%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM850+1 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.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 11:50:24 EDT 2023 % Result : Theorem 8.84s 2.00s % Output : Proof 8.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM850+1 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n013.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Aug 25 09:11:32 EDT 2023 % 0.13/0.35 % 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 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.53/1.21 Prover 1: Preprocessing ... % 3.53/1.21 Prover 4: Preprocessing ... % 3.53/1.25 Prover 2: Preprocessing ... % 3.53/1.25 Prover 3: Preprocessing ... % 3.53/1.25 Prover 5: Preprocessing ... % 3.53/1.25 Prover 6: Preprocessing ... % 3.53/1.25 Prover 0: Preprocessing ... % 7.43/1.77 Prover 1: Warning: ignoring some quantifiers % 7.43/1.79 Prover 5: Proving ... % 7.43/1.81 Prover 3: Warning: ignoring some quantifiers % 7.43/1.82 Prover 1: Constructing countermodel ... % 8.03/1.84 Prover 3: Constructing countermodel ... % 8.03/1.85 Prover 4: Warning: ignoring some quantifiers % 8.03/1.87 Prover 6: Proving ... % 8.36/1.89 Prover 2: Proving ... % 8.36/1.91 Prover 4: Constructing countermodel ... % 8.84/1.96 Prover 0: Proving ... % 8.84/1.99 Prover 3: proved (1338ms) % 8.84/1.99 Prover 1: Found proof (size 8) % 8.84/1.99 Prover 1: proved (1352ms) % 8.84/2.00 Prover 2: stopped % 8.84/2.00 Prover 0: stopped % 8.84/2.00 Prover 6: stopped % 8.84/2.00 Prover 4: stopped % 8.84/2.00 Prover 5: proved (1345ms) % 8.84/2.00 % 8.84/2.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.84/2.00 % 8.84/2.00 % SZS output start Proof for theBenchmark % 8.84/2.01 Assumptions after simplification: % 8.84/2.01 --------------------------------- % 8.84/2.01 % 8.84/2.01 (def(cond(conseq(axiom(3)), 11), 1)) % 8.84/2.05 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, v0) = v2) % 8.84/2.05 | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, v3) = v1) | ~ % 8.84/2.05 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ % 8.84/2.05 $i(v1) | ~ $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2))) % 8.84/2.05 % 8.84/2.05 (holds(antec(302), 472, 0)) % 8.84/2.05 greater(vd470, vd471) = 0 & $i(vd470) & $i(vd471) % 8.84/2.05 % 8.84/2.05 (qe(conseq_conjunct1(conseq(302)))) % 8.84/2.05 $i(vd470) & $i(vd471) & ! [v0: $i] : ( ~ (vplus(vd471, v0) = vd470) | ~ % 8.84/2.05 $i(v0)) % 8.84/2.05 % 8.84/2.05 Further assumptions not needed in the proof: % 8.84/2.05 -------------------------------------------- % 8.84/2.05 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158, % 8.84/2.05 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), % 8.84/2.05 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223, % 8.84/2.05 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), % 8.84/2.05 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(270, 0), 0), ass(cond(281, % 8.84/2.05 0), 0), ass(cond(290, 0), 0), ass(cond(33, 0), 0), ass(cond(43, 0), 0), % 8.84/2.05 ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0), 0), ass(cond(73, 0), % 8.84/2.05 0), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), % 8.84/2.05 1), ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), % 8.84/2.05 ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), % 8.84/2.05 1), ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), % 8.84/2.05 ass(cond(goal(202), 0), 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), % 8.84/2.05 0), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), % 8.84/2.05 0), 2), ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 12), 1), % 8.84/2.05 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1), % 8.84/2.05 qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3), % 8.84/2.05 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), % 8.84/2.05 qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), % 8.84/2.05 holds(definiens(249), 398, 0))), qu(restrictor(axiom(1)), % 8.84/2.05 holds(scope(axiom(1)), 2, 0)) % 8.84/2.05 % 8.84/2.05 Those formulas are unsatisfiable: % 8.84/2.05 --------------------------------- % 8.84/2.05 % 8.84/2.05 Begin of proof % 8.84/2.05 | % 8.84/2.05 | ALPHA: (holds(antec(302), 472, 0)) implies: % 8.84/2.05 | (1) greater(vd470, vd471) = 0 % 8.84/2.05 | % 8.84/2.05 | ALPHA: (def(cond(conseq(axiom(3)), 11), 1)) implies: % 8.84/2.06 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ $i(v1) | ~ % 8.84/2.06 | $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2))) % 8.84/2.06 | % 8.84/2.06 | ALPHA: (qe(conseq_conjunct1(conseq(302)))) implies: % 8.84/2.06 | (3) $i(vd471) % 8.84/2.06 | (4) $i(vd470) % 8.84/2.06 | (5) ! [v0: $i] : ( ~ (vplus(vd471, v0) = vd470) | ~ $i(v0)) % 8.84/2.06 | % 8.84/2.06 | GROUND_INST: instantiating (2) with vd471, vd470, simplifying with (1), (3), % 8.84/2.06 | (4) gives: % 8.84/2.06 | (6) ? [v0: $i] : (vplus(vd471, v0) = vd470 & $i(v0)) % 8.84/2.06 | % 8.84/2.06 | DELTA: instantiating (6) with fresh symbol all_63_0 gives: % 8.84/2.06 | (7) vplus(vd471, all_63_0) = vd470 & $i(all_63_0) % 8.84/2.06 | % 8.84/2.06 | ALPHA: (7) implies: % 8.84/2.06 | (8) $i(all_63_0) % 8.84/2.06 | (9) vplus(vd471, all_63_0) = vd470 % 8.84/2.06 | % 8.84/2.06 | GROUND_INST: instantiating (5) with all_63_0, simplifying with (8), (9) gives: % 8.84/2.06 | (10) $false % 8.84/2.06 | % 8.84/2.06 | CLOSE: (10) is inconsistent. % 8.84/2.06 | % 8.84/2.06 End of proof % 8.84/2.07 % SZS output end Proof for theBenchmark % 8.84/2.07 % 8.84/2.07 1447ms %------------------------------------------------------------------------------