TSTP Solution File: LCL666+1.001 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL666+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 08:12:15 EDT 2023
% Result : Theorem 2.75s 0.96s
% Output : Proof 3.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : LCL666+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Fri Aug 25 07:10:42 EDT 2023
% 0.09/0.27 % CPUTime :
% 0.13/0.47 ________ _____
% 0.13/0.47 ___ __ \_________(_)________________________________
% 0.13/0.47 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.13/0.47 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.13/0.47 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.13/0.47
% 0.13/0.47 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.13/0.47 (2023-06-19)
% 0.13/0.47
% 0.13/0.47 (c) Philipp Rümmer, 2009-2023
% 0.13/0.47 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.13/0.47 Amanda Stjerna.
% 0.13/0.47 Free software under BSD-3-Clause.
% 0.13/0.47
% 0.13/0.47 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.13/0.47
% 0.13/0.47 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.13/0.48 Running up to 7 provers in parallel.
% 0.13/0.49 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.13/0.49 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.13/0.49 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.13/0.49 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.13/0.49 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.13/0.49 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.13/0.49 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.13/0.77 Prover 4: Preprocessing ...
% 0.13/0.77 Prover 1: Preprocessing ...
% 1.15/0.81 Prover 5: Preprocessing ...
% 1.15/0.81 Prover 3: Preprocessing ...
% 1.15/0.81 Prover 0: Preprocessing ...
% 1.15/0.81 Prover 6: Preprocessing ...
% 1.15/0.81 Prover 2: Preprocessing ...
% 2.13/0.88 Prover 2: Proving ...
% 2.13/0.88 Prover 5: Proving ...
% 2.13/0.88 Prover 6: Proving ...
% 2.13/0.88 Prover 3: Constructing countermodel ...
% 2.13/0.88 Prover 1: Constructing countermodel ...
% 2.13/0.88 Prover 4: Constructing countermodel ...
% 2.13/0.91 Prover 0: Proving ...
% 2.55/0.96 Prover 3: gave up
% 2.55/0.96 Prover 1: gave up
% 2.75/0.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 2.75/0.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 2.75/0.96 Prover 5: proved (473ms)
% 2.75/0.96 Prover 2: proved (475ms)
% 2.75/0.96
% 2.75/0.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.75/0.96
% 2.75/0.97
% 2.75/0.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.75/0.97
% 2.75/0.97 Prover 6: stopped
% 2.75/0.97 Prover 0: stopped
% 2.75/0.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 2.75/0.98 Prover 7: Preprocessing ...
% 2.75/0.98 Prover 8: Preprocessing ...
% 2.75/0.98 Prover 7: Warning: ignoring some quantifiers
% 2.75/0.98 Prover 10: Preprocessing ...
% 2.75/0.98 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 2.75/0.98 Prover 7: Constructing countermodel ...
% 2.75/0.98 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 2.75/0.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 2.75/0.99 Prover 13: Preprocessing ...
% 2.75/0.99 Prover 16: Preprocessing ...
% 2.75/0.99 Prover 10: Warning: ignoring some quantifiers
% 2.75/0.99 Prover 11: Preprocessing ...
% 2.75/0.99 Prover 10: Constructing countermodel ...
% 2.75/1.00 Prover 13: Warning: ignoring some quantifiers
% 2.75/1.00 Prover 16: Warning: ignoring some quantifiers
% 2.75/1.00 Prover 13: Constructing countermodel ...
% 2.75/1.00 Prover 16: Constructing countermodel ...
% 2.75/1.00 Prover 10: gave up
% 2.75/1.01 Prover 8: Warning: ignoring some quantifiers
% 2.75/1.01 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 2.75/1.01 Prover 13: gave up
% 2.75/1.01 Prover 8: Constructing countermodel ...
% 2.75/1.01 Prover 16: gave up
% 2.75/1.01 Prover 7: gave up
% 2.75/1.02 Prover 19: Preprocessing ...
% 3.26/1.03 Prover 4: Found proof (size 19)
% 3.26/1.03 Prover 4: proved (547ms)
% 3.26/1.04 Prover 8: gave up
% 3.26/1.04 Prover 11: Constructing countermodel ...
% 3.26/1.05 Prover 11: stopped
% 3.26/1.05 Prover 19: Warning: ignoring some quantifiers
% 3.26/1.05 Prover 19: Constructing countermodel ...
% 3.26/1.06 Prover 19: stopped
% 3.26/1.06
% 3.26/1.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.26/1.06
% 3.26/1.06 % SZS output start Proof for theBenchmark
% 3.49/1.07 Assumptions after simplification:
% 3.49/1.07 ---------------------------------
% 3.49/1.07
% 3.49/1.07 (main)
% 3.49/1.10 ? [v0: $i] : (p201(v0) = 0 & p101(v0) = 0 & $i(v0) & ! [v1: $i] : ( ~
% 3.49/1.10 (p201(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (p101(v1) = v3
% 3.49/1.10 & r1(v0, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v1: $i] : ( ~
% 3.49/1.10 (p101(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (p201(v1) = v3
% 3.49/1.10 & r1(v0, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v1: $i] : ( ~
% 3.49/1.10 (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (p201(v1) =
% 3.49/1.10 v2 & p101(v1) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 3.49/1.10
% 3.49/1.10 (reflexivity)
% 3.49/1.10 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (r1(v0, v0) = v1) | ~ $i(v0))
% 3.49/1.10
% 3.49/1.11 (function-axioms)
% 3.49/1.11 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 3.49/1.11 [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0:
% 3.49/1.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 3.49/1.11 ~ (p201(v2) = v1) | ~ (p201(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 3.49/1.11 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (p101(v2) = v1) | ~
% 3.49/1.11 (p101(v2) = v0))
% 3.49/1.11
% 3.49/1.11 Those formulas are unsatisfiable:
% 3.49/1.11 ---------------------------------
% 3.49/1.11
% 3.49/1.11 Begin of proof
% 3.49/1.11 |
% 3.49/1.11 | ALPHA: (function-axioms) implies:
% 3.49/1.11 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 3.49/1.11 | (v1 = v0 | ~ (p201(v2) = v1) | ~ (p201(v2) = v0))
% 3.49/1.11 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 3.49/1.11 | ! [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0))
% 3.49/1.11 |
% 3.49/1.11 | DELTA: instantiating (main) with fresh symbol all_4_0 gives:
% 3.49/1.12 | (3) p201(all_4_0) = 0 & p101(all_4_0) = 0 & $i(all_4_0) & ! [v0: $i] : ( ~
% 3.49/1.12 | (p201(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (p101(v0)
% 3.49/1.12 | = v2 & r1(all_4_0, v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) & !
% 3.49/1.12 | [v0: $i] : ( ~ (p101(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any]
% 3.49/1.12 | : (p201(v0) = v2 & r1(all_4_0, v0) = v1 & ( ~ (v2 = 0) | ~ (v1 =
% 3.49/1.12 | 0)))) & ! [v0: $i] : ( ~ (r1(all_4_0, v0) = 0) | ~ $i(v0) |
% 3.49/1.12 | ? [v1: any] : ? [v2: any] : (p201(v0) = v1 & p101(v0) = v2 & ( ~ (v2
% 3.49/1.12 | = 0) | ~ (v1 = 0))))
% 3.49/1.12 |
% 3.49/1.12 | ALPHA: (3) implies:
% 3.49/1.12 | (4) $i(all_4_0)
% 3.49/1.12 | (5) p101(all_4_0) = 0
% 3.49/1.12 | (6) p201(all_4_0) = 0
% 3.49/1.12 | (7) ! [v0: $i] : ( ~ (p101(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 3.49/1.12 | any] : (p201(v0) = v2 & r1(all_4_0, v0) = v1 & ( ~ (v2 = 0) | ~
% 3.49/1.12 | (v1 = 0))))
% 3.49/1.12 | (8) ! [v0: $i] : ( ~ (p201(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 3.49/1.12 | any] : (p101(v0) = v2 & r1(all_4_0, v0) = v1 & ( ~ (v2 = 0) | ~
% 3.49/1.12 | (v1 = 0))))
% 3.49/1.12 |
% 3.49/1.12 | GROUND_INST: instantiating (7) with all_4_0, simplifying with (4), (5) gives:
% 3.49/1.12 | (9) ? [v0: any] : ? [v1: any] : (p201(all_4_0) = v1 & r1(all_4_0,
% 3.49/1.12 | all_4_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 3.49/1.12 |
% 3.49/1.12 | GROUND_INST: instantiating (8) with all_4_0, simplifying with (4), (6) gives:
% 3.49/1.13 | (10) ? [v0: any] : ? [v1: any] : (p101(all_4_0) = v1 & r1(all_4_0,
% 3.49/1.13 | all_4_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 3.49/1.13 |
% 3.49/1.13 | DELTA: instantiating (10) with fresh symbols all_12_0, all_12_1 gives:
% 3.49/1.13 | (11) p101(all_4_0) = all_12_0 & r1(all_4_0, all_4_0) = all_12_1 & ( ~
% 3.49/1.13 | (all_12_0 = 0) | ~ (all_12_1 = 0))
% 3.49/1.13 |
% 3.49/1.13 | ALPHA: (11) implies:
% 3.49/1.13 | (12) r1(all_4_0, all_4_0) = all_12_1
% 3.49/1.13 |
% 3.49/1.13 | DELTA: instantiating (9) with fresh symbols all_14_0, all_14_1 gives:
% 3.49/1.13 | (13) p201(all_4_0) = all_14_0 & r1(all_4_0, all_4_0) = all_14_1 & ( ~
% 3.49/1.13 | (all_14_0 = 0) | ~ (all_14_1 = 0))
% 3.49/1.13 |
% 3.49/1.13 | ALPHA: (13) implies:
% 3.49/1.13 | (14) r1(all_4_0, all_4_0) = all_14_1
% 3.49/1.13 | (15) p201(all_4_0) = all_14_0
% 3.49/1.13 | (16) ~ (all_14_0 = 0) | ~ (all_14_1 = 0)
% 3.49/1.13 |
% 3.49/1.13 | GROUND_INST: instantiating (2) with all_12_1, all_14_1, all_4_0, all_4_0,
% 3.49/1.13 | simplifying with (12), (14) gives:
% 3.49/1.13 | (17) all_14_1 = all_12_1
% 3.49/1.13 |
% 3.49/1.13 | GROUND_INST: instantiating (1) with 0, all_14_0, all_4_0, simplifying with
% 3.49/1.13 | (6), (15) gives:
% 3.49/1.13 | (18) all_14_0 = 0
% 3.49/1.13 |
% 3.49/1.13 | BETA: splitting (16) gives:
% 3.49/1.13 |
% 3.49/1.13 | Case 1:
% 3.49/1.13 | |
% 3.49/1.13 | | (19) ~ (all_14_0 = 0)
% 3.49/1.13 | |
% 3.49/1.13 | | REDUCE: (18), (19) imply:
% 3.49/1.13 | | (20) $false
% 3.49/1.13 | |
% 3.49/1.13 | | CLOSE: (20) is inconsistent.
% 3.49/1.13 | |
% 3.49/1.13 | Case 2:
% 3.49/1.13 | |
% 3.49/1.13 | | (21) ~ (all_14_1 = 0)
% 3.49/1.13 | |
% 3.49/1.13 | | REDUCE: (17), (21) imply:
% 3.49/1.13 | | (22) ~ (all_12_1 = 0)
% 3.49/1.13 | |
% 3.49/1.13 | | GROUND_INST: instantiating (reflexivity) with all_4_0, all_12_1, simplifying
% 3.49/1.13 | | with (4), (12) gives:
% 3.49/1.13 | | (23) all_12_1 = 0
% 3.49/1.13 | |
% 3.49/1.13 | | REDUCE: (22), (23) imply:
% 3.49/1.13 | | (24) $false
% 3.49/1.13 | |
% 3.49/1.13 | | CLOSE: (24) is inconsistent.
% 3.49/1.13 | |
% 3.49/1.13 | End of split
% 3.49/1.13 |
% 3.49/1.13 End of proof
% 3.49/1.13 % SZS output end Proof for theBenchmark
% 3.49/1.13
% 3.49/1.13 666ms
%------------------------------------------------------------------------------