%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE058+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 : n032.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 05:34:25 EDT 2023 % Result : Theorem 6.20s 1.46s % Output : Proof 8.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.10 % Problem : KLE058+1 : TPTP v8.1.2. Released v4.0.0. % 0.05/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.30 % Computer : n032.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Tue Aug 29 12:16:31 EDT 2023 % 0.10/0.30 % CPUTime : % 0.14/0.53 ________ _____ % 0.14/0.53 ___ __ \_________(_)________________________________ % 0.14/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.14/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.14/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.14/0.53 % 0.14/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.14/0.53 (2023-06-19) % 0.14/0.53 % 0.14/0.53 (c) Philipp Rümmer, 2009-2023 % 0.14/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.14/0.53 Amanda Stjerna. % 0.14/0.53 Free software under BSD-3-Clause. % 0.14/0.54 % 0.14/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.14/0.54 % 0.14/0.54 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.14/0.55 Running up to 7 provers in parallel. % 0.14/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.14/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.14/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.14/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.14/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.14/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.14/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 1.74/0.90 Prover 4: Preprocessing ... % 1.74/0.90 Prover 1: Preprocessing ... % 2.32/0.94 Prover 6: Preprocessing ... % 2.32/0.94 Prover 2: Preprocessing ... % 2.32/0.94 Prover 0: Preprocessing ... % 2.32/0.94 Prover 5: Preprocessing ... % 2.32/0.94 Prover 3: Preprocessing ... % 4.42/1.23 Prover 6: Constructing countermodel ... % 4.42/1.23 Prover 1: Constructing countermodel ... % 4.42/1.24 Prover 4: Constructing countermodel ... % 4.42/1.25 Prover 3: Constructing countermodel ... % 4.42/1.25 Prover 5: Proving ... % 5.08/1.31 Prover 0: Proving ... % 5.50/1.38 Prover 2: Proving ... % 6.20/1.46 Prover 0: proved (904ms) % 6.20/1.46 % 6.20/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.20/1.46 % 6.20/1.46 Prover 5: stopped % 6.20/1.46 Prover 2: stopped % 6.20/1.46 Prover 3: stopped % 6.20/1.46 Prover 6: stopped % 6.20/1.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.20/1.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.20/1.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.20/1.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.20/1.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.20/1.50 Prover 13: Preprocessing ... % 6.20/1.50 Prover 10: Preprocessing ... % 6.20/1.51 Prover 11: Preprocessing ... % 6.20/1.51 Prover 7: Preprocessing ... % 6.20/1.52 Prover 8: Preprocessing ... % 6.93/1.58 Prover 8: Warning: ignoring some quantifiers % 6.93/1.58 Prover 10: Constructing countermodel ... % 6.93/1.58 Prover 13: Warning: ignoring some quantifiers % 6.93/1.59 Prover 13: Constructing countermodel ... % 6.93/1.59 Prover 8: Constructing countermodel ... % 7.33/1.61 Prover 11: Constructing countermodel ... % 7.33/1.62 Prover 7: Constructing countermodel ... % 8.10/1.81 Prover 4: Found proof (size 34) % 8.10/1.81 Prover 4: proved (1254ms) % 8.10/1.81 Prover 1: stopped % 8.10/1.81 Prover 10: stopped % 8.10/1.81 Prover 7: stopped % 8.10/1.81 Prover 13: stopped % 8.84/1.81 Prover 11: stopped % 8.84/1.81 Prover 8: stopped % 8.84/1.81 % 8.84/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.84/1.81 % 8.84/1.82 % SZS output start Proof for theBenchmark % 8.84/1.83 Assumptions after simplification: % 8.84/1.83 --------------------------------- % 8.84/1.83 % 8.84/1.83 (additive_associativity) % 8.84/1.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 8.84/1.85 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 8.84/1.85 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 & % 8.84/1.86 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 8.84/1.86 : ! [v4: $i] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ % 8.84/1.86 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 & % 8.84/1.86 addition(v2, v1) = v5 & $i(v5) & $i(v4))) % 8.84/1.86 % 8.84/1.86 (additive_commutativity) % 8.84/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~ % 8.84/1.86 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 8.84/1.86 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 8.84/1.86 (addition(v1, v0) = v2 & $i(v2))) % 8.84/1.86 % 8.84/1.86 (domain1) % 8.84/1.86 ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 8.84/1.86 (multiplication(v1, v0) = v2 & addition(v0, v2) = v2 & $i(v2))) % 8.84/1.86 % 8.84/1.86 (domain3) % 8.84/1.86 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | % 8.84/1.86 addition(v1, one) = one) % 8.84/1.86 % 8.84/1.86 (domain4) % 8.84/1.86 domain(zero) = zero & $i(zero) % 8.84/1.86 % 8.84/1.86 (goals) % 8.84/1.86 $i(one) & ? [v0: $i] : ( ~ (v0 = one) & domain(one) = v0 & $i(v0)) % 8.84/1.86 % 8.84/1.86 (multiplicative_right_identity) % 8.84/1.86 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 8.84/1.86 v1) | ~ $i(v0)) % 8.84/1.86 % 8.84/1.86 (function-axioms) % 8.84/1.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.84/1.87 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 8.84/1.87 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.84/1.87 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0: % 8.84/1.87 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3, % 8.84/1.87 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 8.84/1.87 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) % 8.84/1.87 % 8.84/1.87 Further assumptions not needed in the proof: % 8.84/1.87 -------------------------------------------- % 8.84/1.87 additive_idempotence, additive_identity, domain2, domain5, left_annihilation, % 8.84/1.87 left_distributivity, multiplicative_associativity, multiplicative_left_identity, % 8.84/1.87 order, right_annihilation, right_distributivity % 8.84/1.87 % 8.84/1.87 Those formulas are unsatisfiable: % 8.84/1.87 --------------------------------- % 8.84/1.87 % 8.84/1.87 Begin of proof % 8.84/1.87 | % 8.84/1.87 | ALPHA: (additive_commutativity) implies: % 8.84/1.87 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | % 8.84/1.87 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) % 8.84/1.87 | % 8.84/1.87 | ALPHA: (additive_associativity) implies: % 8.84/1.87 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 8.84/1.87 | ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | % 8.84/1.87 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & % 8.84/1.87 | addition(v1, v0) = v5 & $i(v5) & $i(v4))) % 8.84/1.87 | % 8.84/1.87 | ALPHA: (multiplicative_right_identity) implies: % 8.84/1.87 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) = % 8.84/1.87 | v1) | ~ $i(v0)) % 8.84/1.87 | % 8.84/1.87 | ALPHA: (domain3) implies: % 8.84/1.87 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | % 8.84/1.87 | addition(v1, one) = one) % 8.84/1.87 | % 8.84/1.87 | ALPHA: (domain4) implies: % 8.84/1.88 | (5) $i(zero) % 8.84/1.88 | (6) domain(zero) = zero % 8.84/1.88 | % 8.84/1.88 | ALPHA: (goals) implies: % 8.84/1.88 | (7) $i(one) % 8.84/1.88 | (8) ? [v0: $i] : ( ~ (v0 = one) & domain(one) = v0 & $i(v0)) % 8.84/1.88 | % 8.84/1.88 | ALPHA: (function-axioms) implies: % 8.84/1.88 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.84/1.88 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 8.84/1.88 | % 8.84/1.88 | DELTA: instantiating (8) with fresh symbol all_20_0 gives: % 8.84/1.88 | (10) ~ (all_20_0 = one) & domain(one) = all_20_0 & $i(all_20_0) % 8.84/1.88 | % 8.84/1.88 | ALPHA: (10) implies: % 8.84/1.88 | (11) ~ (all_20_0 = one) % 8.84/1.88 | (12) $i(all_20_0) % 8.84/1.88 | (13) domain(one) = all_20_0 % 8.84/1.88 | % 8.84/1.88 | GROUND_INST: instantiating (4) with zero, zero, simplifying with (5), (6) % 8.84/1.88 | gives: % 8.84/1.88 | (14) addition(zero, one) = one % 8.84/1.88 | % 8.84/1.88 | GROUND_INST: instantiating (4) with one, all_20_0, simplifying with (7), (13) % 8.84/1.88 | gives: % 8.84/1.88 | (15) addition(all_20_0, one) = one % 8.84/1.88 | % 8.84/1.88 | GROUND_INST: instantiating (domain1) with one, all_20_0, simplifying with (7), % 8.84/1.88 | (13) gives: % 8.84/1.88 | (16) ? [v0: $i] : (multiplication(all_20_0, one) = v0 & addition(one, v0) % 8.84/1.88 | = v0 & $i(v0)) % 8.84/1.88 | % 8.84/1.88 | DELTA: instantiating (16) with fresh symbol all_28_0 gives: % 8.84/1.88 | (17) multiplication(all_20_0, one) = all_28_0 & addition(one, all_28_0) = % 8.84/1.88 | all_28_0 & $i(all_28_0) % 8.84/1.88 | % 8.84/1.88 | ALPHA: (17) implies: % 8.84/1.88 | (18) $i(all_28_0) % 8.84/1.88 | (19) addition(one, all_28_0) = all_28_0 % 8.84/1.88 | (20) multiplication(all_20_0, one) = all_28_0 % 8.84/1.88 | % 8.84/1.89 | GROUND_INST: instantiating (2) with all_28_0, one, zero, one, all_28_0, % 8.84/1.89 | simplifying with (5), (7), (14), (18), (19) gives: % 8.84/1.89 | (21) ? [v0: $i] : (addition(one, all_28_0) = v0 & addition(zero, v0) = % 8.84/1.89 | all_28_0 & $i(v0)) % 8.84/1.89 | % 8.84/1.89 | GROUND_INST: instantiating (2) with all_28_0, one, all_20_0, one, all_28_0, % 8.84/1.89 | simplifying with (7), (12), (15), (18), (19) gives: % 8.84/1.89 | (22) ? [v0: $i] : (addition(all_20_0, v0) = all_28_0 & addition(one, % 8.84/1.89 | all_28_0) = v0 & $i(v0)) % 8.84/1.89 | % 8.84/1.89 | GROUND_INST: instantiating (1) with one, all_20_0, one, simplifying with (7), % 8.84/1.89 | (12), (15) gives: % 8.84/1.89 | (23) addition(one, all_20_0) = one % 8.84/1.89 | % 8.84/1.89 | GROUND_INST: instantiating (3) with all_20_0, all_28_0, simplifying with (12), % 8.84/1.89 | (20) gives: % 8.84/1.89 | (24) all_28_0 = all_20_0 % 8.84/1.89 | % 8.84/1.89 | DELTA: instantiating (22) with fresh symbol all_46_0 gives: % 8.84/1.89 | (25) addition(all_20_0, all_46_0) = all_28_0 & addition(one, all_28_0) = % 8.84/1.89 | all_46_0 & $i(all_46_0) % 8.84/1.89 | % 8.84/1.89 | ALPHA: (25) implies: % 8.84/1.89 | (26) addition(one, all_28_0) = all_46_0 % 8.84/1.89 | % 8.84/1.89 | DELTA: instantiating (21) with fresh symbol all_48_0 gives: % 8.84/1.89 | (27) addition(one, all_28_0) = all_48_0 & addition(zero, all_48_0) = % 8.84/1.89 | all_28_0 & $i(all_48_0) % 8.84/1.89 | % 8.84/1.89 | ALPHA: (27) implies: % 8.84/1.89 | (28) addition(one, all_28_0) = all_48_0 % 8.84/1.89 | % 8.84/1.89 | REDUCE: (24), (28) imply: % 8.84/1.89 | (29) addition(one, all_20_0) = all_48_0 % 8.84/1.89 | % 8.84/1.89 | REDUCE: (24), (26) imply: % 8.84/1.89 | (30) addition(one, all_20_0) = all_46_0 % 8.84/1.89 | % 8.84/1.89 | REDUCE: (19), (24) imply: % 8.84/1.89 | (31) addition(one, all_20_0) = all_20_0 % 8.84/1.89 | % 8.84/1.89 | GROUND_INST: instantiating (9) with one, all_46_0, all_20_0, one, simplifying % 8.84/1.89 | with (23), (30) gives: % 8.84/1.89 | (32) all_46_0 = one % 8.84/1.89 | % 8.84/1.89 | GROUND_INST: instantiating (9) with all_46_0, all_48_0, all_20_0, one, % 8.84/1.89 | simplifying with (29), (30) gives: % 8.84/1.89 | (33) all_48_0 = all_46_0 % 8.84/1.89 | % 8.84/1.89 | GROUND_INST: instantiating (9) with all_20_0, all_48_0, all_20_0, one, % 8.84/1.89 | simplifying with (29), (31) gives: % 8.84/1.89 | (34) all_48_0 = all_20_0 % 8.84/1.89 | % 8.84/1.89 | COMBINE_EQS: (33), (34) imply: % 8.84/1.89 | (35) all_46_0 = all_20_0 % 8.84/1.89 | % 8.84/1.89 | SIMP: (35) implies: % 8.84/1.89 | (36) all_46_0 = all_20_0 % 8.84/1.89 | % 8.84/1.89 | COMBINE_EQS: (32), (36) imply: % 8.84/1.89 | (37) all_20_0 = one % 8.84/1.89 | % 8.84/1.89 | SIMP: (37) implies: % 8.84/1.89 | (38) all_20_0 = one % 8.84/1.89 | % 8.84/1.89 | REDUCE: (11), (38) imply: % 8.84/1.89 | (39) $false % 8.84/1.90 | % 8.84/1.90 | CLOSE: (39) is inconsistent. % 8.84/1.90 | % 8.84/1.90 End of proof % 8.84/1.90 % SZS output end Proof for theBenchmark % 8.84/1.90 % 8.84/1.90 1360ms %------------------------------------------------------------------------------