%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS003_1 : TPTP v8.1.2. Released v5.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.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 05:50:58 EDT 2023 % Result : Theorem 5.67s 1.55s % Output : Proof 7.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS003_1 : TPTP v8.1.2. Released v5.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n015.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 : Mon Aug 28 02:24:09 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.33/1.06 Prover 1: Preprocessing ... % 2.33/1.07 Prover 4: Preprocessing ... % 2.83/1.11 Prover 5: Preprocessing ... % 2.83/1.11 Prover 3: Preprocessing ... % 2.83/1.11 Prover 0: Preprocessing ... % 2.83/1.11 Prover 2: Preprocessing ... % 2.83/1.11 Prover 6: Preprocessing ... % 3.76/1.35 Prover 2: Proving ... % 3.76/1.35 Prover 5: Proving ... % 3.76/1.37 Prover 1: Constructing countermodel ... % 3.76/1.37 Prover 6: Constructing countermodel ... % 3.76/1.39 Prover 3: Constructing countermodel ... % 5.09/1.44 Prover 0: Proving ... % 5.09/1.45 Prover 4: Constructing countermodel ... % 5.09/1.50 Prover 6: gave up % 5.09/1.50 Prover 3: gave up % 5.09/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.09/1.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.67/1.53 Prover 7: Preprocessing ... % 5.67/1.53 Prover 1: gave up % 5.67/1.53 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.67/1.55 Prover 2: proved (906ms) % 5.67/1.55 Prover 5: proved (904ms) % 5.67/1.55 % 5.67/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.67/1.55 % 5.67/1.55 Prover 8: Preprocessing ... % 5.67/1.55 % 5.67/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.67/1.55 % 5.67/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.67/1.55 Prover 0: stopped % 5.67/1.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.67/1.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.67/1.57 Prover 9: Preprocessing ... % 6.19/1.59 Prover 10: Preprocessing ... % 6.19/1.59 Prover 13: Preprocessing ... % 6.19/1.61 Prover 11: Preprocessing ... % 6.19/1.61 Prover 7: Constructing countermodel ... % 6.19/1.62 Prover 13: Warning: ignoring some quantifiers % 6.19/1.63 Prover 7: gave up % 6.19/1.63 Prover 13: Constructing countermodel ... % 6.19/1.64 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.19/1.64 Prover 10: Constructing countermodel ... % 6.19/1.65 Prover 8: Warning: ignoring some quantifiers % 6.19/1.66 Prover 8: Constructing countermodel ... % 6.19/1.66 Prover 10: gave up % 6.19/1.67 Prover 16: Preprocessing ... % 6.86/1.69 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 6.97/1.69 Prover 16: Warning: ignoring some quantifiers % 6.97/1.70 Prover 16: Constructing countermodel ... % 7.14/1.72 Prover 19: Preprocessing ... % 7.23/1.73 Prover 9: Constructing countermodel ... % 7.23/1.73 Prover 8: gave up % 7.23/1.73 Prover 9: stopped % 7.23/1.74 Prover 13: Found proof (size 25) % 7.23/1.74 Prover 13: proved (179ms) % 7.23/1.74 Prover 4: stopped % 7.23/1.74 Prover 16: stopped % 7.23/1.77 Prover 11: Constructing countermodel ... % 7.23/1.77 Prover 19: Warning: ignoring some quantifiers % 7.23/1.78 Prover 19: Constructing countermodel ... % 7.23/1.79 Prover 19: stopped % 7.23/1.79 Prover 11: stopped % 7.23/1.79 % 7.23/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.23/1.79 % 7.23/1.79 % SZS output start Proof for theBenchmark % 7.23/1.80 Assumptions after simplification: % 7.23/1.80 --------------------------------- % 7.23/1.80 % 7.23/1.80 (clause_11) % 7.23/1.80 ! [v0: real] : ! [v1: real] : ! [v2: unreal] : ( ~ real(v1) | ~ real(v0) | % 7.23/1.80 ~ unreal(v2) | ~ s(v2, v1) | ~ s(v2, v0) | ~ s1most(v2) | equalish(v1, % 7.23/1.80 v0)) % 7.23/1.80 % 7.23/1.80 (clause_15) % 7.23/1.80 ! [v0: unreal] : ( ~ unreal(v0) | ~ e(v0) | c(v0)) % 7.23/1.80 % 7.23/1.80 (clause_16) % 7.23/1.80 ! [v0: unreal] : ( ~ unreal(v0) | ~ f(v0) | d(v0)) % 7.23/1.80 % 7.23/1.80 (clause_1__clause_2) % 7.23/1.80 unreal(exist) & e(exist) & f(exist) % 7.23/1.80 % 7.23/1.80 (clause_3) % 7.23/1.80 ! [v0: unreal] : ( ~ unreal(v0) | ~ c(v0) | s2least(v0)) % 7.23/1.80 % 7.23/1.80 (clause_5) % 7.75/1.83 ! [v0: unreal] : ! [v1: real] : ( ~ (u1r2(v0) = v1) | ~ unreal(v0) | ~ % 7.75/1.83 s2least(v0) | ? [v2: real] : (u1r1(v0) = v2 & real(v2) & ~ equalish(v1, % 7.75/1.83 v2))) & ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0) | ? [v1: % 7.75/1.83 real] : ? [v2: real] : (u1r2(v0) = v1 & u1r1(v0) = v2 & real(v2) & % 7.75/1.83 real(v1) & ~ equalish(v1, v2))) % 7.75/1.83 % 7.75/1.83 (clause_6) % 7.75/1.83 ! [v0: unreal] : ! [v1: real] : ( ~ (u1r1(v0) = v1) | ~ unreal(v0) | ~ % 7.75/1.83 s2least(v0) | s(v0, v1)) & ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0) % 7.75/1.83 | ? [v1: real] : (u1r1(v0) = v1 & real(v1) & s(v0, v1))) % 7.75/1.83 % 7.75/1.83 (clause_7) % 7.75/1.83 ! [v0: unreal] : ! [v1: real] : ( ~ (u1r2(v0) = v1) | ~ unreal(v0) | ~ % 7.75/1.83 s2least(v0) | s(v0, v1)) & ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0) % 7.75/1.83 | ? [v1: real] : (u1r2(v0) = v1 & real(v1) & s(v0, v1))) % 7.75/1.83 % 7.75/1.83 (clause_9) % 7.75/1.83 ! [v0: unreal] : ( ~ unreal(v0) | ~ d(v0) | s1most(v0)) % 7.75/1.83 % 7.75/1.83 (function-axioms) % 7.75/1.84 ! [v0: real] : ! [v1: real] : ! [v2: unreal] : (v1 = v0 | ~ (u3r2(v2) = % 7.75/1.84 v1) | ~ (u3r2(v2) = v0)) & ! [v0: real] : ! [v1: real] : ! [v2: % 7.75/1.84 unreal] : (v1 = v0 | ~ (u3r1(v2) = v1) | ~ (u3r1(v2) = v0)) & ! [v0: % 7.75/1.84 real] : ! [v1: real] : ! [v2: unreal] : (v1 = v0 | ~ (u1r2(v2) = v1) | ~ % 7.75/1.84 (u1r2(v2) = v0)) & ! [v0: real] : ! [v1: real] : ! [v2: unreal] : (v1 = % 7.75/1.84 v0 | ~ (u1r1(v2) = v1) | ~ (u1r1(v2) = v0)) % 7.75/1.84 % 7.75/1.84 Further assumptions not needed in the proof: % 7.75/1.84 -------------------------------------------- % 7.75/1.84 clause_10, clause_12, clause_13, clause_14, clause_4, clause_8 % 7.75/1.84 % 7.75/1.84 Those formulas are unsatisfiable: % 7.75/1.84 --------------------------------- % 7.75/1.84 % 7.75/1.84 Begin of proof % 7.75/1.84 | % 7.75/1.84 | ALPHA: (clause_5) implies: % 7.75/1.84 | (1) ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0) | ? [v1: real] : ? % 7.75/1.84 | [v2: real] : (u1r2(v0) = v1 & u1r1(v0) = v2 & real(v2) & real(v1) & % 7.75/1.84 | ~ equalish(v1, v2))) % 7.75/1.84 | % 7.75/1.84 | ALPHA: (clause_6) implies: % 7.75/1.84 | (2) ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0) | ? [v1: real] : % 7.75/1.84 | (u1r1(v0) = v1 & real(v1) & s(v0, v1))) % 7.75/1.84 | % 7.75/1.84 | ALPHA: (clause_7) implies: % 7.75/1.84 | (3) ! [v0: unreal] : ( ~ unreal(v0) | ~ s2least(v0) | ? [v1: real] : % 7.75/1.84 | (u1r2(v0) = v1 & real(v1) & s(v0, v1))) % 7.75/1.84 | % 7.75/1.84 | ALPHA: (clause_1__clause_2) implies: % 7.75/1.84 | (4) f(exist) % 7.75/1.84 | (5) e(exist) % 7.75/1.84 | (6) unreal(exist) % 7.75/1.84 | % 7.75/1.84 | ALPHA: (function-axioms) implies: % 7.75/1.84 | (7) ! [v0: real] : ! [v1: real] : ! [v2: unreal] : (v1 = v0 | ~ % 7.75/1.84 | (u1r1(v2) = v1) | ~ (u1r1(v2) = v0)) % 7.75/1.85 | (8) ! [v0: real] : ! [v1: real] : ! [v2: unreal] : (v1 = v0 | ~ % 7.75/1.85 | (u1r2(v2) = v1) | ~ (u1r2(v2) = v0)) % 7.75/1.85 | % 7.75/1.85 | GROUND_INST: instantiating (clause_16) with exist, simplifying with (4), (6) % 7.75/1.85 | gives: % 7.75/1.85 | (9) d(exist) % 7.75/1.85 | % 7.75/1.85 | GROUND_INST: instantiating (clause_15) with exist, simplifying with (5), (6) % 7.75/1.85 | gives: % 7.75/1.85 | (10) c(exist) % 7.75/1.85 | % 7.75/1.85 | GROUND_INST: instantiating (clause_9) with exist, simplifying with (6), (9) % 7.75/1.85 | gives: % 7.75/1.85 | (11) s1most(exist) % 7.75/1.85 | % 7.75/1.85 | GROUND_INST: instantiating (clause_3) with exist, simplifying with (6), (10) % 7.75/1.85 | gives: % 7.75/1.85 | (12) s2least(exist) % 7.75/1.85 | % 7.75/1.85 | GROUND_INST: instantiating (1) with exist, simplifying with (6), (12) gives: % 7.75/1.85 | (13) ? [v0: real] : ? [v1: real] : (u1r2(exist) = v0 & u1r1(exist) = v1 & % 7.75/1.85 | real(v1) & real(v0) & ~ equalish(v0, v1)) % 7.75/1.85 | % 7.75/1.85 | GROUND_INST: instantiating (3) with exist, simplifying with (6), (12) gives: % 7.75/1.85 | (14) ? [v0: real] : (u1r2(exist) = v0 & real(v0) & s(exist, v0)) % 7.75/1.85 | % 7.75/1.85 | GROUND_INST: instantiating (2) with exist, simplifying with (6), (12) gives: % 7.75/1.85 | (15) ? [v0: real] : (u1r1(exist) = v0 & real(v0) & s(exist, v0)) % 7.75/1.85 | % 7.75/1.85 | DELTA: instantiating (15) with fresh symbol all_42_0 gives: % 7.75/1.85 | (16) u1r1(exist) = all_42_0 & real(all_42_0) & s(exist, all_42_0) % 7.75/1.85 | % 7.75/1.85 | ALPHA: (16) implies: % 7.75/1.85 | (17) s(exist, all_42_0) % 7.75/1.85 | (18) u1r1(exist) = all_42_0 % 7.75/1.85 | % 7.75/1.85 | DELTA: instantiating (14) with fresh symbol all_44_0 gives: % 7.75/1.85 | (19) u1r2(exist) = all_44_0 & real(all_44_0) & s(exist, all_44_0) % 7.75/1.85 | % 7.75/1.85 | ALPHA: (19) implies: % 7.75/1.85 | (20) s(exist, all_44_0) % 7.75/1.85 | (21) u1r2(exist) = all_44_0 % 7.75/1.85 | % 7.75/1.85 | DELTA: instantiating (13) with fresh symbols all_46_0, all_46_1 gives: % 7.75/1.86 | (22) u1r2(exist) = all_46_1 & u1r1(exist) = all_46_0 & real(all_46_0) & % 7.75/1.86 | real(all_46_1) & ~ equalish(all_46_1, all_46_0) % 7.75/1.86 | % 7.75/1.86 | ALPHA: (22) implies: % 7.75/1.86 | (23) ~ equalish(all_46_1, all_46_0) % 7.75/1.86 | (24) real(all_46_1) % 7.75/1.86 | (25) real(all_46_0) % 7.75/1.86 | (26) u1r1(exist) = all_46_0 % 7.75/1.86 | (27) u1r2(exist) = all_46_1 % 7.75/1.86 | % 7.75/1.86 | GROUND_INST: instantiating (7) with all_42_0, all_46_0, exist, simplifying % 7.75/1.86 | with (18), (26) gives: % 7.75/1.86 | (28) all_46_0 = all_42_0 % 7.75/1.86 | % 7.75/1.86 | GROUND_INST: instantiating (8) with all_44_0, all_46_1, exist, simplifying % 7.75/1.86 | with (21), (27) gives: % 7.75/1.86 | (29) all_46_1 = all_44_0 % 7.75/1.86 | % 7.75/1.86 | REDUCE: (25), (28) imply: % 7.75/1.86 | (30) real(all_42_0) % 7.75/1.86 | % 7.75/1.86 | REDUCE: (24), (29) imply: % 7.75/1.86 | (31) real(all_44_0) % 7.75/1.86 | % 7.75/1.86 | REDUCE: (23), (28), (29) imply: % 7.75/1.86 | (32) ~ equalish(all_44_0, all_42_0) % 7.75/1.86 | % 7.75/1.86 | GROUND_INST: instantiating (clause_11) with all_42_0, all_44_0, exist, % 7.75/1.86 | simplifying with (6), (11), (17), (20), (30), (31), (32) gives: % 7.75/1.86 | (33) $false % 7.75/1.86 | % 7.75/1.86 | CLOSE: (33) is inconsistent. % 7.75/1.86 | % 7.75/1.86 End of proof % 7.75/1.86 % SZS output end Proof for theBenchmark % 7.75/1.86 % 7.75/1.86 1251ms %------------------------------------------------------------------------------