%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE035+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 : n022.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 05:34:19 EDT 2023 % Result : Theorem 8.14s 1.81s % Output : Proof 13.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : KLE035+1 : TPTP v8.1.2. Released v4.0.0. % 0.14/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n022.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 11:49:38 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.15/1.03 Prover 4: Preprocessing ... % 2.15/1.03 Prover 1: Preprocessing ... % 2.81/1.07 Prover 3: Preprocessing ... % 2.81/1.07 Prover 0: Preprocessing ... % 2.81/1.07 Prover 2: Preprocessing ... % 2.81/1.07 Prover 6: Preprocessing ... % 2.81/1.07 Prover 5: Preprocessing ... % 4.94/1.40 Prover 1: Constructing countermodel ... % 4.94/1.41 Prover 6: Proving ... % 4.94/1.42 Prover 3: Constructing countermodel ... % 4.94/1.43 Prover 5: Proving ... % 5.62/1.46 Prover 0: Proving ... % 5.62/1.46 Prover 4: Constructing countermodel ... % 6.34/1.56 Prover 2: Proving ... % 8.14/1.81 Prover 0: proved (1166ms) % 8.14/1.81 % 8.14/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.14/1.81 % 8.14/1.81 Prover 3: stopped % 8.14/1.82 Prover 2: stopped % 8.14/1.82 Prover 5: stopped % 8.14/1.83 Prover 6: stopped % 8.14/1.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.14/1.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.14/1.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.14/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.14/1.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.57/1.86 Prover 8: Preprocessing ... % 8.57/1.87 Prover 11: Preprocessing ... % 8.57/1.87 Prover 13: Preprocessing ... % 8.57/1.88 Prover 7: Preprocessing ... % 8.57/1.89 Prover 10: Preprocessing ... % 8.81/1.93 Prover 8: Warning: ignoring some quantifiers % 8.81/1.94 Prover 8: Constructing countermodel ... % 9.46/1.98 Prover 13: Warning: ignoring some quantifiers % 9.46/1.99 Prover 10: Constructing countermodel ... % 9.46/1.99 Prover 7: Constructing countermodel ... % 9.46/2.00 Prover 13: Constructing countermodel ... % 9.78/2.02 Prover 11: Constructing countermodel ... % 9.98/2.09 Prover 10: gave up % 9.98/2.10 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.98/2.11 Prover 16: Preprocessing ... % 11.01/2.21 Prover 16: Warning: ignoring some quantifiers % 11.01/2.23 Prover 16: Constructing countermodel ... % 12.14/2.34 Prover 13: gave up % 12.33/2.35 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.33/2.37 Prover 19: Preprocessing ... % 12.95/2.43 Prover 11: Found proof (size 83) % 12.95/2.43 Prover 11: proved (593ms) % 12.95/2.43 Prover 7: stopped % 12.95/2.43 Prover 8: stopped % 12.95/2.43 Prover 4: stopped % 12.95/2.43 Prover 1: stopped % 12.95/2.43 Prover 16: stopped % 12.95/2.43 Prover 19: Warning: ignoring some quantifiers % 12.95/2.44 Prover 19: Constructing countermodel ... % 12.95/2.44 Prover 19: stopped % 12.95/2.44 % 12.95/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.95/2.44 % 12.95/2.45 % SZS output start Proof for theBenchmark % 12.95/2.45 Assumptions after simplification: % 12.95/2.45 --------------------------------- % 12.95/2.45 % 12.95/2.45 (additive_associativity) % 12.95/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 12.95/2.48 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 12.95/2.48 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 & % 12.95/2.48 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 12.95/2.48 : ! [v4: $i] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ % 12.95/2.48 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 & % 12.95/2.48 addition(v2, v1) = v5 & $i(v5) & $i(v4))) % 12.95/2.48 % 12.95/2.48 (additive_commutativity) % 12.95/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~ % 12.95/2.48 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 12.95/2.48 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 12.95/2.48 (addition(v1, v0) = v2 & $i(v2))) % 12.95/2.48 % 12.95/2.48 (additive_identity) % 12.95/2.48 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) % 12.95/2.48 | ~ $i(v0)) % 12.95/2.48 % 12.95/2.48 (goals) % 12.95/2.48 $i(zero) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 12.95/2.48 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 12.95/2.48 [v10: $i] : ? [v11: $i] : ? [v12: int] : ( ~ (v12 = 0) & c(v3) = v5 & % 12.95/2.48 test(v3) = 0 & test(v2) = 0 & leq(v11, zero) = v12 & leq(v8, zero) = 0 & % 12.95/2.48 leq(v6, zero) = 0 & multiplication(v10, v5) = v11 & multiplication(v7, v5) = % 12.95/2.48 v8 & multiplication(v4, v5) = v6 & multiplication(v2, v9) = v10 & % 12.95/2.48 multiplication(v2, v1) = v7 & multiplication(v2, v0) = v4 & addition(v0, v1) % 12.95/2.48 = v9 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 12.95/2.48 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.95/2.48 % 12.95/2.48 (left_distributivity) % 12.95/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 12.95/2.49 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | % 12.95/2.49 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 12.95/2.49 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) & % 12.95/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 12.95/2.49 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~ % 12.95/2.49 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) = % 12.95/2.49 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5) % 12.95/2.49 & $i(v4))) % 12.95/2.49 % 12.95/2.49 (multiplicative_associativity) % 12.95/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 12.95/2.49 (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ $i(v2) % 12.95/2.49 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, v2) = v5 & % 12.95/2.49 multiplication(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: % 12.95/2.49 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (multiplication(v1, v2) % 12.95/2.49 = v3) | ~ (multiplication(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 12.95/2.49 $i(v0) | ? [v5: $i] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) % 12.95/2.49 = v5 & $i(v5) & $i(v4))) % 12.95/2.49 % 12.95/2.49 (order) % 12.95/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) = % 12.95/2.49 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) = % 12.95/2.49 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, % 12.95/2.49 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) & % 12.95/2.49 addition(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 12.95/2.49 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | addition(v0, v1) = v1) & ! [v0: % 12.95/2.49 $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) | % 12.95/2.49 leq(v0, v1) = 0) % 12.95/2.49 % 12.95/2.49 (right_distributivity) % 12.95/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 12.95/2.49 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | % 12.95/2.49 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 12.95/2.49 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) & % 12.95/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 12.95/2.49 (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ $i(v2) | ~ % 12.95/2.49 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v0, v2) = % 12.95/2.49 v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5) % 12.95/2.49 & $i(v4))) % 12.95/2.49 % 12.95/2.49 (function-axioms) % 12.95/2.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.95/2.49 [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) = % 12.95/2.49 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.95/2.49 $i] : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 12.95/2.49 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 12.95/2.49 ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! % 12.95/2.49 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.95/2.49 (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! % 12.95/2.49 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & ! % 12.95/2.49 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 12.95/2.49 | ~ (test(v2) = v1) | ~ (test(v2) = v0)) % 12.95/2.49 % 12.95/2.49 Further assumptions not needed in the proof: % 12.95/2.49 -------------------------------------------- % 12.95/2.49 additive_idempotence, left_annihilation, multiplicative_left_identity, % 12.95/2.49 multiplicative_right_identity, right_annihilation, test_1, test_2, test_3, % 12.95/2.49 test_4 % 12.95/2.49 % 12.95/2.49 Those formulas are unsatisfiable: % 12.95/2.49 --------------------------------- % 12.95/2.49 % 12.95/2.49 Begin of proof % 12.95/2.50 | % 12.95/2.50 | ALPHA: (additive_commutativity) implies: % 12.95/2.50 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | % 12.95/2.50 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) % 12.95/2.50 | % 12.95/2.50 | ALPHA: (additive_associativity) implies: % 12.95/2.50 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 12.95/2.50 | ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ $i(v2) | % 12.95/2.50 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 & % 12.95/2.50 | addition(v2, v1) = v5 & $i(v5) & $i(v4))) % 12.95/2.50 | % 12.95/2.50 | ALPHA: (additive_identity) implies: % 12.95/2.50 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) | % 12.95/2.50 | ~ $i(v0)) % 12.95/2.50 | % 12.95/2.50 | ALPHA: (multiplicative_associativity) implies: % 12.95/2.50 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 12.95/2.50 | ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | % 12.95/2.50 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, % 12.95/2.50 | v2) = v5 & multiplication(v0, v5) = v4 & $i(v5) & $i(v4))) % 12.95/2.50 | % 12.95/2.50 | ALPHA: (right_distributivity) implies: % 12.95/2.50 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 12.95/2.50 | ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ % 12.95/2.50 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 12.95/2.50 | (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & % 12.95/2.50 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 12.95/2.50 | % 12.95/2.50 | ALPHA: (left_distributivity) implies: % 12.95/2.50 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 12.95/2.50 | ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ % 12.95/2.50 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 12.95/2.50 | (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & % 12.95/2.50 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 12.95/2.50 | % 12.95/2.50 | ALPHA: (order) implies: % 12.95/2.50 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v0, v1) = 0) | ~ $i(v1) | ~ % 12.95/2.50 | $i(v0) | addition(v0, v1) = v1) % 12.95/2.50 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) = % 12.95/2.50 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) & % 12.95/2.50 | addition(v0, v1) = v3 & $i(v3))) % 12.95/2.50 | % 12.95/2.50 | ALPHA: (goals) implies: % 12.95/2.50 | (9) $i(zero) % 12.95/2.51 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.95/2.51 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 12.95/2.51 | ? [v10: $i] : ? [v11: $i] : ? [v12: int] : ( ~ (v12 = 0) & c(v3) = % 12.95/2.51 | v5 & test(v3) = 0 & test(v2) = 0 & leq(v11, zero) = v12 & leq(v8, % 12.95/2.51 | zero) = 0 & leq(v6, zero) = 0 & multiplication(v10, v5) = v11 & % 12.95/2.51 | multiplication(v7, v5) = v8 & multiplication(v4, v5) = v6 & % 12.95/2.51 | multiplication(v2, v9) = v10 & multiplication(v2, v1) = v7 & % 12.95/2.51 | multiplication(v2, v0) = v4 & addition(v0, v1) = v9 & $i(v11) & % 12.95/2.51 | $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 12.95/2.51 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.95/2.51 | % 12.95/2.51 | ALPHA: (function-axioms) implies: % 12.95/2.51 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.95/2.51 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 12.95/2.51 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.95/2.51 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 12.95/2.51 | % 12.95/2.51 | DELTA: instantiating (10) with fresh symbols all_20_0, all_20_1, all_20_2, % 12.95/2.51 | all_20_3, all_20_4, all_20_5, all_20_6, all_20_7, all_20_8, all_20_9, % 12.95/2.51 | all_20_10, all_20_11, all_20_12 gives: % 12.95/2.51 | (13) ~ (all_20_0 = 0) & c(all_20_9) = all_20_7 & test(all_20_9) = 0 & % 12.95/2.51 | test(all_20_10) = 0 & leq(all_20_1, zero) = all_20_0 & leq(all_20_4, % 12.95/2.51 | zero) = 0 & leq(all_20_6, zero) = 0 & multiplication(all_20_2, % 12.95/2.51 | all_20_7) = all_20_1 & multiplication(all_20_5, all_20_7) = all_20_4 % 12.95/2.51 | & multiplication(all_20_8, all_20_7) = all_20_6 & % 12.95/2.51 | multiplication(all_20_10, all_20_3) = all_20_2 & % 12.95/2.51 | multiplication(all_20_10, all_20_11) = all_20_5 & % 12.95/2.51 | multiplication(all_20_10, all_20_12) = all_20_8 & addition(all_20_12, % 12.95/2.51 | all_20_11) = all_20_3 & $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & % 12.95/2.51 | $i(all_20_4) & $i(all_20_5) & $i(all_20_6) & $i(all_20_7) & % 12.95/2.51 | $i(all_20_8) & $i(all_20_9) & $i(all_20_10) & $i(all_20_11) & % 12.95/2.51 | $i(all_20_12) % 12.95/2.51 | % 12.95/2.51 | ALPHA: (13) implies: % 12.95/2.51 | (14) ~ (all_20_0 = 0) % 12.95/2.51 | (15) $i(all_20_12) % 12.95/2.51 | (16) $i(all_20_11) % 12.95/2.51 | (17) $i(all_20_10) % 12.95/2.51 | (18) $i(all_20_7) % 12.95/2.51 | (19) $i(all_20_6) % 12.95/2.51 | (20) $i(all_20_4) % 12.95/2.51 | (21) $i(all_20_1) % 12.95/2.51 | (22) addition(all_20_12, all_20_11) = all_20_3 % 12.95/2.51 | (23) multiplication(all_20_10, all_20_12) = all_20_8 % 12.95/2.51 | (24) multiplication(all_20_10, all_20_11) = all_20_5 % 12.95/2.51 | (25) multiplication(all_20_10, all_20_3) = all_20_2 % 12.95/2.51 | (26) multiplication(all_20_8, all_20_7) = all_20_6 % 12.95/2.51 | (27) multiplication(all_20_5, all_20_7) = all_20_4 % 12.95/2.51 | (28) multiplication(all_20_2, all_20_7) = all_20_1 % 12.95/2.51 | (29) leq(all_20_6, zero) = 0 % 12.95/2.51 | (30) leq(all_20_4, zero) = 0 % 12.95/2.51 | (31) leq(all_20_1, zero) = all_20_0 % 12.95/2.51 | % 12.95/2.51 | GROUND_INST: instantiating (1) with all_20_11, all_20_12, all_20_3, % 12.95/2.51 | simplifying with (15), (16), (22) gives: % 12.95/2.51 | (32) addition(all_20_11, all_20_12) = all_20_3 & $i(all_20_3) % 12.95/2.51 | % 12.95/2.51 | ALPHA: (32) implies: % 12.95/2.51 | (33) $i(all_20_3) % 12.95/2.51 | % 12.95/2.51 | GROUND_INST: instantiating (5) with all_20_10, all_20_12, all_20_11, all_20_3, % 12.95/2.51 | all_20_2, simplifying with (15), (16), (17), (22), (25) gives: % 12.95/2.51 | (34) ? [v0: $i] : ? [v1: $i] : (multiplication(all_20_10, all_20_11) = v1 % 12.95/2.51 | & multiplication(all_20_10, all_20_12) = v0 & addition(v0, v1) = % 12.95/2.51 | all_20_2 & $i(v1) & $i(v0) & $i(all_20_2)) % 12.95/2.51 | % 12.95/2.51 | GROUND_INST: instantiating (4) with all_20_10, all_20_12, all_20_7, all_20_8, % 12.95/2.52 | all_20_6, simplifying with (15), (17), (18), (23), (26) gives: % 12.95/2.52 | (35) ? [v0: $i] : (multiplication(all_20_10, v0) = all_20_6 & % 12.95/2.52 | multiplication(all_20_12, all_20_7) = v0 & $i(v0) & $i(all_20_6)) % 12.95/2.52 | % 12.95/2.52 | GROUND_INST: instantiating (4) with all_20_10, all_20_11, all_20_7, all_20_5, % 12.95/2.52 | all_20_4, simplifying with (16), (17), (18), (24), (27) gives: % 12.95/2.52 | (36) ? [v0: $i] : (multiplication(all_20_10, v0) = all_20_4 & % 12.95/2.52 | multiplication(all_20_11, all_20_7) = v0 & $i(v0) & $i(all_20_4)) % 12.95/2.52 | % 12.95/2.52 | GROUND_INST: instantiating (4) with all_20_10, all_20_3, all_20_7, all_20_2, % 12.95/2.52 | all_20_1, simplifying with (17), (18), (25), (28), (33) gives: % 12.95/2.52 | (37) ? [v0: $i] : (multiplication(all_20_3, all_20_7) = v0 & % 12.95/2.52 | multiplication(all_20_10, v0) = all_20_1 & $i(v0) & $i(all_20_1)) % 12.95/2.52 | % 12.95/2.52 | GROUND_INST: instantiating (7) with all_20_6, zero, simplifying with (9), % 12.95/2.52 | (19), (29) gives: % 12.95/2.52 | (38) addition(all_20_6, zero) = zero % 12.95/2.52 | % 12.95/2.52 | GROUND_INST: instantiating (7) with all_20_4, zero, simplifying with (9), % 12.95/2.52 | (20), (30) gives: % 12.95/2.52 | (39) addition(all_20_4, zero) = zero % 12.95/2.52 | % 12.95/2.52 | GROUND_INST: instantiating (8) with all_20_1, zero, all_20_0, simplifying with % 12.95/2.52 | (9), (21), (31) gives: % 12.95/2.52 | (40) all_20_0 = 0 | ? [v0: $i] : ( ~ (v0 = zero) & addition(all_20_1, % 12.95/2.52 | zero) = v0 & $i(v0)) % 12.95/2.52 | % 12.95/2.52 | DELTA: instantiating (36) with fresh symbol all_32_0 gives: % 12.95/2.52 | (41) multiplication(all_20_10, all_32_0) = all_20_4 & % 12.95/2.52 | multiplication(all_20_11, all_20_7) = all_32_0 & $i(all_32_0) & % 12.95/2.52 | $i(all_20_4) % 12.95/2.52 | % 12.95/2.52 | DELTA: instantiating (37) with fresh symbol all_34_0 gives: % 12.95/2.52 | (42) multiplication(all_20_3, all_20_7) = all_34_0 & % 12.95/2.52 | multiplication(all_20_10, all_34_0) = all_20_1 & $i(all_34_0) & % 12.95/2.52 | $i(all_20_1) % 12.95/2.52 | % 12.95/2.52 | DELTA: instantiating (35) with fresh symbol all_36_0 gives: % 12.95/2.52 | (43) multiplication(all_20_10, all_36_0) = all_20_6 & % 12.95/2.52 | multiplication(all_20_12, all_20_7) = all_36_0 & $i(all_36_0) & % 12.95/2.52 | $i(all_20_6) % 12.95/2.52 | % 12.95/2.52 | DELTA: instantiating (34) with fresh symbols all_38_0, all_38_1 gives: % 12.95/2.52 | (44) multiplication(all_20_10, all_20_11) = all_38_0 & % 12.95/2.52 | multiplication(all_20_10, all_20_12) = all_38_1 & addition(all_38_1, % 12.95/2.52 | all_38_0) = all_20_2 & $i(all_38_0) & $i(all_38_1) & $i(all_20_2) % 12.95/2.52 | % 12.95/2.52 | ALPHA: (44) implies: % 12.95/2.52 | (45) $i(all_38_1) % 12.95/2.52 | (46) $i(all_38_0) % 12.95/2.52 | (47) addition(all_38_1, all_38_0) = all_20_2 % 12.95/2.52 | (48) multiplication(all_20_10, all_20_12) = all_38_1 % 12.95/2.52 | (49) multiplication(all_20_10, all_20_11) = all_38_0 % 12.95/2.52 | % 12.95/2.52 | BETA: splitting (40) gives: % 12.95/2.52 | % 12.95/2.52 | Case 1: % 12.95/2.52 | | % 12.95/2.52 | | (50) all_20_0 = 0 % 12.95/2.52 | | % 12.95/2.52 | | REDUCE: (14), (50) imply: % 12.95/2.52 | | (51) $false % 12.95/2.52 | | % 12.95/2.52 | | CLOSE: (51) is inconsistent. % 12.95/2.52 | | % 12.95/2.52 | Case 2: % 12.95/2.52 | | % 12.95/2.52 | | (52) ? [v0: $i] : ( ~ (v0 = zero) & addition(all_20_1, zero) = v0 & % 12.95/2.52 | | $i(v0)) % 12.95/2.53 | | % 12.95/2.53 | | DELTA: instantiating (52) with fresh symbol all_57_0 gives: % 12.95/2.53 | | (53) ~ (all_57_0 = zero) & addition(all_20_1, zero) = all_57_0 & % 12.95/2.53 | | $i(all_57_0) % 12.95/2.53 | | % 12.95/2.53 | | ALPHA: (53) implies: % 12.95/2.53 | | (54) ~ (all_57_0 = zero) % 12.95/2.53 | | (55) addition(all_20_1, zero) = all_57_0 % 12.95/2.53 | | % 12.95/2.53 | | GROUND_INST: instantiating (12) with all_20_8, all_38_1, all_20_12, % 12.95/2.53 | | all_20_10, simplifying with (23), (48) gives: % 12.95/2.53 | | (56) all_38_1 = all_20_8 % 12.95/2.53 | | % 12.95/2.53 | | GROUND_INST: instantiating (12) with all_20_5, all_38_0, all_20_11, % 12.95/2.53 | | all_20_10, simplifying with (24), (49) gives: % 12.95/2.53 | | (57) all_38_0 = all_20_5 % 12.95/2.53 | | % 12.95/2.53 | | REDUCE: (47), (56), (57) imply: % 12.95/2.53 | | (58) addition(all_20_8, all_20_5) = all_20_2 % 12.95/2.53 | | % 12.95/2.53 | | REDUCE: (46), (57) imply: % 12.95/2.53 | | (59) $i(all_20_5) % 12.95/2.53 | | % 12.95/2.53 | | REDUCE: (45), (56) imply: % 12.95/2.53 | | (60) $i(all_20_8) % 12.95/2.53 | | % 12.95/2.53 | | GROUND_INST: instantiating (6) with all_20_8, all_20_5, all_20_7, all_20_2, % 12.95/2.53 | | all_20_1, simplifying with (18), (28), (58), (59), (60) gives: % 12.95/2.53 | | (61) ? [v0: $i] : ? [v1: $i] : (multiplication(all_20_5, all_20_7) = v1 % 12.95/2.53 | | & multiplication(all_20_8, all_20_7) = v0 & addition(v0, v1) = % 12.95/2.53 | | all_20_1 & $i(v1) & $i(v0) & $i(all_20_1)) % 12.95/2.53 | | % 12.95/2.53 | | GROUND_INST: instantiating (2) with zero, all_20_6, all_20_6, zero, zero, % 12.95/2.53 | | simplifying with (9), (19), (38) gives: % 12.95/2.53 | | (62) ? [v0: $i] : (addition(v0, zero) = zero & addition(all_20_6, % 12.95/2.53 | | all_20_6) = v0 & $i(v0)) % 12.95/2.53 | | % 12.95/2.53 | | GROUND_INST: instantiating (3) with all_20_6, zero, simplifying with (19), % 12.95/2.53 | | (38) gives: % 12.95/2.53 | | (63) all_20_6 = zero % 12.95/2.53 | | % 12.95/2.53 | | GROUND_INST: instantiating (1) with zero, all_20_6, zero, simplifying with % 12.95/2.53 | | (9), (19), (38) gives: % 12.95/2.53 | | (64) addition(zero, all_20_6) = zero % 12.95/2.53 | | % 12.95/2.53 | | GROUND_INST: instantiating (2) with zero, all_20_4, all_20_4, zero, zero, % 12.95/2.53 | | simplifying with (9), (20), (39) gives: % 12.95/2.53 | | (65) ? [v0: $i] : (addition(v0, zero) = zero & addition(all_20_4, % 12.95/2.53 | | all_20_4) = v0 & $i(v0)) % 12.95/2.53 | | % 12.95/2.53 | | GROUND_INST: instantiating (2) with zero, all_20_6, all_20_4, zero, zero, % 12.95/2.53 | | simplifying with (9), (19), (20), (38), (39) gives: % 12.95/2.53 | | (66) ? [v0: $i] : (addition(v0, zero) = zero & addition(all_20_4, % 12.95/2.53 | | all_20_6) = v0 & $i(v0)) % 12.95/2.53 | | % 12.95/2.53 | | GROUND_INST: instantiating (2) with zero, all_20_4, all_20_6, zero, zero, % 12.95/2.53 | | simplifying with (9), (19), (20), (38), (39) gives: % 12.95/2.53 | | (67) ? [v0: $i] : (addition(v0, zero) = zero & addition(all_20_6, % 12.95/2.53 | | all_20_4) = v0 & $i(v0)) % 12.95/2.53 | | % 12.95/2.53 | | GROUND_INST: instantiating (3) with all_20_4, zero, simplifying with (20), % 12.95/2.53 | | (39) gives: % 12.95/2.53 | | (68) all_20_4 = zero % 12.95/2.53 | | % 12.95/2.53 | | GROUND_INST: instantiating (3) with all_20_1, all_57_0, simplifying with % 13.40/2.53 | | (21), (55) gives: % 13.40/2.53 | | (69) all_57_0 = all_20_1 % 13.40/2.53 | | % 13.40/2.53 | | DELTA: instantiating (65) with fresh symbol all_69_0 gives: % 13.40/2.53 | | (70) addition(all_69_0, zero) = zero & addition(all_20_4, all_20_4) = % 13.40/2.53 | | all_69_0 & $i(all_69_0) % 13.40/2.53 | | % 13.40/2.53 | | ALPHA: (70) implies: % 13.40/2.54 | | (71) addition(all_20_4, all_20_4) = all_69_0 % 13.40/2.54 | | % 13.40/2.54 | | DELTA: instantiating (67) with fresh symbol all_71_0 gives: % 13.40/2.54 | | (72) addition(all_71_0, zero) = zero & addition(all_20_6, all_20_4) = % 13.40/2.54 | | all_71_0 & $i(all_71_0) % 13.40/2.54 | | % 13.40/2.54 | | ALPHA: (72) implies: % 13.40/2.54 | | (73) addition(all_20_6, all_20_4) = all_71_0 % 13.40/2.54 | | % 13.40/2.54 | | DELTA: instantiating (66) with fresh symbol all_73_0 gives: % 13.40/2.54 | | (74) addition(all_73_0, zero) = zero & addition(all_20_4, all_20_6) = % 13.40/2.54 | | all_73_0 & $i(all_73_0) % 13.40/2.54 | | % 13.40/2.54 | | ALPHA: (74) implies: % 13.40/2.54 | | (75) addition(all_20_4, all_20_6) = all_73_0 % 13.40/2.54 | | % 13.40/2.54 | | DELTA: instantiating (62) with fresh symbol all_75_0 gives: % 13.40/2.54 | | (76) addition(all_75_0, zero) = zero & addition(all_20_6, all_20_6) = % 13.40/2.54 | | all_75_0 & $i(all_75_0) % 13.40/2.54 | | % 13.40/2.54 | | ALPHA: (76) implies: % 13.40/2.54 | | (77) addition(all_20_6, all_20_6) = all_75_0 % 13.40/2.54 | | % 13.40/2.54 | | DELTA: instantiating (61) with fresh symbols all_85_0, all_85_1 gives: % 13.40/2.54 | | (78) multiplication(all_20_5, all_20_7) = all_85_0 & % 13.40/2.54 | | multiplication(all_20_8, all_20_7) = all_85_1 & addition(all_85_1, % 13.40/2.54 | | all_85_0) = all_20_1 & $i(all_85_0) & $i(all_85_1) & $i(all_20_1) % 13.40/2.54 | | % 13.40/2.54 | | ALPHA: (78) implies: % 13.40/2.54 | | (79) addition(all_85_1, all_85_0) = all_20_1 % 13.40/2.54 | | (80) multiplication(all_20_8, all_20_7) = all_85_1 % 13.40/2.54 | | (81) multiplication(all_20_5, all_20_7) = all_85_0 % 13.40/2.54 | | % 13.40/2.54 | | REDUCE: (54), (69) imply: % 13.40/2.54 | | (82) ~ (all_20_1 = zero) % 13.40/2.54 | | % 13.40/2.54 | | REDUCE: (27), (68) imply: % 13.40/2.54 | | (83) multiplication(all_20_5, all_20_7) = zero % 13.40/2.54 | | % 13.40/2.54 | | REDUCE: (26), (63) imply: % 13.40/2.54 | | (84) multiplication(all_20_8, all_20_7) = zero % 13.40/2.54 | | % 13.40/2.54 | | REDUCE: (68), (71) imply: % 13.40/2.54 | | (85) addition(zero, zero) = all_69_0 % 13.40/2.54 | | % 13.40/2.54 | | REDUCE: (63), (68), (75) imply: % 13.40/2.54 | | (86) addition(zero, zero) = all_73_0 % 13.40/2.54 | | % 13.40/2.54 | | REDUCE: (63), (68), (73) imply: % 13.40/2.54 | | (87) addition(zero, zero) = all_71_0 % 13.40/2.54 | | % 13.40/2.54 | | REDUCE: (63), (77) imply: % 13.40/2.54 | | (88) addition(zero, zero) = all_75_0 % 13.40/2.54 | | % 13.40/2.54 | | REDUCE: (63), (64) imply: % 13.40/2.54 | | (89) addition(zero, zero) = zero % 13.40/2.54 | | % 13.40/2.54 | | GROUND_INST: instantiating (11) with zero, all_73_0, zero, zero, simplifying % 13.40/2.54 | | with (86), (89) gives: % 13.40/2.54 | | (90) all_73_0 = zero % 13.40/2.54 | | % 13.40/2.54 | | GROUND_INST: instantiating (11) with all_73_0, all_75_0, zero, zero, % 13.40/2.54 | | simplifying with (86), (88) gives: % 13.40/2.54 | | (91) all_75_0 = all_73_0 % 13.40/2.54 | | % 13.40/2.54 | | GROUND_INST: instantiating (11) with all_71_0, all_75_0, zero, zero, % 13.40/2.54 | | simplifying with (87), (88) gives: % 13.40/2.54 | | (92) all_75_0 = all_71_0 % 13.40/2.54 | | % 13.40/2.54 | | GROUND_INST: instantiating (11) with all_69_0, all_75_0, zero, zero, % 13.40/2.54 | | simplifying with (85), (88) gives: % 13.40/2.54 | | (93) all_75_0 = all_69_0 % 13.40/2.54 | | % 13.40/2.54 | | GROUND_INST: instantiating (12) with zero, all_85_1, all_20_7, all_20_8, % 13.40/2.54 | | simplifying with (80), (84) gives: % 13.40/2.54 | | (94) all_85_1 = zero % 13.40/2.54 | | % 13.40/2.54 | | GROUND_INST: instantiating (12) with zero, all_85_0, all_20_7, all_20_5, % 13.40/2.54 | | simplifying with (81), (83) gives: % 13.40/2.54 | | (95) all_85_0 = zero % 13.40/2.54 | | % 13.40/2.54 | | COMBINE_EQS: (91), (92) imply: % 13.40/2.54 | | (96) all_73_0 = all_71_0 % 13.40/2.54 | | % 13.40/2.54 | | SIMP: (96) implies: % 13.40/2.54 | | (97) all_73_0 = all_71_0 % 13.40/2.54 | | % 13.40/2.54 | | COMBINE_EQS: (92), (93) imply: % 13.40/2.54 | | (98) all_71_0 = all_69_0 % 13.40/2.54 | | % 13.40/2.54 | | COMBINE_EQS: (90), (97) imply: % 13.40/2.54 | | (99) all_71_0 = zero % 13.40/2.54 | | % 13.40/2.54 | | SIMP: (99) implies: % 13.40/2.54 | | (100) all_71_0 = zero % 13.40/2.54 | | % 13.40/2.54 | | COMBINE_EQS: (98), (100) imply: % 13.40/2.54 | | (101) all_69_0 = zero % 13.40/2.54 | | % 13.40/2.54 | | REDUCE: (79), (94), (95) imply: % 13.40/2.54 | | (102) addition(zero, zero) = all_20_1 % 13.40/2.54 | | % 13.40/2.54 | | GROUND_INST: instantiating (11) with zero, all_20_1, zero, zero, simplifying % 13.40/2.54 | | with (89), (102) gives: % 13.40/2.54 | | (103) all_20_1 = zero % 13.40/2.54 | | % 13.40/2.54 | | REDUCE: (82), (103) imply: % 13.40/2.54 | | (104) $false % 13.40/2.54 | | % 13.40/2.54 | | CLOSE: (104) is inconsistent. % 13.40/2.54 | | % 13.40/2.55 | End of split % 13.40/2.55 | % 13.40/2.55 End of proof % 13.40/2.55 % SZS output end Proof for theBenchmark % 13.40/2.55 % 13.40/2.55 1932ms %------------------------------------------------------------------------------