TSTP Solution File: SWC274+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC274+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 : 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 20:50:35 EDT 2023
% Result : Theorem 143.50s 19.43s
% Output : Proof 143.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SWC274+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.08 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.07/0.26 % Computer : n032.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Aug 28 17:28:01 EDT 2023
% 0.07/0.26 % CPUTime :
% 0.12/0.50 ________ _____
% 0.12/0.50 ___ __ \_________(_)________________________________
% 0.12/0.50 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.12/0.50 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.12/0.50 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.12/0.50
% 0.12/0.50 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.12/0.50 (2023-06-19)
% 0.12/0.50
% 0.12/0.50 (c) Philipp Rümmer, 2009-2023
% 0.12/0.50 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.12/0.50 Amanda Stjerna.
% 0.12/0.50 Free software under BSD-3-Clause.
% 0.12/0.50
% 0.12/0.50 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.12/0.50
% 0.12/0.50 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.12/0.51 Running up to 7 provers in parallel.
% 0.12/0.52 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.12/0.52 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.12/0.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.12/0.52 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.12/0.52 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.12/0.52 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.12/0.52 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.36/1.29 Prover 1: Preprocessing ...
% 4.36/1.29 Prover 4: Preprocessing ...
% 5.02/1.33 Prover 2: Preprocessing ...
% 5.02/1.33 Prover 5: Preprocessing ...
% 5.02/1.33 Prover 3: Preprocessing ...
% 5.02/1.33 Prover 0: Preprocessing ...
% 5.02/1.33 Prover 6: Preprocessing ...
% 15.29/2.68 Prover 2: Proving ...
% 15.67/2.72 Prover 6: Proving ...
% 15.67/2.73 Prover 5: Constructing countermodel ...
% 15.81/2.73 Prover 1: Constructing countermodel ...
% 15.81/2.74 Prover 3: Constructing countermodel ...
% 22.42/3.66 Prover 4: Constructing countermodel ...
% 24.21/3.84 Prover 0: Proving ...
% 73.16/10.20 Prover 2: stopped
% 73.59/10.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.54/10.39 Prover 7: Preprocessing ...
% 76.83/10.62 Prover 7: Constructing countermodel ...
% 102.18/13.90 Prover 5: stopped
% 102.18/13.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 102.18/14.04 Prover 8: Preprocessing ...
% 105.27/14.34 Prover 8: Warning: ignoring some quantifiers
% 105.27/14.35 Prover 8: Constructing countermodel ...
% 116.92/15.86 Prover 1: stopped
% 116.92/15.87 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 118.22/16.02 Prover 9: Preprocessing ...
% 125.20/16.93 Prover 9: Constructing countermodel ...
% 130.55/17.77 Prover 6: stopped
% 130.55/17.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 132.21/17.91 Prover 10: Preprocessing ...
% 132.98/18.05 Prover 10: Constructing countermodel ...
% 143.50/19.40 Prover 10: Found proof (size 20)
% 143.50/19.41 Prover 10: proved (1638ms)
% 143.50/19.41 Prover 3: stopped
% 143.50/19.41 Prover 7: stopped
% 143.50/19.41 Prover 8: stopped
% 143.50/19.41 Prover 9: stopped
% 143.50/19.41 Prover 4: stopped
% 143.50/19.43 Prover 0: stopped
% 143.50/19.43
% 143.50/19.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 143.50/19.43
% 143.50/19.43 % SZS output start Proof for theBenchmark
% 143.50/19.43 Assumptions after simplification:
% 143.50/19.43 ---------------------------------
% 143.50/19.43
% 143.50/19.43 (ax11)
% 143.50/19.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 143.50/19.46 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2, v7) = v8) | ~
% 143.50/19.47 (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~
% 143.50/19.47 $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 143.50/19.47 totalorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~
% 143.50/19.47 ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | leq(v1, v2)) & ! [v0: $i] : (
% 143.50/19.47 ~ $i(v0) | ~ ssList(v0) | totalorderedP(v0) | ? [v1: $i] : ? [v2: $i] :
% 143.50/19.47 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 143.50/19.47 $i] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3,
% 143.50/19.47 v5) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 143.50/19.47 & $i(v1) & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1)
% 143.50/19.47 & ~ leq(v1, v2)))
% 143.50/19.47
% 143.50/19.47 (ax12)
% 143.50/19.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 143.50/19.47 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2, v7) = v8) | ~
% 143.50/19.47 (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~
% 143.50/19.47 $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 143.50/19.47 strictorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~
% 143.50/19.47 ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | lt(v1, v2)) & ! [v0: $i] : ( ~
% 143.50/19.47 $i(v0) | ~ ssList(v0) | strictorderedP(v0) | ? [v1: $i] : ? [v2: $i] : ?
% 143.50/19.47 [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 143.50/19.47 $i] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3,
% 143.50/19.47 v5) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 143.50/19.47 & $i(v1) & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1)
% 143.50/19.47 & ~ lt(v1, v2)))
% 143.50/19.47
% 143.50/19.47 (ax17)
% 143.50/19.47 $i(nil) & ssList(nil)
% 143.50/19.47
% 143.50/19.47 (ax58)
% 143.50/19.47 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 143.50/19.47 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 143.50/19.47
% 143.86/19.47 (ax93)
% 143.86/19.48 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1)
% 143.86/19.48 | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) & ! [v0: $i] : ! [v1: $i] :
% 143.86/19.48 ( ~ $i(v1) | ~ $i(v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) |
% 143.86/19.48 leq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ lt(v0, v0) | ~ ssItem(v0))
% 143.86/19.48
% 143.86/19.48 (co1)
% 143.86/19.48 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 143.86/19.48 : (app(v3, v4) = v1 & app(v2, v0) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 143.86/19.48 $i(v0) & strictorderedP(v0) & ssList(v4) & ssList(v2) & ssList(v1) &
% 143.86/19.48 ssList(v0) & ~ totalorderedP(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 143.86/19.48 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ (cons(v8, nil) = v9) | ~
% 143.86/19.48 (cons(v5, nil) = v6) | ~ (app(v10, v9) = v0) | ~ (app(v6, v7) = v4) | ~
% 143.86/19.48 $i(v10) | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ lt(v8, v5) | ~
% 143.86/19.48 ssList(v10) | ~ ssList(v7) | ~ ssItem(v8) | ~ ssItem(v5)) & ! [v5: $i]
% 143.86/19.48 : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 143.86/19.48 (cons(v8, nil) = v9) | ~ (cons(v5, nil) = v6) | ~ (app(v9, v10) = v0) |
% 143.86/19.48 ~ (app(v7, v6) = v2) | ~ $i(v10) | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~
% 143.86/19.48 lt(v5, v8) | ~ ssList(v10) | ~ ssList(v7) | ~ ssItem(v8) | ~
% 143.86/19.48 ssItem(v5)) & ( ~ (v0 = nil) | v1 = nil))
% 143.86/19.48
% 143.86/19.48 Further assumptions not needed in the proof:
% 143.86/19.48 --------------------------------------------
% 143.86/19.48 ax1, ax10, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21, ax22, ax23,
% 143.86/19.48 ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35,
% 143.86/19.48 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47,
% 143.86/19.48 ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6,
% 143.86/19.48 ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71,
% 143.86/19.48 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83,
% 143.86/19.48 ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax94, ax95
% 143.86/19.48
% 143.86/19.48 Those formulas are unsatisfiable:
% 143.86/19.48 ---------------------------------
% 143.86/19.48
% 143.86/19.48 Begin of proof
% 143.86/19.49 |
% 143.86/19.49 | ALPHA: (ax11) implies:
% 143.86/19.49 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | totalorderedP(v0) | ? [v1:
% 143.86/19.49 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 143.86/19.49 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : (cons(v2, v7) = v8 & cons(v1,
% 143.86/19.49 | v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & $i(v8) & $i(v7)
% 143.86/19.49 | & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & ssList(v7)
% 143.86/19.49 | & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) & ~ leq(v1,
% 143.86/19.49 | v2)))
% 143.86/19.49 |
% 143.86/19.49 | ALPHA: (ax12) implies:
% 143.86/19.49 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 143.86/19.49 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2,
% 143.86/19.49 | v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~
% 143.86/19.49 | (app(v3, v5) = v6) | ~ $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 143.86/19.49 | ~ $i(v1) | ~ $i(v0) | ~ strictorderedP(v0) | ~ ssList(v7) | ~
% 143.86/19.49 | ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~
% 143.86/19.49 | ssItem(v1) | lt(v1, v2))
% 143.86/19.49 |
% 143.86/19.49 | ALPHA: (ax17) implies:
% 143.86/19.49 | (3) ssList(nil)
% 143.86/19.49 |
% 143.86/19.49 | ALPHA: (ax58) implies:
% 143.86/19.49 | (4) ~ ssList(nil) | segmentP(nil, nil)
% 143.86/19.49 |
% 143.86/19.49 | ALPHA: (ax93) implies:
% 143.86/19.50 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ lt(v0, v1) | ~
% 143.86/19.50 | ssItem(v1) | ~ ssItem(v0) | leq(v0, v1))
% 143.86/19.50 |
% 143.86/19.50 | ALPHA: (co1) implies:
% 143.86/19.50 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 143.86/19.50 | (app(v3, v4) = v1 & app(v2, v0) = v3 & $i(v4) & $i(v3) & $i(v2) &
% 143.86/19.50 | $i(v1) & $i(v0) & strictorderedP(v0) & ssList(v4) & ssList(v2) &
% 143.86/19.50 | ssList(v1) & ssList(v0) & ~ totalorderedP(v0) & ! [v5: $i] : !
% 143.86/19.50 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (
% 143.86/19.50 | ~ (cons(v8, nil) = v9) | ~ (cons(v5, nil) = v6) | ~ (app(v10, v9)
% 143.86/19.50 | = v0) | ~ (app(v6, v7) = v4) | ~ $i(v10) | ~ $i(v8) | ~
% 143.86/19.50 | $i(v7) | ~ $i(v5) | ~ lt(v8, v5) | ~ ssList(v10) | ~ ssList(v7)
% 143.86/19.50 | | ~ ssItem(v8) | ~ ssItem(v5)) & ! [v5: $i] : ! [v6: $i] : !
% 143.86/19.50 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ (cons(v8,
% 143.86/19.50 | nil) = v9) | ~ (cons(v5, nil) = v6) | ~ (app(v9, v10) = v0) |
% 143.86/19.50 | ~ (app(v7, v6) = v2) | ~ $i(v10) | ~ $i(v8) | ~ $i(v7) | ~
% 143.86/19.50 | $i(v5) | ~ lt(v5, v8) | ~ ssList(v10) | ~ ssList(v7) | ~
% 143.86/19.50 | ssItem(v8) | ~ ssItem(v5)) & ( ~ (v0 = nil) | v1 = nil))
% 143.86/19.50 |
% 143.86/19.50 | DELTA: instantiating (6) with fresh symbols all_91_0, all_91_1, all_91_2,
% 143.86/19.50 | all_91_3, all_91_4 gives:
% 143.86/19.51 | (7) app(all_91_1, all_91_0) = all_91_3 & app(all_91_2, all_91_4) = all_91_1
% 143.86/19.51 | & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 143.86/19.51 | $i(all_91_4) & strictorderedP(all_91_4) & ssList(all_91_0) &
% 143.86/19.51 | ssList(all_91_2) & ssList(all_91_3) & ssList(all_91_4) & ~
% 143.86/19.51 | totalorderedP(all_91_4) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 143.86/19.51 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v3, nil) = v4) | ~
% 143.86/19.51 | (cons(v0, nil) = v1) | ~ (app(v5, v4) = all_91_4) | ~ (app(v1, v2)
% 143.86/19.51 | = all_91_0) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 143.86/19.51 | lt(v3, v0) | ~ ssList(v5) | ~ ssList(v2) | ~ ssItem(v3) | ~
% 143.86/19.51 | ssItem(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 143.86/19.51 | ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v3, nil) = v4) | ~ (cons(v0,
% 143.86/19.51 | nil) = v1) | ~ (app(v4, v5) = all_91_4) | ~ (app(v2, v1) =
% 143.86/19.51 | all_91_2) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 143.86/19.51 | lt(v0, v3) | ~ ssList(v5) | ~ ssList(v2) | ~ ssItem(v3) | ~
% 143.86/19.51 | ssItem(v0)) & ( ~ (all_91_4 = nil) | all_91_3 = nil)
% 143.86/19.51 |
% 143.86/19.51 | ALPHA: (7) implies:
% 143.86/19.51 | (8) ~ totalorderedP(all_91_4)
% 143.86/19.51 | (9) ssList(all_91_4)
% 143.86/19.51 | (10) strictorderedP(all_91_4)
% 143.86/19.51 | (11) $i(all_91_4)
% 143.86/19.51 |
% 143.86/19.51 | BETA: splitting (4) gives:
% 143.86/19.51 |
% 143.86/19.51 | Case 1:
% 143.86/19.51 | |
% 143.86/19.51 | | (12) ~ ssList(nil)
% 143.86/19.51 | |
% 143.86/19.51 | | PRED_UNIFY: (3), (12) imply:
% 143.86/19.51 | | (13) $false
% 143.86/19.51 | |
% 143.86/19.51 | | CLOSE: (13) is inconsistent.
% 143.86/19.51 | |
% 143.86/19.51 | Case 2:
% 143.86/19.51 | |
% 143.86/19.51 | |
% 143.86/19.51 | | GROUND_INST: instantiating (1) with all_91_4, simplifying with (8), (9),
% 143.86/19.51 | | (11) gives:
% 143.86/19.52 | | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 143.86/19.52 | | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (cons(v1, v6) = v7 &
% 143.86/19.52 | | cons(v0, v3) = v4 & app(v5, v7) = all_91_4 & app(v2, v4) = v5 &
% 143.86/19.52 | | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 143.86/19.52 | | $i(v0) & ssList(v6) & ssList(v3) & ssList(v2) & ssItem(v1) &
% 143.86/19.52 | | ssItem(v0) & ~ leq(v0, v1))
% 143.86/19.52 | |
% 143.86/19.52 | | DELTA: instantiating (14) with fresh symbols all_120_0, all_120_1,
% 143.86/19.52 | | all_120_2, all_120_3, all_120_4, all_120_5, all_120_6, all_120_7
% 143.86/19.52 | | gives:
% 143.86/19.52 | | (15) cons(all_120_6, all_120_1) = all_120_0 & cons(all_120_7, all_120_4)
% 143.86/19.52 | | = all_120_3 & app(all_120_2, all_120_0) = all_91_4 & app(all_120_5,
% 143.86/19.52 | | all_120_3) = all_120_2 & $i(all_120_0) & $i(all_120_1) &
% 143.86/19.52 | | $i(all_120_2) & $i(all_120_3) & $i(all_120_4) & $i(all_120_5) &
% 143.86/19.52 | | $i(all_120_6) & $i(all_120_7) & ssList(all_120_1) &
% 143.86/19.52 | | ssList(all_120_4) & ssList(all_120_5) & ssItem(all_120_6) &
% 143.86/19.52 | | ssItem(all_120_7) & ~ leq(all_120_7, all_120_6)
% 143.86/19.52 | |
% 143.86/19.52 | | ALPHA: (15) implies:
% 143.86/19.52 | | (16) ~ leq(all_120_7, all_120_6)
% 143.86/19.52 | | (17) ssItem(all_120_7)
% 143.86/19.52 | | (18) ssItem(all_120_6)
% 143.86/19.52 | | (19) ssList(all_120_5)
% 143.86/19.52 | | (20) ssList(all_120_4)
% 143.86/19.52 | | (21) ssList(all_120_1)
% 143.86/19.52 | | (22) $i(all_120_7)
% 143.86/19.52 | | (23) $i(all_120_6)
% 143.86/19.52 | | (24) $i(all_120_5)
% 143.86/19.52 | | (25) $i(all_120_4)
% 143.86/19.52 | | (26) $i(all_120_1)
% 143.86/19.52 | | (27) app(all_120_5, all_120_3) = all_120_2
% 143.86/19.52 | | (28) app(all_120_2, all_120_0) = all_91_4
% 143.86/19.52 | | (29) cons(all_120_7, all_120_4) = all_120_3
% 143.86/19.52 | | (30) cons(all_120_6, all_120_1) = all_120_0
% 143.86/19.52 | |
% 143.86/19.52 | | GROUND_INST: instantiating (2) with all_91_4, all_120_7, all_120_6,
% 143.86/19.52 | | all_120_5, all_120_4, all_120_3, all_120_2, all_120_1,
% 143.86/19.52 | | all_120_0, simplifying with (9), (10), (11), (17), (18), (19),
% 143.86/19.52 | | (20), (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 143.86/19.52 | | (30) gives:
% 143.86/19.52 | | (31) lt(all_120_7, all_120_6)
% 143.86/19.52 | |
% 143.86/19.52 | | GROUND_INST: instantiating (5) with all_120_7, all_120_6, simplifying with
% 143.86/19.52 | | (16), (17), (18), (22), (23), (31) gives:
% 143.86/19.52 | | (32) $false
% 143.86/19.52 | |
% 143.86/19.52 | | CLOSE: (32) is inconsistent.
% 143.86/19.52 | |
% 143.86/19.52 | End of split
% 143.86/19.52 |
% 143.86/19.52 End of proof
% 143.86/19.53 % SZS output end Proof for theBenchmark
% 143.86/19.53
% 143.86/19.53 19024ms
%------------------------------------------------------------------------------