%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE022+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.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 05:34:16 EDT 2023 % Result : Theorem 10.23s 2.08s % Output : Proof 13.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KLE022+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n002.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 11:31:50 EDT 2023 % 0.14/0.34 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.15/1.00 Prover 4: Preprocessing ... % 2.15/1.01 Prover 1: Preprocessing ... % 2.75/1.06 Prover 3: Preprocessing ... % 2.75/1.06 Prover 6: Preprocessing ... % 2.75/1.06 Prover 5: Preprocessing ... % 2.75/1.06 Prover 0: Preprocessing ... % 2.75/1.06 Prover 2: Preprocessing ... % 5.31/1.39 Prover 1: Constructing countermodel ... % 5.31/1.39 Prover 3: Constructing countermodel ... % 5.31/1.40 Prover 6: Proving ... % 5.31/1.42 Prover 4: Constructing countermodel ... % 5.31/1.43 Prover 5: Proving ... % 6.19/1.51 Prover 0: Proving ... % 6.19/1.53 Prover 2: Proving ... % 6.49/1.64 Prover 3: gave up % 7.14/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.50/1.69 Prover 7: Preprocessing ... % 8.41/1.82 Prover 7: Constructing countermodel ... % 9.92/2.04 Prover 1: gave up % 9.92/2.05 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.23/2.07 Prover 0: proved (1456ms) % 10.23/2.07 % 10.23/2.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.23/2.08 % 10.23/2.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.23/2.08 Prover 2: stopped % 10.23/2.08 Prover 5: stopped % 10.23/2.08 Prover 6: stopped % 10.23/2.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.23/2.10 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.23/2.10 Prover 8: Preprocessing ... % 10.23/2.10 Prover 10: Preprocessing ... % 10.23/2.10 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.23/2.12 Prover 11: Preprocessing ... % 10.23/2.12 Prover 13: Preprocessing ... % 10.23/2.14 Prover 16: Preprocessing ... % 11.39/2.23 Prover 8: Warning: ignoring some quantifiers % 11.39/2.23 Prover 8: Constructing countermodel ... % 11.39/2.24 Prover 10: Constructing countermodel ... % 11.39/2.24 Prover 13: Warning: ignoring some quantifiers % 11.39/2.25 Prover 16: Warning: ignoring some quantifiers % 11.56/2.25 Prover 13: Constructing countermodel ... % 11.56/2.26 Prover 16: Constructing countermodel ... % 11.56/2.27 Prover 11: Constructing countermodel ... % 12.13/2.34 Prover 8: gave up % 12.13/2.36 Prover 10: Found proof (size 25) % 12.13/2.36 Prover 10: proved (275ms) % 12.13/2.36 Prover 11: stopped % 12.13/2.36 Prover 4: stopped % 12.13/2.36 Prover 13: stopped % 12.13/2.36 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.13/2.36 Prover 16: stopped % 12.13/2.36 Prover 7: stopped % 12.49/2.37 Prover 19: Preprocessing ... % 12.49/2.43 Prover 19: Warning: ignoring some quantifiers % 12.49/2.44 Prover 19: Constructing countermodel ... % 12.49/2.44 Prover 19: stopped % 12.49/2.44 % 12.49/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.49/2.44 % 12.88/2.45 % SZS output start Proof for theBenchmark % 12.88/2.45 Assumptions after simplification: % 12.88/2.45 --------------------------------- % 12.88/2.45 % 12.88/2.45 (additive_commutativity) % 12.88/2.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ % 12.88/2.47 $i(v1) | ~ $i(v0) | (addition(v1, v0) = v2 & $i(v2))) % 12.88/2.47 % 12.88/2.47 (goals) % 12.88/2.47 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 12.88/2.47 $i] : ( ~ (v5 = v0) & c(v1) = v3 & multiplication(v0, v3) = v4 & % 12.88/2.47 multiplication(v0, v1) = v2 & addition(v2, v4) = v5 & $i(v5) & $i(v4) & % 12.88/2.47 $i(v3) & $i(v2) & $i(v1) & $i(v0) & test(v1)) % 12.88/2.47 % 12.88/2.47 (multiplicative_right_identity) % 13.01/2.47 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 13.01/2.47 v1) | ~ $i(v0)) % 13.01/2.47 % 13.01/2.47 (right_distributivity) % 13.01/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.01/2.48 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | % 13.01/2.48 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 13.01/2.48 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) % 13.01/2.48 % 13.01/2.48 (test_2) % 13.01/2.48 $i(one) & $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~ % 13.01/2.48 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) & % 13.01/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ % 13.01/2.48 $i(v1) | ~ $i(v0) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero % 13.01/2.48 & multiplication(v0, v1) = zero)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.01/2.48 (addition(v0, v1) = one) | ~ $i(v1) | ~ $i(v0) | complement(v1, v0) | ? % 13.01/2.48 [v2: $i] : ? [v3: $i] : (( ~ (v3 = zero) & multiplication(v1, v0) = v3 & % 13.01/2.48 $i(v3)) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2 & $i(v2)))) % 13.01/2.48 % 13.01/2.48 (test_3) % 13.01/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (c(v0) = v2) | ~ % 13.01/2.48 $i(v1) | ~ $i(v0) | ~ complement(v0, v1) | ~ test(v0)) & ! [v0: $i] : ! % 13.01/2.48 [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ test(v0) | % 13.01/2.48 complement(v0, v1)) % 13.01/2.48 % 13.01/2.48 (function-axioms) % 13.01/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.01/2.48 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0: % 13.01/2.48 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3, % 13.01/2.48 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 13.01/2.48 [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 13.01/2.48 % 13.01/2.48 Further assumptions not needed in the proof: % 13.01/2.48 -------------------------------------------- % 13.01/2.48 additive_associativity, additive_idempotence, additive_identity, % 13.01/2.48 left_annihilation, left_distributivity, multiplicative_associativity, % 13.01/2.48 multiplicative_left_identity, order, right_annihilation, test_1, test_4, % 13.01/2.48 test_deMorgan1, test_deMorgan2 % 13.01/2.48 % 13.01/2.48 Those formulas are unsatisfiable: % 13.01/2.48 --------------------------------- % 13.01/2.48 % 13.01/2.48 Begin of proof % 13.01/2.48 | % 13.01/2.49 | ALPHA: (multiplicative_right_identity) implies: % 13.01/2.49 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 13.01/2.49 | v1) | ~ $i(v0)) % 13.01/2.49 | % 13.01/2.49 | ALPHA: (test_2) implies: % 13.01/2.49 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~ (addition(v0, % 13.01/2.49 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) % 13.01/2.49 | % 13.01/2.49 | ALPHA: (test_3) implies: % 13.01/2.49 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) | % 13.01/2.49 | ~ test(v0) | complement(v0, v1)) % 13.01/2.49 | % 13.01/2.49 | ALPHA: (function-axioms) implies: % 13.01/2.49 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.01/2.49 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 13.01/2.49 | % 13.01/2.49 | DELTA: instantiating (goals) with fresh symbols all_22_0, all_22_1, all_22_2, % 13.01/2.49 | all_22_3, all_22_4, all_22_5 gives: % 13.01/2.49 | (5) ~ (all_22_0 = all_22_5) & c(all_22_4) = all_22_2 & % 13.01/2.49 | multiplication(all_22_5, all_22_2) = all_22_1 & % 13.01/2.49 | multiplication(all_22_5, all_22_4) = all_22_3 & addition(all_22_3, % 13.01/2.49 | all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & % 13.01/2.49 | $i(all_22_3) & $i(all_22_4) & $i(all_22_5) & test(all_22_4) % 13.01/2.49 | % 13.01/2.49 | ALPHA: (5) implies: % 13.01/2.49 | (6) ~ (all_22_0 = all_22_5) % 13.01/2.49 | (7) test(all_22_4) % 13.01/2.49 | (8) $i(all_22_5) % 13.01/2.49 | (9) $i(all_22_4) % 13.01/2.49 | (10) $i(all_22_3) % 13.01/2.49 | (11) $i(all_22_2) % 13.01/2.49 | (12) $i(all_22_1) % 13.01/2.49 | (13) addition(all_22_3, all_22_1) = all_22_0 % 13.01/2.49 | (14) multiplication(all_22_5, all_22_4) = all_22_3 % 13.01/2.49 | (15) multiplication(all_22_5, all_22_2) = all_22_1 % 13.01/2.49 | (16) c(all_22_4) = all_22_2 % 13.01/2.49 | % 13.01/2.49 | GROUND_INST: instantiating (additive_commutativity) with all_22_3, all_22_1, % 13.01/2.49 | all_22_0, simplifying with (10), (12), (13) gives: % 13.01/2.49 | (17) addition(all_22_1, all_22_3) = all_22_0 & $i(all_22_0) % 13.01/2.49 | % 13.01/2.49 | ALPHA: (17) implies: % 13.01/2.49 | (18) addition(all_22_1, all_22_3) = all_22_0 % 13.01/2.49 | % 13.01/2.49 | GROUND_INST: instantiating (right_distributivity) with all_22_5, all_22_4, % 13.01/2.49 | all_22_2, all_22_3, all_22_1, all_22_0, simplifying with (8), % 13.01/2.49 | (9), (11), (13), (14), (15) gives: % 13.01/2.49 | (19) ? [v0: $i] : (multiplication(all_22_5, v0) = all_22_0 & % 13.01/2.49 | addition(all_22_4, all_22_2) = v0 & $i(v0) & $i(all_22_0)) % 13.01/2.49 | % 13.01/2.50 | GROUND_INST: instantiating (3) with all_22_4, all_22_2, simplifying with (7), % 13.01/2.50 | (9), (11), (16) gives: % 13.01/2.50 | (20) complement(all_22_4, all_22_2) % 13.01/2.50 | % 13.01/2.50 | DELTA: instantiating (19) with fresh symbol all_32_0 gives: % 13.01/2.50 | (21) multiplication(all_22_5, all_32_0) = all_22_0 & addition(all_22_4, % 13.01/2.50 | all_22_2) = all_32_0 & $i(all_32_0) & $i(all_22_0) % 13.01/2.50 | % 13.01/2.50 | ALPHA: (21) implies: % 13.01/2.50 | (22) addition(all_22_4, all_22_2) = all_32_0 % 13.01/2.50 | % 13.01/2.50 | GROUND_INST: instantiating (additive_commutativity) with all_22_4, all_22_2, % 13.01/2.50 | all_32_0, simplifying with (9), (11), (22) gives: % 13.01/2.50 | (23) addition(all_22_2, all_22_4) = all_32_0 & $i(all_32_0) % 13.01/2.50 | % 13.01/2.50 | ALPHA: (23) implies: % 13.01/2.50 | (24) addition(all_22_2, all_22_4) = all_32_0 % 13.01/2.50 | % 13.01/2.50 | GROUND_INST: instantiating (right_distributivity) with all_22_5, all_22_2, % 13.01/2.50 | all_22_4, all_22_1, all_22_3, all_22_0, simplifying with (8), % 13.01/2.50 | (9), (11), (14), (15), (18) gives: % 13.01/2.50 | (25) ? [v0: $i] : (multiplication(all_22_5, v0) = all_22_0 & % 13.01/2.50 | addition(all_22_2, all_22_4) = v0 & $i(v0) & $i(all_22_0)) % 13.01/2.50 | % 13.01/2.50 | DELTA: instantiating (25) with fresh symbol all_40_0 gives: % 13.01/2.50 | (26) multiplication(all_22_5, all_40_0) = all_22_0 & addition(all_22_2, % 13.01/2.50 | all_22_4) = all_40_0 & $i(all_40_0) & $i(all_22_0) % 13.01/2.50 | % 13.01/2.50 | ALPHA: (26) implies: % 13.01/2.50 | (27) addition(all_22_2, all_22_4) = all_40_0 % 13.01/2.50 | (28) multiplication(all_22_5, all_40_0) = all_22_0 % 13.01/2.50 | % 13.01/2.50 | GROUND_INST: instantiating (4) with all_32_0, all_40_0, all_22_4, all_22_2, % 13.01/2.50 | simplifying with (24), (27) gives: % 13.01/2.50 | (29) all_40_0 = all_32_0 % 13.01/2.50 | % 13.01/2.50 | REDUCE: (28), (29) imply: % 13.01/2.50 | (30) multiplication(all_22_5, all_32_0) = all_22_0 % 13.01/2.50 | % 13.01/2.50 | GROUND_INST: instantiating (2) with all_22_2, all_22_4, all_32_0, simplifying % 13.01/2.50 | with (9), (11), (20), (24) gives: % 13.01/2.50 | (31) all_32_0 = one % 13.01/2.50 | % 13.01/2.50 | REDUCE: (30), (31) imply: % 13.01/2.50 | (32) multiplication(all_22_5, one) = all_22_0 % 13.01/2.50 | % 13.01/2.50 | GROUND_INST: instantiating (1) with all_22_5, all_22_0, simplifying with (8), % 13.01/2.50 | (32) gives: % 13.01/2.50 | (33) all_22_0 = all_22_5 % 13.01/2.50 | % 13.01/2.50 | REDUCE: (6), (33) imply: % 13.01/2.50 | (34) $false % 13.01/2.50 | % 13.01/2.50 | CLOSE: (34) is inconsistent. % 13.01/2.50 | % 13.01/2.50 End of proof % 13.01/2.50 % SZS output end Proof for theBenchmark % 13.01/2.50 % 13.01/2.50 1903ms %------------------------------------------------------------------------------