%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE056+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 : n015.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 05:34:24 EDT 2023 % Result : Theorem 8.46s 1.87s % Output : Proof 10.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : KLE056+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n015.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 12:25:41 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.51/1.03 Prover 1: Preprocessing ... % 2.51/1.04 Prover 4: Preprocessing ... % 2.82/1.10 Prover 5: Preprocessing ... % 2.82/1.10 Prover 6: Preprocessing ... % 2.82/1.10 Prover 0: Preprocessing ... % 2.82/1.10 Prover 3: Preprocessing ... % 2.82/1.10 Prover 2: Preprocessing ... % 4.57/1.38 Prover 3: Constructing countermodel ... % 4.57/1.38 Prover 6: Constructing countermodel ... % 4.57/1.39 Prover 1: Constructing countermodel ... % 4.57/1.40 Prover 4: Constructing countermodel ... % 4.57/1.48 Prover 5: Proving ... % 4.57/1.49 Prover 0: Proving ... % 6.21/1.57 Prover 2: Proving ... % 7.34/1.72 Prover 3: gave up % 7.34/1.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.34/1.76 Prover 7: Preprocessing ... % 8.46/1.87 Prover 0: proved (1220ms) % 8.46/1.87 % 8.46/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.46/1.87 % 8.46/1.87 Prover 6: stopped % 8.46/1.87 Prover 2: stopped % 8.56/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.56/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.56/1.89 Prover 7: Constructing countermodel ... % 8.56/1.89 Prover 5: stopped % 8.56/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.56/1.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.56/1.90 Prover 8: Preprocessing ... % 8.78/1.92 Prover 10: Preprocessing ... % 8.78/1.92 Prover 11: Preprocessing ... % 8.78/1.93 Prover 13: Preprocessing ... % 8.99/1.98 Prover 8: Warning: ignoring some quantifiers % 8.99/1.98 Prover 8: Constructing countermodel ... % 8.99/2.00 Prover 10: Constructing countermodel ... % 8.99/2.00 Prover 13: Warning: ignoring some quantifiers % 8.99/2.01 Prover 11: Constructing countermodel ... % 8.99/2.02 Prover 13: Constructing countermodel ... % 8.99/2.07 Prover 1: gave up % 8.99/2.09 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.99/2.11 Prover 16: Preprocessing ... % 9.80/2.15 Prover 7: Found proof (size 17) % 9.80/2.15 Prover 7: proved (412ms) % 9.80/2.15 Prover 10: stopped % 9.80/2.15 Prover 8: stopped % 9.80/2.15 Prover 13: stopped % 9.80/2.15 Prover 4: stopped % 9.80/2.15 Prover 16: stopped % 9.80/2.16 Prover 11: stopped % 9.80/2.16 % 9.80/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.80/2.16 % 9.80/2.16 % SZS output start Proof for theBenchmark % 9.80/2.16 Assumptions after simplification: % 9.80/2.16 --------------------------------- % 9.80/2.16 % 9.80/2.16 (additive_identity) % 9.80/2.19 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) % 9.80/2.19 | ~ $i(v0)) % 9.80/2.19 % 9.80/2.19 (domain1) % 9.80/2.19 ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 9.80/2.19 (multiplication(v1, v0) = v2 & addition(v0, v2) = v2 & $i(v2))) % 9.80/2.19 % 9.80/2.19 (goals) % 9.80/2.19 $i(zero) & ? [v0: $i] : ( ~ (v0 = zero) & domain(v0) = zero & $i(v0)) % 9.80/2.19 % 9.80/2.19 (left_annihilation) % 9.80/2.19 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, % 9.80/2.19 v0) = v1) | ~ $i(v0)) % 10.68/2.19 % 10.68/2.19 Further assumptions not needed in the proof: % 10.68/2.19 -------------------------------------------- % 10.68/2.19 additive_associativity, additive_commutativity, additive_idempotence, domain2, % 10.68/2.19 domain3, domain4, domain5, left_distributivity, multiplicative_associativity, % 10.68/2.19 multiplicative_left_identity, multiplicative_right_identity, order, % 10.68/2.19 right_annihilation, right_distributivity % 10.68/2.19 % 10.68/2.19 Those formulas are unsatisfiable: % 10.68/2.19 --------------------------------- % 10.68/2.19 % 10.68/2.19 Begin of proof % 10.68/2.19 | % 10.68/2.19 | ALPHA: (additive_identity) implies: % 10.68/2.19 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) | % 10.68/2.19 | ~ $i(v0)) % 10.68/2.19 | % 10.68/2.20 | ALPHA: (left_annihilation) implies: % 10.68/2.20 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, v0) = % 10.68/2.20 | v1) | ~ $i(v0)) % 10.68/2.20 | % 10.68/2.20 | ALPHA: (goals) implies: % 10.68/2.20 | (3) ? [v0: $i] : ( ~ (v0 = zero) & domain(v0) = zero & $i(v0)) % 10.68/2.20 | % 10.68/2.20 | DELTA: instantiating (3) with fresh symbol all_20_0 gives: % 10.68/2.20 | (4) ~ (all_20_0 = zero) & domain(all_20_0) = zero & $i(all_20_0) % 10.68/2.20 | % 10.68/2.20 | ALPHA: (4) implies: % 10.68/2.20 | (5) ~ (all_20_0 = zero) % 10.68/2.20 | (6) $i(all_20_0) % 10.68/2.20 | (7) domain(all_20_0) = zero % 10.68/2.20 | % 10.68/2.20 | GROUND_INST: instantiating (domain1) with all_20_0, zero, simplifying with % 10.68/2.20 | (6), (7) gives: % 10.68/2.20 | (8) ? [v0: $i] : (multiplication(zero, all_20_0) = v0 & addition(all_20_0, % 10.68/2.20 | v0) = v0 & $i(v0)) % 10.68/2.20 | % 10.68/2.20 | DELTA: instantiating (8) with fresh symbol all_28_0 gives: % 10.68/2.20 | (9) multiplication(zero, all_20_0) = all_28_0 & addition(all_20_0, % 10.68/2.20 | all_28_0) = all_28_0 & $i(all_28_0) % 10.68/2.20 | % 10.68/2.20 | ALPHA: (9) implies: % 10.68/2.20 | (10) addition(all_20_0, all_28_0) = all_28_0 % 10.68/2.20 | (11) multiplication(zero, all_20_0) = all_28_0 % 10.68/2.20 | % 10.68/2.20 | GROUND_INST: instantiating (1) with all_20_0, zero, simplifying with (6) % 10.68/2.20 | gives: % 10.68/2.20 | (12) all_20_0 = zero | ~ (addition(all_20_0, zero) = zero) % 10.68/2.20 | % 10.68/2.20 | GROUND_INST: instantiating (2) with all_20_0, all_28_0, simplifying with (6), % 10.68/2.20 | (11) gives: % 10.68/2.20 | (13) all_28_0 = zero % 10.68/2.20 | % 10.68/2.20 | REDUCE: (10), (13) imply: % 10.68/2.20 | (14) addition(all_20_0, zero) = zero % 10.68/2.20 | % 10.68/2.20 | BETA: splitting (12) gives: % 10.68/2.21 | % 10.68/2.21 | Case 1: % 10.68/2.21 | | % 10.68/2.21 | | (15) ~ (addition(all_20_0, zero) = zero) % 10.68/2.21 | | % 10.68/2.21 | | PRED_UNIFY: (14), (15) imply: % 10.68/2.21 | | (16) $false % 10.68/2.21 | | % 10.68/2.21 | | CLOSE: (16) is inconsistent. % 10.68/2.21 | | % 10.68/2.21 | Case 2: % 10.68/2.21 | | % 10.68/2.21 | | (17) all_20_0 = zero % 10.68/2.21 | | % 10.68/2.21 | | REDUCE: (5), (17) imply: % 10.68/2.21 | | (18) $false % 10.68/2.21 | | % 10.68/2.21 | | CLOSE: (18) is inconsistent. % 10.68/2.21 | | % 10.68/2.21 | End of split % 10.68/2.21 | % 10.68/2.21 End of proof % 10.68/2.21 % SZS output end Proof for theBenchmark % 10.68/2.21 % 10.68/2.21 1579ms %------------------------------------------------------------------------------