TSTP Solution File: SWC340+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC340+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 : n016.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 20:50:55 EDT 2023
% Result : Theorem 139.51s 18.92s
% Output : Proof 139.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC340+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n016.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 : Mon Aug 28 18:01:45 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.63/0.61 ________ _____
% 0.63/0.61 ___ __ \_________(_)________________________________
% 0.63/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.63/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.63/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.63/0.61
% 0.63/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.63/0.61 (2023-06-19)
% 0.63/0.61
% 0.63/0.61 (c) Philipp Rümmer, 2009-2023
% 0.63/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.63/0.61 Amanda Stjerna.
% 0.63/0.61 Free software under BSD-3-Clause.
% 0.63/0.61
% 0.63/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.63/0.61
% 0.63/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.62 Running up to 7 provers in parallel.
% 0.73/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.73/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.73/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.73/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.73/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.73/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.73/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.49/1.61 Prover 1: Preprocessing ...
% 6.49/1.61 Prover 4: Preprocessing ...
% 6.93/1.63 Prover 2: Preprocessing ...
% 6.93/1.63 Prover 6: Preprocessing ...
% 6.93/1.63 Prover 0: Preprocessing ...
% 6.93/1.63 Prover 5: Preprocessing ...
% 6.93/1.64 Prover 3: Preprocessing ...
% 16.03/2.83 Prover 2: Proving ...
% 16.03/2.87 Prover 1: Constructing countermodel ...
% 16.03/2.87 Prover 5: Constructing countermodel ...
% 16.55/2.90 Prover 6: Proving ...
% 16.55/2.91 Prover 3: Constructing countermodel ...
% 20.77/3.47 Prover 4: Constructing countermodel ...
% 21.21/3.55 Prover 0: Proving ...
% 74.27/10.37 Prover 2: stopped
% 74.27/10.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 75.10/10.53 Prover 7: Preprocessing ...
% 77.32/10.77 Prover 7: Constructing countermodel ...
% 102.22/13.98 Prover 5: stopped
% 102.22/13.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 102.92/14.12 Prover 8: Preprocessing ...
% 105.11/14.35 Prover 8: Warning: ignoring some quantifiers
% 105.25/14.37 Prover 8: Constructing countermodel ...
% 117.29/15.98 Prover 1: stopped
% 117.29/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 118.32/16.09 Prover 9: Preprocessing ...
% 123.52/16.77 Prover 9: Constructing countermodel ...
% 131.59/17.88 Prover 6: stopped
% 131.59/17.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 132.44/18.01 Prover 10: Preprocessing ...
% 133.54/18.14 Prover 10: Constructing countermodel ...
% 139.51/18.90 Prover 10: Found proof (size 19)
% 139.51/18.90 Prover 10: proved (1023ms)
% 139.51/18.91 Prover 3: stopped
% 139.51/18.91 Prover 0: stopped
% 139.51/18.91 Prover 9: stopped
% 139.51/18.91 Prover 8: stopped
% 139.51/18.91 Prover 7: stopped
% 139.51/18.91 Prover 4: stopped
% 139.51/18.92
% 139.51/18.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 139.51/18.92
% 139.51/18.92 % SZS output start Proof for theBenchmark
% 139.69/18.92 Assumptions after simplification:
% 139.69/18.92 ---------------------------------
% 139.69/18.92
% 139.69/18.92 (ax11)
% 139.72/18.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 139.72/18.96 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2, v7) = v8) | ~
% 139.72/18.96 (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~
% 139.72/18.96 $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 139.72/18.96 totalorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~
% 139.72/18.96 ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | leq(v1, v2)) & ! [v0: $i] : (
% 139.72/18.96 ~ $i(v0) | ~ ssList(v0) | totalorderedP(v0) | ? [v1: $i] : ? [v2: $i] :
% 139.72/18.96 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 139.72/18.96 $i] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3,
% 139.72/18.96 v5) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 139.72/18.96 & $i(v1) & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1)
% 139.72/18.96 & ~ leq(v1, v2)))
% 139.72/18.96
% 139.72/18.96 (ax12)
% 139.72/18.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 139.72/18.96 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2, v7) = v8) | ~
% 139.72/18.96 (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~
% 139.72/18.96 $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 139.72/18.96 strictorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~
% 139.72/18.96 ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | lt(v1, v2)) & ! [v0: $i] : ( ~
% 139.72/18.96 $i(v0) | ~ ssList(v0) | strictorderedP(v0) | ? [v1: $i] : ? [v2: $i] : ?
% 139.72/18.96 [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 139.72/18.96 $i] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3,
% 139.72/18.96 v5) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 139.72/18.96 & $i(v1) & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1)
% 139.72/18.96 & ~ lt(v1, v2)))
% 139.72/18.96
% 139.72/18.96 (ax17)
% 139.72/18.96 $i(nil) & ssList(nil)
% 139.72/18.96
% 139.72/18.96 (ax58)
% 139.72/18.96 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 139.72/18.96 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 139.72/18.96
% 139.72/18.96 (ax93)
% 139.72/18.97 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1)
% 139.72/18.97 | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) & ! [v0: $i] : ! [v1: $i] :
% 139.72/18.97 ( ~ $i(v1) | ~ $i(v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) |
% 139.72/18.97 leq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ lt(v0, v0) | ~ ssItem(v0))
% 139.72/18.97
% 139.72/18.97 (co1)
% 139.72/18.97 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & strictorderedP(v0) &
% 139.72/18.97 segmentP(v1, v0) & ssList(v1) & ssList(v0) & ~ totalorderedP(v0))
% 139.72/18.97
% 139.72/18.97 Further assumptions not needed in the proof:
% 139.72/18.97 --------------------------------------------
% 139.72/18.97 ax1, ax10, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21, ax22, ax23,
% 139.72/18.97 ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35,
% 139.72/18.97 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47,
% 139.72/18.97 ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6,
% 139.72/18.97 ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71,
% 139.72/18.97 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83,
% 139.72/18.97 ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax94, ax95
% 139.72/18.97
% 139.72/18.97 Those formulas are unsatisfiable:
% 139.72/18.97 ---------------------------------
% 139.72/18.97
% 139.72/18.97 Begin of proof
% 139.72/18.97 |
% 139.72/18.97 | ALPHA: (ax11) implies:
% 139.72/18.97 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | totalorderedP(v0) | ? [v1:
% 139.72/18.97 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 139.72/18.97 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : (cons(v2, v7) = v8 & cons(v1,
% 139.72/18.97 | v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & $i(v8) & $i(v7)
% 139.72/18.97 | & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & ssList(v7)
% 139.72/18.98 | & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) & ~ leq(v1,
% 139.72/18.98 | v2)))
% 139.72/18.98 |
% 139.72/18.98 | ALPHA: (ax12) implies:
% 139.72/18.98 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 139.72/18.98 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2,
% 139.72/18.98 | v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~
% 139.72/18.98 | (app(v3, v5) = v6) | ~ $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 139.72/18.98 | ~ $i(v1) | ~ $i(v0) | ~ strictorderedP(v0) | ~ ssList(v7) | ~
% 139.72/18.98 | ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~
% 139.72/18.98 | ssItem(v1) | lt(v1, v2))
% 139.72/18.98 |
% 139.72/18.98 | ALPHA: (ax17) implies:
% 139.72/18.98 | (3) ssList(nil)
% 139.72/18.98 |
% 139.72/18.98 | ALPHA: (ax58) implies:
% 139.72/18.98 | (4) ~ ssList(nil) | segmentP(nil, nil)
% 139.72/18.98 |
% 139.72/18.98 | ALPHA: (ax93) implies:
% 139.72/18.98 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ lt(v0, v1) | ~
% 139.72/18.98 | ssItem(v1) | ~ ssItem(v0) | leq(v0, v1))
% 139.72/18.98 |
% 139.72/18.98 | DELTA: instantiating (co1) with fresh symbols all_91_0, all_91_1 gives:
% 139.72/18.98 | (6) $i(all_91_0) & $i(all_91_1) & strictorderedP(all_91_1) &
% 139.72/18.98 | segmentP(all_91_0, all_91_1) & ssList(all_91_0) & ssList(all_91_1) & ~
% 139.72/18.98 | totalorderedP(all_91_1)
% 139.72/18.98 |
% 139.72/18.98 | ALPHA: (6) implies:
% 139.72/18.98 | (7) ~ totalorderedP(all_91_1)
% 139.72/18.98 | (8) ssList(all_91_1)
% 139.72/18.98 | (9) strictorderedP(all_91_1)
% 139.72/18.98 | (10) $i(all_91_1)
% 139.72/18.98 |
% 139.72/18.98 | BETA: splitting (4) gives:
% 139.72/18.98 |
% 139.72/18.98 | Case 1:
% 139.72/18.98 | |
% 139.72/18.98 | | (11) ~ ssList(nil)
% 139.72/18.98 | |
% 139.72/18.98 | | PRED_UNIFY: (3), (11) imply:
% 139.72/18.98 | | (12) $false
% 139.72/18.98 | |
% 139.72/18.98 | | CLOSE: (12) is inconsistent.
% 139.72/18.98 | |
% 139.72/18.98 | Case 2:
% 139.72/18.98 | |
% 139.72/18.98 | |
% 139.72/18.99 | | GROUND_INST: instantiating (1) with all_91_1, simplifying with (7), (8),
% 139.72/18.99 | | (10) gives:
% 139.72/18.99 | | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 139.72/18.99 | | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (cons(v1, v6) = v7 &
% 139.72/18.99 | | cons(v0, v3) = v4 & app(v5, v7) = all_91_1 & app(v2, v4) = v5 &
% 139.72/18.99 | | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 139.72/18.99 | | $i(v0) & ssList(v6) & ssList(v3) & ssList(v2) & ssItem(v1) &
% 139.72/18.99 | | ssItem(v0) & ~ leq(v0, v1))
% 139.72/18.99 | |
% 139.72/18.99 | | DELTA: instantiating (13) with fresh symbols all_119_0, all_119_1,
% 139.72/18.99 | | all_119_2, all_119_3, all_119_4, all_119_5, all_119_6, all_119_7
% 139.72/18.99 | | gives:
% 139.72/18.99 | | (14) cons(all_119_6, all_119_1) = all_119_0 & cons(all_119_7, all_119_4)
% 139.72/18.99 | | = all_119_3 & app(all_119_2, all_119_0) = all_91_1 & app(all_119_5,
% 139.72/18.99 | | all_119_3) = all_119_2 & $i(all_119_0) & $i(all_119_1) &
% 139.72/18.99 | | $i(all_119_2) & $i(all_119_3) & $i(all_119_4) & $i(all_119_5) &
% 139.72/18.99 | | $i(all_119_6) & $i(all_119_7) & ssList(all_119_1) &
% 139.72/18.99 | | ssList(all_119_4) & ssList(all_119_5) & ssItem(all_119_6) &
% 139.72/18.99 | | ssItem(all_119_7) & ~ leq(all_119_7, all_119_6)
% 139.72/18.99 | |
% 139.72/18.99 | | ALPHA: (14) implies:
% 139.72/18.99 | | (15) ~ leq(all_119_7, all_119_6)
% 139.72/18.99 | | (16) ssItem(all_119_7)
% 139.72/18.99 | | (17) ssItem(all_119_6)
% 139.72/18.99 | | (18) ssList(all_119_5)
% 139.72/18.99 | | (19) ssList(all_119_4)
% 139.72/18.99 | | (20) ssList(all_119_1)
% 139.72/18.99 | | (21) $i(all_119_7)
% 139.72/18.99 | | (22) $i(all_119_6)
% 139.72/18.99 | | (23) $i(all_119_5)
% 139.72/18.99 | | (24) $i(all_119_4)
% 139.72/18.99 | | (25) $i(all_119_1)
% 139.72/18.99 | | (26) app(all_119_5, all_119_3) = all_119_2
% 139.72/18.99 | | (27) app(all_119_2, all_119_0) = all_91_1
% 139.72/18.99 | | (28) cons(all_119_7, all_119_4) = all_119_3
% 139.72/18.99 | | (29) cons(all_119_6, all_119_1) = all_119_0
% 139.72/18.99 | |
% 139.72/18.99 | | GROUND_INST: instantiating (2) with all_91_1, all_119_7, all_119_6,
% 139.72/18.99 | | all_119_5, all_119_4, all_119_3, all_119_2, all_119_1,
% 139.72/18.99 | | all_119_0, simplifying with (8), (9), (10), (16), (17), (18),
% 139.72/18.99 | | (19), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 139.72/18.99 | | (29) gives:
% 139.72/18.99 | | (30) lt(all_119_7, all_119_6)
% 139.72/18.99 | |
% 139.72/18.99 | | GROUND_INST: instantiating (5) with all_119_7, all_119_6, simplifying with
% 139.72/18.99 | | (15), (16), (17), (21), (22), (30) gives:
% 139.72/18.99 | | (31) $false
% 139.72/18.99 | |
% 139.72/18.99 | | CLOSE: (31) is inconsistent.
% 139.72/18.99 | |
% 139.72/18.99 | End of split
% 139.72/18.99 |
% 139.72/18.99 End of proof
% 139.72/18.99 % SZS output end Proof for theBenchmark
% 139.72/18.99
% 139.72/18.99 18384ms
%------------------------------------------------------------------------------