%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE022+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 05:34:15 EDT 2023 % Result : Theorem 8.16s 1.83s % Output : Proof 10.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : KLE022+1 : TPTP v8.1.2. Released v4.0.0. % 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n022.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 12:32:38 EDT 2023 % 0.13/0.35 % 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 ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.49/1.03 Prover 1: Preprocessing ... % 2.49/1.03 Prover 4: Preprocessing ... % 2.49/1.07 Prover 3: Preprocessing ... % 2.49/1.07 Prover 6: Preprocessing ... % 2.49/1.07 Prover 5: Preprocessing ... % 2.49/1.07 Prover 0: Preprocessing ... % 2.49/1.07 Prover 2: Preprocessing ... % 4.22/1.36 Prover 3: Constructing countermodel ... % 5.11/1.41 Prover 1: Constructing countermodel ... % 5.11/1.42 Prover 6: Proving ... % 5.11/1.48 Prover 5: Proving ... % 5.11/1.48 Prover 4: Constructing countermodel ... % 5.80/1.52 Prover 0: Proving ... % 5.80/1.55 Prover 2: Proving ... % 6.51/1.60 Prover 3: gave up % 6.51/1.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.51/1.62 Prover 7: Preprocessing ... % 7.40/1.76 Prover 7: Constructing countermodel ... % 8.16/1.82 Prover 1: gave up % 8.16/1.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.16/1.83 Prover 0: proved (1188ms) % 8.16/1.83 % 8.16/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.16/1.83 % 8.16/1.83 Prover 6: stopped % 8.16/1.83 Prover 5: stopped % 8.16/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.16/1.84 Prover 2: stopped % 8.16/1.85 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.16/1.85 Prover 8: Preprocessing ... % 8.16/1.85 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.16/1.85 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.16/1.85 Prover 10: Preprocessing ... % 8.16/1.87 Prover 11: Preprocessing ... % 8.16/1.88 Prover 16: Preprocessing ... % 8.16/1.89 Prover 13: Preprocessing ... % 8.84/1.92 Prover 8: Warning: ignoring some quantifiers % 8.84/1.92 Prover 8: Constructing countermodel ... % 8.84/1.96 Prover 10: Constructing countermodel ... % 9.47/1.99 Prover 11: Constructing countermodel ... % 9.47/2.01 Prover 16: Warning: ignoring some quantifiers % 9.47/2.01 Prover 13: Warning: ignoring some quantifiers % 9.47/2.02 Prover 13: Constructing countermodel ... % 9.47/2.03 Prover 16: Constructing countermodel ... % 9.47/2.08 Prover 10: Found proof (size 25) % 9.47/2.08 Prover 10: proved (247ms) % 9.47/2.08 Prover 16: stopped % 9.47/2.08 Prover 4: stopped % 9.47/2.08 Prover 11: stopped % 9.47/2.08 Prover 7: stopped % 9.47/2.08 Prover 13: stopped % 9.47/2.08 Prover 8: stopped % 9.47/2.08 % 9.47/2.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.47/2.08 % 9.47/2.09 % SZS output start Proof for theBenchmark % 9.47/2.10 Assumptions after simplification: % 9.47/2.10 --------------------------------- % 9.47/2.10 % 9.47/2.10 (additive_commutativity) % 9.47/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ % 9.47/2.12 $i(v1) | ~ $i(v0) | (addition(v1, v0) = v2 & $i(v2))) % 9.47/2.12 % 9.47/2.12 (goals) % 9.47/2.13 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 9.47/2.13 $i] : ( ~ (v5 = v0) & c(v1) = v3 & multiplication(v0, v3) = v4 & % 9.47/2.13 multiplication(v0, v1) = v2 & addition(v2, v4) = v5 & $i(v5) & $i(v4) & % 9.47/2.13 $i(v3) & $i(v2) & $i(v1) & $i(v0) & test(v1)) % 9.47/2.13 % 9.47/2.13 (multiplicative_right_identity) % 9.47/2.13 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 9.47/2.13 v1) | ~ $i(v0)) % 9.47/2.13 % 9.47/2.13 (right_distributivity) % 9.47/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 9.47/2.13 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | % 9.47/2.13 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 9.47/2.13 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) % 9.47/2.13 % 9.47/2.13 (test_2) % 9.47/2.13 $i(one) & $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~ % 9.47/2.13 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) & % 9.47/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ % 9.47/2.13 $i(v1) | ~ $i(v0) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero % 9.47/2.13 & multiplication(v0, v1) = zero)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 9.47/2.14 (addition(v0, v1) = one) | ~ $i(v1) | ~ $i(v0) | complement(v1, v0) | ? % 9.47/2.14 [v2: $i] : ? [v3: $i] : (( ~ (v3 = zero) & multiplication(v1, v0) = v3 & % 9.47/2.14 $i(v3)) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2 & $i(v2)))) % 9.47/2.14 % 9.47/2.14 (test_3) % 9.47/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (c(v0) = v2) | ~ % 9.47/2.14 $i(v1) | ~ $i(v0) | ~ complement(v0, v1) | ~ test(v0)) & ! [v0: $i] : ! % 9.47/2.14 [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ test(v0) | % 9.47/2.14 complement(v0, v1)) % 9.47/2.14 % 9.47/2.14 (function-axioms) % 9.47/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.47/2.14 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0: % 9.47/2.14 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3, % 9.47/2.14 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 9.47/2.14 [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 9.47/2.14 % 9.47/2.14 Further assumptions not needed in the proof: % 9.47/2.14 -------------------------------------------- % 9.47/2.14 additive_associativity, additive_idempotence, additive_identity, % 9.47/2.14 left_annihilation, left_distributivity, multiplicative_associativity, % 9.47/2.14 multiplicative_left_identity, order, right_annihilation, test_1, test_4 % 9.47/2.14 % 9.47/2.14 Those formulas are unsatisfiable: % 9.47/2.14 --------------------------------- % 9.47/2.14 % 9.47/2.14 Begin of proof % 9.47/2.14 | % 9.47/2.14 | ALPHA: (multiplicative_right_identity) implies: % 9.47/2.14 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 9.47/2.14 | v1) | ~ $i(v0)) % 9.47/2.14 | % 9.47/2.14 | ALPHA: (test_2) implies: % 9.47/2.15 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~ (addition(v0, % 9.47/2.15 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) % 9.47/2.15 | % 9.47/2.15 | ALPHA: (test_3) implies: % 9.47/2.15 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) | % 9.47/2.15 | ~ test(v0) | complement(v0, v1)) % 9.47/2.15 | % 9.47/2.15 | ALPHA: (function-axioms) implies: % 9.47/2.15 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.47/2.15 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 9.47/2.15 | % 9.47/2.15 | DELTA: instantiating (goals) with fresh symbols all_20_0, all_20_1, all_20_2, % 9.47/2.15 | all_20_3, all_20_4, all_20_5 gives: % 9.47/2.15 | (5) ~ (all_20_0 = all_20_5) & c(all_20_4) = all_20_2 & % 9.47/2.15 | multiplication(all_20_5, all_20_2) = all_20_1 & % 9.47/2.15 | multiplication(all_20_5, all_20_4) = all_20_3 & addition(all_20_3, % 9.47/2.15 | all_20_1) = all_20_0 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & % 9.47/2.15 | $i(all_20_3) & $i(all_20_4) & $i(all_20_5) & test(all_20_4) % 9.47/2.15 | % 9.47/2.15 | ALPHA: (5) implies: % 10.55/2.15 | (6) ~ (all_20_0 = all_20_5) % 10.55/2.15 | (7) test(all_20_4) % 10.55/2.15 | (8) $i(all_20_5) % 10.55/2.15 | (9) $i(all_20_4) % 10.55/2.15 | (10) $i(all_20_3) % 10.55/2.15 | (11) $i(all_20_2) % 10.55/2.15 | (12) $i(all_20_1) % 10.55/2.15 | (13) addition(all_20_3, all_20_1) = all_20_0 % 10.55/2.15 | (14) multiplication(all_20_5, all_20_4) = all_20_3 % 10.55/2.15 | (15) multiplication(all_20_5, all_20_2) = all_20_1 % 10.55/2.15 | (16) c(all_20_4) = all_20_2 % 10.55/2.15 | % 10.55/2.15 | GROUND_INST: instantiating (additive_commutativity) with all_20_3, all_20_1, % 10.55/2.15 | all_20_0, simplifying with (10), (12), (13) gives: % 10.55/2.15 | (17) addition(all_20_1, all_20_3) = all_20_0 & $i(all_20_0) % 10.55/2.15 | % 10.55/2.15 | ALPHA: (17) implies: % 10.55/2.15 | (18) addition(all_20_1, all_20_3) = all_20_0 % 10.55/2.15 | % 10.55/2.16 | GROUND_INST: instantiating (right_distributivity) with all_20_5, all_20_4, % 10.55/2.16 | all_20_2, all_20_3, all_20_1, all_20_0, simplifying with (8), % 10.55/2.16 | (9), (11), (13), (14), (15) gives: % 10.55/2.16 | (19) ? [v0: $i] : (multiplication(all_20_5, v0) = all_20_0 & % 10.55/2.16 | addition(all_20_4, all_20_2) = v0 & $i(v0) & $i(all_20_0)) % 10.55/2.16 | % 10.55/2.16 | GROUND_INST: instantiating (3) with all_20_4, all_20_2, simplifying with (7), % 10.55/2.16 | (9), (11), (16) gives: % 10.55/2.16 | (20) complement(all_20_4, all_20_2) % 10.55/2.16 | % 10.55/2.16 | DELTA: instantiating (19) with fresh symbol all_30_0 gives: % 10.55/2.16 | (21) multiplication(all_20_5, all_30_0) = all_20_0 & addition(all_20_4, % 10.55/2.16 | all_20_2) = all_30_0 & $i(all_30_0) & $i(all_20_0) % 10.55/2.16 | % 10.55/2.16 | ALPHA: (21) implies: % 10.55/2.16 | (22) addition(all_20_4, all_20_2) = all_30_0 % 10.55/2.16 | % 10.55/2.16 | GROUND_INST: instantiating (additive_commutativity) with all_20_4, all_20_2, % 10.55/2.16 | all_30_0, simplifying with (9), (11), (22) gives: % 10.55/2.16 | (23) addition(all_20_2, all_20_4) = all_30_0 & $i(all_30_0) % 10.55/2.16 | % 10.55/2.16 | ALPHA: (23) implies: % 10.55/2.16 | (24) addition(all_20_2, all_20_4) = all_30_0 % 10.55/2.16 | % 10.55/2.16 | GROUND_INST: instantiating (right_distributivity) with all_20_5, all_20_2, % 10.55/2.16 | all_20_4, all_20_1, all_20_3, all_20_0, simplifying with (8), % 10.55/2.16 | (9), (11), (14), (15), (18) gives: % 10.55/2.16 | (25) ? [v0: $i] : (multiplication(all_20_5, v0) = all_20_0 & % 10.55/2.16 | addition(all_20_2, all_20_4) = v0 & $i(v0) & $i(all_20_0)) % 10.55/2.16 | % 10.55/2.16 | DELTA: instantiating (25) with fresh symbol all_38_0 gives: % 10.55/2.16 | (26) multiplication(all_20_5, all_38_0) = all_20_0 & addition(all_20_2, % 10.55/2.16 | all_20_4) = all_38_0 & $i(all_38_0) & $i(all_20_0) % 10.55/2.16 | % 10.55/2.16 | ALPHA: (26) implies: % 10.55/2.16 | (27) addition(all_20_2, all_20_4) = all_38_0 % 10.55/2.16 | (28) multiplication(all_20_5, all_38_0) = all_20_0 % 10.55/2.16 | % 10.55/2.16 | GROUND_INST: instantiating (4) with all_30_0, all_38_0, all_20_4, all_20_2, % 10.55/2.16 | simplifying with (24), (27) gives: % 10.55/2.16 | (29) all_38_0 = all_30_0 % 10.55/2.16 | % 10.55/2.16 | REDUCE: (28), (29) imply: % 10.55/2.16 | (30) multiplication(all_20_5, all_30_0) = all_20_0 % 10.55/2.16 | % 10.65/2.16 | GROUND_INST: instantiating (2) with all_20_2, all_20_4, all_30_0, simplifying % 10.65/2.16 | with (9), (11), (20), (24) gives: % 10.65/2.16 | (31) all_30_0 = one % 10.65/2.16 | % 10.65/2.16 | REDUCE: (30), (31) imply: % 10.65/2.16 | (32) multiplication(all_20_5, one) = all_20_0 % 10.65/2.16 | % 10.65/2.16 | GROUND_INST: instantiating (1) with all_20_5, all_20_0, simplifying with (8), % 10.65/2.16 | (32) gives: % 10.65/2.17 | (33) all_20_0 = all_20_5 % 10.65/2.17 | % 10.65/2.17 | REDUCE: (6), (33) imply: % 10.65/2.17 | (34) $false % 10.65/2.17 | % 10.65/2.17 | CLOSE: (34) is inconsistent. % 10.65/2.17 | % 10.65/2.17 End of proof % 10.65/2.17 % SZS output end Proof for theBenchmark % 10.65/2.17 % 10.65/2.17 1542ms %------------------------------------------------------------------------------