%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE066+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 : n032.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 05:34:26 EDT 2023 % Result : Theorem 34.83s 5.26s % Output : Proof 141.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.09 % Problem : KLE066+1 : TPTP v8.1.2. Released v4.0.0. % 0.05/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.28 % Computer : n032.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.28 % CPULimit : 300 % 0.13/0.28 % WCLimit : 300 % 0.13/0.28 % DateTime : Tue Aug 29 12:27:01 EDT 2023 % 0.13/0.29 % CPUTime : % 0.13/0.48 ________ _____ % 0.13/0.48 ___ __ \_________(_)________________________________ % 0.13/0.48 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.13/0.48 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.13/0.48 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.13/0.48 % 0.13/0.48 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.13/0.48 (2023-06-19) % 0.13/0.48 % 0.13/0.48 (c) Philipp Rümmer, 2009-2023 % 0.13/0.48 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.13/0.48 Amanda Stjerna. % 0.13/0.48 Free software under BSD-3-Clause. % 0.13/0.48 % 0.13/0.48 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.13/0.48 % 0.13/0.48 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.13/0.49 Running up to 7 provers in parallel. % 0.13/0.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.13/0.50 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.13/0.50 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.13/0.50 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.13/0.50 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.13/0.50 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.13/0.50 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.19/0.85 Prover 4: Preprocessing ... % 2.19/0.85 Prover 1: Preprocessing ... % 2.19/0.89 Prover 5: Preprocessing ... % 2.19/0.89 Prover 3: Preprocessing ... % 2.19/0.89 Prover 6: Preprocessing ... % 2.19/0.89 Prover 2: Preprocessing ... % 2.19/0.89 Prover 0: Preprocessing ... % 4.42/1.19 Prover 6: Constructing countermodel ... % 4.42/1.20 Prover 1: Constructing countermodel ... % 4.42/1.21 Prover 3: Constructing countermodel ... % 4.42/1.25 Prover 4: Constructing countermodel ... % 4.42/1.27 Prover 5: Proving ... % 4.42/1.32 Prover 0: Proving ... % 6.68/1.48 Prover 2: Proving ... % 34.83/5.25 Prover 0: proved (4736ms) % 34.83/5.26 % 34.83/5.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 34.83/5.26 % 34.83/5.26 Prover 6: stopped % 34.83/5.26 Prover 3: stopped % 34.83/5.27 Prover 2: stopped % 34.83/5.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 34.83/5.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 34.83/5.28 Prover 5: stopped % 34.83/5.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 34.83/5.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 34.83/5.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 34.83/5.31 Prover 8: Preprocessing ... % 35.37/5.32 Prover 13: Preprocessing ... % 35.37/5.32 Prover 7: Preprocessing ... % 35.37/5.33 Prover 10: Preprocessing ... % 35.37/5.34 Prover 11: Preprocessing ... % 35.78/5.39 Prover 10: Constructing countermodel ... % 35.78/5.40 Prover 8: Warning: ignoring some quantifiers % 35.78/5.40 Prover 8: Constructing countermodel ... % 35.78/5.45 Prover 13: Warning: ignoring some quantifiers % 36.41/5.46 Prover 13: Constructing countermodel ... % 36.41/5.46 Prover 7: Constructing countermodel ... % 36.41/5.47 Prover 11: Constructing countermodel ... % 71.94/10.26 Prover 13: stopped % 71.94/10.26 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 71.94/10.29 Prover 16: Preprocessing ... % 73.05/10.38 Prover 16: Warning: ignoring some quantifiers % 73.05/10.40 Prover 16: Constructing countermodel ... % 114.54/15.78 Prover 16: stopped % 114.54/15.79 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 114.81/15.83 Prover 19: Preprocessing ... % 114.81/15.85 Prover 1: stopped % 114.81/15.88 Prover 19: Warning: ignoring some quantifiers % 114.81/15.88 Prover 19: Constructing countermodel ... % 140.50/19.53 Prover 19: stopped % 140.50/19.58 Prover 7: Found proof (size 146) % 140.50/19.58 Prover 7: proved (14238ms) % 140.50/19.59 Prover 4: stopped % 140.50/19.59 Prover 10: stopped % 140.50/19.59 Prover 8: stopped % 140.50/19.59 Prover 11: stopped % 140.50/19.60 % 140.50/19.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 140.50/19.60 % 140.90/19.62 % SZS output start Proof for theBenchmark % 140.90/19.62 Assumptions after simplification: % 140.90/19.62 --------------------------------- % 140.90/19.62 % 140.90/19.62 (additive_identity) % 140.90/19.66 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) % 140.90/19.66 | ~ $i(v0)) % 140.90/19.66 % 140.90/19.66 (domain1) % 140.90/19.66 ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 140.90/19.67 (multiplication(v1, v0) = v2 & addition(v0, v2) = v2 & $i(v2))) % 140.90/19.67 % 140.90/19.67 (domain2) % 141.21/19.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1) = v2) % 141.21/19.67 | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 141.21/19.67 ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = % 141.21/19.67 v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 141.21/19.67 (multiplication(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 141.21/19.67 [v4: $i] : ? [v5: $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = % 141.21/19.67 v4 & multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3))) % 141.21/19.67 % 141.21/19.67 (domain3) % 141.21/19.67 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | % 141.21/19.67 addition(v1, one) = one) % 141.21/19.67 % 141.21/19.67 (domain4) % 141.21/19.67 domain(zero) = zero & $i(zero) % 141.21/19.67 % 141.21/19.67 (domain5) % 141.21/19.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 141.21/19.68 (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ~ % 141.21/19.68 $i(v1) | ~ $i(v0) | ? [v5: $i] : (domain(v5) = v4 & addition(v0, v1) = v5 % 141.21/19.68 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 141.21/19.68 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] % 141.21/19.68 : ? [v5: $i] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & % 141.21/19.68 addition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 141.21/19.68 % 141.21/19.68 (goals) % 141.21/19.68 $i(zero) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = % 141.21/19.68 zero) & domain(v1) = v2 & multiplication(v0, v2) = zero & % 141.21/19.68 multiplication(v0, v1) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 141.21/19.68 % 141.21/19.68 (left_annihilation) % 141.21/19.68 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, % 141.21/19.68 v0) = v1) | ~ $i(v0)) % 141.21/19.68 % 141.21/19.68 (left_distributivity) % 141.21/19.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 141.21/19.69 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | % 141.21/19.69 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 141.21/19.69 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) & % 141.21/19.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 141.21/19.69 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~ % 141.21/19.69 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) = % 141.21/19.69 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5) % 141.21/19.69 & $i(v4))) % 141.21/19.69 % 141.21/19.69 (multiplicative_right_identity) % 141.21/19.69 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 141.21/19.69 v1) | ~ $i(v0)) % 141.21/19.69 % 141.21/19.69 (right_annihilation) % 141.21/19.69 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(v0, % 141.21/19.69 zero) = v1) | ~ $i(v0)) % 141.21/19.69 % 141.21/19.69 (function-axioms) % 141.21/19.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 141.21/19.70 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0: % 141.21/19.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3, % 141.21/19.70 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 141.21/19.70 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) % 141.21/19.70 % 141.21/19.70 Further assumptions not needed in the proof: % 141.21/19.70 -------------------------------------------- % 141.21/19.70 additive_associativity, additive_commutativity, additive_idempotence, % 141.21/19.70 multiplicative_associativity, multiplicative_left_identity, order, % 141.21/19.70 right_distributivity % 141.21/19.70 % 141.21/19.70 Those formulas are unsatisfiable: % 141.21/19.70 --------------------------------- % 141.21/19.70 % 141.21/19.70 Begin of proof % 141.21/19.70 | % 141.21/19.70 | ALPHA: (additive_identity) implies: % 141.21/19.70 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) | % 141.21/19.70 | ~ $i(v0)) % 141.21/19.70 | % 141.21/19.70 | ALPHA: (multiplicative_right_identity) implies: % 141.21/19.70 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 141.21/19.70 | v1) | ~ $i(v0)) % 141.21/19.70 | % 141.21/19.70 | ALPHA: (left_distributivity) implies: % 141.21/19.70 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 141.21/19.70 | ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ % 141.21/19.70 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 141.21/19.70 | (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & % 141.21/19.70 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 141.21/19.70 | % 141.21/19.70 | ALPHA: (right_annihilation) implies: % 141.21/19.70 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(v0, zero) = % 141.21/19.70 | v1) | ~ $i(v0)) % 141.21/19.70 | % 141.21/19.70 | ALPHA: (left_annihilation) implies: % 141.21/19.71 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, v0) = % 141.21/19.71 | v1) | ~ $i(v0)) % 141.21/19.71 | % 141.21/19.71 | ALPHA: (domain2) implies: % 141.21/19.71 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v0, v1) = % 141.21/19.71 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 141.21/19.71 | $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & % 141.21/19.71 | multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3))) % 141.21/19.71 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1) % 141.21/19.71 | = v2) | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | % 141.21/19.71 | ? [v4: $i] : ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 & % 141.21/19.71 | multiplication(v0, v1) = v4 & $i(v5) & $i(v4))) % 141.21/19.71 | % 141.21/19.71 | ALPHA: (domain3) implies: % 141.21/19.71 | (8) $i(one) % 141.21/19.71 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | % 141.21/19.71 | addition(v1, one) = one) % 141.21/19.71 | % 141.21/19.71 | ALPHA: (domain4) implies: % 141.21/19.71 | (10) domain(zero) = zero % 141.21/19.71 | % 141.21/19.71 | ALPHA: (domain5) implies: % 141.21/19.71 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) % 141.21/19.71 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 141.21/19.71 | (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, % 141.21/19.71 | v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 141.21/19.72 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 141.21/19.72 | ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = % 141.21/19.72 | v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (domain(v5) = v4 & % 141.21/19.72 | addition(v0, v1) = v5 & $i(v5) & $i(v4))) % 141.21/19.72 | % 141.21/19.72 | ALPHA: (goals) implies: % 141.21/19.72 | (13) $i(zero) % 141.21/19.72 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = % 141.21/19.72 | zero) & domain(v1) = v2 & multiplication(v0, v2) = zero & % 141.21/19.72 | multiplication(v0, v1) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 141.21/19.72 | % 141.21/19.72 | ALPHA: (function-axioms) implies: % 141.21/19.72 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain(v2) = % 141.21/19.72 | v1) | ~ (domain(v2) = v0)) % 141.21/19.72 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 141.21/19.72 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 141.21/19.72 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 141.21/19.72 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 141.21/19.72 | % 141.21/19.72 | DELTA: instantiating (14) with fresh symbols all_20_0, all_20_1, all_20_2, % 141.21/19.72 | all_20_3 gives: % 141.21/19.72 | (18) ~ (all_20_0 = zero) & domain(all_20_2) = all_20_1 & % 141.21/19.72 | multiplication(all_20_3, all_20_1) = zero & multiplication(all_20_3, % 141.21/19.72 | all_20_2) = all_20_0 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & % 141.21/19.72 | $i(all_20_3) % 141.21/19.72 | % 141.21/19.72 | ALPHA: (18) implies: % 141.21/19.72 | (19) ~ (all_20_0 = zero) % 141.21/19.72 | (20) $i(all_20_3) % 141.21/19.72 | (21) $i(all_20_2) % 141.21/19.72 | (22) $i(all_20_1) % 141.21/19.72 | (23) multiplication(all_20_3, all_20_2) = all_20_0 % 141.21/19.72 | (24) multiplication(all_20_3, all_20_1) = zero % 141.21/19.73 | (25) domain(all_20_2) = all_20_1 % 141.21/19.73 | % 141.21/19.73 | GROUND_INST: instantiating (5) with all_20_2, all_20_0, simplifying with (21) % 141.21/19.73 | gives: % 141.21/19.73 | (26) all_20_0 = zero | ~ (multiplication(zero, all_20_2) = all_20_0) % 141.21/19.73 | % 141.21/19.73 | GROUND_INST: instantiating (2) with all_20_3, zero, simplifying with (20) % 141.21/19.73 | gives: % 141.21/19.73 | (27) all_20_3 = zero | ~ (multiplication(all_20_3, one) = zero) % 141.21/19.73 | % 141.21/19.73 | GROUND_INST: instantiating (6) with all_20_3, all_20_1, zero, simplifying with % 141.21/19.73 | (20), (22), (24) gives: % 141.21/19.73 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 & % 141.21/19.73 | domain(all_20_1) = v1 & domain(zero) = v0 & multiplication(all_20_3, % 141.21/19.73 | v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 141.21/19.73 | % 141.21/19.73 | GROUND_INST: instantiating (9) with zero, zero, simplifying with (10), (13) % 141.21/19.73 | gives: % 141.21/19.73 | (29) addition(zero, one) = one % 141.21/19.73 | % 141.21/19.73 | GROUND_INST: instantiating (domain1) with zero, zero, simplifying with (10), % 141.21/19.73 | (13) gives: % 141.21/19.73 | (30) ? [v0: $i] : (multiplication(zero, zero) = v0 & addition(zero, v0) = % 141.21/19.73 | v0 & $i(v0)) % 141.21/19.73 | % 141.21/19.73 | GROUND_INST: instantiating (7) with all_20_3, all_20_2, all_20_1, zero, % 141.21/19.73 | simplifying with (20), (21), (24), (25) gives: % 141.21/19.73 | (31) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(zero) = v1 & % 141.21/19.73 | multiplication(all_20_3, all_20_2) = v0 & $i(v1) & $i(v0)) % 141.21/19.73 | % 141.21/19.73 | DELTA: instantiating (30) with fresh symbol all_30_0 gives: % 141.21/19.73 | (32) multiplication(zero, zero) = all_30_0 & addition(zero, all_30_0) = % 141.21/19.73 | all_30_0 & $i(all_30_0) % 141.21/19.73 | % 141.21/19.73 | ALPHA: (32) implies: % 141.21/19.73 | (33) $i(all_30_0) % 141.21/19.73 | (34) addition(zero, all_30_0) = all_30_0 % 141.21/19.74 | (35) multiplication(zero, zero) = all_30_0 % 141.21/19.74 | % 141.21/19.74 | DELTA: instantiating (31) with fresh symbols all_32_0, all_32_1 gives: % 141.21/19.74 | (36) domain(all_32_1) = all_32_0 & domain(zero) = all_32_0 & % 141.21/19.74 | multiplication(all_20_3, all_20_2) = all_32_1 & $i(all_32_0) & % 141.21/19.74 | $i(all_32_1) % 141.21/19.74 | % 141.21/19.74 | ALPHA: (36) implies: % 141.21/19.74 | (37) $i(all_32_1) % 141.21/19.74 | (38) $i(all_32_0) % 141.21/19.74 | (39) multiplication(all_20_3, all_20_2) = all_32_1 % 141.21/19.74 | (40) domain(zero) = all_32_0 % 141.21/19.74 | (41) domain(all_32_1) = all_32_0 % 141.21/19.74 | % 141.21/19.74 | DELTA: instantiating (28) with fresh symbols all_34_0, all_34_1, all_34_2 % 141.21/19.74 | gives: % 141.21/19.74 | (42) domain(all_34_0) = all_34_2 & domain(all_20_1) = all_34_1 & % 141.21/19.74 | domain(zero) = all_34_2 & multiplication(all_20_3, all_34_1) = % 141.21/19.74 | all_34_0 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) % 141.21/19.74 | % 141.21/19.74 | ALPHA: (42) implies: % 141.21/19.74 | (43) domain(zero) = all_34_2 % 141.21/19.74 | % 141.21/19.74 | BETA: splitting (26) gives: % 141.21/19.74 | % 141.21/19.74 | Case 1: % 141.21/19.74 | | % 141.21/19.74 | | (44) ~ (multiplication(zero, all_20_2) = all_20_0) % 141.21/19.74 | | % 141.21/19.74 | | GROUND_INST: instantiating (17) with all_20_0, all_32_1, all_20_2, all_20_3, % 141.21/19.74 | | simplifying with (23), (39) gives: % 141.21/19.74 | | (45) all_32_1 = all_20_0 % 141.21/19.74 | | % 141.21/19.74 | | GROUND_INST: instantiating (15) with zero, all_34_2, zero, simplifying with % 141.21/19.74 | | (10), (43) gives: % 141.21/19.74 | | (46) all_34_2 = zero % 141.21/19.74 | | % 141.21/19.74 | | GROUND_INST: instantiating (15) with all_32_0, all_34_2, zero, simplifying % 141.21/19.74 | | with (40), (43) gives: % 141.21/19.74 | | (47) all_34_2 = all_32_0 % 141.21/19.74 | | % 141.21/19.74 | | PRED_UNIFY: (23), (44) imply: % 141.21/19.74 | | (48) ~ (all_20_3 = zero) % 141.21/19.74 | | % 141.21/19.74 | | COMBINE_EQS: (46), (47) imply: % 141.21/19.74 | | (49) all_32_0 = zero % 141.21/19.74 | | % 141.21/19.74 | | REDUCE: (41), (45), (49) imply: % 141.21/19.74 | | (50) domain(all_20_0) = zero % 141.21/19.74 | | % 141.21/19.74 | | REDUCE: (37), (45) imply: % 141.21/19.74 | | (51) $i(all_20_0) % 141.21/19.74 | | % 141.21/19.74 | | BETA: splitting (27) gives: % 141.21/19.74 | | % 141.21/19.74 | | Case 1: % 141.21/19.74 | | | % 141.21/19.75 | | | % 141.21/19.75 | | | GROUND_INST: instantiating (11) with zero, one, one, simplifying with (8), % 141.21/19.75 | | | (13), (29) gives: % 141.21/19.75 | | | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(one) = v2 & % 141.21/19.75 | | | domain(one) = v0 & domain(zero) = v1 & addition(v1, v2) = v0 & % 141.21/19.75 | | | $i(v2) & $i(v1) & $i(v0)) % 141.21/19.75 | | | % 141.21/19.75 | | | GROUND_INST: instantiating (11) with zero, all_30_0, all_30_0, simplifying % 141.21/19.75 | | | with (13), (33), (34) gives: % 141.21/19.75 | | | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_30_0) = v2 & % 141.21/19.75 | | | domain(all_30_0) = v0 & domain(zero) = v1 & addition(v1, v2) = % 141.21/19.75 | | | v0 & $i(v2) & $i(v1) & $i(v0)) % 141.21/19.75 | | | % 141.21/19.75 | | | GROUND_INST: instantiating (3) with zero, zero, zero, zero, zero, % 141.21/19.75 | | | simplifying with (13) gives: % 141.21/19.75 | | | (54) ~ (multiplication(zero, zero) = zero) | ~ (addition(zero, zero) % 141.21/19.75 | | | = zero) | ? [v0: $i] : ? [v1: $i] : (multiplication(zero, % 141.21/19.75 | | | zero) = v1 & multiplication(zero, zero) = v0 & addition(v0, % 141.21/19.75 | | | v1) = zero & $i(v1) & $i(v0)) % 141.21/19.75 | | | % 141.21/19.75 | | | GROUND_INST: instantiating (3) with zero, zero, zero, zero, all_30_0, % 141.21/19.75 | | | simplifying with (13), (35) gives: % 141.21/19.75 | | | (55) ~ (addition(zero, zero) = zero) | ? [v0: $i] : ? [v1: $i] : % 141.21/19.75 | | | (multiplication(zero, zero) = v1 & multiplication(zero, zero) = v0 % 141.21/19.75 | | | & addition(v0, v1) = all_30_0 & $i(v1) & $i(v0) & $i(all_30_0)) % 141.21/19.75 | | | % 141.21/19.75 | | | GROUND_INST: instantiating (7) with zero, zero, zero, all_30_0, % 141.21/19.75 | | | simplifying with (10), (13), (35) gives: % 141.21/19.76 | | | (56) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_30_0) = % 141.21/19.76 | | | v1 & multiplication(zero, zero) = v0 & $i(v1) & $i(v0)) % 141.21/19.76 | | | % 141.21/19.76 | | | GROUND_INST: instantiating (4) with zero, all_30_0, simplifying with (13), % 141.21/19.76 | | | (35) gives: % 141.21/19.76 | | | (57) all_30_0 = zero % 141.21/19.76 | | | % 141.21/19.76 | | | GROUND_INST: instantiating (6) with zero, zero, all_30_0, simplifying with % 141.21/19.76 | | | (13), (35) gives: % 141.21/19.76 | | | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 & % 141.21/19.76 | | | domain(all_30_0) = v0 & domain(zero) = v1 & multiplication(zero, % 141.21/19.76 | | | v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 141.21/19.76 | | | % 141.21/19.76 | | | GROUND_INST: instantiating (12) with all_20_0, zero, zero, zero, zero, % 141.21/19.76 | | | simplifying with (10), (13), (50), (51) gives: % 141.21/19.76 | | | (59) ~ (addition(zero, zero) = zero) | ? [v0: $i] : (domain(v0) = % 141.21/19.76 | | | zero & addition(all_20_0, zero) = v0 & $i(v0)) % 141.21/19.76 | | | % 141.21/19.76 | | | GROUND_INST: instantiating (7) with zero, all_20_0, zero, all_30_0, % 141.21/19.76 | | | simplifying with (13), (35), (50), (51) gives: % 141.21/19.76 | | | (60) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_30_0) = % 141.21/19.76 | | | v1 & multiplication(zero, all_20_0) = v0 & $i(v1) & $i(v0)) % 141.21/19.76 | | | % 141.21/19.76 | | | GROUND_INST: instantiating (domain1) with all_20_0, zero, simplifying with % 141.21/19.76 | | | (50), (51) gives: % 141.21/19.76 | | | (61) ? [v0: $i] : (multiplication(zero, all_20_0) = v0 & % 141.21/19.76 | | | addition(all_20_0, v0) = v0 & $i(v0)) % 141.21/19.76 | | | % 141.21/19.76 | | | DELTA: instantiating (61) with fresh symbol all_78_0 gives: % 141.21/19.76 | | | (62) multiplication(zero, all_20_0) = all_78_0 & addition(all_20_0, % 141.21/19.77 | | | all_78_0) = all_78_0 & $i(all_78_0) % 141.21/19.77 | | | % 141.21/19.77 | | | ALPHA: (62) implies: % 141.21/19.77 | | | (63) addition(all_20_0, all_78_0) = all_78_0 % 141.71/19.77 | | | (64) multiplication(zero, all_20_0) = all_78_0 % 141.71/19.77 | | | % 141.71/19.77 | | | DELTA: instantiating (56) with fresh symbols all_94_0, all_94_1 gives: % 141.71/19.77 | | | (65) domain(all_94_1) = all_94_0 & domain(all_30_0) = all_94_0 & % 141.71/19.77 | | | multiplication(zero, zero) = all_94_1 & $i(all_94_0) & % 141.71/19.77 | | | $i(all_94_1) % 141.71/19.77 | | | % 141.71/19.77 | | | ALPHA: (65) implies: % 141.71/19.77 | | | (66) multiplication(zero, zero) = all_94_1 % 141.71/19.77 | | | % 141.71/19.77 | | | DELTA: instantiating (60) with fresh symbols all_98_0, all_98_1 gives: % 141.71/19.77 | | | (67) domain(all_98_1) = all_98_0 & domain(all_30_0) = all_98_0 & % 141.71/19.77 | | | multiplication(zero, all_20_0) = all_98_1 & $i(all_98_0) & % 141.71/19.77 | | | $i(all_98_1) % 141.71/19.77 | | | % 141.71/19.77 | | | ALPHA: (67) implies: % 141.71/19.77 | | | (68) multiplication(zero, all_20_0) = all_98_1 % 141.71/19.77 | | | (69) domain(all_30_0) = all_98_0 % 141.71/19.77 | | | % 141.71/19.77 | | | DELTA: instantiating (58) with fresh symbols all_100_0, all_100_1, % 141.71/19.77 | | | all_100_2 gives: % 141.71/19.77 | | | (70) domain(all_100_0) = all_100_2 & domain(all_30_0) = all_100_2 & % 141.71/19.77 | | | domain(zero) = all_100_1 & multiplication(zero, all_100_1) = % 141.71/19.77 | | | all_100_0 & $i(all_100_0) & $i(all_100_1) & $i(all_100_2) % 141.71/19.77 | | | % 141.71/19.77 | | | ALPHA: (70) implies: % 141.71/19.77 | | | (71) multiplication(zero, all_100_1) = all_100_0 % 141.71/19.77 | | | (72) domain(zero) = all_100_1 % 141.71/19.77 | | | (73) domain(all_30_0) = all_100_2 % 141.71/19.77 | | | % 141.71/19.77 | | | DELTA: instantiating (53) with fresh symbols all_104_0, all_104_1, % 141.71/19.77 | | | all_104_2 gives: % 141.71/19.77 | | | (74) domain(all_30_0) = all_104_0 & domain(all_30_0) = all_104_2 & % 141.71/19.77 | | | domain(zero) = all_104_1 & addition(all_104_1, all_104_0) = % 141.71/19.77 | | | all_104_2 & $i(all_104_0) & $i(all_104_1) & $i(all_104_2) % 141.71/19.77 | | | % 141.71/19.77 | | | ALPHA: (74) implies: % 141.71/19.77 | | | (75) domain(zero) = all_104_1 % 141.71/19.77 | | | (76) domain(all_30_0) = all_104_2 % 141.71/19.77 | | | % 141.71/19.77 | | | DELTA: instantiating (52) with fresh symbols all_106_0, all_106_1, % 141.71/19.77 | | | all_106_2 gives: % 141.71/19.77 | | | (77) domain(one) = all_106_0 & domain(one) = all_106_2 & domain(zero) = % 141.71/19.77 | | | all_106_1 & addition(all_106_1, all_106_0) = all_106_2 & % 141.71/19.77 | | | $i(all_106_0) & $i(all_106_1) & $i(all_106_2) % 141.71/19.78 | | | % 141.71/19.78 | | | ALPHA: (77) implies: % 141.71/19.78 | | | (78) domain(zero) = all_106_1 % 141.71/19.78 | | | % 141.71/19.78 | | | REDUCE: (57), (76) imply: % 141.71/19.78 | | | (79) domain(zero) = all_104_2 % 141.71/19.78 | | | % 141.71/19.78 | | | REDUCE: (57), (73) imply: % 141.71/19.78 | | | (80) domain(zero) = all_100_2 % 141.71/19.78 | | | % 141.71/19.78 | | | REDUCE: (57), (69) imply: % 141.71/19.78 | | | (81) domain(zero) = all_98_0 % 141.71/19.78 | | | % 141.71/19.78 | | | REDUCE: (35), (57) imply: % 141.71/19.78 | | | (82) multiplication(zero, zero) = zero % 141.71/19.78 | | | % 141.71/19.78 | | | REDUCE: (34), (57) imply: % 141.71/19.78 | | | (83) addition(zero, zero) = zero % 141.71/19.78 | | | % 141.71/19.78 | | | BETA: splitting (59) gives: % 141.71/19.78 | | | % 141.71/19.78 | | | Case 1: % 141.71/19.78 | | | | % 141.71/19.78 | | | | (84) ~ (addition(zero, zero) = zero) % 141.71/19.78 | | | | % 141.71/19.78 | | | | PRED_UNIFY: (83), (84) imply: % 141.71/19.78 | | | | (85) $false % 141.71/19.78 | | | | % 141.71/19.78 | | | | CLOSE: (85) is inconsistent. % 141.71/19.78 | | | | % 141.71/19.78 | | | Case 2: % 141.71/19.78 | | | | % 141.71/19.78 | | | | (86) ? [v0: $i] : (domain(v0) = zero & addition(all_20_0, zero) = v0 % 141.71/19.78 | | | | & $i(v0)) % 141.71/19.78 | | | | % 141.71/19.78 | | | | DELTA: instantiating (86) with fresh symbol all_131_0 gives: % 141.71/19.78 | | | | (87) domain(all_131_0) = zero & addition(all_20_0, zero) = all_131_0 % 141.71/19.78 | | | | & $i(all_131_0) % 141.71/19.78 | | | | % 141.71/19.78 | | | | ALPHA: (87) implies: % 141.71/19.78 | | | | (88) addition(all_20_0, zero) = all_131_0 % 141.71/19.78 | | | | % 141.71/19.78 | | | | BETA: splitting (55) gives: % 141.71/19.78 | | | | % 141.71/19.78 | | | | Case 1: % 141.71/19.78 | | | | | % 141.71/19.78 | | | | | (89) ~ (addition(zero, zero) = zero) % 141.71/19.78 | | | | | % 141.71/19.78 | | | | | PRED_UNIFY: (83), (89) imply: % 141.71/19.78 | | | | | (90) $false % 141.71/19.78 | | | | | % 141.71/19.78 | | | | | CLOSE: (90) is inconsistent. % 141.71/19.78 | | | | | % 141.71/19.78 | | | | Case 2: % 141.71/19.78 | | | | | % 141.71/19.79 | | | | | (91) ? [v0: $i] : ? [v1: $i] : (multiplication(zero, zero) = v1 & % 141.71/19.79 | | | | | multiplication(zero, zero) = v0 & addition(v0, v1) = % 141.71/19.79 | | | | | all_30_0 & $i(v1) & $i(v0) & $i(all_30_0)) % 141.71/19.79 | | | | | % 141.71/19.79 | | | | | DELTA: instantiating (91) with fresh symbols all_143_0, all_143_1 % 141.71/19.79 | | | | | gives: % 141.71/19.79 | | | | | (92) multiplication(zero, zero) = all_143_0 & multiplication(zero, % 141.71/19.79 | | | | | zero) = all_143_1 & addition(all_143_1, all_143_0) = % 141.71/19.79 | | | | | all_30_0 & $i(all_143_0) & $i(all_143_1) & $i(all_30_0) % 141.71/19.79 | | | | | % 141.71/19.79 | | | | | ALPHA: (92) implies: % 141.71/19.79 | | | | | (93) multiplication(zero, zero) = all_143_1 % 141.71/19.79 | | | | | (94) multiplication(zero, zero) = all_143_0 % 141.71/19.79 | | | | | % 141.71/19.79 | | | | | BETA: splitting (54) gives: % 141.71/19.79 | | | | | % 141.71/19.79 | | | | | Case 1: % 141.71/19.79 | | | | | | % 141.71/19.79 | | | | | | (95) ~ (multiplication(zero, zero) = zero) % 141.71/19.79 | | | | | | % 141.71/19.79 | | | | | | PRED_UNIFY: (82), (95) imply: % 141.71/19.79 | | | | | | (96) $false % 141.71/19.79 | | | | | | % 141.71/19.79 | | | | | | CLOSE: (96) is inconsistent. % 141.71/19.79 | | | | | | % 141.71/19.79 | | | | | Case 2: % 141.71/19.79 | | | | | | % 141.71/19.79 | | | | | | (97) ~ (addition(zero, zero) = zero) | ? [v0: $i] : ? [v1: $i] % 141.71/19.79 | | | | | | : (multiplication(zero, zero) = v1 & multiplication(zero, % 141.71/19.79 | | | | | | zero) = v0 & addition(v0, v1) = zero & $i(v1) & $i(v0)) % 141.71/19.79 | | | | | | % 141.71/19.79 | | | | | | BETA: splitting (97) gives: % 141.71/19.79 | | | | | | % 141.71/19.79 | | | | | | Case 1: % 141.71/19.79 | | | | | | | % 141.71/19.79 | | | | | | | (98) ~ (addition(zero, zero) = zero) % 141.71/19.79 | | | | | | | % 141.71/19.79 | | | | | | | PRED_UNIFY: (83), (98) imply: % 141.71/19.79 | | | | | | | (99) $false % 141.71/19.79 | | | | | | | % 141.71/19.79 | | | | | | | CLOSE: (99) is inconsistent. % 141.71/19.79 | | | | | | | % 141.71/19.79 | | | | | | Case 2: % 141.71/19.79 | | | | | | | % 141.71/19.79 | | | | | | | (100) ? [v0: $i] : ? [v1: $i] : (multiplication(zero, zero) = % 141.71/19.79 | | | | | | | v1 & multiplication(zero, zero) = v0 & addition(v0, v1) % 141.71/19.79 | | | | | | | = zero & $i(v1) & $i(v0)) % 141.71/19.79 | | | | | | | % 141.71/19.79 | | | | | | | DELTA: instantiating (100) with fresh symbols all_188_0, all_188_1 % 141.71/19.79 | | | | | | | gives: % 141.71/19.79 | | | | | | | (101) multiplication(zero, zero) = all_188_0 & % 141.71/19.79 | | | | | | | multiplication(zero, zero) = all_188_1 & % 141.71/19.79 | | | | | | | addition(all_188_1, all_188_0) = zero & $i(all_188_0) & % 141.71/19.79 | | | | | | | $i(all_188_1) % 141.71/19.79 | | | | | | | % 141.71/19.79 | | | | | | | ALPHA: (101) implies: % 141.71/19.79 | | | | | | | (102) multiplication(zero, zero) = all_188_1 % 141.71/19.79 | | | | | | | (103) multiplication(zero, zero) = all_188_0 % 141.71/19.79 | | | | | | | % 141.71/19.79 | | | | | | | GROUND_INST: instantiating (16) with all_131_0, zero, zero, % 141.71/19.79 | | | | | | | all_20_0, simplifying with (88) gives: % 141.71/19.80 | | | | | | | (104) all_131_0 = zero | ~ (addition(all_20_0, zero) = zero) % 141.71/19.80 | | | | | | | % 141.71/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_94_1, all_143_1, zero, % 141.71/19.80 | | | | | | | zero, simplifying with (66), (93) gives: % 141.71/19.80 | | | | | | | (105) all_143_1 = all_94_1 % 141.71/19.80 | | | | | | | % 141.71/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_143_1, all_143_0, zero, % 141.71/19.80 | | | | | | | zero, simplifying with (93), (94) gives: % 141.85/19.80 | | | | | | | (106) all_143_0 = all_143_1 % 141.85/19.80 | | | | | | | % 141.85/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_143_0, all_188_1, zero, % 141.85/19.80 | | | | | | | zero, simplifying with (94), (102) gives: % 141.85/19.80 | | | | | | | (107) all_188_1 = all_143_0 % 141.85/19.80 | | | | | | | % 141.85/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_188_1, all_188_0, zero, % 141.85/19.80 | | | | | | | zero, simplifying with (102), (103) gives: % 141.85/19.80 | | | | | | | (108) all_188_0 = all_188_1 % 141.85/19.80 | | | | | | | % 141.85/19.80 | | | | | | | GROUND_INST: instantiating (17) with zero, all_188_0, zero, zero, % 141.85/19.80 | | | | | | | simplifying with (82), (103) gives: % 141.85/19.80 | | | | | | | (109) all_188_0 = zero % 141.85/19.80 | | | | | | | % 141.85/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_78_0, all_98_1, all_20_0, % 141.85/19.80 | | | | | | | zero, simplifying with (64), (68) gives: % 141.85/19.80 | | | | | | | (110) all_98_1 = all_78_0 % 141.85/19.80 | | | | | | | % 141.85/19.80 | | | | | | | GROUND_INST: instantiating (17) with all_100_0, zero, all_100_1, % 141.85/19.80 | | | | | | | zero, simplifying with (71) gives: % 141.85/19.80 | | | | | | | (111) all_100_0 = zero | ~ (multiplication(zero, all_100_1) = % 141.85/19.80 | | | | | | | zero) % 141.85/19.80 | | | | | | | % 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with zero, all_104_2, zero, % 141.85/19.80 | | | | | | | simplifying with (10), (79) gives: % 141.85/19.80 | | | | | | | (112) all_104_2 = zero % 141.85/19.80 | | | | | | | % 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with all_100_2, all_104_1, zero, % 141.85/19.80 | | | | | | | simplifying with (75), (80) gives: % 141.85/19.80 | | | | | | | (113) all_104_1 = all_100_2 % 141.85/19.80 | | | | | | | % 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with all_104_1, all_106_1, zero, % 141.85/19.80 | | | | | | | simplifying with (75), (78) gives: % 141.85/19.80 | | | | | | | (114) all_106_1 = all_104_1 % 141.85/19.80 | | | | | | | % 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with all_104_2, all_106_1, zero, % 141.85/19.80 | | | | | | | simplifying with (78), (79) gives: % 141.85/19.80 | | | | | | | (115) all_106_1 = all_104_2 % 141.85/19.80 | | | | | | | % 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with all_100_1, all_106_1, zero, % 141.85/19.80 | | | | | | | simplifying with (72), (78) gives: % 141.85/19.80 | | | | | | | (116) all_106_1 = all_100_1 % 141.85/19.80 | | | | | | | % 141.85/19.80 | | | | | | | GROUND_INST: instantiating (15) with all_98_0, all_106_1, zero, % 141.85/19.80 | | | | | | | simplifying with (78), (81) gives: % 141.85/19.80 | | | | | | | (117) all_106_1 = all_98_0 % 141.85/19.80 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (108), (109) imply: % 141.85/19.81 | | | | | | | (118) all_188_1 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | SIMP: (118) implies: % 141.85/19.81 | | | | | | | (119) all_188_1 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (107), (119) imply: % 141.85/19.81 | | | | | | | (120) all_143_0 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | SIMP: (120) implies: % 141.85/19.81 | | | | | | | (121) all_143_0 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (106), (121) imply: % 141.85/19.81 | | | | | | | (122) all_143_1 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | SIMP: (122) implies: % 141.85/19.81 | | | | | | | (123) all_143_1 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (105), (123) imply: % 141.85/19.81 | | | | | | | (124) all_94_1 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | SIMP: (124) implies: % 141.85/19.81 | | | | | | | (125) all_94_1 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (115), (116) imply: % 141.85/19.81 | | | | | | | (126) all_104_2 = all_100_1 % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | SIMP: (126) implies: % 141.85/19.81 | | | | | | | (127) all_104_2 = all_100_1 % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (114), (116) imply: % 141.85/19.81 | | | | | | | (128) all_104_1 = all_100_1 % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | SIMP: (128) implies: % 141.85/19.81 | | | | | | | (129) all_104_1 = all_100_1 % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (116), (117) imply: % 141.85/19.81 | | | | | | | (130) all_100_1 = all_98_0 % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (113), (129) imply: % 141.85/19.81 | | | | | | | (131) all_100_1 = all_100_2 % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | SIMP: (131) implies: % 141.85/19.81 | | | | | | | (132) all_100_1 = all_100_2 % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (112), (127) imply: % 141.85/19.81 | | | | | | | (133) all_100_1 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | SIMP: (133) implies: % 141.85/19.81 | | | | | | | (134) all_100_1 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (132), (134) imply: % 141.85/19.81 | | | | | | | (135) all_100_2 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (130), (132) imply: % 141.85/19.81 | | | | | | | (136) all_100_2 = all_98_0 % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | COMBINE_EQS: (135), (136) imply: % 141.85/19.81 | | | | | | | (137) all_98_0 = zero % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | BETA: splitting (111) gives: % 141.85/19.81 | | | | | | | % 141.85/19.81 | | | | | | | Case 1: % 141.85/19.81 | | | | | | | | % 141.85/19.81 | | | | | | | | (138) ~ (multiplication(zero, all_100_1) = zero) % 141.85/19.81 | | | | | | | | % 141.85/19.81 | | | | | | | | REDUCE: (134), (138) imply: % 141.85/19.81 | | | | | | | | (139) ~ (multiplication(zero, zero) = zero) % 141.85/19.81 | | | | | | | | % 141.85/19.81 | | | | | | | | PRED_UNIFY: (82), (139) imply: % 141.85/19.81 | | | | | | | | (140) $false % 141.85/19.81 | | | | | | | | % 141.85/19.81 | | | | | | | | CLOSE: (140) is inconsistent. % 141.85/19.81 | | | | | | | | % 141.85/19.81 | | | | | | | Case 2: % 141.85/19.81 | | | | | | | | % 141.85/19.81 | | | | | | | | % 141.85/19.81 | | | | | | | | GROUND_INST: instantiating (1) with all_20_0, all_131_0, % 141.85/19.81 | | | | | | | | simplifying with (51), (88) gives: % 141.85/19.82 | | | | | | | | (141) all_131_0 = all_20_0 % 141.85/19.82 | | | | | | | | % 141.85/19.82 | | | | | | | | GROUND_INST: instantiating (5) with all_20_0, all_78_0, % 141.85/19.82 | | | | | | | | simplifying with (51), (64) gives: % 141.85/19.82 | | | | | | | | (142) all_78_0 = zero % 141.85/19.82 | | | | | | | | % 141.85/19.82 | | | | | | | | REDUCE: (63), (142) imply: % 141.85/19.82 | | | | | | | | (143) addition(all_20_0, zero) = zero % 141.85/19.82 | | | | | | | | % 141.85/19.82 | | | | | | | | BETA: splitting (104) gives: % 141.85/19.82 | | | | | | | | % 141.85/19.82 | | | | | | | | Case 1: % 141.85/19.82 | | | | | | | | | % 141.85/19.82 | | | | | | | | | (144) ~ (addition(all_20_0, zero) = zero) % 141.85/19.82 | | | | | | | | | % 141.85/19.82 | | | | | | | | | PRED_UNIFY: (143), (144) imply: % 141.85/19.82 | | | | | | | | | (145) $false % 141.85/19.82 | | | | | | | | | % 141.85/19.82 | | | | | | | | | CLOSE: (145) is inconsistent. % 141.85/19.82 | | | | | | | | | % 141.85/19.82 | | | | | | | | Case 2: % 141.85/19.82 | | | | | | | | | % 141.85/19.82 | | | | | | | | | (146) all_131_0 = zero % 141.85/19.82 | | | | | | | | | % 141.85/19.82 | | | | | | | | | COMBINE_EQS: (141), (146) imply: % 141.85/19.82 | | | | | | | | | (147) all_20_0 = zero % 141.85/19.82 | | | | | | | | | % 141.85/19.82 | | | | | | | | | SIMP: (147) implies: % 141.85/19.82 | | | | | | | | | (148) all_20_0 = zero % 141.85/19.82 | | | | | | | | | % 141.85/19.82 | | | | | | | | | REDUCE: (19), (148) imply: % 141.85/19.82 | | | | | | | | | (149) $false % 141.85/19.82 | | | | | | | | | % 141.85/19.82 | | | | | | | | | CLOSE: (149) is inconsistent. % 141.85/19.82 | | | | | | | | | % 141.85/19.82 | | | | | | | | End of split % 141.85/19.82 | | | | | | | | % 141.85/19.82 | | | | | | | End of split % 141.85/19.82 | | | | | | | % 141.85/19.82 | | | | | | End of split % 141.85/19.82 | | | | | | % 141.85/19.82 | | | | | End of split % 141.85/19.82 | | | | | % 141.85/19.82 | | | | End of split % 141.85/19.82 | | | | % 141.85/19.82 | | | End of split % 141.85/19.82 | | | % 141.85/19.82 | | Case 2: % 141.85/19.82 | | | % 141.85/19.82 | | | (150) all_20_3 = zero % 141.85/19.82 | | | % 141.85/19.82 | | | REDUCE: (48), (150) imply: % 141.85/19.82 | | | (151) $false % 141.85/19.82 | | | % 141.85/19.82 | | | CLOSE: (151) is inconsistent. % 141.85/19.82 | | | % 141.85/19.82 | | End of split % 141.85/19.82 | | % 141.85/19.82 | Case 2: % 141.85/19.82 | | % 141.85/19.82 | | (152) all_20_0 = zero % 141.85/19.82 | | % 141.85/19.82 | | REDUCE: (19), (152) imply: % 141.85/19.82 | | (153) $false % 141.85/19.82 | | % 141.85/19.82 | | CLOSE: (153) is inconsistent. % 141.85/19.82 | | % 141.85/19.82 | End of split % 141.85/19.82 | % 141.85/19.82 End of proof % 141.85/19.82 % SZS output end Proof for theBenchmark % 141.85/19.82 % 141.85/19.82 19340ms %------------------------------------------------------------------------------