%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE035+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 05:34:20 EDT 2023 % Result : Theorem 8.63s 1.91s % Output : Proof 14.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : KLE035+2 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 11:28:35 EDT 2023 % 0.13/0.34 % CPUTime : % 0.64/0.61 ________ _____ % 0.64/0.61 ___ __ \_________(_)________________________________ % 0.64/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.64/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.64/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.64/0.61 % 0.64/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.64/0.61 (2023-06-19) % 0.64/0.61 % 0.64/0.61 (c) Philipp Rümmer, 2009-2023 % 0.64/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.64/0.61 Amanda Stjerna. % 0.64/0.61 Free software under BSD-3-Clause. % 0.64/0.61 % 0.64/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.64/0.61 % 0.64/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.64/0.62 Running up to 7 provers in parallel. % 0.68/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.68/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.68/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.68/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.68/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.68/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.68/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.56/1.05 Prover 1: Preprocessing ... % 2.56/1.05 Prover 4: Preprocessing ... % 2.94/1.09 Prover 5: Preprocessing ... % 2.94/1.09 Prover 2: Preprocessing ... % 2.94/1.09 Prover 6: Preprocessing ... % 2.94/1.09 Prover 3: Preprocessing ... % 2.94/1.09 Prover 0: Preprocessing ... % 5.04/1.41 Prover 1: Constructing countermodel ... % 5.04/1.43 Prover 6: Proving ... % 5.04/1.43 Prover 3: Constructing countermodel ... % 6.03/1.50 Prover 4: Constructing countermodel ... % 6.03/1.53 Prover 5: Proving ... % 6.37/1.54 Prover 0: Proving ... % 6.43/1.59 Prover 2: Proving ... % 8.63/1.90 Prover 0: proved (1276ms) % 8.63/1.91 % 8.63/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.63/1.91 % 8.63/1.91 Prover 3: stopped % 8.63/1.91 Prover 2: stopped % 8.63/1.91 Prover 6: stopped % 8.63/1.93 Prover 5: stopped % 9.36/1.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.36/1.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.36/1.94 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.36/1.94 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.36/1.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.36/1.98 Prover 7: Preprocessing ... % 9.36/1.98 Prover 11: Preprocessing ... % 9.36/1.98 Prover 8: Preprocessing ... % 9.36/1.98 Prover 10: Preprocessing ... % 9.36/1.99 Prover 13: Preprocessing ... % 10.32/2.07 Prover 8: Warning: ignoring some quantifiers % 10.32/2.08 Prover 8: Constructing countermodel ... % 10.32/2.09 Prover 13: Warning: ignoring some quantifiers % 10.32/2.09 Prover 10: Constructing countermodel ... % 10.32/2.10 Prover 13: Constructing countermodel ... % 10.61/2.11 Prover 7: Constructing countermodel ... % 10.89/2.15 Prover 11: Constructing countermodel ... % 10.89/2.21 Prover 10: gave up % 10.89/2.21 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.60/2.24 Prover 16: Preprocessing ... % 12.13/2.35 Prover 16: Warning: ignoring some quantifiers % 12.13/2.35 Prover 16: Constructing countermodel ... % 13.10/2.52 Prover 11: Found proof (size 83) % 13.10/2.52 Prover 11: proved (591ms) % 13.10/2.52 Prover 16: stopped % 13.10/2.52 Prover 1: stopped % 13.10/2.52 Prover 13: stopped % 13.10/2.52 Prover 8: stopped % 13.10/2.52 Prover 7: stopped % 13.10/2.52 Prover 4: stopped % 13.10/2.52 % 13.10/2.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.10/2.52 % 13.84/2.53 % SZS output start Proof for theBenchmark % 13.84/2.53 Assumptions after simplification: % 13.84/2.53 --------------------------------- % 13.84/2.53 % 13.84/2.53 (additive_associativity) % 13.84/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 13.84/2.56 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 13.84/2.56 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 & % 13.84/2.56 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 13.84/2.56 : ! [v4: $i] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ % 13.84/2.56 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 & % 13.84/2.56 addition(v2, v1) = v5 & $i(v5) & $i(v4))) % 13.84/2.56 % 13.84/2.56 (additive_commutativity) % 13.84/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~ % 13.84/2.56 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 13.84/2.56 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 13.84/2.56 (addition(v1, v0) = v2 & $i(v2))) % 13.84/2.56 % 13.84/2.56 (additive_identity) % 13.84/2.56 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) % 13.84/2.56 | ~ $i(v0)) % 13.84/2.56 % 13.84/2.56 (goals) % 13.84/2.57 $i(zero) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 13.84/2.57 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 13.84/2.57 [v10: $i] : ? [v11: $i] : ? [v12: int] : ( ~ (v12 = 0) & c(v3) = v5 & % 13.84/2.57 test(v3) = 0 & test(v2) = 0 & leq(v11, zero) = v12 & leq(v8, zero) = 0 & % 13.84/2.57 leq(v6, zero) = 0 & multiplication(v10, v5) = v11 & multiplication(v7, v5) = % 13.84/2.57 v8 & multiplication(v4, v5) = v6 & multiplication(v2, v9) = v10 & % 13.84/2.57 multiplication(v2, v1) = v7 & multiplication(v2, v0) = v4 & addition(v0, v1) % 13.84/2.57 = v9 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 13.84/2.57 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 13.84/2.57 % 13.84/2.57 (left_distributivity) % 13.84/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.84/2.57 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | % 13.84/2.57 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 13.84/2.57 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) & % 13.84/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 13.84/2.57 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~ % 13.84/2.57 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) = % 13.84/2.57 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5) % 13.84/2.57 & $i(v4))) % 13.84/2.57 % 13.84/2.57 (multiplicative_associativity) % 13.84/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 13.84/2.58 (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ $i(v2) % 13.84/2.58 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, v2) = v5 & % 13.84/2.58 multiplication(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: % 13.84/2.58 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (multiplication(v1, v2) % 13.84/2.58 = v3) | ~ (multiplication(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 13.84/2.58 $i(v0) | ? [v5: $i] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) % 13.84/2.58 = v5 & $i(v5) & $i(v4))) % 13.84/2.58 % 13.84/2.58 (order) % 13.84/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) = % 13.84/2.58 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) = % 13.84/2.58 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, % 13.84/2.58 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) & % 13.84/2.58 addition(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.84/2.58 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | addition(v0, v1) = v1) & ! [v0: % 13.84/2.58 $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) | % 13.84/2.58 leq(v0, v1) = 0) % 13.84/2.58 % 13.84/2.58 (right_distributivity) % 13.84/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.84/2.58 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | % 13.84/2.58 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 13.84/2.58 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) & % 13.84/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 13.84/2.58 (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ $i(v2) | ~ % 13.84/2.58 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v0, v2) = % 13.84/2.58 v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5) % 13.84/2.58 & $i(v4))) % 13.84/2.58 % 13.84/2.58 (function-axioms) % 13.84/2.58 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.84/2.58 [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) = % 13.84/2.58 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.84/2.58 $i] : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 13.84/2.58 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 13.84/2.58 ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! % 13.84/2.58 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.84/2.58 (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! % 13.84/2.58 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & ! % 13.84/2.58 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 13.84/2.58 | ~ (test(v2) = v1) | ~ (test(v2) = v0)) % 13.84/2.58 % 13.84/2.58 Further assumptions not needed in the proof: % 13.84/2.58 -------------------------------------------- % 13.84/2.59 additive_idempotence, left_annihilation, multiplicative_left_identity, % 13.84/2.59 multiplicative_right_identity, right_annihilation, test_1, test_2, test_3, % 13.84/2.59 test_4, test_deMorgan1, test_deMorgan2 % 13.84/2.59 % 13.84/2.59 Those formulas are unsatisfiable: % 13.84/2.59 --------------------------------- % 13.84/2.59 % 13.84/2.59 Begin of proof % 13.84/2.59 | % 13.84/2.59 | ALPHA: (additive_commutativity) implies: % 13.84/2.59 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | % 13.84/2.59 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) % 13.84/2.59 | % 13.84/2.59 | ALPHA: (additive_associativity) implies: % 13.84/2.59 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 13.84/2.59 | ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ $i(v2) | % 13.84/2.59 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 & % 13.84/2.59 | addition(v2, v1) = v5 & $i(v5) & $i(v4))) % 13.84/2.59 | % 13.84/2.59 | ALPHA: (additive_identity) implies: % 13.84/2.59 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) | % 13.84/2.59 | ~ $i(v0)) % 13.84/2.59 | % 13.84/2.59 | ALPHA: (multiplicative_associativity) implies: % 13.84/2.59 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 13.84/2.59 | ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | % 13.84/2.59 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, % 13.84/2.59 | v2) = v5 & multiplication(v0, v5) = v4 & $i(v5) & $i(v4))) % 13.84/2.59 | % 13.84/2.59 | ALPHA: (right_distributivity) implies: % 14.19/2.59 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 14.19/2.59 | ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ % 14.19/2.59 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 14.19/2.59 | (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & % 14.19/2.59 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 14.19/2.59 | % 14.19/2.59 | ALPHA: (left_distributivity) implies: % 14.19/2.59 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 14.19/2.59 | ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ % 14.19/2.59 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 14.19/2.59 | (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & % 14.19/2.59 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 14.19/2.59 | % 14.19/2.59 | ALPHA: (order) implies: % 14.19/2.59 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v0, v1) = 0) | ~ $i(v1) | ~ % 14.19/2.59 | $i(v0) | addition(v0, v1) = v1) % 14.19/2.59 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) = % 14.19/2.59 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) & % 14.19/2.59 | addition(v0, v1) = v3 & $i(v3))) % 14.19/2.59 | % 14.19/2.59 | ALPHA: (goals) implies: % 14.19/2.59 | (9) $i(zero) % 14.19/2.60 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 14.19/2.60 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 14.19/2.60 | ? [v10: $i] : ? [v11: $i] : ? [v12: int] : ( ~ (v12 = 0) & c(v3) = % 14.19/2.60 | v5 & test(v3) = 0 & test(v2) = 0 & leq(v11, zero) = v12 & leq(v8, % 14.19/2.60 | zero) = 0 & leq(v6, zero) = 0 & multiplication(v10, v5) = v11 & % 14.19/2.60 | multiplication(v7, v5) = v8 & multiplication(v4, v5) = v6 & % 14.19/2.60 | multiplication(v2, v9) = v10 & multiplication(v2, v1) = v7 & % 14.19/2.60 | multiplication(v2, v0) = v4 & addition(v0, v1) = v9 & $i(v11) & % 14.19/2.60 | $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 14.19/2.60 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.19/2.60 | % 14.19/2.60 | ALPHA: (function-axioms) implies: % 14.19/2.60 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.19/2.60 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 14.19/2.60 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.19/2.60 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 14.19/2.60 | % 14.19/2.60 | DELTA: instantiating (10) with fresh symbols all_22_0, all_22_1, all_22_2, % 14.19/2.60 | all_22_3, all_22_4, all_22_5, all_22_6, all_22_7, all_22_8, all_22_9, % 14.19/2.60 | all_22_10, all_22_11, all_22_12 gives: % 14.19/2.60 | (13) ~ (all_22_0 = 0) & c(all_22_9) = all_22_7 & test(all_22_9) = 0 & % 14.19/2.60 | test(all_22_10) = 0 & leq(all_22_1, zero) = all_22_0 & leq(all_22_4, % 14.19/2.60 | zero) = 0 & leq(all_22_6, zero) = 0 & multiplication(all_22_2, % 14.19/2.60 | all_22_7) = all_22_1 & multiplication(all_22_5, all_22_7) = all_22_4 % 14.19/2.60 | & multiplication(all_22_8, all_22_7) = all_22_6 & % 14.19/2.60 | multiplication(all_22_10, all_22_3) = all_22_2 & % 14.19/2.60 | multiplication(all_22_10, all_22_11) = all_22_5 & % 14.19/2.60 | multiplication(all_22_10, all_22_12) = all_22_8 & addition(all_22_12, % 14.19/2.60 | all_22_11) = all_22_3 & $i(all_22_1) & $i(all_22_2) & $i(all_22_3) & % 14.19/2.60 | $i(all_22_4) & $i(all_22_5) & $i(all_22_6) & $i(all_22_7) & % 14.19/2.60 | $i(all_22_8) & $i(all_22_9) & $i(all_22_10) & $i(all_22_11) & % 14.19/2.60 | $i(all_22_12) % 14.19/2.60 | % 14.19/2.60 | ALPHA: (13) implies: % 14.19/2.60 | (14) ~ (all_22_0 = 0) % 14.19/2.60 | (15) $i(all_22_12) % 14.19/2.60 | (16) $i(all_22_11) % 14.19/2.60 | (17) $i(all_22_10) % 14.19/2.60 | (18) $i(all_22_7) % 14.19/2.60 | (19) $i(all_22_6) % 14.19/2.60 | (20) $i(all_22_4) % 14.19/2.60 | (21) $i(all_22_1) % 14.19/2.60 | (22) addition(all_22_12, all_22_11) = all_22_3 % 14.19/2.60 | (23) multiplication(all_22_10, all_22_12) = all_22_8 % 14.19/2.60 | (24) multiplication(all_22_10, all_22_11) = all_22_5 % 14.19/2.60 | (25) multiplication(all_22_10, all_22_3) = all_22_2 % 14.19/2.60 | (26) multiplication(all_22_8, all_22_7) = all_22_6 % 14.19/2.60 | (27) multiplication(all_22_5, all_22_7) = all_22_4 % 14.19/2.60 | (28) multiplication(all_22_2, all_22_7) = all_22_1 % 14.19/2.60 | (29) leq(all_22_6, zero) = 0 % 14.19/2.60 | (30) leq(all_22_4, zero) = 0 % 14.19/2.60 | (31) leq(all_22_1, zero) = all_22_0 % 14.19/2.60 | % 14.19/2.60 | GROUND_INST: instantiating (1) with all_22_11, all_22_12, all_22_3, % 14.19/2.60 | simplifying with (15), (16), (22) gives: % 14.19/2.60 | (32) addition(all_22_11, all_22_12) = all_22_3 & $i(all_22_3) % 14.19/2.60 | % 14.19/2.60 | ALPHA: (32) implies: % 14.19/2.60 | (33) $i(all_22_3) % 14.19/2.60 | % 14.19/2.61 | GROUND_INST: instantiating (5) with all_22_10, all_22_12, all_22_11, all_22_3, % 14.19/2.61 | all_22_2, simplifying with (15), (16), (17), (22), (25) gives: % 14.19/2.61 | (34) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_10, all_22_11) = v1 % 14.19/2.61 | & multiplication(all_22_10, all_22_12) = v0 & addition(v0, v1) = % 14.19/2.61 | all_22_2 & $i(v1) & $i(v0) & $i(all_22_2)) % 14.19/2.61 | % 14.19/2.61 | GROUND_INST: instantiating (4) with all_22_10, all_22_12, all_22_7, all_22_8, % 14.19/2.61 | all_22_6, simplifying with (15), (17), (18), (23), (26) gives: % 14.19/2.61 | (35) ? [v0: $i] : (multiplication(all_22_10, v0) = all_22_6 & % 14.19/2.61 | multiplication(all_22_12, all_22_7) = v0 & $i(v0) & $i(all_22_6)) % 14.19/2.61 | % 14.19/2.61 | GROUND_INST: instantiating (4) with all_22_10, all_22_11, all_22_7, all_22_5, % 14.19/2.61 | all_22_4, simplifying with (16), (17), (18), (24), (27) gives: % 14.19/2.61 | (36) ? [v0: $i] : (multiplication(all_22_10, v0) = all_22_4 & % 14.19/2.61 | multiplication(all_22_11, all_22_7) = v0 & $i(v0) & $i(all_22_4)) % 14.19/2.61 | % 14.19/2.61 | GROUND_INST: instantiating (4) with all_22_10, all_22_3, all_22_7, all_22_2, % 14.19/2.61 | all_22_1, simplifying with (17), (18), (25), (28), (33) gives: % 14.19/2.61 | (37) ? [v0: $i] : (multiplication(all_22_3, all_22_7) = v0 & % 14.19/2.61 | multiplication(all_22_10, v0) = all_22_1 & $i(v0) & $i(all_22_1)) % 14.19/2.61 | % 14.19/2.61 | GROUND_INST: instantiating (7) with all_22_6, zero, simplifying with (9), % 14.19/2.61 | (19), (29) gives: % 14.19/2.61 | (38) addition(all_22_6, zero) = zero % 14.19/2.61 | % 14.19/2.61 | GROUND_INST: instantiating (7) with all_22_4, zero, simplifying with (9), % 14.19/2.61 | (20), (30) gives: % 14.19/2.61 | (39) addition(all_22_4, zero) = zero % 14.19/2.61 | % 14.19/2.61 | GROUND_INST: instantiating (8) with all_22_1, zero, all_22_0, simplifying with % 14.19/2.61 | (9), (21), (31) gives: % 14.19/2.61 | (40) all_22_0 = 0 | ? [v0: $i] : ( ~ (v0 = zero) & addition(all_22_1, % 14.19/2.61 | zero) = v0 & $i(v0)) % 14.19/2.61 | % 14.19/2.61 | DELTA: instantiating (37) with fresh symbol all_34_0 gives: % 14.19/2.61 | (41) multiplication(all_22_3, all_22_7) = all_34_0 & % 14.19/2.61 | multiplication(all_22_10, all_34_0) = all_22_1 & $i(all_34_0) & % 14.19/2.61 | $i(all_22_1) % 14.19/2.61 | % 14.19/2.61 | DELTA: instantiating (36) with fresh symbol all_36_0 gives: % 14.19/2.61 | (42) multiplication(all_22_10, all_36_0) = all_22_4 & % 14.19/2.61 | multiplication(all_22_11, all_22_7) = all_36_0 & $i(all_36_0) & % 14.19/2.61 | $i(all_22_4) % 14.19/2.61 | % 14.19/2.61 | DELTA: instantiating (35) with fresh symbol all_38_0 gives: % 14.19/2.61 | (43) multiplication(all_22_10, all_38_0) = all_22_6 & % 14.19/2.61 | multiplication(all_22_12, all_22_7) = all_38_0 & $i(all_38_0) & % 14.19/2.61 | $i(all_22_6) % 14.19/2.61 | % 14.19/2.61 | DELTA: instantiating (34) with fresh symbols all_40_0, all_40_1 gives: % 14.19/2.61 | (44) multiplication(all_22_10, all_22_11) = all_40_0 & % 14.19/2.61 | multiplication(all_22_10, all_22_12) = all_40_1 & addition(all_40_1, % 14.19/2.61 | all_40_0) = all_22_2 & $i(all_40_0) & $i(all_40_1) & $i(all_22_2) % 14.19/2.61 | % 14.19/2.61 | ALPHA: (44) implies: % 14.19/2.61 | (45) $i(all_40_1) % 14.19/2.61 | (46) $i(all_40_0) % 14.19/2.61 | (47) addition(all_40_1, all_40_0) = all_22_2 % 14.19/2.61 | (48) multiplication(all_22_10, all_22_12) = all_40_1 % 14.19/2.61 | (49) multiplication(all_22_10, all_22_11) = all_40_0 % 14.19/2.61 | % 14.19/2.61 | BETA: splitting (40) gives: % 14.19/2.61 | % 14.19/2.61 | Case 1: % 14.19/2.61 | | % 14.19/2.61 | | (50) all_22_0 = 0 % 14.19/2.61 | | % 14.19/2.61 | | REDUCE: (14), (50) imply: % 14.19/2.61 | | (51) $false % 14.19/2.62 | | % 14.19/2.62 | | CLOSE: (51) is inconsistent. % 14.19/2.62 | | % 14.19/2.62 | Case 2: % 14.19/2.62 | | % 14.19/2.62 | | (52) ? [v0: $i] : ( ~ (v0 = zero) & addition(all_22_1, zero) = v0 & % 14.19/2.62 | | $i(v0)) % 14.19/2.62 | | % 14.19/2.62 | | DELTA: instantiating (52) with fresh symbol all_66_0 gives: % 14.19/2.62 | | (53) ~ (all_66_0 = zero) & addition(all_22_1, zero) = all_66_0 & % 14.19/2.62 | | $i(all_66_0) % 14.19/2.62 | | % 14.19/2.62 | | ALPHA: (53) implies: % 14.19/2.62 | | (54) ~ (all_66_0 = zero) % 14.19/2.62 | | (55) addition(all_22_1, zero) = all_66_0 % 14.19/2.62 | | % 14.19/2.62 | | GROUND_INST: instantiating (12) with all_22_8, all_40_1, all_22_12, % 14.19/2.62 | | all_22_10, simplifying with (23), (48) gives: % 14.19/2.62 | | (56) all_40_1 = all_22_8 % 14.19/2.62 | | % 14.19/2.62 | | GROUND_INST: instantiating (12) with all_22_5, all_40_0, all_22_11, % 14.19/2.62 | | all_22_10, simplifying with (24), (49) gives: % 14.19/2.62 | | (57) all_40_0 = all_22_5 % 14.19/2.62 | | % 14.19/2.62 | | REDUCE: (47), (56), (57) imply: % 14.19/2.62 | | (58) addition(all_22_8, all_22_5) = all_22_2 % 14.19/2.62 | | % 14.19/2.62 | | REDUCE: (46), (57) imply: % 14.19/2.62 | | (59) $i(all_22_5) % 14.19/2.62 | | % 14.19/2.62 | | REDUCE: (45), (56) imply: % 14.19/2.62 | | (60) $i(all_22_8) % 14.19/2.62 | | % 14.19/2.62 | | GROUND_INST: instantiating (6) with all_22_8, all_22_5, all_22_7, all_22_2, % 14.19/2.62 | | all_22_1, simplifying with (18), (28), (58), (59), (60) gives: % 14.19/2.62 | | (61) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_5, all_22_7) = v1 % 14.19/2.62 | | & multiplication(all_22_8, all_22_7) = v0 & addition(v0, v1) = % 14.19/2.62 | | all_22_1 & $i(v1) & $i(v0) & $i(all_22_1)) % 14.19/2.62 | | % 14.19/2.62 | | GROUND_INST: instantiating (2) with zero, all_22_6, all_22_6, zero, zero, % 14.19/2.62 | | simplifying with (9), (19), (38) gives: % 14.19/2.62 | | (62) ? [v0: $i] : (addition(v0, zero) = zero & addition(all_22_6, % 14.19/2.62 | | all_22_6) = v0 & $i(v0)) % 14.19/2.62 | | % 14.19/2.62 | | GROUND_INST: instantiating (3) with all_22_6, zero, simplifying with (19), % 14.19/2.62 | | (38) gives: % 14.19/2.62 | | (63) all_22_6 = zero % 14.19/2.62 | | % 14.19/2.62 | | GROUND_INST: instantiating (1) with zero, all_22_6, zero, simplifying with % 14.19/2.62 | | (9), (19), (38) gives: % 14.19/2.62 | | (64) addition(zero, all_22_6) = zero % 14.19/2.62 | | % 14.19/2.62 | | GROUND_INST: instantiating (2) with zero, all_22_4, all_22_4, zero, zero, % 14.19/2.62 | | simplifying with (9), (20), (39) gives: % 14.19/2.62 | | (65) ? [v0: $i] : (addition(v0, zero) = zero & addition(all_22_4, % 14.19/2.62 | | all_22_4) = v0 & $i(v0)) % 14.19/2.62 | | % 14.19/2.62 | | GROUND_INST: instantiating (2) with zero, all_22_6, all_22_4, zero, zero, % 14.19/2.62 | | simplifying with (9), (19), (20), (38), (39) gives: % 14.19/2.62 | | (66) ? [v0: $i] : (addition(v0, zero) = zero & addition(all_22_4, % 14.19/2.62 | | all_22_6) = v0 & $i(v0)) % 14.19/2.62 | | % 14.19/2.62 | | GROUND_INST: instantiating (2) with zero, all_22_4, all_22_6, zero, zero, % 14.19/2.62 | | simplifying with (9), (19), (20), (38), (39) gives: % 14.19/2.62 | | (67) ? [v0: $i] : (addition(v0, zero) = zero & addition(all_22_6, % 14.19/2.62 | | all_22_4) = v0 & $i(v0)) % 14.19/2.62 | | % 14.19/2.62 | | GROUND_INST: instantiating (3) with all_22_4, zero, simplifying with (20), % 14.19/2.62 | | (39) gives: % 14.19/2.62 | | (68) all_22_4 = zero % 14.19/2.62 | | % 14.19/2.62 | | GROUND_INST: instantiating (3) with all_22_1, all_66_0, simplifying with % 14.19/2.62 | | (21), (55) gives: % 14.19/2.62 | | (69) all_66_0 = all_22_1 % 14.19/2.63 | | % 14.19/2.63 | | DELTA: instantiating (62) with fresh symbol all_78_0 gives: % 14.19/2.63 | | (70) addition(all_78_0, zero) = zero & addition(all_22_6, all_22_6) = % 14.19/2.63 | | all_78_0 & $i(all_78_0) % 14.19/2.63 | | % 14.19/2.63 | | ALPHA: (70) implies: % 14.19/2.63 | | (71) addition(all_22_6, all_22_6) = all_78_0 % 14.19/2.63 | | % 14.19/2.63 | | DELTA: instantiating (66) with fresh symbol all_80_0 gives: % 14.19/2.63 | | (72) addition(all_80_0, zero) = zero & addition(all_22_4, all_22_6) = % 14.19/2.63 | | all_80_0 & $i(all_80_0) % 14.19/2.63 | | % 14.19/2.63 | | ALPHA: (72) implies: % 14.19/2.63 | | (73) addition(all_22_4, all_22_6) = all_80_0 % 14.19/2.63 | | % 14.19/2.63 | | DELTA: instantiating (65) with fresh symbol all_82_0 gives: % 14.19/2.63 | | (74) addition(all_82_0, zero) = zero & addition(all_22_4, all_22_4) = % 14.19/2.63 | | all_82_0 & $i(all_82_0) % 14.19/2.63 | | % 14.19/2.63 | | ALPHA: (74) implies: % 14.19/2.63 | | (75) addition(all_22_4, all_22_4) = all_82_0 % 14.19/2.63 | | % 14.19/2.63 | | DELTA: instantiating (67) with fresh symbol all_84_0 gives: % 14.19/2.63 | | (76) addition(all_84_0, zero) = zero & addition(all_22_6, all_22_4) = % 14.19/2.63 | | all_84_0 & $i(all_84_0) % 14.19/2.63 | | % 14.19/2.63 | | ALPHA: (76) implies: % 14.19/2.63 | | (77) addition(all_22_6, all_22_4) = all_84_0 % 14.19/2.63 | | % 14.19/2.63 | | DELTA: instantiating (61) with fresh symbols all_98_0, all_98_1 gives: % 14.19/2.63 | | (78) multiplication(all_22_5, all_22_7) = all_98_0 & % 14.19/2.63 | | multiplication(all_22_8, all_22_7) = all_98_1 & addition(all_98_1, % 14.19/2.63 | | all_98_0) = all_22_1 & $i(all_98_0) & $i(all_98_1) & $i(all_22_1) % 14.19/2.63 | | % 14.19/2.63 | | ALPHA: (78) implies: % 14.19/2.63 | | (79) addition(all_98_1, all_98_0) = all_22_1 % 14.19/2.63 | | (80) multiplication(all_22_8, all_22_7) = all_98_1 % 14.19/2.63 | | (81) multiplication(all_22_5, all_22_7) = all_98_0 % 14.19/2.63 | | % 14.19/2.63 | | REDUCE: (54), (69) imply: % 14.19/2.63 | | (82) ~ (all_22_1 = zero) % 14.19/2.63 | | % 14.19/2.63 | | REDUCE: (27), (68) imply: % 14.19/2.63 | | (83) multiplication(all_22_5, all_22_7) = zero % 14.19/2.63 | | % 14.19/2.63 | | REDUCE: (26), (63) imply: % 14.19/2.63 | | (84) multiplication(all_22_8, all_22_7) = zero % 14.19/2.63 | | % 14.19/2.63 | | REDUCE: (68), (75) imply: % 14.19/2.63 | | (85) addition(zero, zero) = all_82_0 % 14.19/2.63 | | % 14.19/2.63 | | REDUCE: (63), (68), (73) imply: % 14.19/2.63 | | (86) addition(zero, zero) = all_80_0 % 14.19/2.63 | | % 14.19/2.63 | | REDUCE: (63), (68), (77) imply: % 14.19/2.63 | | (87) addition(zero, zero) = all_84_0 % 14.19/2.63 | | % 14.19/2.63 | | REDUCE: (63), (71) imply: % 14.19/2.63 | | (88) addition(zero, zero) = all_78_0 % 14.19/2.63 | | % 14.19/2.63 | | REDUCE: (63), (64) imply: % 14.19/2.63 | | (89) addition(zero, zero) = zero % 14.19/2.63 | | % 14.19/2.63 | | GROUND_INST: instantiating (11) with zero, all_82_0, zero, zero, simplifying % 14.19/2.63 | | with (85), (89) gives: % 14.19/2.63 | | (90) all_82_0 = zero % 14.19/2.63 | | % 14.19/2.63 | | GROUND_INST: instantiating (11) with all_82_0, all_84_0, zero, zero, % 14.19/2.63 | | simplifying with (85), (87) gives: % 14.19/2.63 | | (91) all_84_0 = all_82_0 % 14.19/2.63 | | % 14.19/2.63 | | GROUND_INST: instantiating (11) with all_80_0, all_84_0, zero, zero, % 14.19/2.63 | | simplifying with (86), (87) gives: % 14.19/2.63 | | (92) all_84_0 = all_80_0 % 14.19/2.63 | | % 14.19/2.63 | | GROUND_INST: instantiating (11) with all_78_0, all_84_0, zero, zero, % 14.19/2.63 | | simplifying with (87), (88) gives: % 14.19/2.63 | | (93) all_84_0 = all_78_0 % 14.19/2.63 | | % 14.19/2.63 | | GROUND_INST: instantiating (12) with zero, all_98_1, all_22_7, all_22_8, % 14.19/2.63 | | simplifying with (80), (84) gives: % 14.19/2.63 | | (94) all_98_1 = zero % 14.19/2.63 | | % 14.19/2.63 | | GROUND_INST: instantiating (12) with zero, all_98_0, all_22_7, all_22_5, % 14.19/2.63 | | simplifying with (81), (83) gives: % 14.19/2.63 | | (95) all_98_0 = zero % 14.19/2.63 | | % 14.19/2.63 | | COMBINE_EQS: (91), (92) imply: % 14.19/2.63 | | (96) all_82_0 = all_80_0 % 14.19/2.63 | | % 14.19/2.63 | | SIMP: (96) implies: % 14.19/2.63 | | (97) all_82_0 = all_80_0 % 14.19/2.63 | | % 14.19/2.63 | | COMBINE_EQS: (92), (93) imply: % 14.19/2.63 | | (98) all_80_0 = all_78_0 % 14.19/2.63 | | % 14.19/2.63 | | COMBINE_EQS: (90), (97) imply: % 14.19/2.63 | | (99) all_80_0 = zero % 14.19/2.63 | | % 14.19/2.63 | | SIMP: (99) implies: % 14.19/2.63 | | (100) all_80_0 = zero % 14.19/2.63 | | % 14.19/2.63 | | COMBINE_EQS: (98), (100) imply: % 14.19/2.64 | | (101) all_78_0 = zero % 14.19/2.64 | | % 14.19/2.64 | | REDUCE: (79), (94), (95) imply: % 14.19/2.64 | | (102) addition(zero, zero) = all_22_1 % 14.19/2.64 | | % 14.19/2.64 | | GROUND_INST: instantiating (11) with zero, all_22_1, zero, zero, simplifying % 14.19/2.64 | | with (89), (102) gives: % 14.19/2.64 | | (103) all_22_1 = zero % 14.19/2.64 | | % 14.19/2.64 | | REDUCE: (82), (103) imply: % 14.19/2.64 | | (104) $false % 14.19/2.64 | | % 14.19/2.64 | | CLOSE: (104) is inconsistent. % 14.19/2.64 | | % 14.19/2.64 | End of split % 14.19/2.64 | % 14.19/2.64 End of proof % 14.19/2.64 % SZS output end Proof for theBenchmark % 14.19/2.64 % 14.19/2.64 2028ms %------------------------------------------------------------------------------