%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM854+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 : n008.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 11:50:26 EDT 2023 % Result : Theorem 6.68s 1.63s % Output : Proof 8.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM854+2 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n008.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 14:10:02 EDT 2023 % 0.12/0.35 % 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/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.33/1.09 Prover 1: Preprocessing ... % 2.33/1.09 Prover 4: Preprocessing ... % 2.96/1.13 Prover 3: Preprocessing ... % 2.96/1.13 Prover 2: Preprocessing ... % 2.96/1.13 Prover 6: Preprocessing ... % 2.96/1.13 Prover 5: Preprocessing ... % 2.96/1.13 Prover 0: Preprocessing ... % 4.93/1.47 Prover 1: Warning: ignoring some quantifiers % 4.93/1.48 Prover 3: Warning: ignoring some quantifiers % 4.93/1.49 Prover 4: Warning: ignoring some quantifiers % 4.93/1.51 Prover 3: Constructing countermodel ... % 5.99/1.53 Prover 1: Constructing countermodel ... % 5.99/1.53 Prover 6: Proving ... % 5.99/1.53 Prover 5: Proving ... % 5.99/1.54 Prover 4: Constructing countermodel ... % 5.99/1.56 Prover 0: Proving ... % 5.99/1.58 Prover 2: Proving ... % 6.68/1.63 Prover 3: proved (1001ms) % 6.68/1.63 % 6.68/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.68/1.63 % 6.68/1.63 Prover 5: stopped % 6.68/1.63 Prover 2: stopped % 6.68/1.64 Prover 6: stopped % 6.68/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.68/1.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.68/1.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.68/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.68/1.65 Prover 0: proved (1021ms) % 6.68/1.65 % 6.68/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.68/1.65 % 6.68/1.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.18/1.71 Prover 7: Preprocessing ... % 7.18/1.71 Prover 8: Preprocessing ... % 7.18/1.71 Prover 11: Preprocessing ... % 7.18/1.71 Prover 13: Preprocessing ... % 7.18/1.71 Prover 10: Preprocessing ... % 7.18/1.72 Prover 1: Found proof (size 15) % 7.18/1.72 Prover 1: proved (1091ms) % 7.18/1.72 Prover 4: stopped % 7.18/1.73 Prover 7: stopped % 7.18/1.75 Prover 10: stopped % 7.18/1.75 Prover 11: stopped % 7.18/1.75 Prover 13: stopped % 7.95/1.82 Prover 8: Warning: ignoring some quantifiers % 8.02/1.83 Prover 8: Constructing countermodel ... % 8.02/1.84 Prover 8: stopped % 8.02/1.84 % 8.02/1.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.02/1.84 % 8.02/1.84 % SZS output start Proof for theBenchmark % 8.02/1.84 Assumptions after simplification: % 8.02/1.84 --------------------------------- % 8.02/1.84 % 8.02/1.84 (ass(cond(299, 0), 2)) % 8.02/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 8.02/1.87 int] : (v5 = 0 | ~ (vmul(v2, v0) = v4) | ~ (vmul(v1, v0) = v3) | ~ % 8.02/1.87 (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : % 8.02/1.87 ( ~ (v6 = 0) & greater(v1, v2) = v6)) % 8.02/1.87 % 8.02/1.87 (holds(conjunct1(314), 510, 0)) % 8.02/1.87 greater(vd508, vd509) = 0 & $i(vd509) & $i(vd508) % 8.02/1.87 % 8.02/1.87 (holds(conjunct1(315), 514, 0)) % 8.02/1.87 $i(vd509) & $i(vd511) & $i(vd508) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : % 8.02/1.87 ( ~ (v2 = 0) & vmul(vd509, vd511) = v1 & vmul(vd508, vd511) = v0 & greater(v0, % 8.02/1.87 v1) = v2 & $i(v1) & $i(v0)) % 8.02/1.87 % 8.02/1.87 (function-axioms) % 8.02/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.02/1.88 (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 8.02/1.88 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, % 8.02/1.88 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.02/1.88 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, % 8.02/1.88 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.02/1.88 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ % 8.02/1.88 (greater(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 8.02/1.88 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 8.02/1.88 % 8.02/1.88 Further assumptions not needed in the proof: % 8.02/1.88 -------------------------------------------- % 8.02/1.88 ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(253, 0), 0), ass(cond(261, % 8.02/1.88 0), 0), ass(cond(270, 0), 0), ass(cond(281, 0), 0), ass(cond(290, 0), 0), % 8.02/1.88 ass(cond(299, 0), 0), ass(cond(299, 0), 1), ass(cond(conjunct1(307), 0), 0), % 8.02/1.88 ass(cond(conjunct1(conjunct2(307)), 0), 0), ass(cond(conjunct2(conjunct2(307)), % 8.02/1.88 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), % 8.02/1.88 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(88), 0), % 8.02/1.88 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), % 8.02/1.88 0), 3), def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 12), % 8.02/1.88 1), holds(conjunct2(314), 513, 0), qu(cond(conseq(axiom(3)), 32), % 8.02/1.88 and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))) % 8.02/1.88 % 8.02/1.88 Those formulas are unsatisfiable: % 8.02/1.88 --------------------------------- % 8.02/1.88 % 8.02/1.88 Begin of proof % 8.02/1.88 | % 8.02/1.88 | ALPHA: (holds(conjunct1(314), 510, 0)) implies: % 8.02/1.88 | (1) greater(vd508, vd509) = 0 % 8.02/1.88 | % 8.02/1.88 | ALPHA: (holds(conjunct1(315), 514, 0)) implies: % 8.02/1.88 | (2) $i(vd508) % 8.02/1.88 | (3) $i(vd511) % 8.02/1.88 | (4) $i(vd509) % 8.02/1.89 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & vmul(vd509, % 8.02/1.89 | vd511) = v1 & vmul(vd508, vd511) = v0 & greater(v0, v1) = v2 & % 8.02/1.89 | $i(v1) & $i(v0)) % 8.02/1.89 | % 8.02/1.89 | ALPHA: (function-axioms) implies: % 8.02/1.89 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.02/1.89 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 8.02/1.89 | v2) = v0)) % 8.02/1.89 | % 8.02/1.89 | DELTA: instantiating (5) with fresh symbols all_27_0, all_27_1, all_27_2 % 8.02/1.89 | gives: % 8.02/1.89 | (7) ~ (all_27_0 = 0) & vmul(vd509, vd511) = all_27_1 & vmul(vd508, vd511) % 8.02/1.89 | = all_27_2 & greater(all_27_2, all_27_1) = all_27_0 & $i(all_27_1) & % 8.02/1.89 | $i(all_27_2) % 8.02/1.89 | % 8.02/1.89 | ALPHA: (7) implies: % 8.02/1.89 | (8) ~ (all_27_0 = 0) % 8.02/1.89 | (9) greater(all_27_2, all_27_1) = all_27_0 % 8.02/1.89 | (10) vmul(vd508, vd511) = all_27_2 % 8.02/1.89 | (11) vmul(vd509, vd511) = all_27_1 % 8.02/1.89 | % 8.02/1.89 | GROUND_INST: instantiating (ass(cond(299, 0), 2)) with vd511, vd508, vd509, % 8.02/1.89 | all_27_2, all_27_1, all_27_0, simplifying with (2), (3), (4), % 8.02/1.89 | (9), (10), (11) gives: % 8.02/1.89 | (12) all_27_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd508, vd509) = % 8.02/1.89 | v0) % 8.02/1.89 | % 8.02/1.89 | BETA: splitting (12) gives: % 8.02/1.89 | % 8.02/1.89 | Case 1: % 8.02/1.89 | | % 8.02/1.89 | | (13) all_27_0 = 0 % 8.02/1.89 | | % 8.02/1.89 | | REDUCE: (8), (13) imply: % 8.02/1.89 | | (14) $false % 8.02/1.89 | | % 8.02/1.89 | | CLOSE: (14) is inconsistent. % 8.02/1.89 | | % 8.02/1.89 | Case 2: % 8.02/1.89 | | % 8.02/1.90 | | (15) ? [v0: int] : ( ~ (v0 = 0) & greater(vd508, vd509) = v0) % 8.02/1.90 | | % 8.02/1.90 | | DELTA: instantiating (15) with fresh symbol all_49_0 gives: % 8.02/1.90 | | (16) ~ (all_49_0 = 0) & greater(vd508, vd509) = all_49_0 % 8.02/1.90 | | % 8.02/1.90 | | ALPHA: (16) implies: % 8.02/1.90 | | (17) ~ (all_49_0 = 0) % 8.02/1.90 | | (18) greater(vd508, vd509) = all_49_0 % 8.02/1.90 | | % 8.02/1.90 | | GROUND_INST: instantiating (6) with 0, all_49_0, vd509, vd508, simplifying % 8.02/1.90 | | with (1), (18) gives: % 8.02/1.90 | | (19) all_49_0 = 0 % 8.02/1.90 | | % 8.02/1.90 | | REDUCE: (17), (19) imply: % 8.02/1.90 | | (20) $false % 8.02/1.90 | | % 8.02/1.90 | | CLOSE: (20) is inconsistent. % 8.02/1.90 | | % 8.02/1.90 | End of split % 8.02/1.90 | % 8.02/1.90 End of proof % 8.02/1.90 % SZS output end Proof for theBenchmark % 8.02/1.90 % 8.02/1.90 1289ms %------------------------------------------------------------------------------