%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM838+2 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 11:50:18 EDT 2023 % Result : Theorem 6.73s 1.68s % Output : Proof 8.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM838+2 : TPTP v8.1.2. Released v4.1.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n009.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 11:35:51 EDT 2023 % 0.12/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.62/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.62/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.62/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.62/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.62/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.62/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.62/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.67/1.08 Prover 1: Preprocessing ... % 2.67/1.08 Prover 4: Preprocessing ... % 3.16/1.12 Prover 2: Preprocessing ... % 3.16/1.12 Prover 5: Preprocessing ... % 3.16/1.12 Prover 0: Preprocessing ... % 3.16/1.12 Prover 6: Preprocessing ... % 3.16/1.12 Prover 3: Preprocessing ... % 5.38/1.46 Prover 1: Warning: ignoring some quantifiers % 5.38/1.50 Prover 1: Constructing countermodel ... % 6.10/1.52 Prover 4: Warning: ignoring some quantifiers % 6.10/1.56 Prover 5: Proving ... % 6.10/1.56 Prover 3: Warning: ignoring some quantifiers % 6.10/1.58 Prover 4: Constructing countermodel ... % 6.10/1.58 Prover 3: Constructing countermodel ... % 6.10/1.59 Prover 2: Proving ... % 6.10/1.59 Prover 0: Proving ... % 6.10/1.59 Prover 6: Proving ... % 6.73/1.67 Prover 3: proved (1018ms) % 6.73/1.68 % 6.73/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.73/1.68 % 6.73/1.68 Prover 5: stopped % 7.40/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.40/1.69 Prover 0: stopped % 7.51/1.70 Prover 2: stopped % 7.51/1.70 Prover 6: stopped % 7.56/1.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.56/1.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.56/1.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.56/1.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.56/1.74 Prover 8: Preprocessing ... % 7.56/1.75 Prover 7: Preprocessing ... % 7.56/1.75 Prover 11: Preprocessing ... % 7.56/1.76 Prover 13: Preprocessing ... % 7.56/1.76 Prover 10: Preprocessing ... % 7.56/1.77 Prover 1: Found proof (size 20) % 7.56/1.77 Prover 1: proved (1125ms) % 7.56/1.77 Prover 4: stopped % 7.56/1.79 Prover 7: stopped % 7.56/1.79 Prover 10: stopped % 7.56/1.80 Prover 13: stopped % 7.56/1.80 Prover 11: stopped % 7.56/1.85 Prover 8: Warning: ignoring some quantifiers % 7.56/1.86 Prover 8: Constructing countermodel ... % 8.42/1.87 Prover 8: stopped % 8.42/1.87 % 8.42/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.42/1.87 % 8.42/1.88 % SZS output start Proof for theBenchmark % 8.42/1.88 Assumptions after simplification: % 8.42/1.88 --------------------------------- % 8.42/1.88 % 8.42/1.88 (ass(cond(proof(196), 0), 4)) % 8.42/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 8.42/1.92 int] : (v5 = 0 | ~ (vplus(v2, v0) = v4) | ~ (vplus(v1, v0) = v3) | ~ % 8.42/1.92 (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : % 8.42/1.92 ( ~ (v6 = 0) & greater(v1, v2) = v6)) % 8.42/1.92 % 8.42/1.92 (def(cond(conseq(axiom(3)), 11), 1)) % 8.42/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, v0) = v2) % 8.42/1.92 | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, v3) = v1) | ~ % 8.42/1.92 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ % 8.42/1.92 $i(v1) | ~ $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2))) % 8.42/1.92 % 8.42/1.92 (holds(antec(195), 304, 0)) % 8.42/1.92 greater(vd301, vd302) = 0 & $i(vd302) & $i(vd301) % 8.42/1.92 % 8.42/1.92 (holds(conseq(195), 305, 0)) % 8.42/1.93 $i(vd302) & $i(vd303) & $i(vd301) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : % 8.42/1.93 ( ~ (v2 = 0) & vplus(vd302, vd303) = v1 & vplus(vd301, vd303) = v0 & % 8.42/1.93 greater(v0, v1) = v2 & $i(v1) & $i(v0)) % 8.42/1.93 % 8.42/1.93 (function-axioms) % 8.42/1.93 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.42/1.93 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 8.42/1.93 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vskolem7(v3, % 8.42/1.93 v2) = v1) | ~ (vskolem7(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 8.42/1.93 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, % 8.42/1.93 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.42/1.93 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, % 8.42/1.93 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.42/1.93 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ % 8.42/1.93 (greater(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 8.42/1.93 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 8.42/1.93 % 8.42/1.93 Further assumptions not needed in the proof: % 8.42/1.93 -------------------------------------------- % 8.42/1.93 ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(184, 0), 0), ass(cond(189, % 8.42/1.93 0), 0), ass(cond(33, 0), 0), ass(cond(52, 0), 0), ass(cond(61, 0), 0), % 8.42/1.93 ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0), % 8.42/1.93 2), ass(cond(goal(130), 0), 3), ass(cond(goal(88), 0), 0), ass(cond(goal(88), % 8.42/1.93 0), 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), 0), 3), % 8.42/1.93 ass(cond(proof(196), 0), 0), ass(cond(proof(196), 0), 1), ass(cond(proof(196), % 8.42/1.93 0), 2), ass(cond(proof(196), 0), 3), ass(cond(proof(196), 0), 5), % 8.42/1.93 ass(cond(proof(196), 0), 6), ass(cond(proof(196), 0), 7), ass(cond(proof(196), % 8.42/1.93 0), 8), ass(cond(proof(196), 0), 9), def(cond(conseq(axiom(3)), 12), 1), % 8.42/1.93 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), % 8.42/1.93 holds(definiens(29), 44, 0))) % 8.42/1.93 % 8.42/1.93 Those formulas are unsatisfiable: % 8.42/1.93 --------------------------------- % 8.42/1.93 % 8.42/1.93 Begin of proof % 8.42/1.93 | % 8.42/1.93 | ALPHA: (holds(antec(195), 304, 0)) implies: % 8.42/1.93 | (1) greater(vd301, vd302) = 0 % 8.42/1.93 | % 8.42/1.93 | ALPHA: (def(cond(conseq(axiom(3)), 11), 1)) implies: % 8.42/1.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, % 8.42/1.94 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, % 8.42/1.94 | v3) = v1) | ~ $i(v3))) % 8.42/1.94 | % 8.42/1.94 | ALPHA: (holds(conseq(195), 305, 0)) implies: % 8.42/1.94 | (3) $i(vd301) % 8.42/1.94 | (4) $i(vd303) % 8.42/1.94 | (5) $i(vd302) % 8.42/1.94 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & vplus(vd302, % 8.42/1.94 | vd303) = v1 & vplus(vd301, vd303) = v0 & greater(v0, v1) = v2 & % 8.42/1.94 | $i(v1) & $i(v0)) % 8.42/1.94 | % 8.42/1.94 | ALPHA: (function-axioms) implies: % 8.42/1.94 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.42/1.94 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 8.42/1.94 | v2) = v0)) % 8.42/1.94 | % 8.42/1.94 | DELTA: instantiating (6) with fresh symbols all_32_0, all_32_1, all_32_2 % 8.42/1.94 | gives: % 8.42/1.94 | (8) ~ (all_32_0 = 0) & vplus(vd302, vd303) = all_32_1 & vplus(vd301, % 8.42/1.94 | vd303) = all_32_2 & greater(all_32_2, all_32_1) = all_32_0 & % 8.42/1.94 | $i(all_32_1) & $i(all_32_2) % 8.42/1.94 | % 8.42/1.94 | ALPHA: (8) implies: % 8.42/1.94 | (9) ~ (all_32_0 = 0) % 8.42/1.94 | (10) $i(all_32_2) % 8.42/1.94 | (11) $i(all_32_1) % 8.42/1.94 | (12) greater(all_32_2, all_32_1) = all_32_0 % 8.42/1.94 | (13) vplus(vd301, vd303) = all_32_2 % 8.42/1.94 | (14) vplus(vd302, vd303) = all_32_1 % 8.42/1.95 | % 8.42/1.95 | GROUND_INST: instantiating (2) with all_32_1, all_32_2, all_32_0, simplifying % 8.42/1.95 | with (10), (11), (12) gives: % 8.42/1.95 | (15) all_32_0 = 0 | ! [v0: $i] : ( ~ (vplus(all_32_1, v0) = all_32_2) | ~ % 8.42/1.95 | $i(v0)) % 8.42/1.95 | % 8.42/1.95 | GROUND_INST: instantiating (ass(cond(proof(196), 0), 4)) with vd303, vd301, % 8.42/1.95 | vd302, all_32_2, all_32_1, all_32_0, simplifying with (3), (4), % 8.42/1.95 | (5), (12), (13), (14) gives: % 8.42/1.95 | (16) all_32_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd301, vd302) = % 8.42/1.95 | v0) % 8.42/1.95 | % 8.42/1.95 | BETA: splitting (16) gives: % 8.42/1.95 | % 8.42/1.95 | Case 1: % 8.42/1.95 | | % 8.42/1.95 | | (17) all_32_0 = 0 % 8.42/1.95 | | % 8.95/1.95 | | REDUCE: (9), (17) imply: % 8.95/1.95 | | (18) $false % 8.95/1.95 | | % 8.95/1.95 | | CLOSE: (18) is inconsistent. % 8.95/1.95 | | % 8.95/1.95 | Case 2: % 8.95/1.95 | | % 8.95/1.95 | | (19) ? [v0: int] : ( ~ (v0 = 0) & greater(vd301, vd302) = v0) % 8.95/1.95 | | % 8.95/1.95 | | BETA: splitting (15) gives: % 8.95/1.95 | | % 8.95/1.95 | | Case 1: % 8.95/1.95 | | | % 8.95/1.95 | | | (20) all_32_0 = 0 % 8.95/1.95 | | | % 8.95/1.95 | | | REDUCE: (9), (20) imply: % 8.95/1.95 | | | (21) $false % 8.95/1.95 | | | % 8.95/1.95 | | | CLOSE: (21) is inconsistent. % 8.95/1.95 | | | % 8.95/1.95 | | Case 2: % 8.95/1.95 | | | % 8.95/1.95 | | | % 8.95/1.95 | | | DELTA: instantiating (19) with fresh symbol all_53_0 gives: % 8.95/1.95 | | | (22) ~ (all_53_0 = 0) & greater(vd301, vd302) = all_53_0 % 8.95/1.95 | | | % 8.95/1.95 | | | ALPHA: (22) implies: % 8.95/1.95 | | | (23) ~ (all_53_0 = 0) % 8.95/1.95 | | | (24) greater(vd301, vd302) = all_53_0 % 8.95/1.95 | | | % 8.95/1.95 | | | GROUND_INST: instantiating (7) with 0, all_53_0, vd302, vd301, simplifying % 8.95/1.95 | | | with (1), (24) gives: % 8.95/1.95 | | | (25) all_53_0 = 0 % 8.95/1.95 | | | % 8.95/1.95 | | | REDUCE: (23), (25) imply: % 8.95/1.95 | | | (26) $false % 8.95/1.95 | | | % 8.95/1.95 | | | CLOSE: (26) is inconsistent. % 8.95/1.95 | | | % 8.95/1.95 | | End of split % 8.95/1.95 | | % 8.95/1.95 | End of split % 8.95/1.95 | % 8.95/1.95 End of proof % 8.95/1.95 % SZS output end Proof for theBenchmark % 8.95/1.95 % 8.95/1.95 1328ms %------------------------------------------------------------------------------