TSTP Solution File: SWC206+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC206+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n020.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 20:50:14 EDT 2023
% Result : Theorem 26.54s 4.18s
% Output : Proof 34.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SWC206+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.30 % Computer : n020.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Aug 28 15:12:13 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.14/0.54 ________ _____
% 0.14/0.54 ___ __ \_________(_)________________________________
% 0.14/0.54 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.54 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.54 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.54
% 0.14/0.54 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.54 (2023-06-19)
% 0.14/0.54
% 0.14/0.54 (c) Philipp Rümmer, 2009-2023
% 0.14/0.54 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.54 Amanda Stjerna.
% 0.14/0.54 Free software under BSD-3-Clause.
% 0.14/0.54
% 0.14/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.54
% 0.14/0.54 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.14/0.55 Running up to 7 provers in parallel.
% 0.14/0.57 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.57 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.57 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.57 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.57 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.57 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.14/0.57 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 4.90/1.38 Prover 4: Preprocessing ...
% 4.90/1.38 Prover 1: Preprocessing ...
% 5.49/1.42 Prover 2: Preprocessing ...
% 5.49/1.42 Prover 5: Preprocessing ...
% 5.49/1.42 Prover 6: Preprocessing ...
% 5.49/1.42 Prover 3: Preprocessing ...
% 5.49/1.43 Prover 0: Preprocessing ...
% 14.66/2.59 Prover 2: Proving ...
% 14.97/2.63 Prover 1: Constructing countermodel ...
% 14.97/2.63 Prover 5: Constructing countermodel ...
% 14.97/2.69 Prover 3: Constructing countermodel ...
% 15.52/2.71 Prover 6: Proving ...
% 20.61/3.43 Prover 4: Constructing countermodel ...
% 21.34/3.50 Prover 0: Proving ...
% 26.54/4.18 Prover 3: proved (3597ms)
% 26.54/4.18
% 26.54/4.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.54/4.18
% 26.54/4.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 26.54/4.19 Prover 2: stopped
% 26.54/4.19 Prover 0: stopped
% 26.54/4.19 Prover 5: stopped
% 27.01/4.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 27.01/4.21 Prover 6: stopped
% 27.01/4.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 27.01/4.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 27.01/4.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 28.17/4.38 Prover 10: Preprocessing ...
% 28.86/4.44 Prover 13: Preprocessing ...
% 28.86/4.44 Prover 7: Preprocessing ...
% 28.93/4.45 Prover 8: Preprocessing ...
% 28.93/4.46 Prover 11: Preprocessing ...
% 29.81/4.64 Prover 7: Constructing countermodel ...
% 30.85/4.72 Prover 10: Constructing countermodel ...
% 31.30/4.75 Prover 13: Constructing countermodel ...
% 32.56/4.91 Prover 7: Found proof (size 23)
% 32.56/4.91 Prover 7: proved (726ms)
% 32.56/4.91 Prover 13: stopped
% 32.56/4.91 Prover 1: stopped
% 32.56/4.91 Prover 4: stopped
% 32.56/4.92 Prover 10: stopped
% 32.56/4.92 Prover 8: Warning: ignoring some quantifiers
% 32.56/4.93 Prover 8: Constructing countermodel ...
% 32.56/4.94 Prover 8: stopped
% 34.52/5.43 Prover 11: Constructing countermodel ...
% 34.52/5.45 Prover 11: stopped
% 34.52/5.45
% 34.52/5.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.52/5.45
% 34.52/5.46 % SZS output start Proof for theBenchmark
% 34.52/5.47 Assumptions after simplification:
% 34.52/5.47 ---------------------------------
% 34.52/5.47
% 34.52/5.47 (ax15)
% 34.52/5.48 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) |
% 34.52/5.48 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~
% 34.52/5.48 neq(v0, v0))
% 34.52/5.48
% 34.52/5.48 (ax17)
% 34.52/5.48 $i(nil) & ssList(nil)
% 34.52/5.48
% 34.52/5.48 (ax46)
% 34.91/5.48 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 34.91/5.48 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 34.91/5.48
% 34.91/5.48 (ax58)
% 34.91/5.49 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 34.91/5.49 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 34.91/5.49
% 34.91/5.49 (co1)
% 34.91/5.49 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0)
% 34.91/5.49 & segmentP(v1, v2) & segmentP(v0, v2) & ssList(v2) & ssList(v1) & ssList(v0)
% 34.91/5.49 & neq(v2, nil) & neq(v1, nil) & ~ neq(v0, nil) & ( ~ (v1 = nil) | v0 =
% 34.91/5.49 nil))
% 34.91/5.49
% 34.91/5.49 Further assumptions not needed in the proof:
% 34.91/5.49 --------------------------------------------
% 34.91/5.49 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 34.91/5.49 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 34.91/5.49 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax47,
% 34.91/5.49 ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6,
% 34.91/5.49 ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71,
% 34.91/5.49 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83,
% 34.91/5.49 ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 34.91/5.49
% 34.91/5.49 Those formulas are unsatisfiable:
% 34.91/5.49 ---------------------------------
% 34.91/5.49
% 34.91/5.49 Begin of proof
% 34.91/5.49 |
% 34.91/5.49 | ALPHA: (ax15) implies:
% 34.91/5.50 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 34.91/5.50 | ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 34.91/5.50 |
% 34.91/5.50 | ALPHA: (ax17) implies:
% 34.91/5.50 | (2) ssList(nil)
% 34.91/5.50 |
% 34.91/5.50 | ALPHA: (ax46) implies:
% 34.91/5.50 | (3) ~ ssList(nil) | frontsegP(nil, nil)
% 34.91/5.50 |
% 34.91/5.50 | ALPHA: (ax58) implies:
% 34.91/5.50 | (4) ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 34.91/5.50 | ssList(v0))
% 34.91/5.50 |
% 34.91/5.50 | ALPHA: (co1) implies:
% 34.91/5.50 | (5) $i(nil)
% 34.91/5.50 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) &
% 34.91/5.50 | segmentP(v1, v2) & segmentP(v0, v2) & ssList(v2) & ssList(v1) &
% 34.91/5.50 | ssList(v0) & neq(v2, nil) & neq(v1, nil) & ~ neq(v0, nil) & ( ~ (v1
% 34.91/5.50 | = nil) | v0 = nil))
% 34.91/5.50 |
% 34.91/5.50 | DELTA: instantiating (6) with fresh symbols all_91_0, all_91_1, all_91_2
% 34.91/5.50 | gives:
% 34.91/5.50 | (7) $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & segmentP(all_91_1,
% 34.91/5.50 | all_91_0) & segmentP(all_91_2, all_91_0) & ssList(all_91_0) &
% 34.91/5.50 | ssList(all_91_1) & ssList(all_91_2) & neq(all_91_0, nil) &
% 34.91/5.50 | neq(all_91_1, nil) & ~ neq(all_91_2, nil) & ( ~ (all_91_1 = nil) |
% 34.91/5.50 | all_91_2 = nil)
% 34.91/5.50 |
% 34.91/5.50 | ALPHA: (7) implies:
% 34.91/5.51 | (8) ~ neq(all_91_2, nil)
% 34.91/5.51 | (9) neq(all_91_0, nil)
% 34.91/5.51 | (10) ssList(all_91_2)
% 34.91/5.51 | (11) ssList(all_91_0)
% 34.91/5.51 | (12) segmentP(all_91_2, all_91_0)
% 34.91/5.51 | (13) $i(all_91_2)
% 34.91/5.51 | (14) $i(all_91_0)
% 34.91/5.51 |
% 34.91/5.51 | BETA: splitting (3) gives:
% 34.91/5.51 |
% 34.91/5.51 | Case 1:
% 34.91/5.51 | |
% 34.91/5.51 | | (15) ~ ssList(nil)
% 34.91/5.51 | |
% 34.91/5.51 | | PRED_UNIFY: (2), (15) imply:
% 34.91/5.51 | | (16) $false
% 34.91/5.51 | |
% 34.91/5.51 | | CLOSE: (16) is inconsistent.
% 34.91/5.51 | |
% 34.91/5.51 | Case 2:
% 34.91/5.51 | |
% 34.91/5.51 | |
% 34.91/5.51 | | PRED_UNIFY: (8), (9) imply:
% 34.91/5.51 | | (17) ~ (all_91_0 = all_91_2)
% 34.91/5.51 | |
% 34.91/5.51 | | GROUND_INST: instantiating (1) with all_91_2, nil, simplifying with (2),
% 34.91/5.51 | | (5), (8), (10), (13) gives:
% 34.91/5.51 | | (18) all_91_2 = nil
% 34.91/5.51 | |
% 34.91/5.51 | | GROUND_INST: instantiating (4) with all_91_0, simplifying with (11), (14)
% 34.91/5.51 | | gives:
% 34.91/5.51 | | (19) all_91_0 = nil | ~ segmentP(nil, all_91_0)
% 34.91/5.51 | |
% 34.91/5.51 | | REDUCE: (17), (18) imply:
% 34.91/5.51 | | (20) ~ (all_91_0 = nil)
% 34.91/5.51 | |
% 34.91/5.51 | | REDUCE: (12), (18) imply:
% 34.91/5.51 | | (21) segmentP(nil, all_91_0)
% 34.91/5.51 | |
% 34.91/5.51 | | BETA: splitting (19) gives:
% 34.91/5.51 | |
% 34.91/5.51 | | Case 1:
% 34.91/5.51 | | |
% 34.91/5.51 | | | (22) ~ segmentP(nil, all_91_0)
% 34.91/5.51 | | |
% 34.91/5.51 | | | PRED_UNIFY: (21), (22) imply:
% 34.91/5.51 | | | (23) $false
% 34.91/5.52 | | |
% 34.91/5.52 | | | CLOSE: (23) is inconsistent.
% 34.91/5.52 | | |
% 34.91/5.52 | | Case 2:
% 34.91/5.52 | | |
% 34.91/5.52 | | | (24) all_91_0 = nil
% 34.91/5.52 | | |
% 34.91/5.52 | | | REDUCE: (20), (24) imply:
% 34.91/5.52 | | | (25) $false
% 34.91/5.52 | | |
% 34.91/5.52 | | | CLOSE: (25) is inconsistent.
% 34.91/5.52 | | |
% 34.91/5.52 | | End of split
% 34.91/5.52 | |
% 34.91/5.52 | End of split
% 34.91/5.52 |
% 34.91/5.52 End of proof
% 34.91/5.52 % SZS output end Proof for theBenchmark
% 34.91/5.52
% 34.91/5.52 4973ms
%------------------------------------------------------------------------------