%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE006+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 : n018.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 05:34:09 EDT 2023 % Result : Theorem 7.14s 1.72s % Output : Proof 8.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : KLE006+1 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n018.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 11:40:33 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 2.11/1.06 Prover 4: Preprocessing ... % 2.11/1.06 Prover 1: Preprocessing ... % 2.83/1.10 Prover 5: Preprocessing ... % 2.83/1.10 Prover 3: Preprocessing ... % 2.90/1.11 Prover 0: Preprocessing ... % 2.90/1.11 Prover 6: Preprocessing ... % 2.90/1.11 Prover 2: Preprocessing ... % 4.21/1.41 Prover 6: Proving ... % 4.21/1.42 Prover 3: Constructing countermodel ... % 4.21/1.44 Prover 1: Constructing countermodel ... % 5.55/1.47 Prover 5: Proving ... % 5.74/1.50 Prover 0: Proving ... % 5.87/1.53 Prover 4: Constructing countermodel ... % 5.87/1.54 Prover 2: Proving ... % 6.61/1.65 Prover 3: gave up % 6.61/1.65 Prover 1: gave up % 6.61/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.61/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.61/1.68 Prover 7: Preprocessing ... % 7.14/1.71 Prover 8: Preprocessing ... % 7.14/1.71 Prover 0: proved (1074ms) % 7.14/1.71 % 7.14/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.14/1.72 % 7.14/1.72 Prover 6: stopped % 7.14/1.72 Prover 5: stopped % 7.14/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.14/1.72 Prover 2: stopped % 7.14/1.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.14/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.14/1.74 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.14/1.76 Prover 10: Preprocessing ... % 7.14/1.77 Prover 16: Preprocessing ... % 7.14/1.77 Prover 11: Preprocessing ... % 7.14/1.77 Prover 13: Preprocessing ... % 7.81/1.79 Prover 7: Constructing countermodel ... % 7.81/1.80 Prover 8: Warning: ignoring some quantifiers % 8.00/1.82 Prover 8: Constructing countermodel ... % 8.15/1.83 Prover 10: Constructing countermodel ... % 8.15/1.86 Prover 7: Found proof (size 12) % 8.15/1.86 Prover 7: proved (202ms) % 8.15/1.86 Prover 16: Warning: ignoring some quantifiers % 8.15/1.86 Prover 10: stopped % 8.15/1.87 Prover 4: stopped % 8.15/1.87 Prover 8: stopped % 8.15/1.87 Prover 16: Constructing countermodel ... % 8.15/1.87 Prover 16: stopped % 8.15/1.88 Prover 13: Warning: ignoring some quantifiers % 8.15/1.89 Prover 13: Constructing countermodel ... % 8.15/1.89 Prover 13: stopped % 8.15/1.92 Prover 11: Constructing countermodel ... % 8.15/1.93 Prover 11: stopped % 8.15/1.93 % 8.15/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.15/1.93 % 8.15/1.93 % SZS output start Proof for theBenchmark % 8.15/1.93 Assumptions after simplification: % 8.15/1.93 --------------------------------- % 8.15/1.93 % 8.15/1.93 (additive_commutativity) % 8.15/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~ % 8.15/1.96 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 8.15/1.96 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 8.15/1.96 (addition(v1, v0) = v2 & $i(v2))) % 8.15/1.96 % 8.15/1.96 (goals) % 8.15/1.96 $i(one) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = one) & c(v0) = % 8.15/1.96 v1 & addition(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & test(v0)) % 8.15/1.96 % 8.15/1.96 (test_2) % 8.15/1.97 $i(one) & $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~ % 8.15/1.97 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) & % 8.15/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = zero | ~ (multiplication(v1, % 8.15/1.97 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) & ! [v0: $i] % 8.15/1.97 : ! [v1: $i] : ! [v2: $i] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | % 8.15/1.97 ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) & ! [v0: $i] : ! [v1: $i] : % 8.15/1.97 ! [v2: $i] : ( ~ (multiplication(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 8.15/1.97 complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = % 8.15/1.97 one)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v0, % 8.15/1.97 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0) | % 8.15/1.97 (multiplication(v1, v0) = zero & addition(v0, v1) = one)) & ! [v0: $i] : ! % 8.15/1.97 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 8.15/1.97 ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, % 8.15/1.97 v1) = zero)) & ! [v0: $i] : ! [v1: $i] : ( ~ (multiplication(v1, v0) = % 8.15/1.97 zero) | ~ $i(v1) | ~ $i(v0) | complement(v1, v0) | ? [v2: $i] : ? [v3: % 8.15/1.97 $i] : (( ~ (v3 = one) & addition(v0, v1) = v3 & $i(v3)) | ( ~ (v2 = zero) % 8.15/1.97 & multiplication(v0, v1) = v2 & $i(v2)))) & ! [v0: $i] : ! [v1: $i] : % 8.15/1.97 ( ~ (multiplication(v0, v1) = zero) | ~ $i(v1) | ~ $i(v0) | complement(v1, % 8.15/1.97 v0) | ? [v2: $i] : ? [v3: $i] : (( ~ (v3 = one) & addition(v0, v1) = v3 % 8.15/1.97 & $i(v3)) | ( ~ (v2 = zero) & multiplication(v1, v0) = v2 & $i(v2)))) & % 8.15/1.97 ! [v0: $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = one) | ~ $i(v1) | ~ % 8.15/1.97 $i(v0) | complement(v1, v0) | ? [v2: $i] : ? [v3: $i] : (( ~ (v3 = zero) & % 8.15/1.97 multiplication(v1, v0) = v3 & $i(v3)) | ( ~ (v2 = zero) & % 8.15/1.97 multiplication(v0, v1) = v2 & $i(v2)))) % 8.15/1.97 % 8.15/1.97 (test_3) % 8.85/1.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (c(v0) = v2) | ~ % 8.85/1.98 $i(v1) | ~ $i(v0) | ~ complement(v0, v1) | ~ test(v0)) & ! [v0: $i] : ! % 8.85/1.98 [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ test(v0) | % 8.85/1.98 complement(v0, v1)) % 8.85/1.98 % 8.85/1.98 Further assumptions not needed in the proof: % 8.85/1.98 -------------------------------------------- % 8.85/1.98 additive_associativity, additive_idempotence, additive_identity, % 8.85/1.98 left_annihilation, left_distributivity, multiplicative_associativity, % 8.85/1.98 multiplicative_left_identity, multiplicative_right_identity, order, % 8.85/1.98 right_annihilation, right_distributivity, test_1, test_4 % 8.85/1.98 % 8.85/1.98 Those formulas are unsatisfiable: % 8.85/1.98 --------------------------------- % 8.85/1.98 % 8.85/1.98 Begin of proof % 8.85/1.98 | % 8.85/1.98 | ALPHA: (additive_commutativity) implies: % 8.85/1.98 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | % 8.85/1.98 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) % 8.85/1.98 | % 8.85/1.98 | ALPHA: (test_2) implies: % 8.85/1.98 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~ (addition(v0, % 8.85/1.98 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) % 8.85/1.98 | % 8.85/1.98 | ALPHA: (test_3) implies: % 8.85/1.98 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) | % 8.85/1.98 | ~ test(v0) | complement(v0, v1)) % 8.85/1.98 | % 8.85/1.98 | ALPHA: (goals) implies: % 8.85/1.98 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = one) & c(v0) = v1 & % 8.85/1.98 | addition(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & test(v0)) % 8.85/1.98 | % 8.85/1.98 | DELTA: instantiating (4) with fresh symbols all_20_0, all_20_1, all_20_2 % 8.85/1.98 | gives: % 8.85/1.98 | (5) ~ (all_20_0 = one) & c(all_20_2) = all_20_1 & addition(all_20_2, % 8.85/1.98 | all_20_1) = all_20_0 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & % 8.85/1.98 | test(all_20_2) % 8.85/1.98 | % 8.85/1.98 | ALPHA: (5) implies: % 8.85/1.99 | (6) ~ (all_20_0 = one) % 8.85/1.99 | (7) test(all_20_2) % 8.85/1.99 | (8) $i(all_20_2) % 8.85/1.99 | (9) $i(all_20_1) % 8.85/1.99 | (10) addition(all_20_2, all_20_1) = all_20_0 % 8.85/1.99 | (11) c(all_20_2) = all_20_1 % 8.85/1.99 | % 8.85/1.99 | GROUND_INST: instantiating (1) with all_20_1, all_20_2, all_20_0, simplifying % 8.85/1.99 | with (8), (9), (10) gives: % 8.85/1.99 | (12) addition(all_20_1, all_20_2) = all_20_0 & $i(all_20_0) % 8.85/1.99 | % 8.85/1.99 | ALPHA: (12) implies: % 8.85/1.99 | (13) addition(all_20_1, all_20_2) = all_20_0 % 8.85/1.99 | % 8.85/1.99 | GROUND_INST: instantiating (3) with all_20_2, all_20_1, simplifying with (7), % 8.85/1.99 | (8), (9), (11) gives: % 8.85/1.99 | (14) complement(all_20_2, all_20_1) % 8.85/1.99 | % 8.85/1.99 | GROUND_INST: instantiating (2) with all_20_1, all_20_2, all_20_0, simplifying % 8.85/1.99 | with (8), (9), (13), (14) gives: % 8.85/1.99 | (15) all_20_0 = one % 8.85/1.99 | % 8.85/1.99 | REDUCE: (6), (15) imply: % 8.85/1.99 | (16) $false % 8.85/1.99 | % 8.85/1.99 | CLOSE: (16) is inconsistent. % 8.85/1.99 | % 8.85/1.99 End of proof % 8.85/1.99 % SZS output end Proof for theBenchmark % 8.85/1.99 % 8.85/1.99 1373ms %------------------------------------------------------------------------------