%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KLE138+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 05:34:38 EDT 2023 % Result : Theorem 7.87s 1.70s % Output : Proof 11.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.07 % Problem : KLE138+1 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.08 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.07/0.26 % Computer : n005.cluster.edu % 0.07/0.26 % Model : x86_64 x86_64 % 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.26 % Memory : 8042.1875MB % 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 300 % 0.07/0.26 % DateTime : Tue Aug 29 11:53:22 EDT 2023 % 0.07/0.26 % CPUTime : % 0.10/0.45 ________ _____ % 0.10/0.45 ___ __ \_________(_)________________________________ % 0.10/0.45 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.10/0.45 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.10/0.45 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.10/0.45 % 0.10/0.45 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.10/0.45 (2023-06-19) % 0.10/0.45 % 0.10/0.45 (c) Philipp Rümmer, 2009-2023 % 0.10/0.45 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.10/0.45 Amanda Stjerna. % 0.10/0.45 Free software under BSD-3-Clause. % 0.10/0.45 % 0.10/0.45 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.10/0.45 % 0.10/0.45 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.10/0.46 Running up to 7 provers in parallel. % 0.10/0.47 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.10/0.47 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.10/0.47 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.10/0.47 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.10/0.47 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.10/0.47 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.10/0.47 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.47/0.91 Prover 1: Preprocessing ... % 2.47/0.92 Prover 4: Preprocessing ... % 2.74/0.95 Prover 2: Preprocessing ... % 2.74/0.95 Prover 5: Preprocessing ... % 2.74/0.95 Prover 6: Preprocessing ... % 2.74/0.95 Prover 0: Preprocessing ... % 2.74/0.95 Prover 3: Preprocessing ... % 4.23/1.21 Prover 6: Constructing countermodel ... % 4.72/1.23 Prover 1: Constructing countermodel ... % 4.72/1.24 Prover 3: Constructing countermodel ... % 5.14/1.28 Prover 5: Proving ... % 5.14/1.29 Prover 4: Constructing countermodel ... % 5.14/1.29 Prover 0: Proving ... % 5.59/1.35 Prover 3: gave up % 5.59/1.35 Prover 6: gave up % 5.59/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.59/1.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.59/1.35 Prover 1: gave up % 5.59/1.36 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.59/1.38 Prover 2: Proving ... % 5.59/1.39 Prover 7: Preprocessing ... % 5.59/1.40 Prover 8: Preprocessing ... % 5.59/1.40 Prover 9: Preprocessing ... % 6.67/1.50 Prover 7: Constructing countermodel ... % 6.67/1.52 Prover 8: Warning: ignoring some quantifiers % 6.67/1.53 Prover 8: Constructing countermodel ... % 7.40/1.58 Prover 9: Constructing countermodel ... % 7.40/1.60 Prover 8: gave up % 7.70/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.87/1.64 Prover 10: Preprocessing ... % 7.87/1.70 Prover 0: proved (1230ms) % 7.87/1.70 % 7.87/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.87/1.70 % 7.87/1.70 Prover 9: stopped % 7.87/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.87/1.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.87/1.71 Prover 5: stopped % 7.87/1.72 Prover 2: stopped % 8.51/1.72 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.51/1.72 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.51/1.72 Prover 11: Preprocessing ... % 8.51/1.74 Prover 13: Preprocessing ... % 8.51/1.75 Prover 16: Preprocessing ... % 8.51/1.76 Prover 10: Constructing countermodel ... % 8.51/1.76 Prover 19: Preprocessing ... % 8.51/1.80 Prover 10: gave up % 8.51/1.82 Prover 13: Warning: ignoring some quantifiers % 8.51/1.83 Prover 13: Constructing countermodel ... % 8.51/1.83 Prover 16: Warning: ignoring some quantifiers % 8.51/1.84 Prover 16: Constructing countermodel ... % 8.51/1.85 Prover 11: Constructing countermodel ... % 9.44/1.86 Prover 19: Warning: ignoring some quantifiers % 9.44/1.87 Prover 19: Constructing countermodel ... % 9.44/1.87 Prover 13: gave up % 9.44/1.90 Prover 19: gave up % 10.72/2.06 Prover 4: Found proof (size 24) % 10.72/2.06 Prover 4: proved (1584ms) % 10.72/2.06 Prover 11: stopped % 10.72/2.06 Prover 7: stopped % 10.72/2.06 Prover 16: stopped % 10.72/2.06 % 10.72/2.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.72/2.06 % 11.04/2.06 % SZS output start Proof for theBenchmark % 11.04/2.06 Assumptions after simplification: % 11.04/2.06 --------------------------------- % 11.04/2.06 % 11.04/2.06 (additive_commutativity) % 11.04/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~ % 11.04/2.09 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 11.04/2.09 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 11.04/2.09 (addition(v1, v0) = v2 & $i(v2))) % 11.04/2.09 % 11.04/2.09 (additive_identity) % 11.04/2.09 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) % 11.04/2.09 | ~ $i(v0)) % 11.04/2.09 % 11.04/2.09 (goals) % 11.04/2.09 $i(one) & $i(zero) & ? [v0: $i] : ( ~ (v0 = one) & strong_iteration(zero) = % 11.04/2.09 v0 & $i(v0)) % 11.04/2.09 % 11.04/2.09 (infty_unfold1) % 11.04/2.09 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ % 11.04/2.09 $i(v0) | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1 % 11.04/2.09 & $i(v2) & $i(v1))) % 11.04/2.09 % 11.04/2.09 (isolation) % 11.04/2.10 $i(zero) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ % 11.04/2.10 $i(v0) | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & multiplication(v1, % 11.04/2.10 zero) = v3 & addition(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! % 11.04/2.10 [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 11.04/2.10 [v3: $i] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 & % 11.04/2.10 addition(v1, v3) = v2 & $i(v3) & $i(v2))) % 11.04/2.10 % 11.04/2.10 (left_annihilation) % 11.04/2.10 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, % 11.04/2.10 v0) = v1) | ~ $i(v0)) % 11.04/2.10 % 11.04/2.10 Further assumptions not needed in the proof: % 11.04/2.10 -------------------------------------------- % 11.04/2.10 additive_associativity, distributivity1, distributivity2, idempotence, % 11.04/2.10 infty_coinduction, multiplicative_associativity, multiplicative_left_identity, % 11.04/2.10 multiplicative_right_identity, order, star_induction1, star_induction2, % 11.04/2.10 star_unfold1, star_unfold2 % 11.04/2.10 % 11.04/2.10 Those formulas are unsatisfiable: % 11.04/2.10 --------------------------------- % 11.04/2.10 % 11.04/2.10 Begin of proof % 11.04/2.10 | % 11.04/2.10 | ALPHA: (additive_commutativity) implies: % 11.04/2.10 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | % 11.04/2.10 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) % 11.04/2.10 | % 11.04/2.10 | ALPHA: (additive_identity) implies: % 11.04/2.10 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) | % 11.04/2.10 | ~ $i(v0)) % 11.04/2.10 | % 11.04/2.10 | ALPHA: (left_annihilation) implies: % 11.04/2.10 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, v0) = % 11.04/2.10 | v1) | ~ $i(v0)) % 11.04/2.10 | % 11.04/2.10 | ALPHA: (infty_unfold1) implies: % 11.04/2.10 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ $i(v0) % 11.04/2.10 | | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1 % 11.04/2.10 | & $i(v2) & $i(v1))) % 11.04/2.10 | % 11.04/2.10 | ALPHA: (isolation) implies: % 11.04/2.10 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ $i(v0) % 11.04/2.10 | | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & multiplication(v1, % 11.04/2.10 | zero) = v3 & addition(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) % 11.04/2.10 | % 11.04/2.10 | ALPHA: (goals) implies: % 11.04/2.10 | (6) $i(zero) % 11.04/2.11 | (7) $i(one) % 11.04/2.11 | (8) ? [v0: $i] : ( ~ (v0 = one) & strong_iteration(zero) = v0 & $i(v0)) % 11.04/2.11 | % 11.04/2.11 | DELTA: instantiating (8) with fresh symbol all_22_0 gives: % 11.04/2.11 | (9) ~ (all_22_0 = one) & strong_iteration(zero) = all_22_0 & $i(all_22_0) % 11.04/2.11 | % 11.04/2.11 | ALPHA: (9) implies: % 11.04/2.11 | (10) ~ (all_22_0 = one) % 11.04/2.11 | (11) strong_iteration(zero) = all_22_0 % 11.04/2.11 | % 11.04/2.11 | GROUND_INST: instantiating (5) with zero, all_22_0, simplifying with (6), (11) % 11.04/2.11 | gives: % 11.04/2.11 | (12) ? [v0: $i] : ? [v1: $i] : (star(zero) = v0 & % 11.04/2.11 | multiplication(all_22_0, zero) = v1 & addition(v0, v1) = all_22_0 & % 11.04/2.11 | $i(v1) & $i(v0) & $i(all_22_0)) % 11.04/2.11 | % 11.04/2.11 | GROUND_INST: instantiating (4) with zero, all_22_0, simplifying with (6), (11) % 11.04/2.11 | gives: % 11.04/2.11 | (13) ? [v0: $i] : (multiplication(zero, all_22_0) = v0 & addition(v0, one) % 11.04/2.11 | = all_22_0 & $i(v0) & $i(all_22_0)) % 11.04/2.11 | % 11.04/2.11 | DELTA: instantiating (13) with fresh symbol all_29_0 gives: % 11.04/2.11 | (14) multiplication(zero, all_22_0) = all_29_0 & addition(all_29_0, one) = % 11.04/2.11 | all_22_0 & $i(all_29_0) & $i(all_22_0) % 11.04/2.11 | % 11.04/2.11 | ALPHA: (14) implies: % 11.04/2.11 | (15) $i(all_29_0) % 11.04/2.11 | (16) addition(all_29_0, one) = all_22_0 % 11.04/2.11 | (17) multiplication(zero, all_22_0) = all_29_0 % 11.04/2.11 | % 11.04/2.11 | DELTA: instantiating (12) with fresh symbols all_31_0, all_31_1 gives: % 11.04/2.11 | (18) star(zero) = all_31_1 & multiplication(all_22_0, zero) = all_31_0 & % 11.04/2.11 | addition(all_31_1, all_31_0) = all_22_0 & $i(all_31_0) & $i(all_31_1) % 11.04/2.11 | & $i(all_22_0) % 11.04/2.11 | % 11.04/2.11 | ALPHA: (18) implies: % 11.04/2.11 | (19) $i(all_31_1) % 11.04/2.11 | (20) $i(all_31_0) % 11.04/2.11 | (21) addition(all_31_1, all_31_0) = all_22_0 % 11.04/2.11 | % 11.04/2.11 | GROUND_INST: instantiating (1) with one, all_29_0, all_22_0, simplifying with % 11.04/2.11 | (7), (15), (16) gives: % 11.04/2.11 | (22) addition(one, all_29_0) = all_22_0 & $i(all_22_0) % 11.04/2.11 | % 11.04/2.11 | ALPHA: (22) implies: % 11.04/2.11 | (23) addition(one, all_29_0) = all_22_0 % 11.04/2.11 | % 11.04/2.11 | GROUND_INST: instantiating (1) with all_31_0, all_31_1, all_22_0, simplifying % 11.04/2.11 | with (19), (20), (21) gives: % 11.04/2.11 | (24) addition(all_31_0, all_31_1) = all_22_0 & $i(all_22_0) % 11.04/2.11 | % 11.04/2.11 | ALPHA: (24) implies: % 11.04/2.11 | (25) $i(all_22_0) % 11.04/2.11 | % 11.04/2.11 | GROUND_INST: instantiating (3) with all_22_0, all_29_0, simplifying with (17), % 11.04/2.11 | (25) gives: % 11.04/2.11 | (26) all_29_0 = zero % 11.04/2.11 | % 11.04/2.11 | REDUCE: (23), (26) imply: % 11.04/2.11 | (27) addition(one, zero) = all_22_0 % 11.04/2.11 | % 11.04/2.11 | GROUND_INST: instantiating (2) with one, all_22_0, simplifying with (7), (27) % 11.04/2.11 | gives: % 11.04/2.11 | (28) all_22_0 = one % 11.04/2.11 | % 11.04/2.11 | REDUCE: (10), (28) imply: % 11.04/2.11 | (29) $false % 11.04/2.12 | % 11.04/2.12 | CLOSE: (29) is inconsistent. % 11.04/2.12 | % 11.04/2.12 End of proof % 11.04/2.12 % SZS output end Proof for theBenchmark % 11.04/2.12 % 11.04/2.12 1664ms %------------------------------------------------------------------------------