TSTP Solution File: NUM838+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM838+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 : n001.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 8.65s 2.07s
% Output : Proof 10.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM838+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.35 % Computer : n001.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 15:59:28 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.63 ________ _____
% 0.22/0.63 ___ __ \_________(_)________________________________
% 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.63
% 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.63 (2023-06-19)
% 0.22/0.63
% 0.22/0.63 (c) Philipp Rümmer, 2009-2023
% 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.63 Amanda Stjerna.
% 0.22/0.63 Free software under BSD-3-Clause.
% 0.22/0.63
% 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.63
% 0.22/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.64 Running up to 7 provers in parallel.
% 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.20/1.23 Prover 1: Preprocessing ...
% 3.20/1.23 Prover 4: Preprocessing ...
% 3.20/1.27 Prover 6: Preprocessing ...
% 3.20/1.27 Prover 5: Preprocessing ...
% 3.20/1.27 Prover 0: Preprocessing ...
% 3.20/1.27 Prover 2: Preprocessing ...
% 3.20/1.27 Prover 3: Preprocessing ...
% 6.71/1.83 Prover 1: Warning: ignoring some quantifiers
% 7.33/1.87 Prover 3: Warning: ignoring some quantifiers
% 7.33/1.89 Prover 1: Constructing countermodel ...
% 7.63/1.90 Prover 6: Proving ...
% 7.63/1.90 Prover 5: Proving ...
% 7.63/1.90 Prover 3: Constructing countermodel ...
% 7.98/1.95 Prover 4: Warning: ignoring some quantifiers
% 8.01/1.98 Prover 2: Proving ...
% 8.35/2.00 Prover 4: Constructing countermodel ...
% 8.65/2.07 Prover 3: proved (1409ms)
% 8.65/2.07
% 8.65/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.65/2.07
% 8.65/2.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.65/2.08 Prover 0: Proving ...
% 8.65/2.08 Prover 0: stopped
% 8.65/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.65/2.08 Prover 2: stopped
% 8.65/2.08 Prover 5: stopped
% 8.65/2.08 Prover 6: stopped
% 8.65/2.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.65/2.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.65/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.65/2.22 Prover 1: Found proof (size 15)
% 8.65/2.22 Prover 1: proved (1578ms)
% 8.65/2.23 Prover 8: Preprocessing ...
% 8.65/2.23 Prover 7: Preprocessing ...
% 8.65/2.23 Prover 4: stopped
% 8.65/2.24 Prover 10: Preprocessing ...
% 8.65/2.24 Prover 13: Preprocessing ...
% 8.65/2.26 Prover 11: Preprocessing ...
% 9.34/2.28 Prover 10: stopped
% 9.34/2.29 Prover 7: stopped
% 10.15/2.31 Prover 13: stopped
% 10.15/2.32 Prover 11: stopped
% 10.15/2.35 Prover 8: Warning: ignoring some quantifiers
% 10.44/2.37 Prover 8: Constructing countermodel ...
% 10.44/2.38 Prover 8: stopped
% 10.44/2.38
% 10.44/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.44/2.38
% 10.44/2.38 % SZS output start Proof for theBenchmark
% 10.44/2.39 Assumptions after simplification:
% 10.44/2.39 ---------------------------------
% 10.44/2.39
% 10.44/2.39 (ass(cond(proof(196), 0), 4))
% 10.44/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 10.44/2.41 int] : (v5 = 0 | ~ (vplus(v2, v0) = v4) | ~ (vplus(v1, v0) = v3) | ~
% 10.44/2.41 (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] :
% 10.44/2.41 ( ~ (v6 = 0) & greater(v1, v2) = v6))
% 10.44/2.41
% 10.44/2.41 (holds(antec(195), 304, 0))
% 10.44/2.41 greater(vd301, vd302) = 0 & $i(vd302) & $i(vd301)
% 10.44/2.41
% 10.44/2.41 (holds(conseq(195), 305, 0))
% 10.44/2.41 $i(vd302) & $i(vd303) & $i(vd301) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] :
% 10.44/2.42 ( ~ (v2 = 0) & vplus(vd302, vd303) = v1 & vplus(vd301, vd303) = v0 &
% 10.44/2.42 greater(v0, v1) = v2 & $i(v1) & $i(v0))
% 10.44/2.42
% 10.44/2.42 (function-axioms)
% 10.44/2.42 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.44/2.42 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 10.44/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.44/2.42 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 10.44/2.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vskolem7(v3, v2) = v1) |
% 10.44/2.42 ~ (vskolem7(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 10.44/2.42 [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & !
% 10.44/2.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 10.44/2.42 $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 10.44/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.44/2.42 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 10.44/2.42 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~
% 10.44/2.42 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 10.44/2.42 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 10.44/2.42
% 10.44/2.42 Further assumptions not needed in the proof:
% 10.44/2.42 --------------------------------------------
% 10.44/2.42 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 10.44/2.42 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 10.44/2.42 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(33, 0), 0), ass(cond(43, 0),
% 10.44/2.42 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0), 0), ass(cond(73,
% 10.44/2.42 0), 0), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130),
% 10.44/2.42 0), 1), ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3),
% 10.44/2.42 ass(cond(goal(177), 0), 0), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0),
% 10.44/2.42 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), 0), 3), ass(cond(proof(196),
% 10.44/2.42 0), 0), ass(cond(proof(196), 0), 1), ass(cond(proof(196), 0), 2),
% 10.44/2.42 ass(cond(proof(196), 0), 3), ass(cond(proof(196), 0), 5), ass(cond(proof(196),
% 10.44/2.42 0), 6), ass(cond(proof(196), 0), 7), ass(cond(proof(196), 0), 8),
% 10.44/2.42 ass(cond(proof(196), 0), 9), def(cond(conseq(axiom(3)), 11), 1),
% 10.44/2.42 def(cond(conseq(axiom(3)), 12), 1), def(cond(conseq(axiom(3)), 16), 1),
% 10.44/2.42 def(cond(conseq(axiom(3)), 17), 1), qu(antec(axiom(3)), imp(antec(axiom(3)))),
% 10.44/2.42 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 10.44/2.42 holds(definiens(29), 44, 0))), qu(restrictor(axiom(1)),
% 10.44/2.42 holds(scope(axiom(1)), 2, 0))
% 10.44/2.42
% 10.44/2.42 Those formulas are unsatisfiable:
% 10.44/2.42 ---------------------------------
% 10.44/2.42
% 10.44/2.42 Begin of proof
% 10.44/2.42 |
% 10.44/2.42 | ALPHA: (holds(antec(195), 304, 0)) implies:
% 10.44/2.43 | (1) greater(vd301, vd302) = 0
% 10.44/2.43 |
% 10.44/2.43 | ALPHA: (holds(conseq(195), 305, 0)) implies:
% 10.44/2.43 | (2) $i(vd301)
% 10.44/2.43 | (3) $i(vd303)
% 10.44/2.43 | (4) $i(vd302)
% 10.44/2.43 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & vplus(vd302,
% 10.44/2.43 | vd303) = v1 & vplus(vd301, vd303) = v0 & greater(v0, v1) = v2 &
% 10.44/2.43 | $i(v1) & $i(v0))
% 10.44/2.43 |
% 10.44/2.43 | ALPHA: (function-axioms) implies:
% 10.44/2.43 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.44/2.43 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 10.44/2.43 | v2) = v0))
% 10.44/2.43 |
% 10.44/2.43 | DELTA: instantiating (5) with fresh symbols all_44_0, all_44_1, all_44_2
% 10.44/2.43 | gives:
% 10.44/2.43 | (7) ~ (all_44_0 = 0) & vplus(vd302, vd303) = all_44_1 & vplus(vd301,
% 10.44/2.43 | vd303) = all_44_2 & greater(all_44_2, all_44_1) = all_44_0 &
% 10.44/2.43 | $i(all_44_1) & $i(all_44_2)
% 10.44/2.43 |
% 10.44/2.43 | ALPHA: (7) implies:
% 10.44/2.43 | (8) ~ (all_44_0 = 0)
% 10.44/2.43 | (9) greater(all_44_2, all_44_1) = all_44_0
% 10.44/2.43 | (10) vplus(vd301, vd303) = all_44_2
% 10.44/2.43 | (11) vplus(vd302, vd303) = all_44_1
% 10.44/2.43 |
% 10.44/2.43 | GROUND_INST: instantiating (ass(cond(proof(196), 0), 4)) with vd303, vd301,
% 10.44/2.43 | vd302, all_44_2, all_44_1, all_44_0, simplifying with (2), (3),
% 10.44/2.43 | (4), (9), (10), (11) gives:
% 10.44/2.43 | (12) all_44_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd301, vd302) =
% 10.44/2.43 | v0)
% 10.44/2.43 |
% 10.44/2.43 | BETA: splitting (12) gives:
% 10.44/2.43 |
% 10.44/2.43 | Case 1:
% 10.44/2.43 | |
% 10.44/2.43 | | (13) all_44_0 = 0
% 10.44/2.43 | |
% 10.44/2.43 | | REDUCE: (8), (13) imply:
% 10.44/2.43 | | (14) $false
% 10.44/2.44 | |
% 10.44/2.44 | | CLOSE: (14) is inconsistent.
% 10.44/2.44 | |
% 10.44/2.44 | Case 2:
% 10.44/2.44 | |
% 10.44/2.44 | | (15) ? [v0: int] : ( ~ (v0 = 0) & greater(vd301, vd302) = v0)
% 10.44/2.44 | |
% 10.44/2.44 | | DELTA: instantiating (15) with fresh symbol all_63_0 gives:
% 10.44/2.44 | | (16) ~ (all_63_0 = 0) & greater(vd301, vd302) = all_63_0
% 10.44/2.44 | |
% 10.44/2.44 | | ALPHA: (16) implies:
% 10.44/2.44 | | (17) ~ (all_63_0 = 0)
% 10.44/2.44 | | (18) greater(vd301, vd302) = all_63_0
% 10.44/2.44 | |
% 10.44/2.44 | | GROUND_INST: instantiating (6) with 0, all_63_0, vd302, vd301, simplifying
% 10.44/2.44 | | with (1), (18) gives:
% 10.44/2.44 | | (19) all_63_0 = 0
% 10.44/2.44 | |
% 10.44/2.44 | | REDUCE: (17), (19) imply:
% 10.44/2.44 | | (20) $false
% 10.44/2.44 | |
% 10.44/2.44 | | CLOSE: (20) is inconsistent.
% 10.44/2.44 | |
% 10.44/2.44 | End of split
% 10.44/2.44 |
% 10.44/2.44 End of proof
% 10.44/2.44 % SZS output end Proof for theBenchmark
% 10.44/2.44
% 10.44/2.44 1811ms
%------------------------------------------------------------------------------