%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE158+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.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 05:34:44 EDT 2023 % Result : Theorem 26.09s 4.19s % Output : Proof 103.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : KLE158+1 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n013.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 12:02:01 EDT 2023 % 0.19/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.30/1.04 Prover 1: Preprocessing ... % 2.30/1.04 Prover 4: Preprocessing ... % 2.69/1.08 Prover 5: Preprocessing ... % 2.69/1.08 Prover 6: Preprocessing ... % 2.69/1.08 Prover 2: Preprocessing ... % 2.69/1.08 Prover 3: Preprocessing ... % 2.69/1.08 Prover 0: Preprocessing ... % 4.83/1.37 Prover 6: Constructing countermodel ... % 4.83/1.40 Prover 3: Constructing countermodel ... % 4.83/1.41 Prover 1: Constructing countermodel ... % 4.83/1.42 Prover 4: Constructing countermodel ... % 5.42/1.47 Prover 5: Proving ... % 5.42/1.47 Prover 0: Proving ... % 6.00/1.55 Prover 2: Proving ... % 8.13/1.88 Prover 3: gave up % 8.89/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.07/1.92 Prover 7: Preprocessing ... % 9.07/1.97 Prover 1: gave up % 9.07/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.07/2.00 Prover 8: Preprocessing ... % 9.83/2.02 Prover 7: Constructing countermodel ... % 10.44/2.10 Prover 8: Warning: ignoring some quantifiers % 10.44/2.11 Prover 8: Constructing countermodel ... % 13.43/2.53 Prover 8: gave up % 13.43/2.54 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 14.02/2.56 Prover 9: Preprocessing ... % 14.56/2.67 Prover 9: Constructing countermodel ... % 14.56/2.68 Prover 6: gave up % 14.56/2.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.56/2.73 Prover 10: Preprocessing ... % 14.56/2.78 Prover 10: Constructing countermodel ... % 14.56/2.81 Prover 10: gave up % 14.56/2.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.60/2.84 Prover 11: Preprocessing ... % 16.46/2.92 Prover 11: Constructing countermodel ... % 26.09/4.19 Prover 0: proved (3551ms) % 26.09/4.19 % 26.09/4.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 26.09/4.19 % 26.09/4.19 Prover 9: stopped % 26.09/4.19 Prover 5: stopped % 26.49/4.20 Prover 2: stopped % 26.49/4.20 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 26.49/4.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 26.49/4.20 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 26.49/4.21 Prover 16: Preprocessing ... % 26.49/4.23 Prover 19: Preprocessing ... % 26.49/4.23 Prover 13: Preprocessing ... % 26.91/4.25 Prover 16: Warning: ignoring some quantifiers % 26.92/4.25 Prover 16: Constructing countermodel ... % 27.31/4.31 Prover 13: Warning: ignoring some quantifiers % 27.31/4.32 Prover 19: Warning: ignoring some quantifiers % 27.31/4.33 Prover 19: Constructing countermodel ... % 27.31/4.33 Prover 13: Constructing countermodel ... % 27.66/4.36 Prover 13: gave up % 28.84/4.50 Prover 19: gave up % 78.63/12.07 Prover 16: stopped % 102.28/17.63 Prover 11: Found proof (size 414) % 102.28/17.63 Prover 11: proved (14819ms) % 102.28/17.64 Prover 7: stopped % 102.28/17.64 Prover 4: stopped % 102.28/17.64 % 102.28/17.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 102.28/17.64 % 102.75/17.73 % SZS output start Proof for theBenchmark % 102.75/17.73 Assumptions after simplification: % 102.75/17.73 --------------------------------- % 102.75/17.73 % 102.75/17.73 (additive_associativity) % 102.75/17.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 102.75/17.76 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 102.75/17.76 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 & % 102.75/17.76 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 102.75/17.76 : ! [v4: $i] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ % 102.75/17.76 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 & % 102.75/17.76 addition(v2, v1) = v5 & $i(v5) & $i(v4))) % 102.75/17.76 % 102.75/17.76 (additive_commutativity) % 102.75/17.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~ % 102.75/17.77 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 102.75/17.77 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 102.75/17.77 (addition(v1, v0) = v2 & $i(v2))) % 102.75/17.77 % 102.75/17.77 (distributivity1) % 102.75/17.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 102.75/17.77 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | % 102.75/17.77 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 102.75/17.77 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) & % 102.75/17.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 102.75/17.77 (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ $i(v2) | ~ % 102.75/17.77 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v0, v2) = % 102.75/17.77 v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5) % 102.75/17.77 & $i(v4))) % 102.75/17.77 % 102.75/17.77 (distributivity2) % 102.75/17.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 102.75/17.78 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | % 102.75/17.78 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 102.75/17.78 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) & % 102.75/17.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 102.75/17.78 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~ % 102.75/17.78 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) = % 102.75/17.78 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5) % 102.75/17.78 & $i(v4))) % 102.75/17.78 % 102.75/17.78 (goals) % 102.75/17.78 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 102.75/17.78 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) % 102.75/17.78 & strong_iteration(v2) = v7 & strong_iteration(v1) = v5 & leq(v6, v8) = v9 & % 102.75/17.78 leq(v3, v4) = 0 & multiplication(v7, v0) = v8 & multiplication(v2, v0) = v4 % 102.75/17.78 & multiplication(v0, v5) = v6 & multiplication(v0, v1) = v3 & $i(v8) & % 102.75/17.78 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 102.75/17.78 % 102.75/17.78 (idempotence) % 102.75/17.78 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0)) % 102.75/17.78 % 102.75/17.78 (infty_coinduction) % 102.75/17.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 102.75/17.79 int] : (v5 = 0 | ~ (strong_iteration(v0) = v3) | ~ (leq(v2, v4) = v5) | ~ % 102.75/17.79 (multiplication(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 102.75/17.79 $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & leq(v2, v7) = v8 & % 102.75/17.79 multiplication(v0, v2) = v6 & addition(v6, v1) = v7 & $i(v7) & $i(v6))) & % 102.75/17.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 102.75/17.79 (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ $i(v2) | ~ % 102.75/17.79 $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] % 102.75/17.79 : ((v8 = 0 & strong_iteration(v0) = v6 & leq(v2, v7) = 0 & % 102.75/17.79 multiplication(v6, v1) = v7 & $i(v7) & $i(v6)) | ( ~ (v5 = 0) & leq(v2, % 102.75/17.79 v4) = v5))) % 102.75/17.79 % 102.75/17.79 (infty_unfold1) % 102.75/17.79 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ % 103.15/17.79 $i(v0) | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1 % 103.15/17.79 & $i(v2) & $i(v1))) % 103.15/17.79 % 103.15/17.79 (isolation) % 103.15/17.79 $i(zero) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ % 103.15/17.79 $i(v0) | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & multiplication(v1, % 103.15/17.79 zero) = v3 & addition(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! % 103.15/17.79 [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 103.15/17.79 [v3: $i] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 & % 103.15/17.79 addition(v1, v3) = v2 & $i(v3) & $i(v2))) % 103.15/17.79 % 103.15/17.79 (multiplicative_associativity) % 103.15/17.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 103.15/17.80 (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ $i(v2) % 103.15/17.80 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, v2) = v5 & % 103.15/17.80 multiplication(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: % 103.15/17.80 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (multiplication(v1, v2) % 103.15/17.80 = v3) | ~ (multiplication(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 103.15/17.80 $i(v0) | ? [v5: $i] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) % 103.15/17.80 = v5 & $i(v5) & $i(v4))) % 103.15/17.80 % 103.15/17.80 (multiplicative_left_identity) % 103.15/17.80 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(one, v0) = % 103.15/17.80 v1) | ~ $i(v0)) % 103.15/17.80 % 103.15/17.80 (multiplicative_right_identity) % 103.15/17.80 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 103.15/17.80 v1) | ~ $i(v0)) % 103.15/17.80 % 103.15/17.80 (order) % 103.15/17.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) = % 103.15/17.80 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) = % 103.15/17.80 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, % 103.15/17.80 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) & % 103.15/17.80 addition(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 103.15/17.80 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | addition(v0, v1) = v1) & ! [v0: % 103.15/17.80 $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) | % 103.15/17.80 leq(v0, v1) = 0) % 103.15/17.80 % 103.15/17.80 (star_unfold1) % 103.15/17.80 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? % 103.15/17.80 [v2: $i] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1 & $i(v2) & % 103.15/17.80 $i(v1))) % 103.15/17.80 % 103.15/17.80 (star_unfold2) % 103.15/17.81 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? % 103.15/17.81 [v2: $i] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1 & $i(v2) & % 103.15/17.81 $i(v1))) % 103.15/17.81 % 103.15/17.81 (function-axioms) % 103.15/17.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 103.15/17.81 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 103.15/17.81 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 103.15/17.81 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0: % 103.15/17.81 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3, % 103.15/17.81 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 103.15/17.81 [v2: $i] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ % 103.15/17.81 (strong_iteration(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 103.15/17.81 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) % 103.15/17.81 % 103.15/17.81 Further assumptions not needed in the proof: % 103.15/17.81 -------------------------------------------- % 103.15/17.81 additive_identity, left_annihilation, star_induction1, star_induction2 % 103.15/17.81 % 103.15/17.81 Those formulas are unsatisfiable: % 103.15/17.81 --------------------------------- % 103.15/17.81 % 103.15/17.81 Begin of proof % 103.15/17.81 | % 103.15/17.81 | ALPHA: (additive_commutativity) implies: % 103.15/17.81 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | % 103.15/17.81 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) % 103.15/17.81 | % 103.15/17.81 | ALPHA: (additive_associativity) implies: % 103.15/17.82 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 103.15/17.82 | ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ $i(v2) | % 103.15/17.82 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 & % 103.15/17.82 | addition(v2, v1) = v5 & $i(v5) & $i(v4))) % 103.15/17.82 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 103.15/17.82 | ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | % 103.15/17.82 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & % 103.15/17.82 | addition(v1, v0) = v5 & $i(v5) & $i(v4))) % 103.15/17.82 | % 103.15/17.82 | ALPHA: (multiplicative_associativity) implies: % 103.15/17.82 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 103.15/17.82 | ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | % 103.15/17.82 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v5, % 103.15/17.82 | v2) = v4 & multiplication(v0, v1) = v5 & $i(v5) & $i(v4))) % 103.15/17.82 | % 103.15/17.82 | ALPHA: (multiplicative_right_identity) implies: % 103.15/17.82 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 103.15/17.82 | v1) | ~ $i(v0)) % 103.15/17.82 | % 103.15/17.82 | ALPHA: (multiplicative_left_identity) implies: % 103.15/17.82 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(one, v0) = % 103.15/17.82 | v1) | ~ $i(v0)) % 103.15/17.82 | % 103.15/17.82 | ALPHA: (distributivity1) implies: % 103.15/17.82 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 103.15/17.82 | ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ % 103.15/17.82 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 103.15/17.82 | (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & % 103.15/17.82 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 103.15/17.82 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 103.15/17.82 | ! [v5: $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, % 103.15/17.82 | v1) = v3) | ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | % 103.15/17.82 | ~ $i(v0) | ? [v6: $i] : (multiplication(v0, v6) = v5 & addition(v1, % 103.15/17.82 | v2) = v6 & $i(v6) & $i(v5))) % 103.15/17.82 | % 103.15/17.82 | ALPHA: (distributivity2) implies: % 103.15/17.82 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 103.15/17.82 | ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ % 103.15/17.82 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 103.15/17.82 | (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & % 103.15/17.82 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 103.15/17.83 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 103.15/17.83 | ! [v5: $i] : ( ~ (multiplication(v1, v2) = v4) | ~ % 103.15/17.83 | (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ~ % 103.15/17.83 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (multiplication(v6, % 103.15/17.83 | v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) % 103.15/17.83 | % 103.15/17.83 | ALPHA: (star_unfold1) implies: % 103.15/17.83 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2: % 103.15/17.83 | $i] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1 & % 103.15/17.83 | $i(v2) & $i(v1))) % 103.15/17.83 | % 103.15/17.83 | ALPHA: (star_unfold2) implies: % 103.15/17.83 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2: % 103.15/17.83 | $i] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1 & % 103.15/17.83 | $i(v2) & $i(v1))) % 103.15/17.83 | % 103.15/17.83 | ALPHA: (infty_unfold1) implies: % 103.15/17.83 | (13) $i(one) % 103.15/17.83 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ % 103.15/17.83 | $i(v0) | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, % 103.15/17.83 | one) = v1 & $i(v2) & $i(v1))) % 103.15/17.83 | % 103.15/17.83 | ALPHA: (infty_coinduction) implies: % 103.15/17.83 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 103.15/17.83 | ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ % 103.15/17.83 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? % 103.15/17.83 | [v7: $i] : ? [v8: int] : ((v8 = 0 & strong_iteration(v0) = v6 & % 103.15/17.83 | leq(v2, v7) = 0 & multiplication(v6, v1) = v7 & $i(v7) & $i(v6)) % 103.15/17.83 | | ( ~ (v5 = 0) & leq(v2, v4) = v5))) % 103.15/17.83 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 103.15/17.83 | ! [v5: int] : (v5 = 0 | ~ (strong_iteration(v0) = v3) | ~ (leq(v2, % 103.15/17.83 | v4) = v5) | ~ (multiplication(v3, v1) = v4) | ~ $i(v2) | ~ % 103.15/17.83 | $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ % 103.15/17.83 | (v8 = 0) & leq(v2, v7) = v8 & multiplication(v0, v2) = v6 & % 103.15/17.83 | addition(v6, v1) = v7 & $i(v7) & $i(v6))) % 103.15/17.83 | % 103.15/17.83 | ALPHA: (isolation) implies: % 103.15/17.83 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ % 103.15/17.83 | $i(v0) | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & % 103.15/17.83 | multiplication(v1, zero) = v3 & addition(v2, v3) = v1 & $i(v3) & % 103.15/17.83 | $i(v2) & $i(v1))) % 103.15/17.83 | % 103.15/17.83 | ALPHA: (order) implies: % 103.15/17.84 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | % 103.15/17.84 | ~ $i(v0) | leq(v0, v1) = 0) % 103.15/17.84 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v0, v1) = 0) | ~ $i(v1) | ~ % 103.15/17.84 | $i(v0) | addition(v0, v1) = v1) % 103.15/17.84 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) = % 103.15/17.84 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) & % 103.15/17.84 | addition(v0, v1) = v3 & $i(v3))) % 103.15/17.84 | % 103.15/17.84 | ALPHA: (function-axioms) implies: % 103.15/17.84 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 103.15/17.84 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 103.15/17.84 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 103.15/17.84 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 103.15/17.84 | (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 103.15/17.84 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 103.15/17.84 | v0)) % 103.15/17.84 | % 103.15/17.84 | DELTA: instantiating (goals) with fresh symbols all_22_0, all_22_1, all_22_2, % 103.15/17.84 | all_22_3, all_22_4, all_22_5, all_22_6, all_22_7, all_22_8, all_22_9 % 103.15/17.84 | gives: % 103.15/17.84 | (24) ~ (all_22_0 = 0) & strong_iteration(all_22_7) = all_22_2 & % 103.15/17.84 | strong_iteration(all_22_8) = all_22_4 & leq(all_22_3, all_22_1) = % 103.15/17.84 | all_22_0 & leq(all_22_6, all_22_5) = 0 & multiplication(all_22_2, % 103.15/17.84 | all_22_9) = all_22_1 & multiplication(all_22_7, all_22_9) = all_22_5 % 103.15/17.84 | & multiplication(all_22_9, all_22_4) = all_22_3 & % 103.15/17.84 | multiplication(all_22_9, all_22_8) = all_22_6 & $i(all_22_1) & % 103.15/17.84 | $i(all_22_2) & $i(all_22_3) & $i(all_22_4) & $i(all_22_5) & % 103.15/17.84 | $i(all_22_6) & $i(all_22_7) & $i(all_22_8) & $i(all_22_9) % 103.15/17.84 | % 103.15/17.84 | ALPHA: (24) implies: % 103.15/17.84 | (25) ~ (all_22_0 = 0) % 103.15/17.84 | (26) $i(all_22_9) % 103.15/17.84 | (27) $i(all_22_8) % 103.15/17.84 | (28) $i(all_22_7) % 103.15/17.84 | (29) $i(all_22_6) % 103.15/17.84 | (30) $i(all_22_5) % 103.15/17.84 | (31) $i(all_22_3) % 103.15/17.84 | (32) $i(all_22_1) % 103.15/17.84 | (33) multiplication(all_22_9, all_22_8) = all_22_6 % 103.15/17.84 | (34) multiplication(all_22_9, all_22_4) = all_22_3 % 103.15/17.84 | (35) multiplication(all_22_7, all_22_9) = all_22_5 % 103.15/17.84 | (36) multiplication(all_22_2, all_22_9) = all_22_1 % 103.15/17.84 | (37) leq(all_22_6, all_22_5) = 0 % 103.15/17.84 | (38) leq(all_22_3, all_22_1) = all_22_0 % 103.15/17.84 | (39) strong_iteration(all_22_8) = all_22_4 % 103.15/17.84 | (40) strong_iteration(all_22_7) = all_22_2 % 103.15/17.84 | % 103.15/17.84 | GROUND_INST: instantiating (19) with all_22_6, all_22_5, simplifying with % 103.15/17.84 | (29), (30), (37) gives: % 103.15/17.85 | (41) addition(all_22_6, all_22_5) = all_22_5 % 103.15/17.85 | % 103.15/17.85 | GROUND_INST: instantiating (20) with all_22_3, all_22_1, all_22_0, simplifying % 103.15/17.85 | with (31), (32), (38) gives: % 103.15/17.85 | (42) all_22_0 = 0 | ? [v0: any] : ( ~ (v0 = all_22_1) & addition(all_22_3, % 103.15/17.85 | all_22_1) = v0 & $i(v0)) % 103.15/17.85 | % 103.15/17.85 | GROUND_INST: instantiating (17) with all_22_8, all_22_4, simplifying with % 103.15/17.85 | (27), (39) gives: % 103.15/17.85 | (43) ? [v0: $i] : ? [v1: $i] : (star(all_22_8) = v0 & % 103.15/17.85 | multiplication(all_22_4, zero) = v1 & addition(v0, v1) = all_22_4 & % 103.15/17.85 | $i(v1) & $i(v0) & $i(all_22_4)) % 103.15/17.85 | % 103.15/17.85 | GROUND_INST: instantiating (14) with all_22_8, all_22_4, simplifying with % 103.15/17.85 | (27), (39) gives: % 103.15/17.85 | (44) ? [v0: $i] : (multiplication(all_22_8, all_22_4) = v0 & addition(v0, % 103.15/17.85 | one) = all_22_4 & $i(v0) & $i(all_22_4)) % 103.15/17.85 | % 103.15/17.85 | GROUND_INST: instantiating (16) with all_22_7, all_22_9, all_22_3, all_22_2, % 103.15/17.85 | all_22_1, all_22_0, simplifying with (26), (28), (31), (36), % 103.15/17.85 | (38), (40) gives: % 103.15/17.85 | (45) all_22_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 103.15/17.85 | & leq(all_22_3, v1) = v2 & multiplication(all_22_7, all_22_3) = v0 & % 103.15/17.85 | addition(v0, all_22_9) = v1 & $i(v1) & $i(v0)) % 103.15/17.85 | % 103.15/17.85 | GROUND_INST: instantiating (17) with all_22_7, all_22_2, simplifying with % 103.15/17.85 | (28), (40) gives: % 103.15/17.85 | (46) ? [v0: $i] : ? [v1: $i] : (star(all_22_7) = v0 & % 103.15/17.85 | multiplication(all_22_2, zero) = v1 & addition(v0, v1) = all_22_2 & % 103.15/17.85 | $i(v1) & $i(v0) & $i(all_22_2)) % 103.15/17.85 | % 103.15/17.85 | GROUND_INST: instantiating (14) with all_22_7, all_22_2, simplifying with % 103.15/17.85 | (28), (40) gives: % 103.15/17.85 | (47) ? [v0: $i] : (multiplication(all_22_7, all_22_2) = v0 & addition(v0, % 103.15/17.85 | one) = all_22_2 & $i(v0) & $i(all_22_2)) % 103.15/17.85 | % 103.15/17.85 | DELTA: instantiating (47) with fresh symbol all_30_0 gives: % 103.15/17.85 | (48) multiplication(all_22_7, all_22_2) = all_30_0 & addition(all_30_0, % 103.15/17.85 | one) = all_22_2 & $i(all_30_0) & $i(all_22_2) % 103.15/17.85 | % 103.15/17.85 | ALPHA: (48) implies: % 103.15/17.85 | (49) $i(all_30_0) % 103.15/17.85 | (50) addition(all_30_0, one) = all_22_2 % 103.15/17.85 | (51) multiplication(all_22_7, all_22_2) = all_30_0 % 103.15/17.85 | % 103.15/17.85 | DELTA: instantiating (44) with fresh symbol all_32_0 gives: % 103.15/17.85 | (52) multiplication(all_22_8, all_22_4) = all_32_0 & addition(all_32_0, % 103.15/17.85 | one) = all_22_4 & $i(all_32_0) & $i(all_22_4) % 103.15/17.85 | % 103.15/17.85 | ALPHA: (52) implies: % 103.15/17.85 | (53) $i(all_32_0) % 103.15/17.85 | (54) addition(all_32_0, one) = all_22_4 % 103.15/17.85 | (55) multiplication(all_22_8, all_22_4) = all_32_0 % 103.15/17.85 | % 103.15/17.85 | DELTA: instantiating (43) with fresh symbols all_34_0, all_34_1 gives: % 103.15/17.85 | (56) star(all_22_8) = all_34_1 & multiplication(all_22_4, zero) = all_34_0 % 103.15/17.85 | & addition(all_34_1, all_34_0) = all_22_4 & $i(all_34_0) & % 103.15/17.85 | $i(all_34_1) & $i(all_22_4) % 103.15/17.85 | % 103.15/17.85 | ALPHA: (56) implies: % 103.15/17.86 | (57) $i(all_34_1) % 103.15/17.86 | (58) $i(all_34_0) % 103.15/17.86 | (59) addition(all_34_1, all_34_0) = all_22_4 % 103.15/17.86 | (60) star(all_22_8) = all_34_1 % 103.15/17.86 | % 103.15/17.86 | DELTA: instantiating (46) with fresh symbols all_36_0, all_36_1 gives: % 103.15/17.86 | (61) star(all_22_7) = all_36_1 & multiplication(all_22_2, zero) = all_36_0 % 103.15/17.86 | & addition(all_36_1, all_36_0) = all_22_2 & $i(all_36_0) & % 103.15/17.86 | $i(all_36_1) & $i(all_22_2) % 103.15/17.86 | % 103.15/17.86 | ALPHA: (61) implies: % 103.15/17.86 | (62) $i(all_36_1) % 103.15/17.86 | (63) $i(all_36_0) % 103.15/17.86 | (64) addition(all_36_1, all_36_0) = all_22_2 % 103.15/17.86 | (65) star(all_22_7) = all_36_1 % 103.15/17.86 | % 103.15/17.86 | BETA: splitting (42) gives: % 103.15/17.86 | % 103.15/17.86 | Case 1: % 103.15/17.86 | | % 103.15/17.86 | | (66) all_22_0 = 0 % 103.15/17.86 | | % 103.15/17.86 | | REDUCE: (25), (66) imply: % 103.15/17.86 | | (67) $false % 103.15/17.86 | | % 103.15/17.86 | | CLOSE: (67) is inconsistent. % 103.15/17.86 | | % 103.15/17.86 | Case 2: % 103.15/17.86 | | % 103.15/17.86 | | (68) ? [v0: any] : ( ~ (v0 = all_22_1) & addition(all_22_3, all_22_1) = % 103.15/17.86 | | v0 & $i(v0)) % 103.15/17.86 | | % 103.15/17.86 | | DELTA: instantiating (68) with fresh symbol all_42_0 gives: % 103.15/17.86 | | (69) ~ (all_42_0 = all_22_1) & addition(all_22_3, all_22_1) = all_42_0 & % 103.15/17.86 | | $i(all_42_0) % 103.15/17.86 | | % 103.15/17.86 | | ALPHA: (69) implies: % 103.15/17.86 | | (70) addition(all_22_3, all_22_1) = all_42_0 % 103.15/17.86 | | % 103.15/17.86 | | BETA: splitting (45) gives: % 103.15/17.86 | | % 103.15/17.86 | | Case 1: % 103.15/17.86 | | | % 103.15/17.86 | | | (71) all_22_0 = 0 % 103.15/17.86 | | | % 103.15/17.86 | | | REDUCE: (25), (71) imply: % 103.15/17.86 | | | (72) $false % 103.15/17.86 | | | % 103.15/17.86 | | | CLOSE: (72) is inconsistent. % 103.15/17.86 | | | % 103.15/17.86 | | Case 2: % 103.15/17.86 | | | % 103.15/17.86 | | | (73) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 103.15/17.86 | | | leq(all_22_3, v1) = v2 & multiplication(all_22_7, all_22_3) = v0 % 103.15/17.86 | | | & addition(v0, all_22_9) = v1 & $i(v1) & $i(v0)) % 103.15/17.86 | | | % 103.15/17.86 | | | DELTA: instantiating (73) with fresh symbols all_47_0, all_47_1, all_47_2 % 103.15/17.86 | | | gives: % 103.15/17.86 | | | (74) ~ (all_47_0 = 0) & leq(all_22_3, all_47_1) = all_47_0 & % 103.15/17.86 | | | multiplication(all_22_7, all_22_3) = all_47_2 & addition(all_47_2, % 103.15/17.86 | | | all_22_9) = all_47_1 & $i(all_47_1) & $i(all_47_2) % 103.15/17.86 | | | % 103.15/17.86 | | | ALPHA: (74) implies: % 103.15/17.86 | | | (75) ~ (all_47_0 = 0) % 103.15/17.86 | | | (76) $i(all_47_2) % 103.15/17.86 | | | (77) addition(all_47_2, all_22_9) = all_47_1 % 103.15/17.86 | | | (78) multiplication(all_22_7, all_22_3) = all_47_2 % 103.15/17.86 | | | (79) leq(all_22_3, all_47_1) = all_47_0 % 103.15/17.86 | | | % 103.15/17.86 | | | GROUND_INST: instantiating (2) with all_22_5, all_22_6, all_22_6, % 103.15/17.86 | | | all_22_5, all_22_5, simplifying with (29), (30), (41) gives: % 103.15/17.87 | | | (80) ? [v0: $i] : (addition(v0, all_22_5) = all_22_5 & % 103.15/17.87 | | | addition(all_22_6, all_22_6) = v0 & $i(v0)) % 103.15/17.87 | | | % 103.15/17.87 | | | GROUND_INST: instantiating (1) with all_22_5, all_22_6, all_22_5, % 103.15/17.87 | | | simplifying with (29), (30), (41) gives: % 103.15/17.87 | | | (81) addition(all_22_5, all_22_6) = all_22_5 % 103.15/17.87 | | | % 103.15/17.87 | | | GROUND_INST: instantiating (1) with all_22_1, all_22_3, all_42_0, % 103.15/17.87 | | | simplifying with (31), (32), (70) gives: % 103.15/17.87 | | | (82) addition(all_22_1, all_22_3) = all_42_0 & $i(all_42_0) % 103.15/17.87 | | | % 103.15/17.87 | | | ALPHA: (82) implies: % 103.15/17.87 | | | (83) addition(all_22_1, all_22_3) = all_42_0 % 103.15/17.87 | | | % 103.15/17.87 | | | GROUND_INST: instantiating (9) with all_30_0, one, all_22_9, all_22_2, % 103.15/17.87 | | | all_22_1, simplifying with (13), (26), (36), (49), (50) % 103.15/17.87 | | | gives: % 103.15/17.87 | | | (84) ? [v0: $i] : ? [v1: $i] : (multiplication(all_30_0, all_22_9) = % 103.15/17.87 | | | v0 & multiplication(one, all_22_9) = v1 & addition(v0, v1) = % 103.15/17.87 | | | all_22_1 & $i(v1) & $i(v0) & $i(all_22_1)) % 103.15/17.87 | | | % 103.15/17.87 | | | GROUND_INST: instantiating (1) with one, all_30_0, all_22_2, simplifying % 103.15/17.87 | | | with (13), (49), (50) gives: % 103.15/17.87 | | | (85) addition(one, all_30_0) = all_22_2 & $i(all_22_2) % 103.15/17.87 | | | % 103.15/17.87 | | | ALPHA: (85) implies: % 103.15/17.87 | | | (86) addition(one, all_30_0) = all_22_2 % 103.15/17.87 | | | % 103.15/17.87 | | | GROUND_INST: instantiating (7) with all_22_9, all_32_0, one, all_22_4, % 103.15/17.87 | | | all_22_3, simplifying with (13), (26), (34), (53), (54) % 103.15/17.87 | | | gives: % 103.15/17.87 | | | (87) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_9, all_32_0) = % 103.15/17.87 | | | v0 & multiplication(all_22_9, one) = v1 & addition(v0, v1) = % 103.15/17.87 | | | all_22_3 & $i(v1) & $i(v0) & $i(all_22_3)) % 103.15/17.87 | | | % 103.15/17.87 | | | GROUND_INST: instantiating (1) with one, all_32_0, all_22_4, simplifying % 103.15/17.87 | | | with (13), (53), (54) gives: % 103.15/17.87 | | | (88) addition(one, all_32_0) = all_22_4 & $i(all_22_4) % 103.15/17.87 | | | % 103.15/17.87 | | | ALPHA: (88) implies: % 103.15/17.87 | | | (89) addition(one, all_32_0) = all_22_4 % 103.15/17.87 | | | % 103.15/17.87 | | | GROUND_INST: instantiating (7) with all_22_9, all_34_1, all_34_0, % 103.15/17.87 | | | all_22_4, all_22_3, simplifying with (26), (34), (57), (58), % 103.15/17.87 | | | (59) gives: % 103.15/17.87 | | | (90) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_9, all_34_0) = % 103.15/17.87 | | | v1 & multiplication(all_22_9, all_34_1) = v0 & addition(v0, v1) % 103.15/17.87 | | | = all_22_3 & $i(v1) & $i(v0) & $i(all_22_3)) % 103.15/17.87 | | | % 103.15/17.87 | | | GROUND_INST: instantiating (1) with all_34_0, all_34_1, all_22_4, % 103.15/17.87 | | | simplifying with (57), (58), (59) gives: % 103.15/17.87 | | | (91) addition(all_34_0, all_34_1) = all_22_4 & $i(all_22_4) % 103.15/17.87 | | | % 103.15/17.87 | | | ALPHA: (91) implies: % 103.15/17.87 | | | (92) $i(all_22_4) % 103.15/17.87 | | | % 103.15/17.87 | | | GROUND_INST: instantiating (9) with all_36_1, all_36_0, all_22_9, % 103.15/17.87 | | | all_22_2, all_22_1, simplifying with (26), (36), (62), (63), % 103.15/17.87 | | | (64) gives: % 103.15/17.87 | | | (93) ? [v0: $i] : ? [v1: $i] : (multiplication(all_36_0, all_22_9) = % 103.15/17.87 | | | v1 & multiplication(all_36_1, all_22_9) = v0 & addition(v0, v1) % 103.15/17.87 | | | = all_22_1 & $i(v1) & $i(v0) & $i(all_22_1)) % 103.15/17.87 | | | % 103.15/17.87 | | | GROUND_INST: instantiating (1) with all_22_9, all_47_2, all_47_1, % 103.15/17.87 | | | simplifying with (26), (76), (77) gives: % 103.15/17.87 | | | (94) addition(all_22_9, all_47_2) = all_47_1 & $i(all_47_1) % 103.15/17.87 | | | % 103.15/17.87 | | | ALPHA: (94) implies: % 103.15/17.87 | | | (95) $i(all_47_1) % 103.15/17.87 | | | (96) addition(all_22_9, all_47_2) = all_47_1 % 103.15/17.87 | | | % 103.15/17.88 | | | GROUND_INST: instantiating (7) with all_22_8, all_34_1, all_34_0, % 103.15/17.88 | | | all_22_4, all_32_0, simplifying with (27), (55), (57), (58), % 103.15/17.88 | | | (59) gives: % 103.15/17.88 | | | (97) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_8, all_34_0) = % 103.15/17.88 | | | v1 & multiplication(all_22_8, all_34_1) = v0 & addition(v0, v1) % 103.15/17.88 | | | = all_32_0 & $i(v1) & $i(v0) & $i(all_32_0)) % 103.15/17.88 | | | % 103.15/17.88 | | | GROUND_INST: instantiating (7) with all_22_8, all_32_0, one, all_22_4, % 103.15/17.88 | | | all_32_0, simplifying with (13), (27), (53), (54), (55) % 103.15/17.88 | | | gives: % 103.15/17.88 | | | (98) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_8, all_32_0) = % 103.15/17.88 | | | v0 & multiplication(all_22_8, one) = v1 & addition(v0, v1) = % 103.15/17.88 | | | all_32_0 & $i(v1) & $i(v0)) % 103.15/17.88 | | | % 103.15/17.88 | | | GROUND_INST: instantiating (4) with all_22_7, all_22_9, all_22_4, % 103.15/17.88 | | | all_22_3, all_47_2, simplifying with (26), (28), (34), (78), % 103.15/17.88 | | | (92) gives: % 103.15/17.88 | | | (99) ? [v0: $i] : (multiplication(v0, all_22_4) = all_47_2 & % 103.15/17.88 | | | multiplication(all_22_7, all_22_9) = v0 & $i(v0) & $i(all_47_2)) % 103.15/17.88 | | | % 103.15/17.88 | | | GROUND_INST: instantiating (7) with all_22_7, all_36_1, all_36_0, % 103.15/17.88 | | | all_22_2, all_30_0, simplifying with (28), (51), (62), (63), % 103.15/17.88 | | | (64) gives: % 103.15/17.88 | | | (100) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_7, all_36_0) = % 103.15/17.88 | | | v1 & multiplication(all_22_7, all_36_1) = v0 & addition(v0, v1) % 103.15/17.88 | | | = all_30_0 & $i(v1) & $i(v0) & $i(all_30_0)) % 103.15/17.88 | | | % 103.15/17.88 | | | GROUND_INST: instantiating (7) with all_22_7, all_30_0, one, all_22_2, % 103.15/17.88 | | | all_30_0, simplifying with (13), (28), (49), (50), (51) % 103.15/17.88 | | | gives: % 103.15/17.88 | | | (101) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_7, all_30_0) = % 103.15/17.88 | | | v0 & multiplication(all_22_7, one) = v1 & addition(v0, v1) = % 103.15/17.88 | | | all_30_0 & $i(v1) & $i(v0)) % 103.15/17.88 | | | % 103.15/17.88 | | | GROUND_INST: instantiating (12) with all_22_8, all_34_1, simplifying with % 103.15/17.88 | | | (27), (60) gives: % 103.15/17.88 | | | (102) ? [v0: $i] : (multiplication(all_34_1, all_22_8) = v0 & % 103.15/17.88 | | | addition(one, v0) = all_34_1 & $i(v0) & $i(all_34_1)) % 103.15/17.88 | | | % 103.15/17.88 | | | GROUND_INST: instantiating (11) with all_22_8, all_34_1, simplifying with % 103.15/17.88 | | | (27), (60) gives: % 103.15/17.88 | | | (103) ? [v0: $i] : (multiplication(all_22_8, all_34_1) = v0 & % 103.15/17.88 | | | addition(one, v0) = all_34_1 & $i(v0) & $i(all_34_1)) % 103.15/17.88 | | | % 103.15/17.88 | | | GROUND_INST: instantiating (12) with all_22_7, all_36_1, simplifying with % 103.15/17.88 | | | (28), (65) gives: % 103.15/17.88 | | | (104) ? [v0: $i] : (multiplication(all_36_1, all_22_7) = v0 & % 103.15/17.88 | | | addition(one, v0) = all_36_1 & $i(v0) & $i(all_36_1)) % 103.15/17.88 | | | % 103.15/17.88 | | | GROUND_INST: instantiating (11) with all_22_7, all_36_1, simplifying with % 103.15/17.88 | | | (28), (65) gives: % 103.15/17.88 | | | (105) ? [v0: $i] : (multiplication(all_22_7, all_36_1) = v0 & % 103.15/17.88 | | | addition(one, v0) = all_36_1 & $i(v0) & $i(all_36_1)) % 103.15/17.88 | | | % 103.15/17.88 | | | GROUND_INST: instantiating (20) with all_22_3, all_47_1, all_47_0, % 103.15/17.88 | | | simplifying with (31), (79), (95) gives: % 103.15/17.88 | | | (106) all_47_0 = 0 | ? [v0: any] : ( ~ (v0 = all_47_1) & % 103.15/17.88 | | | addition(all_22_3, all_47_1) = v0 & $i(v0)) % 103.15/17.88 | | | % 103.15/17.88 | | | DELTA: instantiating (80) with fresh symbol all_55_0 gives: % 103.15/17.88 | | | (107) addition(all_55_0, all_22_5) = all_22_5 & addition(all_22_6, % 103.15/17.88 | | | all_22_6) = all_55_0 & $i(all_55_0) % 103.15/17.88 | | | % 103.15/17.88 | | | ALPHA: (107) implies: % 103.15/17.88 | | | (108) $i(all_55_0) % 103.15/17.88 | | | (109) addition(all_22_6, all_22_6) = all_55_0 % 103.15/17.88 | | | (110) addition(all_55_0, all_22_5) = all_22_5 % 103.15/17.88 | | | % 103.15/17.88 | | | DELTA: instantiating (99) with fresh symbol all_57_0 gives: % 103.15/17.88 | | | (111) multiplication(all_57_0, all_22_4) = all_47_2 & % 103.15/17.88 | | | multiplication(all_22_7, all_22_9) = all_57_0 & $i(all_57_0) & % 103.15/17.89 | | | $i(all_47_2) % 103.15/17.89 | | | % 103.15/17.89 | | | ALPHA: (111) implies: % 103.15/17.89 | | | (112) $i(all_57_0) % 103.15/17.89 | | | (113) multiplication(all_22_7, all_22_9) = all_57_0 % 103.15/17.89 | | | (114) multiplication(all_57_0, all_22_4) = all_47_2 % 103.15/17.89 | | | % 103.15/17.89 | | | DELTA: instantiating (105) with fresh symbol all_59_0 gives: % 103.15/17.89 | | | (115) multiplication(all_22_7, all_36_1) = all_59_0 & addition(one, % 103.15/17.89 | | | all_59_0) = all_36_1 & $i(all_59_0) & $i(all_36_1) % 103.15/17.89 | | | % 103.15/17.89 | | | ALPHA: (115) implies: % 103.15/17.89 | | | (116) addition(one, all_59_0) = all_36_1 % 103.15/17.89 | | | (117) multiplication(all_22_7, all_36_1) = all_59_0 % 103.15/17.89 | | | % 103.15/17.89 | | | DELTA: instantiating (103) with fresh symbol all_61_0 gives: % 103.63/17.89 | | | (118) multiplication(all_22_8, all_34_1) = all_61_0 & addition(one, % 103.63/17.89 | | | all_61_0) = all_34_1 & $i(all_61_0) & $i(all_34_1) % 103.63/17.89 | | | % 103.63/17.89 | | | ALPHA: (118) implies: % 103.63/17.89 | | | (119) addition(one, all_61_0) = all_34_1 % 103.63/17.89 | | | (120) multiplication(all_22_8, all_34_1) = all_61_0 % 103.63/17.89 | | | % 103.63/17.89 | | | DELTA: instantiating (102) with fresh symbol all_63_0 gives: % 103.63/17.89 | | | (121) multiplication(all_34_1, all_22_8) = all_63_0 & addition(one, % 103.63/17.89 | | | all_63_0) = all_34_1 & $i(all_63_0) & $i(all_34_1) % 103.63/17.89 | | | % 103.63/17.89 | | | ALPHA: (121) implies: % 103.63/17.89 | | | (122) $i(all_63_0) % 103.63/17.89 | | | (123) addition(one, all_63_0) = all_34_1 % 103.63/17.89 | | | % 103.63/17.89 | | | DELTA: instantiating (104) with fresh symbol all_65_0 gives: % 103.63/17.89 | | | (124) multiplication(all_36_1, all_22_7) = all_65_0 & addition(one, % 103.63/17.89 | | | all_65_0) = all_36_1 & $i(all_65_0) & $i(all_36_1) % 103.63/17.89 | | | % 103.63/17.89 | | | ALPHA: (124) implies: % 103.63/17.89 | | | (125) $i(all_65_0) % 103.63/17.89 | | | (126) addition(one, all_65_0) = all_36_1 % 103.63/17.89 | | | % 103.63/17.89 | | | DELTA: instantiating (101) with fresh symbols all_69_0, all_69_1 gives: % 103.63/17.89 | | | (127) multiplication(all_22_7, all_30_0) = all_69_1 & % 103.63/17.89 | | | multiplication(all_22_7, one) = all_69_0 & addition(all_69_1, % 103.63/17.89 | | | all_69_0) = all_30_0 & $i(all_69_0) & $i(all_69_1) % 103.63/17.89 | | | % 103.63/17.89 | | | ALPHA: (127) implies: % 103.63/17.89 | | | (128) $i(all_69_1) % 103.63/17.89 | | | (129) $i(all_69_0) % 103.63/17.89 | | | (130) addition(all_69_1, all_69_0) = all_30_0 % 103.63/17.89 | | | (131) multiplication(all_22_7, one) = all_69_0 % 103.63/17.89 | | | % 103.63/17.89 | | | DELTA: instantiating (98) with fresh symbols all_73_0, all_73_1 gives: % 103.63/17.89 | | | (132) multiplication(all_22_8, all_32_0) = all_73_1 & % 103.63/17.89 | | | multiplication(all_22_8, one) = all_73_0 & addition(all_73_1, % 103.63/17.89 | | | all_73_0) = all_32_0 & $i(all_73_0) & $i(all_73_1) % 103.63/17.89 | | | % 103.63/17.89 | | | ALPHA: (132) implies: % 103.63/17.89 | | | (133) $i(all_73_1) % 103.63/17.89 | | | (134) $i(all_73_0) % 103.63/17.89 | | | (135) addition(all_73_1, all_73_0) = all_32_0 % 103.63/17.89 | | | (136) multiplication(all_22_8, one) = all_73_0 % 103.63/17.89 | | | % 103.63/17.89 | | | DELTA: instantiating (100) with fresh symbols all_77_0, all_77_1 gives: % 103.63/17.89 | | | (137) multiplication(all_22_7, all_36_0) = all_77_0 & % 103.63/17.89 | | | multiplication(all_22_7, all_36_1) = all_77_1 & % 103.63/17.89 | | | addition(all_77_1, all_77_0) = all_30_0 & $i(all_77_0) & % 103.63/17.89 | | | $i(all_77_1) & $i(all_30_0) % 103.63/17.89 | | | % 103.63/17.89 | | | ALPHA: (137) implies: % 103.63/17.89 | | | (138) $i(all_77_1) % 103.63/17.89 | | | (139) multiplication(all_22_7, all_36_1) = all_77_1 % 103.63/17.89 | | | % 103.63/17.89 | | | DELTA: instantiating (97) with fresh symbols all_79_0, all_79_1 gives: % 103.63/17.89 | | | (140) multiplication(all_22_8, all_34_0) = all_79_0 & % 103.63/17.89 | | | multiplication(all_22_8, all_34_1) = all_79_1 & % 103.63/17.89 | | | addition(all_79_1, all_79_0) = all_32_0 & $i(all_79_0) & % 103.63/17.89 | | | $i(all_79_1) & $i(all_32_0) % 103.63/17.89 | | | % 103.63/17.89 | | | ALPHA: (140) implies: % 103.63/17.89 | | | (141) $i(all_79_1) % 103.63/17.89 | | | (142) multiplication(all_22_8, all_34_1) = all_79_1 % 103.63/17.89 | | | % 103.63/17.89 | | | DELTA: instantiating (93) with fresh symbols all_81_0, all_81_1 gives: % 103.63/17.89 | | | (143) multiplication(all_36_0, all_22_9) = all_81_0 & % 103.63/17.89 | | | multiplication(all_36_1, all_22_9) = all_81_1 & % 103.63/17.89 | | | addition(all_81_1, all_81_0) = all_22_1 & $i(all_81_0) & % 103.63/17.89 | | | $i(all_81_1) & $i(all_22_1) % 103.63/17.89 | | | % 103.63/17.89 | | | ALPHA: (143) implies: % 103.63/17.89 | | | (144) $i(all_81_1) % 103.63/17.89 | | | (145) $i(all_81_0) % 103.63/17.89 | | | (146) addition(all_81_1, all_81_0) = all_22_1 % 103.66/17.89 | | | (147) multiplication(all_36_1, all_22_9) = all_81_1 % 103.66/17.89 | | | % 103.66/17.89 | | | DELTA: instantiating (90) with fresh symbols all_85_0, all_85_1 gives: % 103.66/17.89 | | | (148) multiplication(all_22_9, all_34_0) = all_85_0 & % 103.66/17.89 | | | multiplication(all_22_9, all_34_1) = all_85_1 & % 103.66/17.89 | | | addition(all_85_1, all_85_0) = all_22_3 & $i(all_85_0) & % 103.66/17.89 | | | $i(all_85_1) & $i(all_22_3) % 103.66/17.89 | | | % 103.66/17.89 | | | ALPHA: (148) implies: % 103.66/17.89 | | | (149) multiplication(all_22_9, all_34_1) = all_85_1 % 103.66/17.89 | | | % 103.66/17.89 | | | DELTA: instantiating (87) with fresh symbols all_87_0, all_87_1 gives: % 103.66/17.89 | | | (150) multiplication(all_22_9, all_32_0) = all_87_1 & % 103.66/17.89 | | | multiplication(all_22_9, one) = all_87_0 & addition(all_87_1, % 103.66/17.89 | | | all_87_0) = all_22_3 & $i(all_87_0) & $i(all_87_1) & % 103.66/17.89 | | | $i(all_22_3) % 103.66/17.89 | | | % 103.66/17.89 | | | ALPHA: (150) implies: % 103.66/17.89 | | | (151) $i(all_87_1) % 103.66/17.89 | | | (152) $i(all_87_0) % 103.66/17.89 | | | (153) addition(all_87_1, all_87_0) = all_22_3 % 103.66/17.89 | | | (154) multiplication(all_22_9, one) = all_87_0 % 103.66/17.89 | | | (155) multiplication(all_22_9, all_32_0) = all_87_1 % 103.66/17.89 | | | % 103.66/17.89 | | | DELTA: instantiating (84) with fresh symbols all_89_0, all_89_1 gives: % 103.66/17.90 | | | (156) multiplication(all_30_0, all_22_9) = all_89_1 & % 103.66/17.90 | | | multiplication(one, all_22_9) = all_89_0 & addition(all_89_1, % 103.66/17.90 | | | all_89_0) = all_22_1 & $i(all_89_0) & $i(all_89_1) & % 103.66/17.90 | | | $i(all_22_1) % 103.66/17.90 | | | % 103.66/17.90 | | | ALPHA: (156) implies: % 103.66/17.90 | | | (157) $i(all_89_1) % 103.66/17.90 | | | (158) $i(all_89_0) % 103.66/17.90 | | | (159) addition(all_89_1, all_89_0) = all_22_1 % 103.66/17.90 | | | (160) multiplication(one, all_22_9) = all_89_0 % 103.66/17.90 | | | (161) multiplication(all_30_0, all_22_9) = all_89_1 % 103.66/17.90 | | | % 103.66/17.90 | | | BETA: splitting (106) gives: % 103.66/17.90 | | | % 103.66/17.90 | | | Case 1: % 103.66/17.90 | | | | % 103.66/17.90 | | | | (162) all_47_0 = 0 % 103.66/17.90 | | | | % 103.66/17.90 | | | | REDUCE: (75), (162) imply: % 103.66/17.90 | | | | (163) $false % 103.66/17.90 | | | | % 103.66/17.90 | | | | CLOSE: (163) is inconsistent. % 103.66/17.90 | | | | % 103.66/17.90 | | | Case 2: % 103.66/17.90 | | | | % 103.66/17.90 | | | | (164) ? [v0: any] : ( ~ (v0 = all_47_1) & addition(all_22_3, % 103.66/17.90 | | | | all_47_1) = v0 & $i(v0)) % 103.66/17.90 | | | | % 103.66/17.90 | | | | DELTA: instantiating (164) with fresh symbol all_109_0 gives: % 103.66/17.90 | | | | (165) ~ (all_109_0 = all_47_1) & addition(all_22_3, all_47_1) = % 103.66/17.90 | | | | all_109_0 & $i(all_109_0) % 103.66/17.90 | | | | % 103.66/17.90 | | | | ALPHA: (165) implies: % 103.66/17.90 | | | | (166) ~ (all_109_0 = all_47_1) % 103.66/17.90 | | | | (167) addition(all_22_3, all_47_1) = all_109_0 % 103.66/17.90 | | | | % 103.66/17.90 | | | | GROUND_INST: instantiating (22) with all_61_0, all_79_1, all_34_1, % 103.66/17.90 | | | | all_22_8, simplifying with (120), (142) gives: % 103.66/17.90 | | | | (168) all_79_1 = all_61_0 % 103.66/17.90 | | | | % 103.66/17.90 | | | | GROUND_INST: instantiating (22) with all_22_5, all_57_0, all_22_9, % 103.66/17.90 | | | | all_22_7, simplifying with (35), (113) gives: % 103.66/17.90 | | | | (169) all_57_0 = all_22_5 % 103.66/17.90 | | | | % 103.66/17.90 | | | | GROUND_INST: instantiating (22) with all_59_0, all_77_1, all_36_1, % 103.66/17.90 | | | | all_22_7, simplifying with (117), (139) gives: % 103.66/17.90 | | | | (170) all_77_1 = all_59_0 % 103.66/17.90 | | | | % 103.66/17.90 | | | | REDUCE: (114), (169) imply: % 103.66/17.90 | | | | (171) multiplication(all_22_5, all_22_4) = all_47_2 % 103.66/17.90 | | | | % 103.66/17.90 | | | | REDUCE: (141), (168) imply: % 103.66/17.90 | | | | (172) $i(all_61_0) % 103.66/17.90 | | | | % 103.66/17.90 | | | | REDUCE: (138), (170) imply: % 103.66/17.90 | | | | (173) $i(all_59_0) % 103.66/17.90 | | | | % 103.66/17.90 | | | | GROUND_INST: instantiating (9) with one, all_30_0, all_22_9, all_22_2, % 103.66/17.90 | | | | all_22_1, simplifying with (13), (26), (36), (49), (86) % 103.66/17.90 | | | | gives: % 103.66/17.90 | | | | (174) ? [v0: $i] : ? [v1: $i] : (multiplication(all_30_0, all_22_9) % 103.66/17.90 | | | | = v1 & multiplication(one, all_22_9) = v0 & addition(v0, v1) % 103.66/17.90 | | | | = all_22_1 & $i(v1) & $i(v0) & $i(all_22_1)) % 103.66/17.90 | | | | % 103.66/17.90 | | | | GROUND_INST: instantiating (7) with all_22_7, one, all_30_0, all_22_2, % 103.66/17.90 | | | | all_30_0, simplifying with (13), (28), (49), (51), (86) % 103.71/17.90 | | | | gives: % 103.71/17.90 | | | | (175) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_7, all_30_0) % 103.71/17.90 | | | | = v1 & multiplication(all_22_7, one) = v0 & addition(v0, v1) % 103.71/17.90 | | | | = all_30_0 & $i(v1) & $i(v0)) % 103.71/17.90 | | | | % 103.71/17.90 | | | | GROUND_INST: instantiating (7) with all_22_8, one, all_32_0, all_22_4, % 103.71/17.90 | | | | all_32_0, simplifying with (13), (27), (53), (55), (89) % 103.71/17.90 | | | | gives: % 103.71/17.90 | | | | (176) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_8, all_32_0) % 103.71/17.90 | | | | = v1 & multiplication(all_22_8, one) = v0 & addition(v0, v1) % 103.71/17.90 | | | | = all_32_0 & $i(v1) & $i(v0)) % 103.71/17.90 | | | | % 103.71/17.90 | | | | GROUND_INST: instantiating (7) with all_22_9, one, all_32_0, all_22_4, % 103.71/17.90 | | | | all_22_3, simplifying with (13), (26), (34), (53), (89) % 103.71/17.90 | | | | gives: % 103.71/17.90 | | | | (177) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_9, all_32_0) % 103.71/17.90 | | | | = v1 & multiplication(all_22_9, one) = v0 & addition(v0, v1) % 103.71/17.90 | | | | = all_22_3 & $i(v1) & $i(v0) & $i(all_22_3)) % 103.71/17.90 | | | | % 103.71/17.90 | | | | GROUND_INST: instantiating (10) with all_22_9, all_22_9, all_22_8, % 103.71/17.90 | | | | all_22_6, all_22_6, all_55_0, simplifying with (26), (27), % 103.71/17.90 | | | | (33), (109) gives: % 103.71/17.91 | | | | (178) ? [v0: $i] : (multiplication(v0, all_22_8) = all_55_0 & % 103.71/17.91 | | | | addition(all_22_9, all_22_9) = v0 & $i(v0) & $i(all_55_0)) % 103.71/17.91 | | | | % 103.71/17.91 | | | | GROUND_INST: instantiating (8) with all_22_9, all_22_8, all_22_8, % 103.71/17.91 | | | | all_22_6, all_22_6, all_55_0, simplifying with (26), (27), % 103.71/17.91 | | | | (33), (109) gives: % 103.72/17.91 | | | | (179) ? [v0: $i] : (multiplication(all_22_9, v0) = all_55_0 & % 103.72/17.91 | | | | addition(all_22_8, all_22_8) = v0 & $i(v0) & $i(all_55_0)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (idempotence) with all_22_6, all_55_0, % 103.72/17.91 | | | | simplifying with (29), (109) gives: % 103.72/17.91 | | | | (180) all_55_0 = all_22_6 % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (3) with all_22_6, all_22_6, all_22_5, % 103.72/17.91 | | | | all_22_5, all_22_5, simplifying with (29), (30), (81) % 103.72/17.91 | | | | gives: % 103.72/17.91 | | | | (181) ? [v0: $i] : (addition(all_22_5, v0) = all_22_5 & % 103.72/17.91 | | | | addition(all_22_6, all_22_6) = v0 & $i(v0)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (2) with all_22_9, all_47_2, all_22_3, % 103.72/17.91 | | | | all_47_1, all_109_0, simplifying with (26), (31), (76), % 103.72/17.91 | | | | (77), (167) gives: % 103.72/17.91 | | | | (182) ? [v0: $i] : (addition(v0, all_22_9) = all_109_0 & % 103.72/17.91 | | | | addition(all_22_3, all_47_2) = v0 & $i(v0) & $i(all_109_0)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (2) with all_47_2, all_22_9, all_22_3, % 103.72/17.91 | | | | all_47_1, all_109_0, simplifying with (26), (31), (76), % 103.72/17.91 | | | | (96), (167) gives: % 103.72/17.91 | | | | (183) ? [v0: $i] : (addition(v0, all_47_2) = all_109_0 & % 103.72/17.91 | | | | addition(all_22_3, all_22_9) = v0 & $i(v0) & $i(all_109_0)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (2) with all_22_5, all_22_6, all_55_0, % 103.72/17.91 | | | | all_22_5, all_22_5, simplifying with (29), (30), (41), % 103.72/17.91 | | | | (108), (110) gives: % 103.72/17.91 | | | | (184) ? [v0: $i] : (addition(v0, all_22_5) = all_22_5 & % 103.72/17.91 | | | | addition(all_55_0, all_22_6) = v0 & $i(v0)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (2) with all_22_5, all_55_0, all_22_6, % 103.72/17.91 | | | | all_22_5, all_22_5, simplifying with (29), (30), (41), % 103.72/17.91 | | | | (108), (110) gives: % 103.72/17.91 | | | | (185) ? [v0: $i] : (addition(v0, all_22_5) = all_22_5 & % 103.72/17.91 | | | | addition(all_22_6, all_55_0) = v0 & $i(v0)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (2) with all_22_5, all_55_0, all_55_0, % 103.72/17.91 | | | | all_22_5, all_22_5, simplifying with (30), (108), (110) % 103.72/17.91 | | | | gives: % 103.72/17.91 | | | | (186) ? [v0: $i] : (addition(v0, all_22_5) = all_22_5 & % 103.72/17.91 | | | | addition(all_55_0, all_55_0) = v0 & $i(v0)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (1) with all_81_0, all_81_1, all_22_1, % 103.72/17.91 | | | | simplifying with (144), (145), (146) gives: % 103.72/17.91 | | | | (187) addition(all_81_0, all_81_1) = all_22_1 & $i(all_22_1) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (7) with all_22_7, all_87_1, all_87_0, % 103.72/17.91 | | | | all_22_3, all_47_2, simplifying with (28), (78), (151), % 103.72/17.91 | | | | (152), (153) gives: % 103.72/17.91 | | | | (188) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_7, all_87_0) % 103.72/17.91 | | | | = v1 & multiplication(all_22_7, all_87_1) = v0 & addition(v0, % 103.72/17.91 | | | | v1) = all_47_2 & $i(v1) & $i(v0) & $i(all_47_2)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (3) with all_22_1, all_87_0, all_87_1, % 103.72/17.91 | | | | all_22_3, all_42_0, simplifying with (32), (70), (151), % 103.72/17.91 | | | | (152), (153) gives: % 103.72/17.91 | | | | (189) ? [v0: $i] : (addition(all_87_0, all_22_1) = v0 & % 103.72/17.91 | | | | addition(all_87_1, v0) = all_42_0 & $i(v0) & $i(all_42_0)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (3) with all_47_1, all_87_0, all_87_1, % 103.72/17.91 | | | | all_22_3, all_109_0, simplifying with (95), (151), (152), % 103.72/17.91 | | | | (153), (167) gives: % 103.72/17.91 | | | | (190) ? [v0: $i] : (addition(all_87_0, all_47_1) = v0 & % 103.72/17.91 | | | | addition(all_87_1, v0) = all_109_0 & $i(v0) & $i(all_109_0)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (1) with all_87_0, all_87_1, all_22_3, % 103.72/17.91 | | | | simplifying with (151), (152), (153) gives: % 103.72/17.91 | | | | (191) addition(all_87_0, all_87_1) = all_22_3 & $i(all_22_3) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (3) with all_22_3, all_89_0, all_89_1, % 103.72/17.91 | | | | all_22_1, all_42_0, simplifying with (31), (83), (157), % 103.72/17.91 | | | | (158), (159) gives: % 103.72/17.91 | | | | (192) ? [v0: $i] : (addition(all_89_0, all_22_3) = v0 & % 103.72/17.91 | | | | addition(all_89_1, v0) = all_42_0 & $i(v0) & $i(all_42_0)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (6) with all_22_9, all_89_0, simplifying with % 103.72/17.91 | | | | (26), (160) gives: % 103.72/17.91 | | | | (193) all_89_0 = all_22_9 % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (5) with all_22_9, all_87_0, simplifying with % 103.72/17.91 | | | | (26), (154) gives: % 103.72/17.91 | | | | (194) all_87_0 = all_22_9 % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (4) with all_22_9, all_22_8, all_22_4, % 103.72/17.91 | | | | all_32_0, all_87_1, simplifying with (26), (27), (55), % 103.72/17.91 | | | | (92), (155) gives: % 103.72/17.91 | | | | (195) ? [v0: $i] : (multiplication(v0, all_22_4) = all_87_1 & % 103.72/17.91 | | | | multiplication(all_22_9, all_22_8) = v0 & $i(v0) & % 103.72/17.91 | | | | $i(all_87_1)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (7) with all_22_9, all_73_1, all_73_0, % 103.72/17.91 | | | | all_32_0, all_87_1, simplifying with (26), (133), (134), % 103.72/17.91 | | | | (135), (155) gives: % 103.72/17.91 | | | | (196) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_9, all_73_0) % 103.72/17.91 | | | | = v1 & multiplication(all_22_9, all_73_1) = v0 & addition(v0, % 103.72/17.91 | | | | v1) = all_87_1 & $i(v1) & $i(v0) & $i(all_87_1)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (7) with all_22_9, one, all_63_0, all_34_1, % 103.72/17.91 | | | | all_85_1, simplifying with (13), (26), (122), (123), (149) % 103.72/17.91 | | | | gives: % 103.72/17.91 | | | | (197) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_9, all_63_0) % 103.72/17.91 | | | | = v1 & multiplication(all_22_9, one) = v0 & addition(v0, v1) % 103.72/17.91 | | | | = all_85_1 & $i(v1) & $i(v0) & $i(all_85_1)) % 103.72/17.91 | | | | % 103.72/17.91 | | | | GROUND_INST: instantiating (7) with all_22_9, one, all_61_0, all_34_1, % 103.72/17.91 | | | | all_85_1, simplifying with (13), (26), (119), (149), (172) % 103.72/17.91 | | | | gives: % 103.72/17.92 | | | | (198) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_9, all_61_0) % 103.72/17.92 | | | | = v1 & multiplication(all_22_9, one) = v0 & addition(v0, v1) % 103.72/17.92 | | | | = all_85_1 & $i(v1) & $i(v0) & $i(all_85_1)) % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (5) with all_22_8, all_73_0, simplifying with % 103.72/17.92 | | | | (27), (136) gives: % 103.72/17.92 | | | | (199) all_73_0 = all_22_8 % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (7) with all_22_8, one, all_63_0, all_34_1, % 103.72/17.92 | | | | all_61_0, simplifying with (13), (27), (120), (122), (123) % 103.72/17.92 | | | | gives: % 103.72/17.92 | | | | (200) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_8, all_63_0) % 103.72/17.92 | | | | = v1 & multiplication(all_22_8, one) = v0 & addition(v0, v1) % 103.72/17.92 | | | | = all_61_0 & $i(v1) & $i(v0) & $i(all_61_0)) % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (7) with all_22_8, one, all_61_0, all_34_1, % 103.72/17.92 | | | | all_61_0, simplifying with (13), (27), (119), (120), (172) % 103.72/17.92 | | | | gives: % 103.72/17.92 | | | | (201) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_8, all_61_0) % 103.72/17.92 | | | | = v1 & multiplication(all_22_8, one) = v0 & addition(v0, v1) % 103.72/17.92 | | | | = all_61_0 & $i(v1) & $i(v0)) % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (5) with all_22_7, all_69_0, simplifying with % 103.72/17.92 | | | | (28), (131) gives: % 103.72/17.92 | | | | (202) all_69_0 = all_22_7 % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (7) with all_22_7, one, all_65_0, all_36_1, % 103.72/17.92 | | | | all_59_0, simplifying with (13), (28), (117), (125), (126) % 103.72/17.92 | | | | gives: % 103.72/17.92 | | | | (203) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_7, all_65_0) % 103.72/17.92 | | | | = v1 & multiplication(all_22_7, one) = v0 & addition(v0, v1) % 103.72/17.92 | | | | = all_59_0 & $i(v1) & $i(v0) & $i(all_59_0)) % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (7) with all_22_7, one, all_59_0, all_36_1, % 103.72/17.92 | | | | all_59_0, simplifying with (13), (28), (116), (117), (173) % 103.72/17.92 | | | | gives: % 103.72/17.92 | | | | (204) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_7, all_59_0) % 103.72/17.92 | | | | = v1 & multiplication(all_22_7, one) = v0 & addition(v0, v1) % 103.72/17.92 | | | | = all_59_0 & $i(v1) & $i(v0)) % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (9) with all_22_6, all_22_5, all_22_4, % 103.72/17.92 | | | | all_22_5, all_47_2, simplifying with (29), (30), (41), % 103.72/17.92 | | | | (92), (171) gives: % 103.72/17.92 | | | | (205) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_5, all_22_4) % 103.72/17.92 | | | | = v1 & multiplication(all_22_6, all_22_4) = v0 & addition(v0, % 103.72/17.92 | | | | v1) = all_47_2 & $i(v1) & $i(v0) & $i(all_47_2)) % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (9) with all_55_0, all_22_5, all_22_4, % 103.72/17.92 | | | | all_22_5, all_47_2, simplifying with (30), (92), (108), % 103.72/17.92 | | | | (110), (171) gives: % 103.72/17.92 | | | | (206) ? [v0: $i] : ? [v1: $i] : (multiplication(all_55_0, all_22_4) % 103.72/17.92 | | | | = v0 & multiplication(all_22_5, all_22_4) = v1 & addition(v0, % 103.72/17.92 | | | | v1) = all_47_2 & $i(v1) & $i(v0) & $i(all_47_2)) % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (9) with all_22_5, all_22_6, all_22_4, % 103.72/17.92 | | | | all_22_5, all_47_2, simplifying with (29), (30), (81), % 103.72/17.92 | | | | (92), (171) gives: % 103.72/17.92 | | | | (207) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_5, all_22_4) % 103.72/17.92 | | | | = v0 & multiplication(all_22_6, all_22_4) = v1 & addition(v0, % 103.72/17.92 | | | | v1) = all_47_2 & $i(v1) & $i(v0) & $i(all_47_2)) % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (9) with all_69_1, all_69_0, all_22_9, % 103.72/17.92 | | | | all_30_0, all_89_1, simplifying with (26), (128), (129), % 103.72/17.92 | | | | (130), (161) gives: % 103.72/17.92 | | | | (208) ? [v0: $i] : ? [v1: $i] : (multiplication(all_69_0, all_22_9) % 103.72/17.92 | | | | = v1 & multiplication(all_69_1, all_22_9) = v0 & addition(v0, % 103.72/17.92 | | | | v1) = all_89_1 & $i(v1) & $i(v0) & $i(all_89_1)) % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (9) with one, all_65_0, all_22_9, all_36_1, % 103.72/17.92 | | | | all_81_1, simplifying with (13), (26), (125), (126), (147) % 103.72/17.92 | | | | gives: % 103.72/17.92 | | | | (209) ? [v0: $i] : ? [v1: $i] : (multiplication(all_65_0, all_22_9) % 103.72/17.92 | | | | = v1 & multiplication(one, all_22_9) = v0 & addition(v0, v1) % 103.72/17.92 | | | | = all_81_1 & $i(v1) & $i(v0) & $i(all_81_1)) % 103.72/17.92 | | | | % 103.72/17.92 | | | | GROUND_INST: instantiating (9) with one, all_59_0, all_22_9, all_36_1, % 103.72/17.92 | | | | all_81_1, simplifying with (13), (26), (116), (147), (173) % 103.72/17.92 | | | | gives: % 103.72/17.92 | | | | (210) ? [v0: $i] : ? [v1: $i] : (multiplication(all_59_0, all_22_9) % 103.72/17.92 | | | | = v1 & multiplication(one, all_22_9) = v0 & addition(v0, v1) % 103.72/17.92 | | | | = all_81_1 & $i(v1) & $i(v0) & $i(all_81_1)) % 103.72/17.92 | | | | % 103.72/17.92 | | | | DELTA: instantiating (181) with fresh symbol all_121_0 gives: % 103.72/17.92 | | | | (211) addition(all_22_5, all_121_0) = all_22_5 & addition(all_22_6, % 103.72/17.92 | | | | all_22_6) = all_121_0 & $i(all_121_0) % 103.72/17.92 | | | | % 103.72/17.92 | | | | ALPHA: (211) implies: % 103.72/17.92 | | | | (212) $i(all_121_0) % 103.72/17.92 | | | | (213) addition(all_22_6, all_22_6) = all_121_0 % 103.72/17.92 | | | | % 103.72/17.92 | | | | DELTA: instantiating (186) with fresh symbol all_123_0 gives: % 103.72/17.92 | | | | (214) addition(all_123_0, all_22_5) = all_22_5 & addition(all_55_0, % 103.72/17.92 | | | | all_55_0) = all_123_0 & $i(all_123_0) % 103.72/17.92 | | | | % 103.72/17.92 | | | | ALPHA: (214) implies: % 103.72/17.92 | | | | (215) addition(all_55_0, all_55_0) = all_123_0 % 103.72/17.92 | | | | % 103.72/17.92 | | | | DELTA: instantiating (185) with fresh symbol all_125_0 gives: % 103.72/17.92 | | | | (216) addition(all_125_0, all_22_5) = all_22_5 & addition(all_22_6, % 103.72/17.92 | | | | all_55_0) = all_125_0 & $i(all_125_0) % 103.72/17.92 | | | | % 103.72/17.92 | | | | ALPHA: (216) implies: % 103.72/17.92 | | | | (217) addition(all_22_6, all_55_0) = all_125_0 % 103.72/17.92 | | | | % 103.72/17.92 | | | | DELTA: instantiating (184) with fresh symbol all_127_0 gives: % 103.72/17.92 | | | | (218) addition(all_127_0, all_22_5) = all_22_5 & addition(all_55_0, % 103.72/17.92 | | | | all_22_6) = all_127_0 & $i(all_127_0) % 103.72/17.92 | | | | % 103.72/17.92 | | | | ALPHA: (218) implies: % 103.72/17.92 | | | | (219) addition(all_55_0, all_22_6) = all_127_0 % 103.72/17.92 | | | | % 103.72/17.92 | | | | DELTA: instantiating (183) with fresh symbol all_129_0 gives: % 103.72/17.92 | | | | (220) addition(all_129_0, all_47_2) = all_109_0 & addition(all_22_3, % 103.72/17.92 | | | | all_22_9) = all_129_0 & $i(all_129_0) & $i(all_109_0) % 103.72/17.92 | | | | % 103.72/17.92 | | | | ALPHA: (220) implies: % 103.72/17.92 | | | | (221) addition(all_22_3, all_22_9) = all_129_0 % 103.72/17.92 | | | | % 103.72/17.92 | | | | DELTA: instantiating (182) with fresh symbol all_131_0 gives: % 103.72/17.92 | | | | (222) addition(all_131_0, all_22_9) = all_109_0 & addition(all_22_3, % 103.72/17.92 | | | | all_47_2) = all_131_0 & $i(all_131_0) & $i(all_109_0) % 103.72/17.92 | | | | % 103.72/17.92 | | | | ALPHA: (222) implies: % 103.72/17.92 | | | | (223) addition(all_22_3, all_47_2) = all_131_0 % 103.72/17.92 | | | | % 103.72/17.92 | | | | DELTA: instantiating (179) with fresh symbol all_159_0 gives: % 103.72/17.92 | | | | (224) multiplication(all_22_9, all_159_0) = all_55_0 & % 103.72/17.92 | | | | addition(all_22_8, all_22_8) = all_159_0 & $i(all_159_0) & % 103.72/17.92 | | | | $i(all_55_0) % 103.72/17.92 | | | | % 103.72/17.92 | | | | ALPHA: (224) implies: % 103.72/17.92 | | | | (225) $i(all_159_0) % 103.72/17.92 | | | | (226) multiplication(all_22_9, all_159_0) = all_55_0 % 103.72/17.92 | | | | % 103.72/17.92 | | | | DELTA: instantiating (178) with fresh symbol all_161_0 gives: % 103.72/17.92 | | | | (227) multiplication(all_161_0, all_22_8) = all_55_0 & % 103.72/17.92 | | | | addition(all_22_9, all_22_9) = all_161_0 & $i(all_161_0) & % 103.72/17.92 | | | | $i(all_55_0) % 103.72/17.92 | | | | % 103.72/17.92 | | | | ALPHA: (227) implies: % 103.72/17.92 | | | | (228) $i(all_161_0) % 103.72/17.92 | | | | (229) addition(all_22_9, all_22_9) = all_161_0 % 103.72/17.92 | | | | (230) multiplication(all_161_0, all_22_8) = all_55_0 % 103.72/17.92 | | | | % 103.72/17.92 | | | | DELTA: instantiating (195) with fresh symbol all_179_0 gives: % 103.72/17.92 | | | | (231) multiplication(all_179_0, all_22_4) = all_87_1 & % 103.72/17.92 | | | | multiplication(all_22_9, all_22_8) = all_179_0 & $i(all_179_0) % 103.72/17.92 | | | | & $i(all_87_1) % 103.72/17.92 | | | | % 103.72/17.92 | | | | ALPHA: (231) implies: % 103.72/17.93 | | | | (232) multiplication(all_22_9, all_22_8) = all_179_0 % 103.72/17.93 | | | | (233) multiplication(all_179_0, all_22_4) = all_87_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (190) with fresh symbol all_181_0 gives: % 103.72/17.93 | | | | (234) addition(all_87_0, all_47_1) = all_181_0 & addition(all_87_1, % 103.72/17.93 | | | | all_181_0) = all_109_0 & $i(all_181_0) & $i(all_109_0) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (234) implies: % 103.72/17.93 | | | | (235) addition(all_87_1, all_181_0) = all_109_0 % 103.72/17.93 | | | | (236) addition(all_87_0, all_47_1) = all_181_0 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (189) with fresh symbol all_183_0 gives: % 103.72/17.93 | | | | (237) addition(all_87_0, all_22_1) = all_183_0 & addition(all_87_1, % 103.72/17.93 | | | | all_183_0) = all_42_0 & $i(all_183_0) & $i(all_42_0) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (237) implies: % 103.72/17.93 | | | | (238) addition(all_87_0, all_22_1) = all_183_0 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (192) with fresh symbol all_205_0 gives: % 103.72/17.93 | | | | (239) addition(all_89_0, all_22_3) = all_205_0 & addition(all_89_1, % 103.72/17.93 | | | | all_205_0) = all_42_0 & $i(all_205_0) & $i(all_42_0) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (239) implies: % 103.72/17.93 | | | | (240) addition(all_89_0, all_22_3) = all_205_0 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (201) with fresh symbols all_229_0, all_229_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (241) multiplication(all_22_8, all_61_0) = all_229_0 & % 103.72/17.93 | | | | multiplication(all_22_8, one) = all_229_1 & addition(all_229_1, % 103.72/17.93 | | | | all_229_0) = all_61_0 & $i(all_229_0) & $i(all_229_1) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (241) implies: % 103.72/17.93 | | | | (242) $i(all_229_1) % 103.72/17.93 | | | | (243) multiplication(all_22_8, one) = all_229_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (176) with fresh symbols all_241_0, all_241_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (244) multiplication(all_22_8, all_32_0) = all_241_0 & % 103.72/17.93 | | | | multiplication(all_22_8, one) = all_241_1 & addition(all_241_1, % 103.72/17.93 | | | | all_241_0) = all_32_0 & $i(all_241_0) & $i(all_241_1) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (244) implies: % 103.72/17.93 | | | | (245) multiplication(all_22_8, one) = all_241_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (175) with fresh symbols all_243_0, all_243_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (246) multiplication(all_22_7, all_30_0) = all_243_0 & % 103.72/17.93 | | | | multiplication(all_22_7, one) = all_243_1 & addition(all_243_1, % 103.72/17.93 | | | | all_243_0) = all_30_0 & $i(all_243_0) & $i(all_243_1) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (246) implies: % 103.72/17.93 | | | | (247) $i(all_243_1) % 103.72/17.93 | | | | (248) multiplication(all_22_7, one) = all_243_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (204) with fresh symbols all_249_0, all_249_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (249) multiplication(all_22_7, all_59_0) = all_249_0 & % 103.72/17.93 | | | | multiplication(all_22_7, one) = all_249_1 & addition(all_249_1, % 103.72/17.93 | | | | all_249_0) = all_59_0 & $i(all_249_0) & $i(all_249_1) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (249) implies: % 103.72/17.93 | | | | (250) multiplication(all_22_7, one) = all_249_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (174) with fresh symbols all_259_0, all_259_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (251) multiplication(all_30_0, all_22_9) = all_259_0 & % 103.72/17.93 | | | | multiplication(one, all_22_9) = all_259_1 & addition(all_259_1, % 103.72/17.93 | | | | all_259_0) = all_22_1 & $i(all_259_0) & $i(all_259_1) & % 103.72/17.93 | | | | $i(all_22_1) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (251) implies: % 103.72/17.93 | | | | (252) $i(all_259_1) % 103.72/17.93 | | | | (253) $i(all_259_0) % 103.72/17.93 | | | | (254) addition(all_259_1, all_259_0) = all_22_1 % 103.72/17.93 | | | | (255) multiplication(one, all_22_9) = all_259_1 % 103.72/17.93 | | | | (256) multiplication(all_30_0, all_22_9) = all_259_0 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (198) with fresh symbols all_275_0, all_275_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (257) multiplication(all_22_9, all_61_0) = all_275_0 & % 103.72/17.93 | | | | multiplication(all_22_9, one) = all_275_1 & addition(all_275_1, % 103.72/17.93 | | | | all_275_0) = all_85_1 & $i(all_275_0) & $i(all_275_1) & % 103.72/17.93 | | | | $i(all_85_1) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (257) implies: % 103.72/17.93 | | | | (258) multiplication(all_22_9, one) = all_275_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (197) with fresh symbols all_277_0, all_277_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (259) multiplication(all_22_9, all_63_0) = all_277_0 & % 103.72/17.93 | | | | multiplication(all_22_9, one) = all_277_1 & addition(all_277_1, % 103.72/17.93 | | | | all_277_0) = all_85_1 & $i(all_277_0) & $i(all_277_1) & % 103.72/17.93 | | | | $i(all_85_1) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (259) implies: % 103.72/17.93 | | | | (260) multiplication(all_22_9, one) = all_277_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (210) with fresh symbols all_281_0, all_281_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (261) multiplication(all_59_0, all_22_9) = all_281_0 & % 103.72/17.93 | | | | multiplication(one, all_22_9) = all_281_1 & addition(all_281_1, % 103.72/17.93 | | | | all_281_0) = all_81_1 & $i(all_281_0) & $i(all_281_1) & % 103.72/17.93 | | | | $i(all_81_1) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (261) implies: % 103.72/17.93 | | | | (262) multiplication(one, all_22_9) = all_281_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (177) with fresh symbols all_283_0, all_283_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (263) multiplication(all_22_9, all_32_0) = all_283_0 & % 103.72/17.93 | | | | multiplication(all_22_9, one) = all_283_1 & addition(all_283_1, % 103.72/17.93 | | | | all_283_0) = all_22_3 & $i(all_283_0) & $i(all_283_1) & % 103.72/17.93 | | | | $i(all_22_3) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (263) implies: % 103.72/17.93 | | | | (264) addition(all_283_1, all_283_0) = all_22_3 % 103.72/17.93 | | | | (265) multiplication(all_22_9, one) = all_283_1 % 103.72/17.93 | | | | (266) multiplication(all_22_9, all_32_0) = all_283_0 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (196) with fresh symbols all_297_0, all_297_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (267) multiplication(all_22_9, all_73_0) = all_297_0 & % 103.72/17.93 | | | | multiplication(all_22_9, all_73_1) = all_297_1 & % 103.72/17.93 | | | | addition(all_297_1, all_297_0) = all_87_1 & $i(all_297_0) & % 103.72/17.93 | | | | $i(all_297_1) & $i(all_87_1) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (267) implies: % 103.72/17.93 | | | | (268) $i(all_297_1) % 103.72/17.93 | | | | (269) addition(all_297_1, all_297_0) = all_87_1 % 103.72/17.93 | | | | (270) multiplication(all_22_9, all_73_0) = all_297_0 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (208) with fresh symbols all_299_0, all_299_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (271) multiplication(all_69_0, all_22_9) = all_299_0 & % 103.72/17.93 | | | | multiplication(all_69_1, all_22_9) = all_299_1 & % 103.72/17.93 | | | | addition(all_299_1, all_299_0) = all_89_1 & $i(all_299_0) & % 103.72/17.93 | | | | $i(all_299_1) & $i(all_89_1) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (271) implies: % 103.72/17.93 | | | | (272) $i(all_299_0) % 103.72/17.93 | | | | (273) multiplication(all_69_0, all_22_9) = all_299_0 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (209) with fresh symbols all_325_0, all_325_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (274) multiplication(all_65_0, all_22_9) = all_325_0 & % 103.72/17.93 | | | | multiplication(one, all_22_9) = all_325_1 & addition(all_325_1, % 103.72/17.93 | | | | all_325_0) = all_81_1 & $i(all_325_0) & $i(all_325_1) & % 103.72/17.93 | | | | $i(all_81_1) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (274) implies: % 103.72/17.93 | | | | (275) multiplication(one, all_22_9) = all_325_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (207) with fresh symbols all_327_0, all_327_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (276) multiplication(all_22_5, all_22_4) = all_327_1 & % 103.72/17.93 | | | | multiplication(all_22_6, all_22_4) = all_327_0 & % 103.72/17.93 | | | | addition(all_327_1, all_327_0) = all_47_2 & $i(all_327_0) & % 103.72/17.93 | | | | $i(all_327_1) & $i(all_47_2) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (276) implies: % 103.72/17.93 | | | | (277) $i(all_327_1) % 103.72/17.93 | | | | (278) addition(all_327_1, all_327_0) = all_47_2 % 103.72/17.93 | | | | (279) multiplication(all_22_6, all_22_4) = all_327_0 % 103.72/17.93 | | | | (280) multiplication(all_22_5, all_22_4) = all_327_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (188) with fresh symbols all_329_0, all_329_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (281) multiplication(all_22_7, all_87_0) = all_329_0 & % 103.72/17.93 | | | | multiplication(all_22_7, all_87_1) = all_329_1 & % 103.72/17.93 | | | | addition(all_329_1, all_329_0) = all_47_2 & $i(all_329_0) & % 103.72/17.93 | | | | $i(all_329_1) & $i(all_47_2) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (281) implies: % 103.72/17.93 | | | | (282) addition(all_329_1, all_329_0) = all_47_2 % 103.72/17.93 | | | | (283) multiplication(all_22_7, all_87_1) = all_329_1 % 103.72/17.93 | | | | (284) multiplication(all_22_7, all_87_0) = all_329_0 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (200) with fresh symbols all_335_0, all_335_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (285) multiplication(all_22_8, all_63_0) = all_335_0 & % 103.72/17.93 | | | | multiplication(all_22_8, one) = all_335_1 & addition(all_335_1, % 103.72/17.93 | | | | all_335_0) = all_61_0 & $i(all_335_0) & $i(all_335_1) & % 103.72/17.93 | | | | $i(all_61_0) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (285) implies: % 103.72/17.93 | | | | (286) multiplication(all_22_8, one) = all_335_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (203) with fresh symbols all_339_0, all_339_1 % 103.72/17.93 | | | | gives: % 103.72/17.93 | | | | (287) multiplication(all_22_7, all_65_0) = all_339_0 & % 103.72/17.93 | | | | multiplication(all_22_7, one) = all_339_1 & addition(all_339_1, % 103.72/17.93 | | | | all_339_0) = all_59_0 & $i(all_339_0) & $i(all_339_1) & % 103.72/17.93 | | | | $i(all_59_0) % 103.72/17.93 | | | | % 103.72/17.93 | | | | ALPHA: (287) implies: % 103.72/17.93 | | | | (288) multiplication(all_22_7, one) = all_339_1 % 103.72/17.93 | | | | % 103.72/17.93 | | | | DELTA: instantiating (206) with fresh symbols all_343_0, all_343_1 % 103.72/17.93 | | | | gives: % 103.72/17.94 | | | | (289) multiplication(all_55_0, all_22_4) = all_343_1 & % 103.72/17.94 | | | | multiplication(all_22_5, all_22_4) = all_343_0 & % 103.72/17.94 | | | | addition(all_343_1, all_343_0) = all_47_2 & $i(all_343_0) & % 103.72/17.94 | | | | $i(all_343_1) & $i(all_47_2) % 103.72/17.94 | | | | % 103.72/17.94 | | | | ALPHA: (289) implies: % 103.72/17.94 | | | | (290) $i(all_343_1) % 103.72/17.94 | | | | (291) addition(all_343_1, all_343_0) = all_47_2 % 103.72/17.94 | | | | (292) multiplication(all_22_5, all_22_4) = all_343_0 % 103.72/17.94 | | | | (293) multiplication(all_55_0, all_22_4) = all_343_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | DELTA: instantiating (205) with fresh symbols all_345_0, all_345_1 % 103.72/17.94 | | | | gives: % 103.72/17.94 | | | | (294) multiplication(all_22_5, all_22_4) = all_345_0 & % 103.72/17.94 | | | | multiplication(all_22_6, all_22_4) = all_345_1 & % 103.72/17.94 | | | | addition(all_345_1, all_345_0) = all_47_2 & $i(all_345_0) & % 103.72/17.94 | | | | $i(all_345_1) & $i(all_47_2) % 103.72/17.94 | | | | % 103.72/17.94 | | | | ALPHA: (294) implies: % 103.72/17.94 | | | | (295) multiplication(all_22_6, all_22_4) = all_345_1 % 103.72/17.94 | | | | (296) multiplication(all_22_5, all_22_4) = all_345_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (180), (230) imply: % 103.72/17.94 | | | | (297) multiplication(all_161_0, all_22_8) = all_22_6 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (202), (273) imply: % 103.72/17.94 | | | | (298) multiplication(all_22_7, all_22_9) = all_299_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (180), (293) imply: % 103.72/17.94 | | | | (299) multiplication(all_22_6, all_22_4) = all_343_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (194), (284) imply: % 103.72/17.94 | | | | (300) multiplication(all_22_7, all_22_9) = all_329_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (131), (202) imply: % 103.72/17.94 | | | | (301) multiplication(all_22_7, one) = all_22_7 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (136), (199) imply: % 103.72/17.94 | | | | (302) multiplication(all_22_8, one) = all_22_8 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (180), (226) imply: % 103.72/17.94 | | | | (303) multiplication(all_22_9, all_159_0) = all_22_6 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (199), (270) imply: % 103.72/17.94 | | | | (304) multiplication(all_22_9, all_22_8) = all_297_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (154), (194) imply: % 103.72/17.94 | | | | (305) multiplication(all_22_9, one) = all_22_9 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (160), (193) imply: % 103.72/17.94 | | | | (306) multiplication(one, all_22_9) = all_22_9 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (193), (240) imply: % 103.72/17.94 | | | | (307) addition(all_22_9, all_22_3) = all_205_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (194), (236) imply: % 103.72/17.94 | | | | (308) addition(all_22_9, all_47_1) = all_181_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (194), (238) imply: % 103.72/17.94 | | | | (309) addition(all_22_9, all_22_1) = all_183_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (153), (194) imply: % 103.72/17.94 | | | | (310) addition(all_87_1, all_22_9) = all_22_3 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (180), (215) imply: % 103.72/17.94 | | | | (311) addition(all_22_6, all_22_6) = all_123_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (180), (219) imply: % 103.72/17.94 | | | | (312) addition(all_22_6, all_22_6) = all_127_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (180), (217) imply: % 103.72/17.94 | | | | (313) addition(all_22_6, all_22_6) = all_125_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | REDUCE: (109), (180) imply: % 103.72/17.94 | | | | (314) addition(all_22_6, all_22_6) = all_22_6 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (21) with all_125_0, all_127_0, all_22_6, % 103.72/17.94 | | | | all_22_6, simplifying with (312), (313) gives: % 103.72/17.94 | | | | (315) all_127_0 = all_125_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (21) with all_123_0, all_127_0, all_22_6, % 103.72/17.94 | | | | all_22_6, simplifying with (311), (312) gives: % 103.72/17.94 | | | | (316) all_127_0 = all_123_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (21) with all_121_0, all_127_0, all_22_6, % 103.72/17.94 | | | | all_22_6, simplifying with (213), (312) gives: % 103.72/17.94 | | | | (317) all_127_0 = all_121_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (21) with all_22_6, all_127_0, all_22_6, % 103.72/17.94 | | | | all_22_6, simplifying with (312), (314) gives: % 103.72/17.94 | | | | (318) all_127_0 = all_22_6 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_259_1, all_281_1, all_22_9, % 103.72/17.94 | | | | one, simplifying with (255), (262) gives: % 103.72/17.94 | | | | (319) all_281_1 = all_259_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_281_1, all_325_1, all_22_9, % 103.72/17.94 | | | | one, simplifying with (262), (275) gives: % 103.72/17.94 | | | | (320) all_325_1 = all_281_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_22_9, all_325_1, all_22_9, one, % 103.72/17.94 | | | | simplifying with (275), (306) gives: % 103.72/17.94 | | | | (321) all_325_1 = all_22_9 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_275_1, all_277_1, one, % 103.72/17.94 | | | | all_22_9, simplifying with (258), (260) gives: % 103.72/17.94 | | | | (322) all_277_1 = all_275_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_277_1, all_283_1, one, % 103.72/17.94 | | | | all_22_9, simplifying with (260), (265) gives: % 103.72/17.94 | | | | (323) all_283_1 = all_277_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_22_9, all_283_1, one, all_22_9, % 103.72/17.94 | | | | simplifying with (265), (305) gives: % 103.72/17.94 | | | | (324) all_283_1 = all_22_9 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_22_6, all_297_0, all_22_8, % 103.72/17.94 | | | | all_22_9, simplifying with (33), (304) gives: % 103.72/17.94 | | | | (325) all_297_0 = all_22_6 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_179_0, all_297_0, all_22_8, % 103.72/17.94 | | | | all_22_9, simplifying with (232), (304) gives: % 103.72/17.94 | | | | (326) all_297_0 = all_179_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_87_1, all_283_0, all_32_0, % 103.72/17.94 | | | | all_22_9, simplifying with (155), (266) gives: % 103.72/17.94 | | | | (327) all_283_0 = all_87_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_229_1, all_241_1, one, % 103.72/17.94 | | | | all_22_8, simplifying with (243), (245) gives: % 103.72/17.94 | | | | (328) all_241_1 = all_229_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_241_1, all_335_1, one, % 103.72/17.94 | | | | all_22_8, simplifying with (245), (286) gives: % 103.72/17.94 | | | | (329) all_335_1 = all_241_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_22_8, all_335_1, one, all_22_8, % 103.72/17.94 | | | | simplifying with (286), (302) gives: % 103.72/17.94 | | | | (330) all_335_1 = all_22_8 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_249_1, all_339_1, one, % 103.72/17.94 | | | | all_22_7, simplifying with (250), (288) gives: % 103.72/17.94 | | | | (331) all_339_1 = all_249_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_243_1, all_339_1, one, % 103.72/17.94 | | | | all_22_7, simplifying with (248), (288) gives: % 103.72/17.94 | | | | (332) all_339_1 = all_243_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_22_7, all_339_1, one, all_22_7, % 103.72/17.94 | | | | simplifying with (288), (301) gives: % 103.72/17.94 | | | | (333) all_339_1 = all_22_7 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_22_5, all_329_0, all_22_9, % 103.72/17.94 | | | | all_22_7, simplifying with (35), (300) gives: % 103.72/17.94 | | | | (334) all_329_0 = all_22_5 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_299_0, all_329_0, all_22_9, % 103.72/17.94 | | | | all_22_7, simplifying with (298), (300) gives: % 103.72/17.94 | | | | (335) all_329_0 = all_299_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_343_1, all_345_1, all_22_4, % 103.72/17.94 | | | | all_22_6, simplifying with (295), (299) gives: % 103.72/17.94 | | | | (336) all_345_1 = all_343_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_327_0, all_345_1, all_22_4, % 103.72/17.94 | | | | all_22_6, simplifying with (279), (295) gives: % 103.72/17.94 | | | | (337) all_345_1 = all_327_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_47_2, all_343_0, all_22_4, % 103.72/17.94 | | | | all_22_5, simplifying with (171), (292) gives: % 103.72/17.94 | | | | (338) all_343_0 = all_47_2 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_343_0, all_345_0, all_22_4, % 103.72/17.94 | | | | all_22_5, simplifying with (292), (296) gives: % 103.72/17.94 | | | | (339) all_345_0 = all_343_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_327_1, all_345_0, all_22_4, % 103.72/17.94 | | | | all_22_5, simplifying with (280), (296) gives: % 103.72/17.94 | | | | (340) all_345_0 = all_327_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | GROUND_INST: instantiating (22) with all_89_1, all_259_0, all_22_9, % 103.72/17.94 | | | | all_30_0, simplifying with (161), (256) gives: % 103.72/17.94 | | | | (341) all_259_0 = all_89_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (339), (340) imply: % 103.72/17.94 | | | | (342) all_343_0 = all_327_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | SIMP: (342) implies: % 103.72/17.94 | | | | (343) all_343_0 = all_327_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (336), (337) imply: % 103.72/17.94 | | | | (344) all_343_1 = all_327_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (338), (343) imply: % 103.72/17.94 | | | | (345) all_327_1 = all_47_2 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (331), (333) imply: % 103.72/17.94 | | | | (346) all_249_1 = all_22_7 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (331), (332) imply: % 103.72/17.94 | | | | (347) all_249_1 = all_243_1 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (329), (330) imply: % 103.72/17.94 | | | | (348) all_241_1 = all_22_8 % 103.72/17.94 | | | | % 103.72/17.94 | | | | SIMP: (348) implies: % 103.72/17.94 | | | | (349) all_241_1 = all_22_8 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (334), (335) imply: % 103.72/17.94 | | | | (350) all_299_0 = all_22_5 % 103.72/17.94 | | | | % 103.72/17.94 | | | | SIMP: (350) implies: % 103.72/17.94 | | | | (351) all_299_0 = all_22_5 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (320), (321) imply: % 103.72/17.94 | | | | (352) all_281_1 = all_22_9 % 103.72/17.94 | | | | % 103.72/17.94 | | | | SIMP: (352) implies: % 103.72/17.94 | | | | (353) all_281_1 = all_22_9 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (325), (326) imply: % 103.72/17.94 | | | | (354) all_179_0 = all_22_6 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (323), (324) imply: % 103.72/17.94 | | | | (355) all_277_1 = all_22_9 % 103.72/17.94 | | | | % 103.72/17.94 | | | | SIMP: (355) implies: % 103.72/17.94 | | | | (356) all_277_1 = all_22_9 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (319), (353) imply: % 103.72/17.94 | | | | (357) all_259_1 = all_22_9 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (322), (356) imply: % 103.72/17.94 | | | | (358) all_275_1 = all_22_9 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (346), (347) imply: % 103.72/17.94 | | | | (359) all_243_1 = all_22_7 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (328), (349) imply: % 103.72/17.94 | | | | (360) all_229_1 = all_22_8 % 103.72/17.94 | | | | % 103.72/17.94 | | | | SIMP: (360) implies: % 103.72/17.94 | | | | (361) all_229_1 = all_22_8 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (315), (317) imply: % 103.72/17.94 | | | | (362) all_125_0 = all_121_0 % 103.72/17.94 | | | | % 103.72/17.94 | | | | COMBINE_EQS: (315), (318) imply: % 103.72/17.95 | | | | (363) all_125_0 = all_22_6 % 103.72/17.95 | | | | % 103.72/17.95 | | | | COMBINE_EQS: (315), (316) imply: % 103.72/17.95 | | | | (364) all_125_0 = all_123_0 % 103.72/17.95 | | | | % 103.72/17.95 | | | | COMBINE_EQS: (362), (364) imply: % 103.72/17.95 | | | | (365) all_123_0 = all_121_0 % 103.72/17.95 | | | | % 103.72/17.95 | | | | COMBINE_EQS: (363), (364) imply: % 103.72/17.95 | | | | (366) all_123_0 = all_22_6 % 103.72/17.95 | | | | % 103.72/17.95 | | | | COMBINE_EQS: (365), (366) imply: % 103.72/17.95 | | | | (367) all_121_0 = all_22_6 % 103.72/17.95 | | | | % 103.72/17.95 | | | | REDUCE: (233), (354) imply: % 103.72/17.95 | | | | (368) multiplication(all_22_6, all_22_4) = all_87_1 % 103.72/17.95 | | | | % 103.72/17.95 | | | | REDUCE: (291), (338), (344) imply: % 103.72/17.95 | | | | (369) addition(all_327_0, all_47_2) = all_47_2 % 103.72/17.95 | | | | % 103.72/17.95 | | | | REDUCE: (282), (334) imply: % 103.72/17.95 | | | | (370) addition(all_329_1, all_22_5) = all_47_2 % 103.72/17.95 | | | | % 103.72/17.95 | | | | REDUCE: (278), (345) imply: % 103.72/17.95 | | | | (371) addition(all_47_2, all_327_0) = all_47_2 % 103.72/17.95 | | | | % 103.72/17.95 | | | | REDUCE: (269), (325) imply: % 103.72/17.95 | | | | (372) addition(all_297_1, all_22_6) = all_87_1 % 103.72/17.95 | | | | % 103.72/17.95 | | | | REDUCE: (264), (324), (327) imply: % 103.72/17.95 | | | | (373) addition(all_22_9, all_87_1) = all_22_3 % 103.72/17.95 | | | | % 103.72/17.95 | | | | REDUCE: (254), (341), (357) imply: % 103.72/17.95 | | | | (374) addition(all_22_9, all_89_1) = all_22_1 % 103.72/17.95 | | | | % 103.72/17.95 | | | | REDUCE: (290), (344) imply: % 103.72/17.95 | | | | (375) $i(all_327_0) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (22) with all_327_0, all_87_1, all_22_4, % 103.72/17.95 | | | | all_22_6, simplifying with (279), (368) gives: % 103.72/17.95 | | | | (376) all_327_0 = all_87_1 % 103.72/17.95 | | | | % 103.72/17.95 | | | | REDUCE: (369), (376) imply: % 103.72/17.95 | | | | (377) addition(all_87_1, all_47_2) = all_47_2 % 103.72/17.95 | | | | % 103.72/17.95 | | | | REDUCE: (371), (376) imply: % 103.72/17.95 | | | | (378) addition(all_47_2, all_87_1) = all_47_2 % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (idempotence) with all_22_9, all_161_0, % 103.72/17.95 | | | | simplifying with (26), (229) gives: % 103.72/17.95 | | | | (379) all_161_0 = all_22_9 % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (2) with all_22_9, all_47_2, all_22_9, % 103.72/17.95 | | | | all_47_1, all_181_0, simplifying with (26), (76), (77), % 103.72/17.95 | | | | (308) gives: % 103.72/17.95 | | | | (380) ? [v0: $i] : (addition(v0, all_22_9) = all_181_0 & % 103.72/17.95 | | | | addition(all_22_9, all_47_2) = v0 & $i(v0) & $i(all_181_0)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (2) with all_47_2, all_22_9, all_22_9, % 103.72/17.95 | | | | all_47_1, all_181_0, simplifying with (26), (76), (96), % 103.72/17.95 | | | | (308) gives: % 103.72/17.95 | | | | (381) ? [v0: $i] : (addition(v0, all_47_2) = all_181_0 & % 103.72/17.95 | | | | addition(all_22_9, all_22_9) = v0 & $i(v0) & $i(all_181_0)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (2) with all_87_1, all_22_9, all_22_9, % 103.72/17.95 | | | | all_22_3, all_205_0, simplifying with (26), (151), (307), % 103.72/17.95 | | | | (373) gives: % 103.72/17.95 | | | | (382) ? [v0: $i] : (addition(v0, all_87_1) = all_205_0 & % 103.72/17.95 | | | | addition(all_22_9, all_22_9) = v0 & $i(v0) & $i(all_205_0)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (2) with all_89_1, all_22_9, all_22_9, % 103.72/17.95 | | | | all_22_1, all_183_0, simplifying with (26), (157), (309), % 103.72/17.95 | | | | (374) gives: % 103.72/17.95 | | | | (383) ? [v0: $i] : (addition(v0, all_89_1) = all_183_0 & % 103.72/17.95 | | | | addition(all_22_9, all_22_9) = v0 & $i(v0) & $i(all_183_0)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (3) with all_47_2, all_87_1, all_22_9, % 103.72/17.95 | | | | all_22_3, all_131_0, simplifying with (26), (76), (151), % 103.72/17.95 | | | | (223), (373) gives: % 103.72/17.95 | | | | (384) ? [v0: $i] : (addition(all_87_1, all_47_2) = v0 & % 103.72/17.95 | | | | addition(all_22_9, v0) = all_131_0 & $i(v0) & $i(all_131_0)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (2) with all_87_1, all_47_2, all_22_9, % 103.72/17.95 | | | | all_47_2, all_47_1, simplifying with (26), (76), (96), % 103.72/17.95 | | | | (151), (378) gives: % 103.72/17.95 | | | | (385) ? [v0: $i] : (addition(v0, all_87_1) = all_47_1 & % 103.72/17.95 | | | | addition(all_22_9, all_47_2) = v0 & $i(v0) & $i(all_47_1)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (3) with all_47_2, all_22_9, all_87_1, % 103.72/17.95 | | | | all_22_3, all_131_0, simplifying with (26), (76), (151), % 103.72/17.95 | | | | (223), (310) gives: % 103.72/17.95 | | | | (386) ? [v0: $i] : (addition(all_87_1, v0) = all_131_0 & % 103.72/17.95 | | | | addition(all_22_9, all_47_2) = v0 & $i(v0) & $i(all_131_0)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (3) with all_22_9, all_22_9, all_87_1, % 103.72/17.95 | | | | all_22_3, all_129_0, simplifying with (26), (151), (221), % 103.72/17.95 | | | | (310) gives: % 103.72/17.95 | | | | (387) ? [v0: $i] : (addition(all_87_1, v0) = all_129_0 & % 103.72/17.95 | | | | addition(all_22_9, all_22_9) = v0 & $i(v0) & $i(all_129_0)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (18) with all_87_1, all_47_2, simplifying % 103.72/17.95 | | | | with (76), (151), (377) gives: % 103.72/17.95 | | | | (388) leq(all_87_1, all_47_2) = 0 % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (1) with all_22_6, all_297_1, all_87_1, % 103.72/17.95 | | | | simplifying with (29), (268), (372) gives: % 103.72/17.95 | | | | (389) addition(all_22_6, all_297_1) = all_87_1 & $i(all_87_1) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (8) with one, all_22_9, all_22_9, all_22_9, % 103.72/17.95 | | | | all_22_9, all_161_0, simplifying with (13), (26), (229), % 103.72/17.95 | | | | (306) gives: % 103.72/17.95 | | | | (390) ? [v0: $i] : (multiplication(one, v0) = all_161_0 & % 103.72/17.95 | | | | addition(all_22_9, all_22_9) = v0 & $i(v0) & $i(all_161_0)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (10) with all_22_9, all_22_9, one, all_22_9, % 103.72/17.95 | | | | all_22_9, all_161_0, simplifying with (13), (26), (229), % 103.72/17.95 | | | | (305) gives: % 103.72/17.95 | | | | (391) ? [v0: $i] : (multiplication(v0, one) = all_161_0 & % 103.72/17.95 | | | | addition(all_22_9, all_22_9) = v0 & $i(v0) & $i(all_161_0)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (10) with all_22_9, all_22_9, all_159_0, % 103.72/17.95 | | | | all_22_6, all_22_6, all_22_6, simplifying with (26), (225), % 103.72/17.95 | | | | (303), (314) gives: % 103.72/17.95 | | | | (392) ? [v0: $i] : (multiplication(v0, all_159_0) = all_22_6 & % 103.72/17.95 | | | | addition(all_22_9, all_22_9) = v0 & $i(v0) & $i(all_22_6)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (15) with all_22_7, all_22_5, all_87_1, % 103.72/17.95 | | | | all_329_1, all_47_2, simplifying with (28), (30), (151), % 103.72/17.95 | | | | (283), (370) gives: % 103.72/17.95 | | | | (393) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ((v3 % 103.72/17.95 | | | | = 0 & strong_iteration(all_22_7) = v1 & leq(all_87_1, v2) = % 103.72/17.95 | | | | 0 & multiplication(v1, all_22_5) = v2 & $i(v2) & $i(v1)) | % 103.72/17.95 | | | | ( ~ (v0 = 0) & leq(all_87_1, all_47_2) = v0)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (10) with all_22_9, all_161_0, all_22_8, % 103.72/17.95 | | | | all_22_6, all_22_6, all_22_6, simplifying with (26), (27), % 103.72/17.95 | | | | (33), (228), (297), (314) gives: % 103.72/17.95 | | | | (394) ? [v0: $i] : (multiplication(v0, all_22_8) = all_22_6 & % 103.72/17.95 | | | | addition(all_22_9, all_161_0) = v0 & $i(v0) & $i(all_22_6)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (10) with all_161_0, all_22_9, all_22_8, % 103.72/17.95 | | | | all_22_6, all_22_6, all_22_6, simplifying with (26), (27), % 103.72/17.95 | | | | (33), (228), (297), (314) gives: % 103.72/17.95 | | | | (395) ? [v0: $i] : (multiplication(v0, all_22_8) = all_22_6 & % 103.72/17.95 | | | | addition(all_161_0, all_22_9) = v0 & $i(v0) & $i(all_22_6)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | GROUND_INST: instantiating (10) with all_161_0, all_161_0, all_22_8, % 103.72/17.95 | | | | all_22_6, all_22_6, all_22_6, simplifying with (27), (228), % 103.72/17.95 | | | | (297), (314) gives: % 103.72/17.95 | | | | (396) ? [v0: $i] : (multiplication(v0, all_22_8) = all_22_6 & % 103.72/17.95 | | | | addition(all_161_0, all_161_0) = v0 & $i(v0) & $i(all_22_6)) % 103.72/17.95 | | | | % 103.72/17.95 | | | | DELTA: instantiating (381) with fresh symbol all_458_0 gives: % 103.72/17.95 | | | | (397) addition(all_458_0, all_47_2) = all_181_0 & addition(all_22_9, % 103.72/17.95 | | | | all_22_9) = all_458_0 & $i(all_458_0) & $i(all_181_0) % 103.72/17.95 | | | | % 103.72/17.95 | | | | ALPHA: (397) implies: % 103.72/17.95 | | | | (398) addition(all_22_9, all_22_9) = all_458_0 % 103.72/17.95 | | | | (399) addition(all_458_0, all_47_2) = all_181_0 % 103.72/17.95 | | | | % 103.72/17.95 | | | | DELTA: instantiating (380) with fresh symbol all_470_0 gives: % 103.72/17.95 | | | | (400) addition(all_470_0, all_22_9) = all_181_0 & addition(all_22_9, % 103.72/17.95 | | | | all_47_2) = all_470_0 & $i(all_470_0) & $i(all_181_0) % 103.72/17.95 | | | | % 103.72/17.95 | | | | ALPHA: (400) implies: % 103.72/17.95 | | | | (401) addition(all_22_9, all_47_2) = all_470_0 % 103.72/17.95 | | | | % 103.72/17.95 | | | | DELTA: instantiating (395) with fresh symbol all_488_0 gives: % 103.72/17.95 | | | | (402) multiplication(all_488_0, all_22_8) = all_22_6 & % 103.72/17.95 | | | | addition(all_161_0, all_22_9) = all_488_0 & $i(all_488_0) & % 103.72/17.95 | | | | $i(all_22_6) % 103.72/17.95 | | | | % 103.72/17.95 | | | | ALPHA: (402) implies: % 103.72/17.95 | | | | (403) addition(all_161_0, all_22_9) = all_488_0 % 103.72/17.95 | | | | % 103.72/17.95 | | | | DELTA: instantiating (394) with fresh symbol all_490_0 gives: % 103.72/17.96 | | | | (404) multiplication(all_490_0, all_22_8) = all_22_6 & % 103.72/17.96 | | | | addition(all_22_9, all_161_0) = all_490_0 & $i(all_490_0) & % 103.72/17.96 | | | | $i(all_22_6) % 103.72/17.96 | | | | % 103.72/17.96 | | | | ALPHA: (404) implies: % 103.72/17.96 | | | | (405) addition(all_22_9, all_161_0) = all_490_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | DELTA: instantiating (390) with fresh symbol all_594_0 gives: % 103.72/17.96 | | | | (406) multiplication(one, all_594_0) = all_161_0 & addition(all_22_9, % 103.72/17.96 | | | | all_22_9) = all_594_0 & $i(all_594_0) & $i(all_161_0) % 103.72/17.96 | | | | % 103.72/17.96 | | | | ALPHA: (406) implies: % 103.72/17.96 | | | | (407) addition(all_22_9, all_22_9) = all_594_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | DELTA: instantiating (382) with fresh symbol all_632_0 gives: % 103.72/17.96 | | | | (408) addition(all_632_0, all_87_1) = all_205_0 & addition(all_22_9, % 103.72/17.96 | | | | all_22_9) = all_632_0 & $i(all_632_0) & $i(all_205_0) % 103.72/17.96 | | | | % 103.72/17.96 | | | | ALPHA: (408) implies: % 103.72/17.96 | | | | (409) addition(all_22_9, all_22_9) = all_632_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | DELTA: instantiating (383) with fresh symbol all_638_0 gives: % 103.72/17.96 | | | | (410) addition(all_638_0, all_89_1) = all_183_0 & addition(all_22_9, % 103.72/17.96 | | | | all_22_9) = all_638_0 & $i(all_638_0) & $i(all_183_0) % 103.72/17.96 | | | | % 103.72/17.96 | | | | ALPHA: (410) implies: % 103.72/17.96 | | | | (411) addition(all_22_9, all_22_9) = all_638_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | DELTA: instantiating (387) with fresh symbol all_728_0 gives: % 103.72/17.96 | | | | (412) addition(all_87_1, all_728_0) = all_129_0 & addition(all_22_9, % 103.72/17.96 | | | | all_22_9) = all_728_0 & $i(all_728_0) & $i(all_129_0) % 103.72/17.96 | | | | % 103.72/17.96 | | | | ALPHA: (412) implies: % 103.72/17.96 | | | | (413) addition(all_22_9, all_22_9) = all_728_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | DELTA: instantiating (386) with fresh symbol all_730_0 gives: % 103.72/17.96 | | | | (414) addition(all_87_1, all_730_0) = all_131_0 & addition(all_22_9, % 103.72/17.96 | | | | all_47_2) = all_730_0 & $i(all_730_0) & $i(all_131_0) % 103.72/17.96 | | | | % 103.72/17.96 | | | | ALPHA: (414) implies: % 103.72/17.96 | | | | (415) addition(all_22_9, all_47_2) = all_730_0 % 103.72/17.96 | | | | (416) addition(all_87_1, all_730_0) = all_131_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | DELTA: instantiating (396) with fresh symbol all_738_0 gives: % 103.72/17.96 | | | | (417) multiplication(all_738_0, all_22_8) = all_22_6 & % 103.72/17.96 | | | | addition(all_161_0, all_161_0) = all_738_0 & $i(all_738_0) & % 103.72/17.96 | | | | $i(all_22_6) % 103.72/17.96 | | | | % 103.72/17.96 | | | | ALPHA: (417) implies: % 103.72/17.96 | | | | (418) addition(all_161_0, all_161_0) = all_738_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | DELTA: instantiating (384) with fresh symbol all_838_0 gives: % 103.72/17.96 | | | | (419) addition(all_87_1, all_47_2) = all_838_0 & addition(all_22_9, % 103.72/17.96 | | | | all_838_0) = all_131_0 & $i(all_838_0) & $i(all_131_0) % 103.72/17.96 | | | | % 103.72/17.96 | | | | ALPHA: (419) implies: % 103.72/17.96 | | | | (420) addition(all_22_9, all_838_0) = all_131_0 % 103.72/17.96 | | | | (421) addition(all_87_1, all_47_2) = all_838_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | DELTA: instantiating (392) with fresh symbol all_1200_0 gives: % 103.72/17.96 | | | | (422) multiplication(all_1200_0, all_159_0) = all_22_6 & % 103.72/17.96 | | | | addition(all_22_9, all_22_9) = all_1200_0 & $i(all_1200_0) & % 103.72/17.96 | | | | $i(all_22_6) % 103.72/17.96 | | | | % 103.72/17.96 | | | | ALPHA: (422) implies: % 103.72/17.96 | | | | (423) addition(all_22_9, all_22_9) = all_1200_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | DELTA: instantiating (385) with fresh symbol all_1236_0 gives: % 103.72/17.96 | | | | (424) addition(all_1236_0, all_87_1) = all_47_1 & addition(all_22_9, % 103.72/17.96 | | | | all_47_2) = all_1236_0 & $i(all_1236_0) & $i(all_47_1) % 103.72/17.96 | | | | % 103.72/17.96 | | | | ALPHA: (424) implies: % 103.72/17.96 | | | | (425) addition(all_22_9, all_47_2) = all_1236_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | DELTA: instantiating (391) with fresh symbol all_1294_0 gives: % 103.72/17.96 | | | | (426) multiplication(all_1294_0, one) = all_161_0 & % 103.72/17.96 | | | | addition(all_22_9, all_22_9) = all_1294_0 & $i(all_1294_0) & % 103.72/17.96 | | | | $i(all_161_0) % 103.72/17.96 | | | | % 103.72/17.96 | | | | ALPHA: (426) implies: % 103.72/17.96 | | | | (427) addition(all_22_9, all_22_9) = all_1294_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | DELTA: instantiating (393) with fresh symbols all_2717_0, all_2717_1, % 103.72/17.96 | | | | all_2717_2, all_2717_3 gives: % 103.72/17.96 | | | | (428) (all_2717_0 = 0 & strong_iteration(all_22_7) = all_2717_2 & % 103.72/17.96 | | | | leq(all_87_1, all_2717_1) = 0 & multiplication(all_2717_2, % 103.72/17.96 | | | | all_22_5) = all_2717_1 & $i(all_2717_1) & $i(all_2717_2)) | % 103.72/17.96 | | | | ( ~ (all_2717_3 = 0) & leq(all_87_1, all_47_2) = all_2717_3) % 103.72/17.96 | | | | % 103.72/17.96 | | | | REDUCE: (379), (418) imply: % 103.72/17.96 | | | | (429) addition(all_22_9, all_22_9) = all_738_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | REDUCE: (379), (403) imply: % 103.72/17.96 | | | | (430) addition(all_22_9, all_22_9) = all_488_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | REDUCE: (379), (405) imply: % 103.72/17.96 | | | | (431) addition(all_22_9, all_22_9) = all_490_0 % 103.72/17.96 | | | | % 103.72/17.96 | | | | REDUCE: (229), (379) imply: % 103.72/17.96 | | | | (432) addition(all_22_9, all_22_9) = all_22_9 % 103.72/17.96 | | | | % 103.72/17.96 | | | | BETA: splitting (428) gives: % 103.72/17.96 | | | | % 103.72/17.96 | | | | Case 1: % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_22_9, all_488_0, all_22_9, % 103.72/17.96 | | | | | all_22_9, simplifying with (430), (432) gives: % 103.72/17.96 | | | | | (433) all_488_0 = all_22_9 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_490_0, all_632_0, all_22_9, % 103.72/17.96 | | | | | all_22_9, simplifying with (409), (431) gives: % 103.72/17.96 | | | | | (434) all_632_0 = all_490_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_488_0, all_632_0, all_22_9, % 103.72/17.96 | | | | | all_22_9, simplifying with (409), (430) gives: % 103.72/17.96 | | | | | (435) all_632_0 = all_488_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_632_0, all_638_0, all_22_9, % 103.72/17.96 | | | | | all_22_9, simplifying with (409), (411) gives: % 103.72/17.96 | | | | | (436) all_638_0 = all_632_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_638_0, all_728_0, all_22_9, % 103.72/17.96 | | | | | all_22_9, simplifying with (411), (413) gives: % 103.72/17.96 | | | | | (437) all_728_0 = all_638_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_594_0, all_728_0, all_22_9, % 103.72/17.96 | | | | | all_22_9, simplifying with (407), (413) gives: % 103.72/17.96 | | | | | (438) all_728_0 = all_594_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_638_0, all_738_0, all_22_9, % 103.72/17.96 | | | | | all_22_9, simplifying with (411), (429) gives: % 103.72/17.96 | | | | | (439) all_738_0 = all_638_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_738_0, all_1200_0, all_22_9, % 103.72/17.96 | | | | | all_22_9, simplifying with (423), (429) gives: % 103.72/17.96 | | | | | (440) all_1200_0 = all_738_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_1200_0, all_1294_0, all_22_9, % 103.72/17.96 | | | | | all_22_9, simplifying with (423), (427) gives: % 103.72/17.96 | | | | | (441) all_1294_0 = all_1200_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_458_0, all_1294_0, all_22_9, % 103.72/17.96 | | | | | all_22_9, simplifying with (398), (427) gives: % 103.72/17.96 | | | | | (442) all_1294_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_47_1, all_730_0, all_47_2, % 103.72/17.96 | | | | | all_22_9, simplifying with (96), (415) gives: % 103.72/17.96 | | | | | (443) all_730_0 = all_47_1 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_730_0, all_1236_0, all_47_2, % 103.72/17.96 | | | | | all_22_9, simplifying with (415), (425) gives: % 103.72/17.96 | | | | | (444) all_1236_0 = all_730_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_470_0, all_1236_0, all_47_2, % 103.72/17.96 | | | | | all_22_9, simplifying with (401), (425) gives: % 103.72/17.96 | | | | | (445) all_1236_0 = all_470_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_47_2, all_838_0, all_47_2, % 103.72/17.96 | | | | | all_87_1, simplifying with (377), (421) gives: % 103.72/17.96 | | | | | (446) all_838_0 = all_47_2 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (441), (442) imply: % 103.72/17.96 | | | | | (447) all_1200_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | SIMP: (447) implies: % 103.72/17.96 | | | | | (448) all_1200_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (444), (445) imply: % 103.72/17.96 | | | | | (449) all_730_0 = all_470_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | SIMP: (449) implies: % 103.72/17.96 | | | | | (450) all_730_0 = all_470_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (440), (448) imply: % 103.72/17.96 | | | | | (451) all_738_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | SIMP: (451) implies: % 103.72/17.96 | | | | | (452) all_738_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (439), (452) imply: % 103.72/17.96 | | | | | (453) all_638_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | SIMP: (453) implies: % 103.72/17.96 | | | | | (454) all_638_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (443), (450) imply: % 103.72/17.96 | | | | | (455) all_470_0 = all_47_1 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (437), (438) imply: % 103.72/17.96 | | | | | (456) all_638_0 = all_594_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | SIMP: (456) implies: % 103.72/17.96 | | | | | (457) all_638_0 = all_594_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (436), (457) imply: % 103.72/17.96 | | | | | (458) all_632_0 = all_594_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | SIMP: (458) implies: % 103.72/17.96 | | | | | (459) all_632_0 = all_594_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (454), (457) imply: % 103.72/17.96 | | | | | (460) all_594_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (434), (459) imply: % 103.72/17.96 | | | | | (461) all_594_0 = all_490_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | SIMP: (461) implies: % 103.72/17.96 | | | | | (462) all_594_0 = all_490_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (434), (435) imply: % 103.72/17.96 | | | | | (463) all_490_0 = all_488_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (460), (462) imply: % 103.72/17.96 | | | | | (464) all_490_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | SIMP: (464) implies: % 103.72/17.96 | | | | | (465) all_490_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (463), (465) imply: % 103.72/17.96 | | | | | (466) all_488_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | SIMP: (466) implies: % 103.72/17.96 | | | | | (467) all_488_0 = all_458_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (433), (467) imply: % 103.72/17.96 | | | | | (468) all_458_0 = all_22_9 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | REDUCE: (399), (468) imply: % 103.72/17.96 | | | | | (469) addition(all_22_9, all_47_2) = all_181_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | REDUCE: (416), (443) imply: % 103.72/17.96 | | | | | (470) addition(all_87_1, all_47_1) = all_131_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | REDUCE: (420), (446) imply: % 103.72/17.96 | | | | | (471) addition(all_22_9, all_47_2) = all_131_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_47_1, all_181_0, all_47_2, % 103.72/17.96 | | | | | all_22_9, simplifying with (96), (469) gives: % 103.72/17.96 | | | | | (472) all_181_0 = all_47_1 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_131_0, all_181_0, all_47_2, % 103.72/17.96 | | | | | all_22_9, simplifying with (469), (471) gives: % 103.72/17.96 | | | | | (473) all_181_0 = all_131_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | COMBINE_EQS: (472), (473) imply: % 103.72/17.96 | | | | | (474) all_131_0 = all_47_1 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | REDUCE: (235), (472) imply: % 103.72/17.96 | | | | | (475) addition(all_87_1, all_47_1) = all_109_0 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | REDUCE: (470), (474) imply: % 103.72/17.96 | | | | | (476) addition(all_87_1, all_47_1) = all_47_1 % 103.72/17.96 | | | | | % 103.72/17.96 | | | | | GROUND_INST: instantiating (21) with all_47_1, all_109_0, all_47_1, % 103.72/17.96 | | | | | all_87_1, simplifying with (475), (476) gives: % 103.72/17.97 | | | | | (477) all_109_0 = all_47_1 % 103.72/17.97 | | | | | % 103.72/17.97 | | | | | REDUCE: (166), (477) imply: % 103.72/17.97 | | | | | (478) $false % 103.72/17.97 | | | | | % 103.72/17.97 | | | | | CLOSE: (478) is inconsistent. % 103.72/17.97 | | | | | % 103.72/17.97 | | | | Case 2: % 103.72/17.97 | | | | | % 103.72/17.97 | | | | | (479) ~ (all_2717_3 = 0) & leq(all_87_1, all_47_2) = all_2717_3 % 103.72/17.97 | | | | | % 103.72/17.97 | | | | | ALPHA: (479) implies: % 103.72/17.97 | | | | | (480) ~ (all_2717_3 = 0) % 103.72/17.97 | | | | | (481) leq(all_87_1, all_47_2) = all_2717_3 % 103.72/17.97 | | | | | % 103.72/17.97 | | | | | GROUND_INST: instantiating (23) with 0, all_2717_3, all_47_2, % 103.72/17.97 | | | | | all_87_1, simplifying with (388), (481) gives: % 103.72/17.97 | | | | | (482) all_2717_3 = 0 % 103.72/17.97 | | | | | % 103.72/17.97 | | | | | REDUCE: (480), (482) imply: % 103.72/17.97 | | | | | (483) $false % 103.72/17.97 | | | | | % 103.72/17.97 | | | | | CLOSE: (483) is inconsistent. % 103.72/17.97 | | | | | % 103.72/17.97 | | | | End of split % 103.72/17.97 | | | | % 103.72/17.97 | | | End of split % 103.72/17.97 | | | % 103.72/17.97 | | End of split % 103.72/17.97 | | % 103.72/17.97 | End of split % 103.72/17.97 | % 103.72/17.97 End of proof % 103.72/17.97 % SZS output end Proof for theBenchmark % 103.72/17.97 % 103.72/17.97 17353ms %------------------------------------------------------------------------------