TSTP Solution File: NUM850+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM850+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 : n022.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 8.67s 2.05s
% Output : Proof 10.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM850+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n022.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Fri Aug 25 10:46:10 EDT 2023
% 0.17/0.34 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.24/1.19 Prover 4: Preprocessing ...
% 3.24/1.19 Prover 1: Preprocessing ...
% 3.63/1.24 Prover 5: Preprocessing ...
% 3.63/1.24 Prover 2: Preprocessing ...
% 3.63/1.24 Prover 3: Preprocessing ...
% 3.63/1.24 Prover 6: Preprocessing ...
% 3.63/1.25 Prover 0: Preprocessing ...
% 7.39/1.79 Prover 1: Warning: ignoring some quantifiers
% 7.39/1.85 Prover 1: Constructing countermodel ...
% 8.12/1.88 Prover 4: Warning: ignoring some quantifiers
% 8.37/1.90 Prover 5: Proving ...
% 8.37/1.90 Prover 6: Proving ...
% 8.37/1.93 Prover 3: Warning: ignoring some quantifiers
% 8.67/1.94 Prover 4: Constructing countermodel ...
% 8.67/1.94 Prover 3: Constructing countermodel ...
% 8.67/1.98 Prover 2: Proving ...
% 8.67/2.04 Prover 3: proved (1389ms)
% 8.67/2.05
% 8.67/2.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.67/2.05
% 8.67/2.05 Prover 2: stopped
% 8.67/2.05 Prover 6: stopped
% 8.67/2.06 Prover 1: Found proof (size 8)
% 8.67/2.06 Prover 1: proved (1405ms)
% 8.67/2.06 Prover 5: stopped
% 8.67/2.06 Prover 0: Proving ...
% 8.67/2.06 Prover 0: stopped
% 8.67/2.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.67/2.06 Prover 4: stopped
% 8.67/2.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.67/2.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.67/2.10 Prover 8: Preprocessing ...
% 8.67/2.11 Prover 7: Preprocessing ...
% 9.88/2.12 Prover 10: Preprocessing ...
% 9.88/2.15 Prover 7: stopped
% 9.88/2.16 Prover 10: stopped
% 10.28/2.23 Prover 8: Warning: ignoring some quantifiers
% 10.28/2.24 Prover 8: Constructing countermodel ...
% 10.28/2.25 Prover 8: stopped
% 10.28/2.25
% 10.28/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.28/2.25
% 10.28/2.26 % SZS output start Proof for theBenchmark
% 10.28/2.26 Assumptions after simplification:
% 10.28/2.26 ---------------------------------
% 10.28/2.26
% 10.28/2.26 (def(cond(conseq(axiom(3)), 11), 1))
% 10.80/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, v0) = v2)
% 10.80/2.30 | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, v3) = v1) | ~
% 10.80/2.30 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~
% 10.80/2.30 $i(v1) | ~ $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2)))
% 10.80/2.30
% 10.80/2.30 (holds(antec(302), 472, 0))
% 10.80/2.30 greater(vd470, vd471) = 0 & $i(vd470) & $i(vd471)
% 10.80/2.30
% 10.80/2.30 (qe(conseq_conjunct1(conseq(302))))
% 10.80/2.31 $i(vd470) & $i(vd471) & ! [v0: $i] : ( ~ (vplus(vd471, v0) = vd470) | ~
% 10.80/2.31 $i(v0))
% 10.80/2.31
% 10.80/2.31 Further assumptions not needed in the proof:
% 10.80/2.31 --------------------------------------------
% 10.80/2.31 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(163,
% 10.80/2.31 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), ass(cond(189, 0), 0),
% 10.80/2.31 ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223, 0), 0), ass(cond(228,
% 10.80/2.31 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), ass(cond(253, 0), 0),
% 10.80/2.31 ass(cond(261, 0), 0), ass(cond(270, 0), 0), ass(cond(281, 0), 0), ass(cond(290,
% 10.80/2.31 0), 0), ass(cond(33, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0),
% 10.80/2.31 ass(cond(6, 0), 0), ass(cond(61, 0), 0), ass(cond(73, 0), 0), ass(cond(81, 0),
% 10.80/2.31 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1),
% 10.80/2.31 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0),
% 10.80/2.31 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1),
% 10.80/2.31 ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0),
% 10.80/2.31 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88),
% 10.80/2.31 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2),
% 10.80/2.31 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 12), 1),
% 10.80/2.31 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1),
% 10.80/2.31 qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3),
% 10.80/2.31 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))),
% 10.80/2.31 qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0),
% 10.80/2.31 holds(definiens(249), 398, 0))), qu(restrictor(axiom(1)),
% 10.80/2.31 holds(scope(axiom(1)), 2, 0))
% 10.80/2.31
% 10.80/2.31 Those formulas are unsatisfiable:
% 10.80/2.31 ---------------------------------
% 10.80/2.31
% 10.80/2.31 Begin of proof
% 10.80/2.31 |
% 10.80/2.31 | ALPHA: (holds(antec(302), 472, 0)) implies:
% 10.80/2.31 | (1) greater(vd470, vd471) = 0
% 10.80/2.31 |
% 10.80/2.31 | ALPHA: (def(cond(conseq(axiom(3)), 11), 1)) implies:
% 10.80/2.31 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ $i(v1) | ~
% 10.80/2.31 | $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2)))
% 10.80/2.31 |
% 10.80/2.31 | ALPHA: (qe(conseq_conjunct1(conseq(302)))) implies:
% 10.92/2.31 | (3) $i(vd471)
% 10.92/2.31 | (4) $i(vd470)
% 10.92/2.31 | (5) ! [v0: $i] : ( ~ (vplus(vd471, v0) = vd470) | ~ $i(v0))
% 10.92/2.31 |
% 10.92/2.32 | GROUND_INST: instantiating (2) with vd471, vd470, simplifying with (1), (3),
% 10.92/2.32 | (4) gives:
% 10.92/2.32 | (6) ? [v0: $i] : (vplus(vd471, v0) = vd470 & $i(v0))
% 10.92/2.32 |
% 10.92/2.32 | DELTA: instantiating (6) with fresh symbol all_62_0 gives:
% 10.92/2.32 | (7) vplus(vd471, all_62_0) = vd470 & $i(all_62_0)
% 10.92/2.32 |
% 10.92/2.32 | ALPHA: (7) implies:
% 10.92/2.32 | (8) $i(all_62_0)
% 10.92/2.32 | (9) vplus(vd471, all_62_0) = vd470
% 10.92/2.32 |
% 10.92/2.32 | GROUND_INST: instantiating (5) with all_62_0, simplifying with (8), (9) gives:
% 10.92/2.32 | (10) $false
% 10.95/2.32 |
% 10.95/2.32 | CLOSE: (10) is inconsistent.
% 10.95/2.32 |
% 10.95/2.32 End of proof
% 10.95/2.32 % SZS output end Proof for theBenchmark
% 10.95/2.32
% 10.95/2.32 1699ms
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