TSTP Solution File: NUM854+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM854+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 : n023.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 9.12s 1.96s
% Output : Proof 11.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM854+1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 15:11:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.57/0.61 ________ _____
% 0.57/0.61 ___ __ \_________(_)________________________________
% 0.57/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.57/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.57/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.57/0.61
% 0.57/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.57/0.61 (2023-06-19)
% 0.57/0.61
% 0.57/0.61 (c) Philipp Rümmer, 2009-2023
% 0.57/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.57/0.61 Amanda Stjerna.
% 0.57/0.61 Free software under BSD-3-Clause.
% 0.57/0.61
% 0.57/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.57/0.61
% 0.57/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.57/0.62 Running up to 7 provers in parallel.
% 0.72/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.72/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.72/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.72/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.72/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.72/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.72/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.50/1.19 Prover 4: Preprocessing ...
% 3.50/1.19 Prover 1: Preprocessing ...
% 4.07/1.23 Prover 0: Preprocessing ...
% 4.07/1.23 Prover 3: Preprocessing ...
% 4.07/1.23 Prover 6: Preprocessing ...
% 4.14/1.25 Prover 5: Preprocessing ...
% 4.14/1.25 Prover 2: Preprocessing ...
% 7.40/1.70 Prover 1: Warning: ignoring some quantifiers
% 8.27/1.80 Prover 3: Warning: ignoring some quantifiers
% 8.27/1.81 Prover 5: Proving ...
% 8.27/1.81 Prover 6: Proving ...
% 8.27/1.82 Prover 1: Constructing countermodel ...
% 8.50/1.82 Prover 3: Constructing countermodel ...
% 8.50/1.82 Prover 2: Proving ...
% 8.50/1.83 Prover 4: Warning: ignoring some quantifiers
% 8.57/1.86 Prover 4: Constructing countermodel ...
% 9.12/1.94 Prover 0: Proving ...
% 9.12/1.96 Prover 3: proved (1324ms)
% 9.12/1.96
% 9.12/1.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.12/1.96
% 9.12/1.96 Prover 5: stopped
% 9.12/1.96 Prover 0: stopped
% 9.12/1.96 Prover 6: stopped
% 9.12/1.97 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.12/1.97 Prover 2: stopped
% 9.12/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.12/1.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.12/1.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.59/1.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.59/2.03 Prover 1: Found proof (size 15)
% 9.59/2.03 Prover 1: proved (1394ms)
% 9.59/2.03 Prover 4: stopped
% 9.59/2.03 Prover 7: Preprocessing ...
% 9.59/2.04 Prover 10: Preprocessing ...
% 9.59/2.04 Prover 11: Preprocessing ...
% 9.59/2.05 Prover 13: Preprocessing ...
% 10.23/2.06 Prover 8: Preprocessing ...
% 10.23/2.08 Prover 10: stopped
% 10.23/2.08 Prover 7: stopped
% 10.39/2.11 Prover 13: stopped
% 10.63/2.12 Prover 11: stopped
% 10.74/2.18 Prover 8: Warning: ignoring some quantifiers
% 10.74/2.19 Prover 8: Constructing countermodel ...
% 10.74/2.20 Prover 8: stopped
% 10.74/2.20
% 10.74/2.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.74/2.20
% 10.74/2.21 % SZS output start Proof for theBenchmark
% 10.74/2.21 Assumptions after simplification:
% 10.74/2.21 ---------------------------------
% 10.74/2.21
% 10.74/2.21 (ass(cond(299, 0), 2))
% 11.12/2.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 11.12/2.24 int] : (v5 = 0 | ~ (vmul(v2, v0) = v4) | ~ (vmul(v1, v0) = v3) | ~
% 11.12/2.24 (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] :
% 11.12/2.24 ( ~ (v6 = 0) & greater(v1, v2) = v6))
% 11.12/2.24
% 11.12/2.24 (holds(conjunct1(314), 510, 0))
% 11.12/2.24 greater(vd508, vd509) = 0 & $i(vd509) & $i(vd508)
% 11.12/2.24
% 11.12/2.24 (holds(conjunct1(315), 514, 0))
% 11.12/2.24 $i(vd509) & $i(vd511) & $i(vd508) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] :
% 11.12/2.24 ( ~ (v2 = 0) & vmul(vd509, vd511) = v1 & vmul(vd508, vd511) = v0 & greater(v0,
% 11.12/2.24 v1) = v2 & $i(v1) & $i(v0))
% 11.12/2.24
% 11.12/2.24 (function-axioms)
% 11.12/2.24 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.12/2.24 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 11.12/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.12/2.24 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 11.12/2.24 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~
% 11.12/2.24 (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 11.12/2.24 $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) & ! [v0:
% 11.12/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.12/2.24 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 11.12/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.12/2.24 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 11.12/2.24 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~
% 11.12/2.24 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 11.12/2.24 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 11.12/2.24
% 11.12/2.24 Further assumptions not needed in the proof:
% 11.12/2.24 --------------------------------------------
% 11.12/2.24 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 11.12/2.24 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 11.12/2.24 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223,
% 11.12/2.24 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0),
% 11.12/2.25 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(270, 0), 0), ass(cond(281,
% 11.12/2.25 0), 0), ass(cond(290, 0), 0), ass(cond(299, 0), 0), ass(cond(299, 0), 1),
% 11.12/2.25 ass(cond(33, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0),
% 11.12/2.25 0), ass(cond(61, 0), 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0),
% 11.12/2.25 ass(cond(conjunct1(307), 0), 0), ass(cond(conjunct1(conjunct2(307)), 0), 0),
% 11.12/2.25 ass(cond(conjunct2(conjunct2(307)), 0), 0), ass(cond(goal(130), 0), 0),
% 11.12/2.25 ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0),
% 11.12/2.25 3), ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0), 0),
% 11.12/2.25 ass(cond(goal(193), 0), 1), ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0),
% 11.12/2.25 0), ass(cond(goal(202), 0), 1), ass(cond(goal(202), 0), 2),
% 11.12/2.25 ass(cond(goal(216), 0), 0), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0),
% 11.12/2.25 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), 0), 3),
% 11.12/2.25 def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 12), 1),
% 11.12/2.25 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1),
% 11.12/2.25 holds(conjunct2(314), 513, 0), qu(antec(axiom(3)), imp(antec(axiom(3)))),
% 11.12/2.25 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 11.12/2.25 holds(definiens(29), 44, 0))), qu(cond(conseq(axiom(3)), 32),
% 11.12/2.25 and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))),
% 11.12/2.25 qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))
% 11.12/2.25
% 11.12/2.25 Those formulas are unsatisfiable:
% 11.12/2.25 ---------------------------------
% 11.12/2.25
% 11.12/2.25 Begin of proof
% 11.12/2.25 |
% 11.12/2.25 | ALPHA: (holds(conjunct1(314), 510, 0)) implies:
% 11.12/2.25 | (1) greater(vd508, vd509) = 0
% 11.12/2.25 |
% 11.12/2.25 | ALPHA: (holds(conjunct1(315), 514, 0)) implies:
% 11.12/2.25 | (2) $i(vd508)
% 11.12/2.25 | (3) $i(vd511)
% 11.12/2.25 | (4) $i(vd509)
% 11.12/2.25 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & vmul(vd509,
% 11.12/2.25 | vd511) = v1 & vmul(vd508, vd511) = v0 & greater(v0, v1) = v2 &
% 11.12/2.25 | $i(v1) & $i(v0))
% 11.12/2.25 |
% 11.12/2.25 | ALPHA: (function-axioms) implies:
% 11.12/2.25 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.12/2.25 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 11.12/2.25 | v2) = v0))
% 11.12/2.25 |
% 11.12/2.25 | DELTA: instantiating (5) with fresh symbols all_59_0, all_59_1, all_59_2
% 11.12/2.25 | gives:
% 11.12/2.25 | (7) ~ (all_59_0 = 0) & vmul(vd509, vd511) = all_59_1 & vmul(vd508, vd511)
% 11.12/2.25 | = all_59_2 & greater(all_59_2, all_59_1) = all_59_0 & $i(all_59_1) &
% 11.12/2.25 | $i(all_59_2)
% 11.12/2.25 |
% 11.12/2.25 | ALPHA: (7) implies:
% 11.12/2.25 | (8) ~ (all_59_0 = 0)
% 11.12/2.25 | (9) greater(all_59_2, all_59_1) = all_59_0
% 11.12/2.25 | (10) vmul(vd508, vd511) = all_59_2
% 11.12/2.25 | (11) vmul(vd509, vd511) = all_59_1
% 11.12/2.25 |
% 11.12/2.25 | GROUND_INST: instantiating (ass(cond(299, 0), 2)) with vd511, vd508, vd509,
% 11.12/2.25 | all_59_2, all_59_1, all_59_0, simplifying with (2), (3), (4),
% 11.12/2.25 | (9), (10), (11) gives:
% 11.12/2.26 | (12) all_59_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd508, vd509) =
% 11.12/2.26 | v0)
% 11.12/2.26 |
% 11.12/2.26 | BETA: splitting (12) gives:
% 11.12/2.26 |
% 11.12/2.26 | Case 1:
% 11.12/2.26 | |
% 11.12/2.26 | | (13) all_59_0 = 0
% 11.12/2.26 | |
% 11.12/2.26 | | REDUCE: (8), (13) imply:
% 11.12/2.26 | | (14) $false
% 11.12/2.26 | |
% 11.12/2.26 | | CLOSE: (14) is inconsistent.
% 11.12/2.26 | |
% 11.12/2.26 | Case 2:
% 11.12/2.26 | |
% 11.12/2.26 | | (15) ? [v0: int] : ( ~ (v0 = 0) & greater(vd508, vd509) = v0)
% 11.12/2.26 | |
% 11.12/2.26 | | DELTA: instantiating (15) with fresh symbol all_82_0 gives:
% 11.12/2.26 | | (16) ~ (all_82_0 = 0) & greater(vd508, vd509) = all_82_0
% 11.12/2.26 | |
% 11.12/2.26 | | ALPHA: (16) implies:
% 11.12/2.26 | | (17) ~ (all_82_0 = 0)
% 11.12/2.26 | | (18) greater(vd508, vd509) = all_82_0
% 11.12/2.26 | |
% 11.12/2.26 | | GROUND_INST: instantiating (6) with 0, all_82_0, vd509, vd508, simplifying
% 11.12/2.26 | | with (1), (18) gives:
% 11.12/2.26 | | (19) all_82_0 = 0
% 11.12/2.26 | |
% 11.12/2.26 | | REDUCE: (17), (19) imply:
% 11.12/2.26 | | (20) $false
% 11.12/2.26 | |
% 11.12/2.26 | | CLOSE: (20) is inconsistent.
% 11.12/2.26 | |
% 11.12/2.26 | End of split
% 11.12/2.26 |
% 11.12/2.26 End of proof
% 11.12/2.26 % SZS output end Proof for theBenchmark
% 11.12/2.26
% 11.12/2.26 1645ms
%------------------------------------------------------------------------------