v10 = v5)))) % 15.89/2.82 | % 15.89/2.82 | ALPHA: (ass(cond(conseq(263), 1), 3)) implies: % 15.89/2.82 | (4) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 15.89/2.82 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~ % 15.89/2.82 | (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411, % 15.89/2.82 | v1) = v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 15.89/2.82 | : ? [v9: $i] : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 & vplus(v2, % 15.89/2.82 | v1) = v7 & vplus(v0, v1) = v8 & $i(v9) & $i(v8) & $i(v7) & % 15.89/2.82 | $i(v6) & ( ~ (v7 = v6) | v9 = v5)))) % 15.89/2.82 | % 15.89/2.82 | ALPHA: (ass(cond(conseq(263), 1), 4)) implies: % 15.89/2.82 | (5) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 15.89/2.82 | ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~ % 15.89/2.82 | (vplus(v2, v3) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v1) | ? % 15.89/2.82 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vmul(v0, v1) % 15.89/2.82 | = v5 & vplus(v2, v7) = v8 & vplus(v2, v1) = v6 & vplus(v1, v0) = % 15.89/2.82 | v7 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = % 15.89/2.82 | v4)))) % 15.89/2.82 | % 15.89/2.82 | ALPHA: (ass(cond(conseq(263), 1), 5)) implies: % 15.89/2.82 | (6) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 15.89/2.82 | ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~ % 15.89/2.82 | (vplus(v2, v3) = v4) | ~ (vplus(v1, v0) = v3) | ~ $i(v1) | ? % 15.89/2.82 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vmul(v0, v1) = v5 & % 15.89/2.82 | vplus(v6, v0) = v7 & vplus(v2, v1) = v6 & $i(v7) & $i(v6) & % 15.89/2.82 | $i(v5) & ( ~ (v6 = v5) | v7 = v4)))) % 15.89/2.82 | % 15.89/2.82 | ALPHA: (ass(cond(conseq(263), 1), 6)) implies: % 15.89/2.82 | (7) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 15.89/2.82 | ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? % 15.89/2.82 | [v5: $i] : ? [v6: $i] : (vmul(vd411, v1) = v3 & vplus(v4, v0) = v6 % 15.89/2.82 | & vplus(v3, v1) = v4 & vplus(v2, v0) = v5 & $i(v6) & $i(v5) & % 15.89/2.82 | $i(v4) & $i(v3) & ( ~ (v4 = v2) | v6 = v5)))) % 15.89/2.82 | % 15.89/2.82 | ALPHA: (ass(cond(conseq(263), 1), 7)) implies: % 15.89/2.83 | (8) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 15.89/2.83 | ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? % 15.89/2.83 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vsucc(v1) = v5 & vmul(v0, % 15.89/2.83 | v5) = v6 & vmul(vd411, v1) = v3 & vplus(v3, v1) = v4 & % 15.89/2.83 | vplus(v2, v0) = v7 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 15.89/2.83 | ( ~ (v4 = v2) | v7 = v6)))) % 15.89/2.83 | % 15.89/2.83 | ALPHA: (holds(264, 412, 2)) implies: % 15.89/2.83 | (9) ? [v0: $i] : ? [v1: $i] : (vsucc(v0) = v1 & vmul(vd411, v1) = v0 & % 15.89/2.83 | vplus(v0, v1) = v1 & $i(v1) & $i(v0)) % 15.89/2.83 | % 15.89/2.83 | ALPHA: (holds(264, 412, 1)) implies: % 15.89/2.83 | (10) ? [v0: $i] : ? [v1: $i] : (vsucc(v1) = v0 & vsucc(vd411) = v0 & % 15.89/2.83 | vmul(vd411, v1) = v1 & $i(v1) & $i(v0)) % 15.89/2.83 | % 15.89/2.83 | ALPHA: (holds(264, 412, 0)) implies: % 15.89/2.83 | (11) ? [v0: $i] : (vsucc(vd411) = v0 & vmul(v0, v1) = v0 & $i(v0)) % 15.89/2.83 | % 15.89/2.83 | ALPHA: (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), % 15.89/2.83 | holds(definiens(249), 398, 0)))) implies: % 15.89/2.83 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v1) % 15.89/2.83 | = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 15.89/2.83 | $i] : (vmul(v0, v1) = v4 & vplus(v4, v0) = v3 & $i(v4) & $i(v3))) % 15.89/2.83 | % 15.89/2.83 | ALPHA: (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), % 15.89/2.83 | holds(definiens(29), 44, 0)))) implies: % 15.89/2.83 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v1) % 15.89/2.83 | = v2) | ~ (vplus(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 15.89/2.83 | $i] : (vsucc(v4) = v3 & vplus(v0, v1) = v4 & $i(v4) & $i(v3))) % 15.89/2.83 | % 15.89/2.83 | ALPHA: (qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))) implies: % 15.89/2.83 | (14) $i(v1) % 15.89/2.83 | % 15.89/2.83 | ALPHA: (qu(ind(267), imp(267))) implies: % 15.89/2.83 | (15) $i(vd411) % 15.89/2.83 | (16) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ? [v1: $i] : ? [v2: $i] % 15.89/2.83 | : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 15.89/2.83 | $i] : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 & % 15.89/2.83 | vmul(v0, v1) = v2 & vmul(vd411, v4) = v6 & vmul(vd411, v1) = v3 & % 15.89/2.83 | vplus(v6, v4) = v7 & vplus(v3, v1) = v2 & $i(v7) & $i(v6) & $i(v5) % 15.89/2.83 | & $i(v4) & $i(v3) & $i(v2) & $i(v1))) % 15.89/2.83 | % 15.89/2.83 | ALPHA: (function-axioms) implies: % 15.89/2.83 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = % 15.89/2.83 | v1) | ~ (vsucc(v2) = v0)) % 15.89/2.83 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.89/2.83 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 15.89/2.83 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.89/2.83 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 15.89/2.83 | % 15.89/2.83 | DELTA: instantiating (11) with fresh symbol all_45_0 gives: % 15.89/2.83 | (20) vsucc(vd411) = all_45_0 & vmul(all_45_0, v1) = all_45_0 & $i(all_45_0) % 15.89/2.83 | % 15.89/2.83 | ALPHA: (20) implies: % 15.89/2.83 | (21) vsucc(vd411) = all_45_0 % 15.89/2.83 | % 15.89/2.83 | DELTA: instantiating (9) with fresh symbols all_52_0, all_52_1 gives: % 15.89/2.83 | (22) vsucc(all_52_1) = all_52_0 & vmul(vd411, v1) = all_52_1 & % 15.89/2.83 | vplus(all_52_1, v1) = all_52_0 & $i(all_52_0) & $i(all_52_1) % 15.89/2.83 | % 15.89/2.83 | ALPHA: (22) implies: % 15.89/2.84 | (23) vplus(all_52_1, v1) = all_52_0 % 15.89/2.84 | (24) vmul(vd411, v1) = all_52_1 % 15.89/2.84 | (25) vsucc(all_52_1) = all_52_0 % 15.89/2.84 | % 15.89/2.84 | DELTA: instantiating (10) with fresh symbols all_54_0, all_54_1 gives: % 15.89/2.84 | (26) vsucc(all_54_0) = all_54_1 & vsucc(vd411) = all_54_1 & vmul(vd411, v1) % 15.89/2.84 | = all_54_0 & $i(all_54_0) & $i(all_54_1) % 15.89/2.84 | % 15.89/2.84 | ALPHA: (26) implies: % 15.89/2.84 | (27) $i(all_54_0) % 15.89/2.84 | (28) vmul(vd411, v1) = all_54_0 % 15.89/2.84 | (29) vsucc(vd411) = all_54_1 % 15.89/2.84 | (30) vsucc(all_54_0) = all_54_1 % 15.89/2.84 | % 15.89/2.84 | DELTA: instantiating (6) with fresh symbol all_59_0 gives: % 15.89/2.84 | (31) vsucc(vd411) = all_59_0 & $i(all_59_0) & ! [v0: $i] : ! [v1: $i] : % 15.89/2.84 | ! [v2: $i] : ! [v3: $i] : ( ~ (vmul(vd411, v0) = v1) | ~ (vplus(v1, % 15.89/2.84 | v2) = v3) | ~ (vplus(v0, all_59_0) = v2) | ~ $i(v0) | ? [v4: % 15.89/2.84 | $i] : ? [v5: $i] : ? [v6: $i] : (vmul(all_59_0, v0) = v4 & % 15.89/2.84 | vplus(v5, all_59_0) = v6 & vplus(v1, v0) = v5 & $i(v6) & $i(v5) & % 15.89/2.84 | $i(v4) & ( ~ (v5 = v4) | v6 = v3))) % 15.89/2.84 | % 15.89/2.84 | ALPHA: (31) implies: % 15.89/2.84 | (32) vsucc(vd411) = all_59_0 % 15.89/2.84 | % 15.89/2.84 | DELTA: instantiating (7) with fresh symbol all_62_0 gives: % 15.89/2.84 | (33) vsucc(vd411) = all_62_0 & $i(all_62_0) & ! [v0: $i] : ! [v1: $i] : ( % 15.89/2.84 | ~ (vmul(all_62_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] % 15.89/2.84 | : ? [v4: $i] : ? [v5: $i] : (vmul(vd411, v0) = v2 & vplus(v3, % 15.89/2.84 | all_62_0) = v5 & vplus(v2, v0) = v3 & vplus(v1, all_62_0) = v4 & % 15.89/2.84 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v5 = v4))) % 15.89/2.84 | % 15.89/2.84 | ALPHA: (33) implies: % 15.89/2.84 | (34) vsucc(vd411) = all_62_0 % 15.89/2.84 | % 15.89/2.84 | DELTA: instantiating (8) with fresh symbol all_65_0 gives: % 15.89/2.84 | (35) vsucc(vd411) = all_65_0 & $i(all_65_0) & ! [v0: $i] : ! [v1: $i] : ( % 15.89/2.84 | ~ (vmul(all_65_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] % 15.89/2.84 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vsucc(v0) = v4 & % 15.89/2.84 | vmul(all_65_0, v4) = v5 & vmul(vd411, v0) = v2 & vplus(v2, v0) = % 15.89/2.84 | v3 & vplus(v1, all_65_0) = v6 & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 15.89/2.84 | & $i(v2) & ( ~ (v3 = v1) | v6 = v5))) % 15.89/2.84 | % 15.89/2.84 | ALPHA: (35) implies: % 15.89/2.84 | (36) vsucc(vd411) = all_65_0 % 15.89/2.84 | % 15.89/2.84 | DELTA: instantiating (5) with fresh symbol all_68_0 gives: % 15.89/2.84 | (37) vsucc(vd411) = all_68_0 & $i(all_68_0) & ! [v0: $i] : ! [v1: $i] : % 15.89/2.84 | ! [v2: $i] : ! [v3: $i] : ( ~ (vmul(vd411, v0) = v1) | ~ (vplus(v1, % 15.89/2.84 | v2) = v3) | ~ (vplus(all_68_0, v0) = v2) | ~ $i(v0) | ? [v4: % 15.89/2.84 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vmul(all_68_0, % 15.89/2.84 | v0) = v4 & vplus(v1, v6) = v7 & vplus(v1, v0) = v5 & vplus(v0, % 15.89/2.84 | all_68_0) = v6 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~ (v5 = % 15.89/2.84 | v4) | v7 = v3))) % 15.89/2.84 | % 15.89/2.84 | ALPHA: (37) implies: % 15.89/2.84 | (38) vsucc(vd411) = all_68_0 % 15.89/2.84 | % 15.89/2.84 | DELTA: instantiating (2) with fresh symbol all_71_0 gives: % 15.89/2.84 | (39) vsucc(vd411) = all_71_0 & $i(all_71_0) & ! [v0: $i] : ! [v1: $i] : % 15.89/2.84 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v0) = v2) | ~ % 15.89/2.84 | (vmul(vd411, v0) = v1) | ~ (vplus(v3, v2) = v4) | ~ (vplus(v1, % 15.89/2.84 | vd411) = v3) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: % 15.89/2.84 | $i] : ? [v8: $i] : (vmul(all_71_0, v0) = v5 & vplus(v1, v7) = v8 % 15.89/2.84 | & vplus(v1, v0) = v6 & vplus(vd411, v2) = v7 & $i(v8) & $i(v7) & % 15.89/2.84 | $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4))) % 15.89/2.84 | % 15.89/2.84 | ALPHA: (39) implies: % 15.89/2.84 | (40) vsucc(vd411) = all_71_0 % 15.89/2.85 | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.89/2.85 | ( ~ (vsucc(v0) = v2) | ~ (vmul(vd411, v0) = v1) | ~ (vplus(v3, v2) = % 15.89/2.85 | v4) | ~ (vplus(v1, vd411) = v3) | ~ $i(v0) | ? [v5: $i] : ? % 15.89/2.85 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vmul(all_71_0, v0) = v5 & % 15.89/2.85 | vplus(v1, v7) = v8 & vplus(v1, v0) = v6 & vplus(vd411, v2) = v7 & % 15.89/2.85 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4))) % 15.89/2.85 | % 15.89/2.85 | DELTA: instantiating (4) with fresh symbol all_74_0 gives: % 15.89/2.85 | (42) vsucc(vd411) = all_74_0 & $i(all_74_0) & ! [v0: $i] : ! [v1: $i] : % 15.89/2.85 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v2) = v3) | ~ % 15.89/2.85 | (vmul(vd411, v0) = v1) | ~ (vplus(v1, v3) = v4) | ~ (vplus(vd411, % 15.89/2.85 | v0) = v2) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 15.89/2.85 | : ? [v8: $i] : (vmul(all_74_0, v0) = v5 & vplus(v1, v7) = v8 & % 15.89/2.85 | vplus(v1, v0) = v6 & vplus(all_74_0, v0) = v7 & $i(v8) & $i(v7) & % 15.89/2.85 | $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4))) % 15.89/2.85 | % 15.89/2.85 | ALPHA: (42) implies: % 15.89/2.85 | (43) vsucc(vd411) = all_74_0 % 15.89/2.85 | % 15.89/2.85 | DELTA: instantiating (16) with fresh symbol all_77_0 gives: % 15.89/2.85 | (44) vsucc(vd411) = all_77_0 & $i(all_77_0) & ? [v0: $i] : ? [v1: $i] : % 15.89/2.85 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( % 15.89/2.85 | ~ (v6 = v4) & vsucc(v0) = v3 & vmul(all_77_0, v3) = v4 & % 15.89/2.85 | vmul(all_77_0, v0) = v1 & vmul(vd411, v3) = v5 & vmul(vd411, v0) = % 15.89/2.85 | v2 & vplus(v5, v3) = v6 & vplus(v2, v0) = v1 & $i(v6) & $i(v5) & % 15.89/2.85 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 15.89/2.85 | % 15.89/2.85 | ALPHA: (44) implies: % 15.89/2.85 | (45) vsucc(vd411) = all_77_0 % 15.89/2.85 | (46) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 15.89/2.85 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & vsucc(v0) = v3 & % 15.89/2.85 | vmul(all_77_0, v3) = v4 & vmul(all_77_0, v0) = v1 & vmul(vd411, v3) % 15.89/2.85 | = v5 & vmul(vd411, v0) = v2 & vplus(v5, v3) = v6 & vplus(v2, v0) = % 15.89/2.85 | v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 15.89/2.85 | % 15.89/2.85 | DELTA: instantiating (1) with fresh symbol all_79_0 gives: % 15.89/2.85 | (47) vsucc(vd411) = all_79_0 & $i(all_79_0) & ! [v0: $i] : ! [v1: $i] : % 15.89/2.85 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v0) = v3) | ~ % 15.89/2.85 | (vmul(vd411, v0) = v1) | ~ (vplus(v2, v3) = v4) | ~ (vplus(v1, % 15.89/2.85 | vd411) = v2) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: % 15.89/2.85 | $i] : ? [v8: $i] : (vmul(all_79_0, v0) = v5 & vmul(vd411, v3) = % 15.89/2.85 | v7 & vplus(v7, v3) = v8 & vplus(v1, v0) = v6 & $i(v8) & $i(v7) & % 15.89/2.85 | $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4))) % 15.89/2.85 | % 15.89/2.85 | ALPHA: (47) implies: % 15.89/2.85 | (48) vsucc(vd411) = all_79_0 % 15.89/2.85 | % 15.89/2.85 | DELTA: instantiating (3) with fresh symbol all_82_0 gives: % 15.89/2.85 | (49) vsucc(vd411) = all_82_0 & $i(all_82_0) & ! [v0: $i] : ! [v1: $i] : % 15.89/2.85 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v2) = v3) | ~ % 15.89/2.85 | (vmul(vd411, v0) = v1) | ~ (vplus(v1, v3) = v4) | ~ (vplus(vd411, % 15.89/2.85 | v0) = v2) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 15.89/2.85 | : ? [v8: $i] : ? [v9: $i] : (vsucc(v0) = v7 & vmul(all_82_0, v0) = % 15.89/2.85 | v5 & vplus(v1, v8) = v9 & vplus(v1, v0) = v6 & vplus(vd411, v7) = % 15.89/2.85 | v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) | % 15.89/2.85 | v9 = v4))) % 15.89/2.85 | % 15.89/2.85 | ALPHA: (49) implies: % 15.89/2.85 | (50) vsucc(vd411) = all_82_0 % 15.89/2.85 | % 15.89/2.85 | DELTA: instantiating (46) with fresh symbols all_85_0, all_85_1, all_85_2, % 15.89/2.85 | all_85_3, all_85_4, all_85_5, all_85_6 gives: % 15.89/2.85 | (51) ~ (all_85_0 = all_85_2) & vsucc(all_85_6) = all_85_3 & vmul(all_77_0, % 15.89/2.85 | all_85_3) = all_85_2 & vmul(all_77_0, all_85_6) = all_85_5 & % 15.89/2.85 | vmul(vd411, all_85_3) = all_85_1 & vmul(vd411, all_85_6) = all_85_4 & % 15.89/2.85 | vplus(all_85_1, all_85_3) = all_85_0 & vplus(all_85_4, all_85_6) = % 15.89/2.85 | all_85_5 & $i(all_85_0) & $i(all_85_1) & $i(all_85_2) & $i(all_85_3) & % 15.89/2.85 | $i(all_85_4) & $i(all_85_5) & $i(all_85_6) % 15.89/2.85 | % 15.89/2.85 | ALPHA: (51) implies: % 15.89/2.85 | (52) ~ (all_85_0 = all_85_2) % 15.89/2.85 | (53) $i(all_85_6) % 15.89/2.85 | (54) $i(all_85_3) % 15.89/2.85 | (55) $i(all_85_1) % 15.89/2.85 | (56) vplus(all_85_4, all_85_6) = all_85_5 % 15.89/2.85 | (57) vplus(all_85_1, all_85_3) = all_85_0 % 15.89/2.85 | (58) vmul(vd411, all_85_6) = all_85_4 % 15.89/2.85 | (59) vmul(vd411, all_85_3) = all_85_1 % 15.89/2.85 | (60) vmul(all_77_0, all_85_6) = all_85_5 % 15.89/2.85 | (61) vmul(all_77_0, all_85_3) = all_85_2 % 15.89/2.85 | (62) vsucc(all_85_6) = all_85_3 % 15.89/2.85 | % 15.89/2.86 | GROUND_INST: instantiating (19) with all_52_1, all_54_0, v1, vd411, % 15.89/2.86 | simplifying with (24), (28) gives: % 15.89/2.86 | (63) all_54_0 = all_52_1 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (17) with all_59_0, all_62_0, vd411, simplifying % 15.89/2.86 | with (32), (34) gives: % 15.89/2.86 | (64) all_62_0 = all_59_0 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (17) with all_62_0, all_65_0, vd411, simplifying % 15.89/2.86 | with (34), (36) gives: % 15.89/2.86 | (65) all_65_0 = all_62_0 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (17) with all_65_0, all_71_0, vd411, simplifying % 15.89/2.86 | with (36), (40) gives: % 15.89/2.86 | (66) all_71_0 = all_65_0 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (17) with all_71_0, all_74_0, vd411, simplifying % 15.89/2.86 | with (40), (43) gives: % 15.89/2.86 | (67) all_74_0 = all_71_0 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (17) with all_71_0, all_77_0, vd411, simplifying % 15.89/2.86 | with (40), (45) gives: % 15.89/2.86 | (68) all_77_0 = all_71_0 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (17) with all_68_0, all_77_0, vd411, simplifying % 15.89/2.86 | with (38), (45) gives: % 15.89/2.86 | (69) all_77_0 = all_68_0 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (17) with all_59_0, all_79_0, vd411, simplifying % 15.89/2.86 | with (32), (48) gives: % 15.89/2.86 | (70) all_79_0 = all_59_0 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (17) with all_54_1, all_79_0, vd411, simplifying % 15.89/2.86 | with (29), (48) gives: % 15.89/2.86 | (71) all_79_0 = all_54_1 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (17) with all_74_0, all_82_0, vd411, simplifying % 15.89/2.86 | with (43), (50) gives: % 15.89/2.86 | (72) all_82_0 = all_74_0 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (17) with all_45_0, all_82_0, vd411, simplifying % 15.89/2.86 | with (21), (50) gives: % 15.89/2.86 | (73) all_82_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | COMBINE_EQS: (72), (73) imply: % 15.89/2.86 | (74) all_74_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | SIMP: (74) implies: % 15.89/2.86 | (75) all_74_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | COMBINE_EQS: (70), (71) imply: % 15.89/2.86 | (76) all_59_0 = all_54_1 % 15.89/2.86 | % 15.89/2.86 | SIMP: (76) implies: % 15.89/2.86 | (77) all_59_0 = all_54_1 % 15.89/2.86 | % 15.89/2.86 | COMBINE_EQS: (68), (69) imply: % 15.89/2.86 | (78) all_71_0 = all_68_0 % 15.89/2.86 | % 15.89/2.86 | SIMP: (78) implies: % 15.89/2.86 | (79) all_71_0 = all_68_0 % 15.89/2.86 | % 15.89/2.86 | COMBINE_EQS: (67), (75) imply: % 15.89/2.86 | (80) all_71_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | SIMP: (80) implies: % 15.89/2.86 | (81) all_71_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | COMBINE_EQS: (79), (81) imply: % 15.89/2.86 | (82) all_68_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | COMBINE_EQS: (66), (79) imply: % 15.89/2.86 | (83) all_68_0 = all_65_0 % 15.89/2.86 | % 15.89/2.86 | COMBINE_EQS: (82), (83) imply: % 15.89/2.86 | (84) all_65_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | SIMP: (84) implies: % 15.89/2.86 | (85) all_65_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | COMBINE_EQS: (65), (85) imply: % 15.89/2.86 | (86) all_62_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | SIMP: (86) implies: % 15.89/2.86 | (87) all_62_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | COMBINE_EQS: (64), (87) imply: % 15.89/2.86 | (88) all_59_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | SIMP: (88) implies: % 15.89/2.86 | (89) all_59_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | COMBINE_EQS: (77), (89) imply: % 15.89/2.86 | (90) all_54_1 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | SIMP: (90) implies: % 15.89/2.86 | (91) all_54_1 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | COMBINE_EQS: (69), (82) imply: % 15.89/2.86 | (92) all_77_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | REDUCE: (30), (63), (91) imply: % 15.89/2.86 | (93) vsucc(all_52_1) = all_45_0 % 15.89/2.86 | % 15.89/2.86 | REDUCE: (61), (92) imply: % 15.89/2.86 | (94) vmul(all_45_0, all_85_3) = all_85_2 % 15.89/2.86 | % 15.89/2.86 | REDUCE: (60), (92) imply: % 15.89/2.86 | (95) vmul(all_45_0, all_85_6) = all_85_5 % 15.89/2.86 | % 15.89/2.86 | REDUCE: (27), (63) imply: % 15.89/2.86 | (96) $i(all_52_1) % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (17) with all_52_0, all_45_0, all_52_1, simplifying % 15.89/2.86 | with (25), (93) gives: % 15.89/2.86 | (97) all_52_0 = all_45_0 % 15.89/2.86 | % 15.89/2.86 | REDUCE: (23), (97) imply: % 15.89/2.86 | (98) vplus(all_52_1, v1) = all_45_0 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_52_1, v1, all_45_0, % 15.89/2.86 | simplifying with (14), (96), (98) gives: % 15.89/2.86 | (99) vplus(v1, all_52_1) = all_45_0 & $i(all_45_0) % 15.89/2.86 | % 15.89/2.86 | ALPHA: (99) implies: % 15.89/2.86 | (100) $i(all_45_0) % 15.89/2.86 | (101) vplus(v1, all_52_1) = all_45_0 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_85_1, all_85_3, % 15.89/2.86 | all_85_0, simplifying with (54), (55), (57) gives: % 15.89/2.86 | (102) vplus(all_85_3, all_85_1) = all_85_0 & $i(all_85_0) % 15.89/2.86 | % 15.89/2.86 | ALPHA: (102) implies: % 15.89/2.86 | (103) vplus(all_85_3, all_85_1) = all_85_0 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (qu(antec(axiom(3)), imp(antec(axiom(3))))) with % 15.89/2.86 | vd411, all_52_1, all_45_0, simplifying with (15), (21), (93), % 15.89/2.86 | (96) gives: % 15.89/2.86 | (104) all_52_1 = vd411 % 15.89/2.86 | % 15.89/2.86 | GROUND_INST: instantiating (12) with all_45_0, all_85_6, all_85_3, all_85_2, % 15.89/2.86 | simplifying with (53), (62), (94), (100) gives: % 15.89/2.87 | (105) ? [v0: $i] : (vmul(all_45_0, all_85_6) = v0 & vplus(v0, all_45_0) = % 15.89/2.87 | all_85_2 & $i(v0) & $i(all_85_2)) % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (12) with vd411, all_85_6, all_85_3, all_85_1, % 15.89/2.87 | simplifying with (15), (53), (59), (62) gives: % 15.89/2.87 | (106) ? [v0: $i] : (vmul(vd411, all_85_6) = v0 & vplus(v0, vd411) = % 15.89/2.87 | all_85_1 & $i(v0) & $i(all_85_1)) % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (13) with all_85_1, all_85_6, all_85_3, all_85_0, % 15.89/2.87 | simplifying with (53), (55), (57), (62) gives: % 15.89/2.87 | (107) ? [v0: $i] : (vsucc(v0) = all_85_0 & vplus(all_85_1, all_85_6) = v0 % 15.89/2.87 | & $i(v0) & $i(all_85_0)) % 15.89/2.87 | % 15.89/2.87 | DELTA: instantiating (107) with fresh symbol all_101_0 gives: % 15.89/2.87 | (108) vsucc(all_101_0) = all_85_0 & vplus(all_85_1, all_85_6) = all_101_0 & % 15.89/2.87 | $i(all_101_0) & $i(all_85_0) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (108) implies: % 15.89/2.87 | (109) vplus(all_85_1, all_85_6) = all_101_0 % 15.89/2.87 | % 15.89/2.87 | DELTA: instantiating (106) with fresh symbol all_103_0 gives: % 15.89/2.87 | (110) vmul(vd411, all_85_6) = all_103_0 & vplus(all_103_0, vd411) = % 15.89/2.87 | all_85_1 & $i(all_103_0) & $i(all_85_1) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (110) implies: % 15.89/2.87 | (111) $i(all_103_0) % 15.89/2.87 | (112) vplus(all_103_0, vd411) = all_85_1 % 15.89/2.87 | (113) vmul(vd411, all_85_6) = all_103_0 % 15.89/2.87 | % 15.89/2.87 | DELTA: instantiating (105) with fresh symbol all_105_0 gives: % 15.89/2.87 | (114) vmul(all_45_0, all_85_6) = all_105_0 & vplus(all_105_0, all_45_0) = % 15.89/2.87 | all_85_2 & $i(all_105_0) & $i(all_85_2) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (114) implies: % 15.89/2.87 | (115) $i(all_105_0) % 15.89/2.87 | (116) vplus(all_105_0, all_45_0) = all_85_2 % 15.89/2.87 | (117) vmul(all_45_0, all_85_6) = all_105_0 % 15.89/2.87 | % 15.89/2.87 | REDUCE: (101), (104) imply: % 15.89/2.87 | (118) vplus(v1, vd411) = all_45_0 % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (19) with all_85_4, all_103_0, all_85_6, vd411, % 15.89/2.87 | simplifying with (58), (113) gives: % 15.89/2.87 | (119) all_103_0 = all_85_4 % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (19) with all_85_5, all_105_0, all_85_6, all_45_0, % 15.89/2.87 | simplifying with (95), (117) gives: % 15.89/2.87 | (120) all_105_0 = all_85_5 % 15.89/2.87 | % 15.89/2.87 | REDUCE: (116), (120) imply: % 15.89/2.87 | (121) vplus(all_85_5, all_45_0) = all_85_2 % 15.89/2.87 | % 15.89/2.87 | REDUCE: (112), (119) imply: % 15.89/2.87 | (122) vplus(all_85_4, vd411) = all_85_1 % 15.89/2.87 | % 15.89/2.87 | REDUCE: (115), (120) imply: % 15.89/2.87 | (123) $i(all_85_5) % 15.89/2.87 | % 15.89/2.87 | REDUCE: (111), (119) imply: % 15.89/2.87 | (124) $i(all_85_4) % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (13) with all_85_5, vd411, all_45_0, all_85_2, % 15.89/2.87 | simplifying with (15), (21), (121), (123) gives: % 15.89/2.87 | (125) ? [v0: $i] : (vsucc(v0) = all_85_2 & vplus(all_85_5, vd411) = v0 & % 15.89/2.87 | $i(v0) & $i(all_85_2)) % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_85_4, all_85_6, % 15.89/2.87 | all_45_0, all_85_5, all_85_2, simplifying with (53), (56), (100), % 15.89/2.87 | (121), (124) gives: % 15.89/2.87 | (126) ? [v0: $i] : (vplus(all_85_4, v0) = all_85_2 & vplus(all_85_6, % 15.89/2.87 | all_45_0) = v0 & $i(v0) & $i(all_85_2)) % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_85_5, all_45_0, % 15.89/2.87 | all_85_2, simplifying with (100), (121), (123) gives: % 15.89/2.87 | (127) vplus(all_45_0, all_85_5) = all_85_2 & $i(all_85_2) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (127) implies: % 15.89/2.87 | (128) vplus(all_45_0, all_85_5) = all_85_2 % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (41) with all_85_6, all_85_4, all_85_3, all_85_1, % 15.89/2.87 | all_85_0, simplifying with (53), (57), (58), (62), (122) gives: % 15.89/2.87 | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 15.89/2.87 | (vmul(all_71_0, all_85_6) = v0 & vplus(all_85_4, v2) = v3 & % 15.89/2.87 | vplus(all_85_4, all_85_6) = v1 & vplus(vd411, all_85_3) = v2 & % 15.89/2.87 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v1 = v0) | v3 = all_85_0)) % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_85_4, vd411, % 15.89/2.87 | all_85_1, simplifying with (15), (122), (124) gives: % 15.89/2.87 | (130) vplus(vd411, all_85_4) = all_85_1 & $i(all_85_1) % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (ass(cond(52, 0), 0)) with all_85_6, all_85_1, % 15.89/2.87 | all_85_3, all_85_0, simplifying with (53), (55), (62), (103) % 15.89/2.87 | gives: % 15.89/2.87 | (131) ? [v0: $i] : (vsucc(v0) = all_85_0 & vplus(all_85_6, all_85_1) = v0 % 15.89/2.87 | & $i(v0) & $i(all_85_0)) % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_85_4, vd411, % 15.89/2.87 | all_85_6, all_85_1, all_101_0, simplifying with (15), (53), % 15.89/2.87 | (109), (122), (124) gives: % 15.89/2.87 | (132) ? [v0: $i] : (vplus(all_85_4, v0) = all_101_0 & vplus(vd411, % 15.89/2.87 | all_85_6) = v0 & $i(v0) & $i(all_101_0)) % 15.89/2.87 | % 15.89/2.87 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_85_1, all_85_6, % 15.89/2.87 | all_101_0, simplifying with (53), (55), (109) gives: % 15.89/2.87 | (133) vplus(all_85_6, all_85_1) = all_101_0 & $i(all_101_0) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (133) implies: % 15.89/2.87 | (134) vplus(all_85_6, all_85_1) = all_101_0 % 15.89/2.87 | % 15.89/2.87 | DELTA: instantiating (131) with fresh symbol all_117_0 gives: % 15.89/2.87 | (135) vsucc(all_117_0) = all_85_0 & vplus(all_85_6, all_85_1) = all_117_0 & % 15.89/2.87 | $i(all_117_0) & $i(all_85_0) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (135) implies: % 15.89/2.87 | (136) vplus(all_85_6, all_85_1) = all_117_0 % 15.89/2.87 | (137) vsucc(all_117_0) = all_85_0 % 15.89/2.87 | % 15.89/2.87 | DELTA: instantiating (126) with fresh symbol all_123_0 gives: % 15.89/2.87 | (138) vplus(all_85_4, all_123_0) = all_85_2 & vplus(all_85_6, all_45_0) = % 15.89/2.87 | all_123_0 & $i(all_123_0) & $i(all_85_2) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (138) implies: % 15.89/2.87 | (139) vplus(all_85_6, all_45_0) = all_123_0 % 15.89/2.87 | % 15.89/2.87 | DELTA: instantiating (132) with fresh symbol all_125_0 gives: % 15.89/2.87 | (140) vplus(all_85_4, all_125_0) = all_101_0 & vplus(vd411, all_85_6) = % 15.89/2.87 | all_125_0 & $i(all_125_0) & $i(all_101_0) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (140) implies: % 15.89/2.88 | (141) vplus(vd411, all_85_6) = all_125_0 % 15.89/2.88 | (142) vplus(all_85_4, all_125_0) = all_101_0 % 15.89/2.88 | % 15.89/2.88 | DELTA: instantiating (125) with fresh symbol all_127_0 gives: % 15.89/2.88 | (143) vsucc(all_127_0) = all_85_2 & vplus(all_85_5, vd411) = all_127_0 & % 15.89/2.88 | $i(all_127_0) & $i(all_85_2) % 15.89/2.88 | % 15.89/2.88 | ALPHA: (143) implies: % 15.89/2.88 | (144) vplus(all_85_5, vd411) = all_127_0 % 15.89/2.88 | % 15.89/2.88 | DELTA: instantiating (129) with fresh symbols all_129_0, all_129_1, all_129_2, % 15.89/2.88 | all_129_3 gives: % 15.89/2.88 | (145) vmul(all_71_0, all_85_6) = all_129_3 & vplus(all_85_4, all_129_1) = % 15.89/2.88 | all_129_0 & vplus(all_85_4, all_85_6) = all_129_2 & vplus(vd411, % 15.89/2.88 | all_85_3) = all_129_1 & $i(all_129_0) & $i(all_129_1) & % 15.89/2.88 | $i(all_129_2) & $i(all_129_3) & ( ~ (all_129_2 = all_129_3) | % 15.89/2.88 | all_129_0 = all_85_0) % 15.89/2.88 | % 15.89/2.88 | ALPHA: (145) implies: % 15.89/2.88 | (146) $i(all_129_3) % 15.89/2.88 | (147) vplus(all_85_4, all_85_6) = all_129_2 % 15.89/2.88 | (148) vmul(all_71_0, all_85_6) = all_129_3 % 15.89/2.88 | % 15.89/2.88 | REDUCE: (81), (148) imply: % 15.89/2.88 | (149) vmul(all_45_0, all_85_6) = all_129_3 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (18) with all_101_0, all_117_0, all_85_1, all_85_6, % 15.89/2.88 | simplifying with (134), (136) gives: % 15.89/2.88 | (150) all_117_0 = all_101_0 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (18) with all_85_5, all_129_2, all_85_6, all_85_4, % 15.89/2.88 | simplifying with (56), (147) gives: % 15.89/2.88 | (151) all_129_2 = all_85_5 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (19) with all_85_5, all_129_3, all_85_6, all_45_0, % 15.89/2.88 | simplifying with (95), (149) gives: % 15.89/2.88 | (152) all_129_3 = all_85_5 % 15.89/2.88 | % 15.89/2.88 | REDUCE: (137), (150) imply: % 15.89/2.88 | (153) vsucc(all_101_0) = all_85_0 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd411, all_85_6, % 15.89/2.88 | all_125_0, simplifying with (15), (53), (141) gives: % 15.89/2.88 | (154) vplus(all_85_6, vd411) = all_125_0 & $i(all_125_0) % 15.89/2.88 | % 15.89/2.88 | ALPHA: (154) implies: % 15.89/2.88 | (155) vplus(all_85_6, vd411) = all_125_0 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (ass(cond(52, 0), 0)) with vd411, all_85_5, % 15.89/2.88 | all_45_0, all_85_2, simplifying with (15), (21), (123), (128) % 15.89/2.88 | gives: % 15.89/2.88 | (156) ? [v0: $i] : (vsucc(v0) = all_85_2 & vplus(vd411, all_85_5) = v0 & % 15.89/2.88 | $i(v0) & $i(all_85_2)) % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with v1, vd411, all_85_5, % 15.89/2.88 | all_45_0, all_85_2, simplifying with (14), (15), (118), (123), % 15.89/2.88 | (128) gives: % 15.89/2.88 | (157) ? [v0: $i] : (vplus(v1, v0) = all_85_2 & vplus(vd411, all_85_5) = v0 % 15.89/2.88 | & $i(v0) & $i(all_85_2)) % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (13) with all_85_6, vd411, all_45_0, all_123_0, % 15.89/2.88 | simplifying with (15), (21), (53), (139) gives: % 15.89/2.88 | (158) ? [v0: $i] : (vsucc(v0) = all_123_0 & vplus(all_85_6, vd411) = v0 & % 15.89/2.88 | $i(v0) & $i(all_123_0)) % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_85_4, all_85_6, % 15.89/2.88 | vd411, all_85_5, all_127_0, simplifying with (15), (53), (56), % 15.89/2.88 | (124), (144) gives: % 15.89/2.88 | (159) ? [v0: $i] : (vplus(all_85_4, v0) = all_127_0 & vplus(all_85_6, % 15.89/2.88 | vd411) = v0 & $i(v0) & $i(all_127_0)) % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_85_5, vd411, % 15.89/2.88 | all_127_0, simplifying with (15), (123), (144) gives: % 15.89/2.88 | (160) vplus(vd411, all_85_5) = all_127_0 & $i(all_127_0) % 15.89/2.88 | % 15.89/2.88 | ALPHA: (160) implies: % 15.89/2.88 | (161) vplus(vd411, all_85_5) = all_127_0 % 15.89/2.88 | % 15.89/2.88 | DELTA: instantiating (156) with fresh symbol all_147_0 gives: % 15.89/2.88 | (162) vsucc(all_147_0) = all_85_2 & vplus(vd411, all_85_5) = all_147_0 & % 15.89/2.88 | $i(all_147_0) & $i(all_85_2) % 15.89/2.88 | % 15.89/2.88 | ALPHA: (162) implies: % 15.89/2.88 | (163) vplus(vd411, all_85_5) = all_147_0 % 15.89/2.88 | (164) vsucc(all_147_0) = all_85_2 % 15.89/2.88 | % 15.89/2.88 | DELTA: instantiating (157) with fresh symbol all_153_0 gives: % 15.89/2.88 | (165) vplus(v1, all_153_0) = all_85_2 & vplus(vd411, all_85_5) = all_153_0 % 15.89/2.88 | & $i(all_153_0) & $i(all_85_2) % 15.89/2.88 | % 15.89/2.88 | ALPHA: (165) implies: % 15.89/2.88 | (166) vplus(vd411, all_85_5) = all_153_0 % 15.89/2.88 | % 15.89/2.88 | DELTA: instantiating (159) with fresh symbol all_157_0 gives: % 15.89/2.88 | (167) vplus(all_85_4, all_157_0) = all_127_0 & vplus(all_85_6, vd411) = % 15.89/2.88 | all_157_0 & $i(all_157_0) & $i(all_127_0) % 15.89/2.88 | % 15.89/2.88 | ALPHA: (167) implies: % 15.89/2.88 | (168) vplus(all_85_6, vd411) = all_157_0 % 15.89/2.88 | (169) vplus(all_85_4, all_157_0) = all_127_0 % 15.89/2.88 | % 15.89/2.88 | DELTA: instantiating (158) with fresh symbol all_161_0 gives: % 15.89/2.88 | (170) vsucc(all_161_0) = all_123_0 & vplus(all_85_6, vd411) = all_161_0 & % 15.89/2.88 | $i(all_161_0) & $i(all_123_0) % 15.89/2.88 | % 15.89/2.88 | ALPHA: (170) implies: % 15.89/2.88 | (171) vplus(all_85_6, vd411) = all_161_0 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (18) with all_147_0, all_153_0, all_85_5, vd411, % 15.89/2.88 | simplifying with (163), (166) gives: % 15.89/2.88 | (172) all_153_0 = all_147_0 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (18) with all_127_0, all_153_0, all_85_5, vd411, % 15.89/2.88 | simplifying with (161), (166) gives: % 15.89/2.88 | (173) all_153_0 = all_127_0 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (18) with all_157_0, all_161_0, vd411, all_85_6, % 15.89/2.88 | simplifying with (168), (171) gives: % 15.89/2.88 | (174) all_161_0 = all_157_0 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (18) with all_125_0, all_161_0, vd411, all_85_6, % 15.89/2.88 | simplifying with (155), (171) gives: % 15.89/2.88 | (175) all_161_0 = all_125_0 % 15.89/2.88 | % 15.89/2.88 | COMBINE_EQS: (174), (175) imply: % 15.89/2.88 | (176) all_157_0 = all_125_0 % 15.89/2.88 | % 15.89/2.88 | SIMP: (176) implies: % 15.89/2.88 | (177) all_157_0 = all_125_0 % 15.89/2.88 | % 15.89/2.88 | COMBINE_EQS: (172), (173) imply: % 15.89/2.88 | (178) all_147_0 = all_127_0 % 15.89/2.88 | % 15.89/2.88 | REDUCE: (164), (178) imply: % 15.89/2.88 | (179) vsucc(all_127_0) = all_85_2 % 15.89/2.88 | % 15.89/2.88 | REDUCE: (169), (177) imply: % 15.89/2.88 | (180) vplus(all_85_4, all_125_0) = all_127_0 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (18) with all_101_0, all_127_0, all_125_0, % 15.89/2.88 | all_85_4, simplifying with (142), (180) gives: % 15.89/2.88 | (181) all_127_0 = all_101_0 % 15.89/2.88 | % 15.89/2.88 | REDUCE: (179), (181) imply: % 15.89/2.88 | (182) vsucc(all_101_0) = all_85_2 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (17) with all_85_0, all_85_2, all_101_0, % 15.89/2.88 | simplifying with (153), (182) gives: % 15.89/2.89 | (183) all_85_0 = all_85_2 % 15.89/2.89 | % 15.89/2.89 | REDUCE: (52), (183) imply: % 15.89/2.89 | (184) $false % 15.89/2.89 | % 15.89/2.89 | CLOSE: (184) is inconsistent. % 15.89/2.89 | % 15.89/2.89 End of proof % 15.89/2.89 % SZS output end Proof for theBenchmark % 15.89/2.89 % 15.89/2.89 2296ms %------------------------------------------------------------------------------