TSTP Solution File: SWC218+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC218+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 20:50:18 EDT 2023
% Result : Theorem 33.76s 5.14s
% Output : Proof 56.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SWC218+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 18:28:01 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.51 ________ _____
% 0.14/0.51 ___ __ \_________(_)________________________________
% 0.14/0.51 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.51 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.51 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.51
% 0.14/0.51 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.51 (2023-06-19)
% 0.14/0.51
% 0.14/0.51 (c) Philipp Rümmer, 2009-2023
% 0.14/0.51 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.51 Amanda Stjerna.
% 0.14/0.51 Free software under BSD-3-Clause.
% 0.14/0.51
% 0.14/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.51
% 0.14/0.51 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.53 Running up to 7 provers in parallel.
% 0.14/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.88/1.26 Prover 4: Preprocessing ...
% 3.88/1.26 Prover 1: Preprocessing ...
% 4.74/1.33 Prover 6: Preprocessing ...
% 4.74/1.33 Prover 2: Preprocessing ...
% 4.74/1.33 Prover 5: Preprocessing ...
% 4.74/1.33 Prover 3: Preprocessing ...
% 4.74/1.33 Prover 0: Preprocessing ...
% 13.51/2.52 Prover 2: Proving ...
% 13.51/2.55 Prover 5: Constructing countermodel ...
% 14.56/2.68 Prover 1: Constructing countermodel ...
% 15.15/2.74 Prover 6: Proving ...
% 15.15/2.76 Prover 3: Constructing countermodel ...
% 20.66/3.42 Prover 4: Constructing countermodel ...
% 22.02/3.60 Prover 0: Proving ...
% 33.76/5.14 Prover 3: proved (4605ms)
% 33.76/5.14
% 33.76/5.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.76/5.14
% 33.76/5.14 Prover 5: stopped
% 33.76/5.16 Prover 0: stopped
% 33.76/5.16 Prover 6: stopped
% 33.76/5.16 Prover 2: stopped
% 33.76/5.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 33.76/5.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 33.76/5.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 33.76/5.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 33.76/5.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 35.69/5.40 Prover 10: Preprocessing ...
% 35.94/5.43 Prover 8: Preprocessing ...
% 35.94/5.45 Prover 7: Preprocessing ...
% 35.94/5.45 Prover 13: Preprocessing ...
% 35.94/5.46 Prover 11: Preprocessing ...
% 37.97/5.69 Prover 10: Constructing countermodel ...
% 37.97/5.76 Prover 7: Constructing countermodel ...
% 39.10/5.89 Prover 8: Warning: ignoring some quantifiers
% 39.10/5.90 Prover 8: Constructing countermodel ...
% 39.75/5.94 Prover 13: Constructing countermodel ...
% 44.77/6.66 Prover 11: Constructing countermodel ...
% 55.60/8.02 Prover 10: Found proof (size 76)
% 55.60/8.02 Prover 10: proved (2861ms)
% 55.60/8.02 Prover 13: stopped
% 55.60/8.02 Prover 11: stopped
% 55.60/8.02 Prover 8: stopped
% 55.60/8.02 Prover 1: stopped
% 55.60/8.02 Prover 7: stopped
% 55.60/8.03 Prover 4: stopped
% 55.60/8.03
% 55.60/8.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 55.60/8.03
% 55.60/8.04 % SZS output start Proof for theBenchmark
% 55.60/8.04 Assumptions after simplification:
% 55.60/8.04 ---------------------------------
% 55.60/8.04
% 55.60/8.04 (ax1)
% 55.60/8.05 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) |
% 55.60/8.05 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) |
% 55.60/8.05 ~ ssItem(v0))
% 55.60/8.05
% 55.60/8.05 (ax15)
% 55.60/8.05 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) |
% 55.60/8.05 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~
% 55.60/8.05 neq(v0, v0))
% 55.60/8.05
% 55.60/8.05 (ax16)
% 56.10/8.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1)
% 56.10/8.07 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2))
% 56.10/8.07
% 56.10/8.07 (ax17)
% 56.10/8.07 $i(nil) & ssList(nil)
% 56.10/8.07
% 56.10/8.07 (ax2)
% 56.10/8.07 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) &
% 56.10/8.07 ssItem(v0))
% 56.10/8.07
% 56.10/8.07 (ax27)
% 56.10/8.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 56.10/8.08 (cons(v3, v2) = v4) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 56.10/8.08 $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v3) | ? [v5: $i] :
% 56.10/8.08 (cons(v3, v1) = v5 & app(v5, v0) = v4 & $i(v5) & $i(v4)))
% 56.10/8.08
% 56.10/8.08 (ax28)
% 56.10/8.08 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 56.10/8.08 $i(v0) | ~ ssList(v0))
% 56.10/8.08
% 56.10/8.08 (ax39)
% 56.10/8.08 $i(nil) & ~ singletonP(nil)
% 56.10/8.08
% 56.10/8.08 (ax4)
% 56.18/8.08 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) |
% 56.18/8.08 ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) & ! [v0: $i] : (
% 56.18/8.08 ~ $i(v0) | ~ singletonP(v0) | ~ ssList(v0) | ? [v1: $i] : (cons(v1, nil)
% 56.18/8.08 = v0 & $i(v1) & ssItem(v1)))
% 56.18/8.08
% 56.18/8.08 (ax46)
% 56.18/8.08 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 56.18/8.08 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 56.18/8.08
% 56.18/8.08 (ax5)
% 56.18/8.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 56.18/8.08 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 56.18/8.08 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 56.18/8.08 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 56.18/8.08 v2) = v0 & $i(v2) & ssList(v2)))
% 56.18/8.08
% 56.18/8.08 (ax52)
% 56.18/8.08 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~
% 56.18/8.08 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 56.18/8.08
% 56.18/8.08 (ax54)
% 56.18/8.08 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ segmentP(v1,
% 56.18/8.08 v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 56.18/8.08
% 56.18/8.08 (ax57)
% 56.18/8.08 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil))
% 56.18/8.08
% 56.18/8.08 (ax58)
% 56.18/8.09 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 56.18/8.09 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 56.18/8.09
% 56.18/8.09 (ax6)
% 56.18/8.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 56.18/8.09 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 56.18/8.09 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 56.18/8.09 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 56.18/8.09 v1) = v0 & $i(v2) & ssList(v2)))
% 56.18/8.09
% 56.18/8.09 (ax7)
% 56.18/8.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 56.18/8.09 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 56.18/8.09 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 56.18/8.09 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 56.18/8.09 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 56.18/8.09 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 56.18/8.09 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 56.18/8.09
% 56.18/8.09 (ax82)
% 56.18/8.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 56.18/8.09 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 56.18/8.09 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 56.18/8.09 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 56.18/8.09
% 56.18/8.09 (ax83)
% 56.18/8.09 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 56.18/8.09 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 56.18/8.09 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 56.18/8.09 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 56.18/8.09 v0) | ~ ssList(nil))
% 56.18/8.09
% 56.18/8.09 (ax84)
% 56.18/8.09 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 56.18/8.09 $i(v0) | ~ ssList(v0))
% 56.18/8.09
% 56.18/8.09 (co1)
% 56.18/8.10 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 56.18/8.10 : ? [v5: $i] : ? [v6: $i] : (cons(v4, nil) = v5 & app(v6, v3) = v0 & app(v2,
% 56.18/8.10 v5) = v6 & app(v2, v3) = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 56.18/8.10 $i(v1) & $i(v0) & ssList(v3) & ssList(v2) & ssList(v1) & ssList(v0) &
% 56.18/8.10 ssItem(v4) & ~ neq(v0, nil))
% 56.18/8.10
% 56.18/8.10 (function-axioms)
% 56.18/8.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 56.18/8.10 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 56.18/8.10 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 56.18/8.10 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 56.18/8.10 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 56.18/8.10 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 56.18/8.10
% 56.18/8.10 Further assumptions not needed in the proof:
% 56.18/8.10 --------------------------------------------
% 56.18/8.10 ax10, ax11, ax12, ax13, ax14, ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25,
% 56.18/8.10 ax26, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax40,
% 56.18/8.10 ax41, ax42, ax43, ax44, ax45, ax47, ax48, ax49, ax50, ax51, ax53, ax55, ax56,
% 56.18/8.10 ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax70, ax71,
% 56.18/8.10 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax85, ax86,
% 56.18/8.10 ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 56.18/8.10
% 56.18/8.10 Those formulas are unsatisfiable:
% 56.18/8.10 ---------------------------------
% 56.18/8.10
% 56.18/8.10 Begin of proof
% 56.18/8.10 |
% 56.18/8.10 | ALPHA: (ax1) implies:
% 56.18/8.10 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 56.18/8.10 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1))
% 56.18/8.10 |
% 56.18/8.10 | ALPHA: (ax4) implies:
% 56.18/8.10 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) | ~
% 56.18/8.10 | $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0))
% 56.18/8.10 |
% 56.18/8.10 | ALPHA: (ax5) implies:
% 56.18/8.11 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 56.18/8.11 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 56.18/8.11 | v0 & $i(v2) & ssList(v2)))
% 56.18/8.11 |
% 56.18/8.11 | ALPHA: (ax6) implies:
% 56.18/8.11 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 56.18/8.11 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 56.18/8.11 | v0 & $i(v2) & ssList(v2)))
% 56.18/8.11 |
% 56.18/8.11 | ALPHA: (ax7) implies:
% 56.18/8.11 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 56.18/8.11 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2)
% 56.18/8.11 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~
% 56.18/8.11 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 56.18/8.11 |
% 56.18/8.11 | ALPHA: (ax15) implies:
% 56.18/8.11 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 56.18/8.11 | ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 56.18/8.11 |
% 56.18/8.11 | ALPHA: (ax17) implies:
% 56.18/8.11 | (7) ssList(nil)
% 56.18/8.11 |
% 56.18/8.11 | ALPHA: (ax28) implies:
% 56.18/8.11 | (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 56.18/8.11 | $i(v0) | ~ ssList(v0))
% 56.18/8.11 |
% 56.18/8.11 | ALPHA: (ax39) implies:
% 56.18/8.11 | (9) ~ singletonP(nil)
% 56.18/8.11 |
% 56.18/8.11 | ALPHA: (ax46) implies:
% 56.18/8.11 | (10) ~ ssList(nil) | frontsegP(nil, nil)
% 56.18/8.11 |
% 56.18/8.11 | ALPHA: (ax52) implies:
% 56.18/8.11 | (11) ~ ssList(nil) | rearsegP(nil, nil)
% 56.18/8.11 |
% 56.18/8.11 | ALPHA: (ax57) implies:
% 56.36/8.11 | (12) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil))
% 56.36/8.11 |
% 56.36/8.11 | ALPHA: (ax58) implies:
% 56.36/8.11 | (13) ~ ssList(nil) | segmentP(nil, nil)
% 56.36/8.11 |
% 56.36/8.11 | ALPHA: (ax83) implies:
% 56.36/8.11 | (14) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 56.36/8.11 |
% 56.36/8.11 | ALPHA: (ax84) implies:
% 56.36/8.11 | (15) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 56.36/8.11 | $i(v0) | ~ ssList(v0))
% 56.36/8.11 |
% 56.36/8.11 | ALPHA: (co1) implies:
% 56.36/8.12 | (16) $i(nil)
% 56.36/8.12 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 56.36/8.12 | ? [v5: $i] : ? [v6: $i] : (cons(v4, nil) = v5 & app(v6, v3) = v0 &
% 56.36/8.12 | app(v2, v5) = v6 & app(v2, v3) = v1 & $i(v6) & $i(v5) & $i(v4) &
% 56.36/8.12 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v3) & ssList(v2) &
% 56.36/8.12 | ssList(v1) & ssList(v0) & ssItem(v4) & ~ neq(v0, nil))
% 56.36/8.12 |
% 56.36/8.12 | ALPHA: (function-axioms) implies:
% 56.36/8.12 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 56.36/8.12 | (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 56.36/8.12 |
% 56.36/8.12 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives:
% 56.36/8.12 | (19) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) &
% 56.36/8.12 | ssItem(all_89_0) & ssItem(all_89_1)
% 56.36/8.12 |
% 56.36/8.12 | ALPHA: (19) implies:
% 56.36/8.12 | (20) ~ (all_89_0 = all_89_1)
% 56.36/8.12 | (21) ssItem(all_89_1)
% 56.36/8.12 | (22) ssItem(all_89_0)
% 56.36/8.12 | (23) $i(all_89_1)
% 56.36/8.12 | (24) $i(all_89_0)
% 56.36/8.12 |
% 56.36/8.12 | DELTA: instantiating (17) with fresh symbols all_91_0, all_91_1, all_91_2,
% 56.36/8.12 | all_91_3, all_91_4, all_91_5, all_91_6 gives:
% 56.36/8.12 | (25) cons(all_91_2, nil) = all_91_1 & app(all_91_0, all_91_3) = all_91_6 &
% 56.36/8.12 | app(all_91_4, all_91_1) = all_91_0 & app(all_91_4, all_91_3) =
% 56.36/8.12 | all_91_5 & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 56.36/8.12 | $i(all_91_4) & $i(all_91_5) & $i(all_91_6) & ssList(all_91_3) &
% 56.36/8.12 | ssList(all_91_4) & ssList(all_91_5) & ssList(all_91_6) &
% 56.36/8.12 | ssItem(all_91_2) & ~ neq(all_91_6, nil)
% 56.36/8.12 |
% 56.36/8.12 | ALPHA: (25) implies:
% 56.36/8.12 | (26) ~ neq(all_91_6, nil)
% 56.36/8.12 | (27) ssItem(all_91_2)
% 56.36/8.12 | (28) ssList(all_91_6)
% 56.36/8.12 | (29) ssList(all_91_4)
% 56.36/8.12 | (30) ssList(all_91_3)
% 56.36/8.12 | (31) $i(all_91_6)
% 56.36/8.12 | (32) $i(all_91_4)
% 56.36/8.12 | (33) $i(all_91_3)
% 56.36/8.12 | (34) $i(all_91_2)
% 56.36/8.12 | (35) $i(all_91_1)
% 56.36/8.12 | (36) app(all_91_4, all_91_1) = all_91_0
% 56.36/8.12 | (37) app(all_91_0, all_91_3) = all_91_6
% 56.36/8.12 | (38) cons(all_91_2, nil) = all_91_1
% 56.36/8.12 |
% 56.36/8.12 | BETA: splitting (10) gives:
% 56.36/8.12 |
% 56.36/8.13 | Case 1:
% 56.36/8.13 | |
% 56.36/8.13 | | (39) ~ ssList(nil)
% 56.36/8.13 | |
% 56.36/8.13 | | PRED_UNIFY: (7), (39) imply:
% 56.36/8.13 | | (40) $false
% 56.36/8.13 | |
% 56.36/8.13 | | CLOSE: (40) is inconsistent.
% 56.36/8.13 | |
% 56.36/8.13 | Case 2:
% 56.36/8.13 | |
% 56.36/8.13 | | (41) frontsegP(nil, nil)
% 56.36/8.13 | |
% 56.36/8.13 | | BETA: splitting (11) gives:
% 56.36/8.13 | |
% 56.36/8.13 | | Case 1:
% 56.36/8.13 | | |
% 56.36/8.13 | | | (42) ~ ssList(nil)
% 56.36/8.13 | | |
% 56.36/8.13 | | | PRED_UNIFY: (7), (42) imply:
% 56.36/8.13 | | | (43) $false
% 56.36/8.13 | | |
% 56.36/8.13 | | | CLOSE: (43) is inconsistent.
% 56.36/8.13 | | |
% 56.36/8.13 | | Case 2:
% 56.36/8.13 | | |
% 56.36/8.13 | | | (44) rearsegP(nil, nil)
% 56.36/8.13 | | |
% 56.36/8.13 | | | BETA: splitting (13) gives:
% 56.36/8.13 | | |
% 56.36/8.13 | | | Case 1:
% 56.36/8.13 | | | |
% 56.36/8.13 | | | | (45) ~ ssList(nil)
% 56.36/8.13 | | | |
% 56.36/8.13 | | | | PRED_UNIFY: (7), (45) imply:
% 56.36/8.13 | | | | (46) $false
% 56.36/8.13 | | | |
% 56.36/8.13 | | | | CLOSE: (46) is inconsistent.
% 56.36/8.13 | | | |
% 56.36/8.13 | | | Case 2:
% 56.36/8.13 | | | |
% 56.45/8.13 | | | |
% 56.45/8.13 | | | | GROUND_INST: instantiating (1) with all_89_1, all_89_0, simplifying with
% 56.45/8.13 | | | | (21), (22), (23), (24) gives:
% 56.45/8.13 | | | | (47) all_89_0 = all_89_1 | neq(all_89_1, all_89_0)
% 56.45/8.13 | | | |
% 56.45/8.13 | | | | GROUND_INST: instantiating (6) with all_91_6, nil, simplifying with (7),
% 56.45/8.13 | | | | (16), (26), (28), (31) gives:
% 56.45/8.13 | | | | (48) all_91_6 = nil
% 56.45/8.13 | | | |
% 56.45/8.13 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (7),
% 56.45/8.13 | | | | (16), (41) gives:
% 56.45/8.13 | | | | (49) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 56.45/8.13 | | | |
% 56.45/8.13 | | | | GROUND_INST: instantiating (4) with nil, nil, simplifying with (7),
% 56.45/8.13 | | | | (16), (44) gives:
% 56.45/8.13 | | | | (50) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0))
% 56.45/8.13 | | | |
% 56.45/8.14 | | | | GROUND_INST: instantiating (ax16) with nil, all_91_2, all_91_1,
% 56.45/8.14 | | | | simplifying with (7), (16), (27), (34), (38) gives:
% 56.45/8.14 | | | | (51) ssList(all_91_1)
% 56.45/8.14 | | | |
% 56.45/8.14 | | | | DELTA: instantiating (50) with fresh symbol all_111_0 gives:
% 56.45/8.14 | | | | (52) app(all_111_0, nil) = nil & $i(all_111_0) & ssList(all_111_0)
% 56.45/8.14 | | | |
% 56.45/8.14 | | | | ALPHA: (52) implies:
% 56.45/8.14 | | | | (53) ssList(all_111_0)
% 56.45/8.14 | | | | (54) $i(all_111_0)
% 56.45/8.14 | | | | (55) app(all_111_0, nil) = nil
% 56.45/8.14 | | | |
% 56.45/8.14 | | | | DELTA: instantiating (49) with fresh symbol all_113_0 gives:
% 56.45/8.14 | | | | (56) app(nil, all_113_0) = nil & $i(all_113_0) & ssList(all_113_0)
% 56.45/8.14 | | | |
% 56.45/8.14 | | | | ALPHA: (56) implies:
% 56.45/8.14 | | | | (57) ssList(all_113_0)
% 56.45/8.14 | | | | (58) $i(all_113_0)
% 56.45/8.14 | | | | (59) app(nil, all_113_0) = nil
% 56.45/8.14 | | | |
% 56.45/8.14 | | | | REDUCE: (37), (48) imply:
% 56.45/8.14 | | | | (60) app(all_91_0, all_91_3) = nil
% 56.45/8.14 | | | |
% 56.45/8.14 | | | | BETA: splitting (47) gives:
% 56.45/8.14 | | | |
% 56.45/8.14 | | | | Case 1:
% 56.45/8.14 | | | | |
% 56.45/8.14 | | | | |
% 56.45/8.14 | | | | | GROUND_INST: instantiating (2) with all_91_1, all_91_2, simplifying
% 56.45/8.14 | | | | | with (27), (34), (35), (38), (51) gives:
% 56.45/8.14 | | | | | (61) singletonP(all_91_1)
% 56.45/8.14 | | | | |
% 56.45/8.14 | | | | | GROUND_INST: instantiating (12) with all_91_1, simplifying with (35),
% 56.45/8.14 | | | | | (51) gives:
% 56.45/8.14 | | | | | (62) segmentP(all_91_1, nil)
% 56.45/8.14 | | | | |
% 56.45/8.14 | | | | | GROUND_INST: instantiating (ax27) with all_113_0, nil, nil, all_91_2,
% 56.45/8.14 | | | | | all_91_1, simplifying with (7), (16), (27), (34), (38),
% 56.45/8.14 | | | | | (57), (58), (59) gives:
% 56.45/8.14 | | | | | (63) ? [v0: $i] : (cons(all_91_2, nil) = v0 & app(v0, all_113_0) =
% 56.45/8.14 | | | | | all_91_1 & $i(v0) & $i(all_91_1))
% 56.45/8.14 | | | | |
% 56.45/8.14 | | | | | GROUND_INST: instantiating (ax82) with nil, all_113_0, nil, all_113_0,
% 56.45/8.14 | | | | | nil, simplifying with (7), (16), (57), (58), (59) gives:
% 56.45/8.15 | | | | | (64) ? [v0: $i] : (app(all_113_0, all_113_0) = v0 & app(nil, v0) =
% 56.45/8.15 | | | | | nil & $i(v0))
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | GROUND_INST: instantiating (8) with all_113_0, nil, simplifying with
% 56.45/8.15 | | | | | (57), (58), (59) gives:
% 56.45/8.15 | | | | | (65) all_113_0 = nil
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | GROUND_INST: instantiating (5) with nil, all_91_1, all_91_4, all_91_0,
% 56.45/8.15 | | | | | all_91_3, simplifying with (7), (16), (29), (30), (32),
% 56.45/8.15 | | | | | (33), (35), (36), (51), (60) gives:
% 56.45/8.15 | | | | | (66) segmentP(nil, all_91_1)
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | GROUND_INST: instantiating (ax27) with nil, all_111_0, nil, all_91_2,
% 56.45/8.15 | | | | | all_91_1, simplifying with (7), (16), (27), (34), (38),
% 56.45/8.15 | | | | | (53), (54), (55) gives:
% 56.45/8.15 | | | | | (67) ? [v0: $i] : (cons(all_91_2, all_111_0) = v0 & app(v0, nil) =
% 56.45/8.15 | | | | | all_91_1 & $i(v0) & $i(all_91_1))
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | GROUND_INST: instantiating (15) with all_111_0, nil, simplifying with
% 56.45/8.15 | | | | | (53), (54), (55) gives:
% 56.45/8.15 | | | | | (68) all_111_0 = nil
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | DELTA: instantiating (64) with fresh symbol all_141_0 gives:
% 56.45/8.15 | | | | | (69) app(all_113_0, all_113_0) = all_141_0 & app(nil, all_141_0) =
% 56.45/8.15 | | | | | nil & $i(all_141_0)
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | ALPHA: (69) implies:
% 56.45/8.15 | | | | | (70) $i(all_141_0)
% 56.45/8.15 | | | | | (71) app(all_113_0, all_113_0) = all_141_0
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | DELTA: instantiating (67) with fresh symbol all_165_0 gives:
% 56.45/8.15 | | | | | (72) cons(all_91_2, all_111_0) = all_165_0 & app(all_165_0, nil) =
% 56.45/8.15 | | | | | all_91_1 & $i(all_165_0) & $i(all_91_1)
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | ALPHA: (72) implies:
% 56.45/8.15 | | | | | (73) $i(all_165_0)
% 56.45/8.15 | | | | | (74) cons(all_91_2, all_111_0) = all_165_0
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | DELTA: instantiating (63) with fresh symbol all_167_0 gives:
% 56.45/8.15 | | | | | (75) cons(all_91_2, nil) = all_167_0 & app(all_167_0, all_113_0) =
% 56.45/8.15 | | | | | all_91_1 & $i(all_167_0) & $i(all_91_1)
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | ALPHA: (75) implies:
% 56.45/8.15 | | | | | (76) cons(all_91_2, nil) = all_167_0
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | REDUCE: (68), (74) imply:
% 56.45/8.15 | | | | | (77) cons(all_91_2, nil) = all_165_0
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | REDUCE: (65), (71) imply:
% 56.45/8.15 | | | | | (78) app(nil, nil) = all_141_0
% 56.45/8.15 | | | | |
% 56.45/8.15 | | | | | GROUND_INST: instantiating (14) with all_141_0, simplifying with (7),
% 56.45/8.16 | | | | | (78) gives:
% 56.45/8.16 | | | | | (79) all_141_0 = nil
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | | GROUND_INST: instantiating (18) with all_91_1, all_167_0, nil,
% 56.45/8.16 | | | | | all_91_2, simplifying with (38), (76) gives:
% 56.45/8.16 | | | | | (80) all_167_0 = all_91_1
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | | GROUND_INST: instantiating (18) with all_165_0, all_167_0, nil,
% 56.45/8.16 | | | | | all_91_2, simplifying with (76), (77) gives:
% 56.45/8.16 | | | | | (81) all_167_0 = all_165_0
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | | COMBINE_EQS: (80), (81) imply:
% 56.45/8.16 | | | | | (82) all_165_0 = all_91_1
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | | GROUND_INST: instantiating (ax54) with nil, all_91_1, simplifying with
% 56.45/8.16 | | | | | (7), (16), (35), (51), (62), (66) gives:
% 56.45/8.16 | | | | | (83) all_91_1 = nil
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | | REDUCE: (61), (83) imply:
% 56.45/8.16 | | | | | (84) singletonP(nil)
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | | PRED_UNIFY: (9), (84) imply:
% 56.45/8.16 | | | | | (85) $false
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | | CLOSE: (85) is inconsistent.
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | Case 2:
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | | (86) all_89_0 = all_89_1
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | | REDUCE: (20), (86) imply:
% 56.45/8.16 | | | | | (87) $false
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | | CLOSE: (87) is inconsistent.
% 56.45/8.16 | | | | |
% 56.45/8.16 | | | | End of split
% 56.45/8.16 | | | |
% 56.45/8.16 | | | End of split
% 56.45/8.16 | | |
% 56.45/8.16 | | End of split
% 56.45/8.16 | |
% 56.45/8.16 | End of split
% 56.45/8.16 |
% 56.45/8.16 End of proof
% 56.45/8.16 % SZS output end Proof for theBenchmark
% 56.45/8.16
% 56.45/8.16 7645ms
%------------------------------------------------------------------------------