%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE074+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 : n005.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 05:34:27 EDT 2023 % Result : Theorem 7.02s 1.84s % Output : Proof 9.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : KLE074+1 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n005.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 11:20:23 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.64 ________ _____ % 0.20/0.64 ___ __ \_________(_)________________________________ % 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.64 % 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.64 (2023-06-19) % 0.20/0.64 % 0.20/0.64 (c) Philipp Rümmer, 2009-2023 % 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.64 Amanda Stjerna. % 0.20/0.64 Free software under BSD-3-Clause. % 0.20/0.64 % 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.64 % 0.20/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.66 Running up to 7 provers in parallel. % 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.31/1.20 Prover 4: Preprocessing ... % 2.31/1.21 Prover 1: Preprocessing ... % 2.96/1.26 Prover 5: Preprocessing ... % 2.96/1.26 Prover 2: Preprocessing ... % 2.96/1.26 Prover 0: Preprocessing ... % 2.96/1.26 Prover 6: Preprocessing ... % 2.96/1.26 Prover 3: Preprocessing ... % 5.69/1.64 Prover 1: Constructing countermodel ... % 5.69/1.64 Prover 6: Constructing countermodel ... % 5.69/1.65 Prover 3: Constructing countermodel ... % 5.69/1.69 Prover 4: Constructing countermodel ... % 6.20/1.72 Prover 5: Proving ... % 6.71/1.78 Prover 0: Proving ... % 7.02/1.83 Prover 3: proved (1157ms) % 7.02/1.84 % 7.02/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.02/1.84 % 7.02/1.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.02/1.85 Prover 5: stopped % 7.02/1.86 Prover 0: stopped % 7.02/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.02/1.87 Prover 6: stopped % 7.02/1.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.02/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.02/1.88 Prover 7: Preprocessing ... % 7.02/1.88 Prover 8: Preprocessing ... % 7.02/1.90 Prover 10: Preprocessing ... % 7.02/1.90 Prover 11: Preprocessing ... % 7.71/1.94 Prover 2: Proving ... % 7.71/1.94 Prover 2: stopped % 7.71/1.96 Prover 1: Found proof (size 23) % 7.71/1.96 Prover 1: proved (1286ms) % 7.71/1.96 Prover 4: stopped % 7.71/1.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.71/1.98 Prover 8: Warning: ignoring some quantifiers % 7.71/1.99 Prover 13: Preprocessing ... % 7.71/1.99 Prover 8: Constructing countermodel ... % 8.22/2.00 Prover 8: stopped % 8.22/2.01 Prover 10: Constructing countermodel ... % 8.22/2.01 Prover 13: stopped % 8.22/2.02 Prover 10: stopped % 8.22/2.04 Prover 7: Constructing countermodel ... % 8.22/2.05 Prover 7: stopped % 8.22/2.05 Prover 11: Constructing countermodel ... % 8.22/2.06 Prover 11: stopped % 8.22/2.07 % 8.22/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.22/2.07 % 8.22/2.07 % SZS output start Proof for theBenchmark % 8.22/2.08 Assumptions after simplification: % 8.22/2.08 --------------------------------- % 8.22/2.08 % 8.22/2.08 (domain2) % 8.22/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1) = v2) % 8.22/2.13 | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 8.22/2.13 ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = % 8.22/2.13 v4 & $i(v5) & $i(v4))) % 8.22/2.13 % 8.22/2.13 (goals) % 8.22/2.14 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.22/2.14 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 8.22/2.14 ( ~ (v10 = v6) & domain(v9) = v10 & domain(v7) = v8 & domain(v5) = v6 & % 8.22/2.14 domain(v2) = v4 & multiplication(v3, v4) = v5 & multiplication(v1, v4) = v7 % 8.22/2.14 & multiplication(v0, v8) = v9 & multiplication(v0, v1) = v3 & $i(v10) & % 8.22/2.14 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 8.22/2.14 $i(v1) & $i(v0)) % 8.22/2.14 % 8.22/2.14 (multiplicative_associativity) % 8.22/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 8.22/2.14 (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ $i(v2) % 8.22/2.14 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, v2) = v5 & % 8.22/2.14 multiplication(v0, v5) = v4 & $i(v5) & $i(v4))) % 8.22/2.14 % 8.22/2.14 (function-axioms) % 8.22/2.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.22/2.15 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 8.22/2.15 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.22/2.15 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0: % 8.22/2.15 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3, % 8.22/2.15 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 8.22/2.15 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) % 8.22/2.15 % 8.22/2.15 Further assumptions not needed in the proof: % 8.22/2.15 -------------------------------------------- % 8.22/2.15 additive_associativity, additive_commutativity, additive_idempotence, % 8.22/2.15 additive_identity, domain1, domain3, domain4, domain5, left_annihilation, % 8.22/2.15 left_distributivity, multiplicative_left_identity, % 8.22/2.15 multiplicative_right_identity, order, right_annihilation, right_distributivity % 8.22/2.15 % 8.22/2.15 Those formulas are unsatisfiable: % 8.22/2.15 --------------------------------- % 8.22/2.15 % 8.22/2.15 Begin of proof % 8.22/2.15 | % 8.22/2.15 | ALPHA: (function-axioms) implies: % 8.22/2.16 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain(v2) = % 8.22/2.16 | v1) | ~ (domain(v2) = v0)) % 8.22/2.16 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.22/2.16 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 8.22/2.16 | % 8.22/2.16 | DELTA: instantiating (goals) with fresh symbols all_20_0, all_20_1, all_20_2, % 8.22/2.16 | all_20_3, all_20_4, all_20_5, all_20_6, all_20_7, all_20_8, all_20_9, % 8.22/2.16 | all_20_10 gives: % 8.22/2.17 | (3) ~ (all_20_0 = all_20_4) & domain(all_20_1) = all_20_0 & % 8.22/2.17 | domain(all_20_3) = all_20_2 & domain(all_20_5) = all_20_4 & % 8.22/2.17 | domain(all_20_8) = all_20_6 & multiplication(all_20_7, all_20_6) = % 8.22/2.17 | all_20_5 & multiplication(all_20_9, all_20_6) = all_20_3 & % 8.22/2.17 | multiplication(all_20_10, all_20_2) = all_20_1 & % 8.22/2.17 | multiplication(all_20_10, all_20_9) = all_20_7 & $i(all_20_0) & % 8.87/2.17 | $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & $i(all_20_4) & % 8.87/2.17 | $i(all_20_5) & $i(all_20_6) & $i(all_20_7) & $i(all_20_8) & % 8.87/2.17 | $i(all_20_9) & $i(all_20_10) % 8.87/2.17 | % 8.87/2.17 | ALPHA: (3) implies: % 9.14/2.17 | (4) ~ (all_20_0 = all_20_4) % 9.14/2.17 | (5) $i(all_20_10) % 9.14/2.17 | (6) $i(all_20_9) % 9.14/2.17 | (7) $i(all_20_8) % 9.14/2.17 | (8) $i(all_20_7) % 9.14/2.17 | (9) $i(all_20_6) % 9.14/2.17 | (10) $i(all_20_3) % 9.14/2.17 | (11) multiplication(all_20_10, all_20_9) = all_20_7 % 9.14/2.17 | (12) multiplication(all_20_10, all_20_2) = all_20_1 % 9.14/2.17 | (13) multiplication(all_20_9, all_20_6) = all_20_3 % 9.14/2.17 | (14) multiplication(all_20_7, all_20_6) = all_20_5 % 9.14/2.17 | (15) domain(all_20_8) = all_20_6 % 9.14/2.17 | (16) domain(all_20_5) = all_20_4 % 9.14/2.18 | (17) domain(all_20_3) = all_20_2 % 9.14/2.18 | (18) domain(all_20_1) = all_20_0 % 9.14/2.18 | % 9.14/2.18 | GROUND_INST: instantiating (multiplicative_associativity) with all_20_10, % 9.14/2.18 | all_20_9, all_20_6, all_20_7, all_20_5, simplifying with (5), % 9.14/2.18 | (6), (9), (11), (14) gives: % 9.14/2.18 | (19) ? [v0: $i] : (multiplication(all_20_9, all_20_6) = v0 & % 9.14/2.18 | multiplication(all_20_10, v0) = all_20_5 & $i(v0) & $i(all_20_5)) % 9.14/2.18 | % 9.14/2.18 | GROUND_INST: instantiating (domain2) with all_20_7, all_20_8, all_20_6, % 9.14/2.18 | all_20_5, simplifying with (7), (8), (14), (15) gives: % 9.14/2.18 | (20) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_20_5) = v1 & % 9.14/2.18 | multiplication(all_20_7, all_20_8) = v0 & $i(v1) & $i(v0)) % 9.14/2.18 | % 9.14/2.18 | GROUND_INST: instantiating (domain2) with all_20_10, all_20_3, all_20_2, % 9.14/2.18 | all_20_1, simplifying with (5), (10), (12), (17) gives: % 9.14/2.19 | (21) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_20_1) = v1 & % 9.14/2.19 | multiplication(all_20_10, all_20_3) = v0 & $i(v1) & $i(v0)) % 9.14/2.19 | % 9.14/2.19 | DELTA: instantiating (19) with fresh symbol all_28_0 gives: % 9.14/2.19 | (22) multiplication(all_20_9, all_20_6) = all_28_0 & % 9.14/2.19 | multiplication(all_20_10, all_28_0) = all_20_5 & $i(all_28_0) & % 9.14/2.19 | $i(all_20_5) % 9.14/2.19 | % 9.14/2.19 | ALPHA: (22) implies: % 9.14/2.19 | (23) multiplication(all_20_10, all_28_0) = all_20_5 % 9.14/2.19 | (24) multiplication(all_20_9, all_20_6) = all_28_0 % 9.14/2.19 | % 9.14/2.19 | DELTA: instantiating (21) with fresh symbols all_30_0, all_30_1 gives: % 9.14/2.19 | (25) domain(all_30_1) = all_30_0 & domain(all_20_1) = all_30_0 & % 9.14/2.19 | multiplication(all_20_10, all_20_3) = all_30_1 & $i(all_30_0) & % 9.14/2.19 | $i(all_30_1) % 9.14/2.19 | % 9.14/2.19 | ALPHA: (25) implies: % 9.14/2.19 | (26) multiplication(all_20_10, all_20_3) = all_30_1 % 9.14/2.19 | (27) domain(all_20_1) = all_30_0 % 9.14/2.19 | (28) domain(all_30_1) = all_30_0 % 9.14/2.19 | % 9.14/2.19 | DELTA: instantiating (20) with fresh symbols all_34_0, all_34_1 gives: % 9.26/2.19 | (29) domain(all_34_1) = all_34_0 & domain(all_20_5) = all_34_0 & % 9.26/2.19 | multiplication(all_20_7, all_20_8) = all_34_1 & $i(all_34_0) & % 9.26/2.19 | $i(all_34_1) % 9.26/2.19 | % 9.26/2.19 | ALPHA: (29) implies: % 9.26/2.19 | (30) domain(all_20_5) = all_34_0 % 9.26/2.19 | % 9.26/2.19 | GROUND_INST: instantiating (2) with all_20_3, all_28_0, all_20_6, all_20_9, % 9.26/2.19 | simplifying with (13), (24) gives: % 9.26/2.20 | (31) all_28_0 = all_20_3 % 9.26/2.20 | % 9.26/2.20 | GROUND_INST: instantiating (1) with all_20_4, all_34_0, all_20_5, simplifying % 9.26/2.20 | with (16), (30) gives: % 9.26/2.20 | (32) all_34_0 = all_20_4 % 9.26/2.20 | % 9.26/2.20 | GROUND_INST: instantiating (1) with all_20_0, all_30_0, all_20_1, simplifying % 9.26/2.20 | with (18), (27) gives: % 9.26/2.20 | (33) all_30_0 = all_20_0 % 9.26/2.20 | % 9.26/2.20 | REDUCE: (28), (33) imply: % 9.26/2.20 | (34) domain(all_30_1) = all_20_0 % 9.26/2.20 | % 9.26/2.20 | REDUCE: (23), (31) imply: % 9.26/2.20 | (35) multiplication(all_20_10, all_20_3) = all_20_5 % 9.26/2.20 | % 9.26/2.20 | GROUND_INST: instantiating (2) with all_30_1, all_20_5, all_20_3, all_20_10, % 9.26/2.20 | simplifying with (26), (35) gives: % 9.26/2.20 | (36) all_30_1 = all_20_5 % 9.26/2.20 | % 9.26/2.20 | REDUCE: (34), (36) imply: % 9.26/2.20 | (37) domain(all_20_5) = all_20_0 % 9.26/2.20 | % 9.26/2.20 | GROUND_INST: instantiating (1) with all_20_4, all_20_0, all_20_5, simplifying % 9.26/2.20 | with (16), (37) gives: % 9.26/2.20 | (38) all_20_0 = all_20_4 % 9.26/2.20 | % 9.26/2.20 | REDUCE: (4), (38) imply: % 9.26/2.20 | (39) $false % 9.26/2.20 | % 9.26/2.20 | CLOSE: (39) is inconsistent. % 9.26/2.20 | % 9.26/2.20 End of proof % 9.26/2.20 % SZS output end Proof for theBenchmark % 9.26/2.20 % 9.26/2.20 1564ms %------------------------------------------------------------------------------