TSTP Solution File: SWC182+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC182+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 : n005.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 20:50:07 EDT 2023
% Result : Theorem 33.11s 7.03s
% Output : Proof 52.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWC182+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 16:12:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.63 ________ _____
% 0.19/0.63 ___ __ \_________(_)________________________________
% 0.19/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.63
% 0.19/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.63 (2023-06-19)
% 0.19/0.63
% 0.19/0.63 (c) Philipp Rümmer, 2009-2023
% 0.19/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.63 Amanda Stjerna.
% 0.19/0.63 Free software under BSD-3-Clause.
% 0.19/0.63
% 0.19/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.63
% 0.19/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.64 Running up to 7 provers in parallel.
% 0.19/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.56/1.68 Prover 4: Preprocessing ...
% 4.56/1.68 Prover 1: Preprocessing ...
% 4.96/1.73 Prover 3: Preprocessing ...
% 4.96/1.73 Prover 6: Preprocessing ...
% 4.96/1.73 Prover 2: Preprocessing ...
% 4.96/1.73 Prover 5: Preprocessing ...
% 4.96/1.73 Prover 0: Preprocessing ...
% 13.82/3.45 Prover 2: Proving ...
% 14.10/3.51 Prover 5: Constructing countermodel ...
% 14.10/3.53 Prover 6: Proving ...
% 14.10/3.54 Prover 1: Constructing countermodel ...
% 14.67/3.60 Prover 3: Constructing countermodel ...
% 19.00/4.45 Prover 4: Constructing countermodel ...
% 20.43/4.73 Prover 0: Proving ...
% 33.11/7.02 Prover 3: proved (6353ms)
% 33.11/7.03
% 33.11/7.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.11/7.03
% 33.11/7.04 Prover 5: stopped
% 33.11/7.04 Prover 2: stopped
% 33.11/7.04 Prover 6: stopped
% 33.11/7.06 Prover 0: stopped
% 33.11/7.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 33.11/7.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 33.11/7.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 33.11/7.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 33.11/7.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 34.74/7.41 Prover 11: Preprocessing ...
% 34.74/7.45 Prover 8: Preprocessing ...
% 34.74/7.47 Prover 10: Preprocessing ...
% 34.74/7.48 Prover 7: Preprocessing ...
% 34.74/7.48 Prover 13: Preprocessing ...
% 36.92/7.74 Prover 10: Constructing countermodel ...
% 37.41/7.81 Prover 7: Constructing countermodel ...
% 37.78/7.89 Prover 13: Constructing countermodel ...
% 38.61/8.00 Prover 8: Warning: ignoring some quantifiers
% 38.61/8.03 Prover 8: Constructing countermodel ...
% 43.44/8.90 Prover 11: Constructing countermodel ...
% 51.51/10.42 Prover 10: Found proof (size 70)
% 51.51/10.42 Prover 10: proved (3374ms)
% 51.51/10.42 Prover 11: stopped
% 51.51/10.42 Prover 7: stopped
% 51.51/10.42 Prover 13: stopped
% 51.51/10.42 Prover 8: stopped
% 52.05/10.43 Prover 1: stopped
% 52.05/10.44 Prover 4: stopped
% 52.05/10.44
% 52.05/10.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 52.05/10.44
% 52.05/10.44 % SZS output start Proof for theBenchmark
% 52.05/10.45 Assumptions after simplification:
% 52.05/10.45 ---------------------------------
% 52.05/10.45
% 52.05/10.45 (ax1)
% 52.05/10.46 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) |
% 52.05/10.46 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) |
% 52.05/10.46 ~ ssItem(v0))
% 52.05/10.46
% 52.05/10.46 (ax16)
% 52.30/10.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1)
% 52.30/10.50 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2))
% 52.30/10.50
% 52.30/10.50 (ax2)
% 52.30/10.50 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) &
% 52.30/10.50 ssItem(v0))
% 52.30/10.50
% 52.30/10.50 (ax27)
% 52.30/10.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 52.30/10.50 (cons(v3, v2) = v4) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 52.30/10.50 $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v3) | ? [v5: $i] :
% 52.30/10.50 (cons(v3, v1) = v5 & app(v5, v0) = v4 & $i(v5) & $i(v4)))
% 52.30/10.50
% 52.30/10.50 (ax28)
% 52.30/10.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 52.30/10.50 $i(v0) | ~ ssList(v0))
% 52.30/10.50
% 52.30/10.50 (ax39)
% 52.30/10.50 $i(nil) & ~ singletonP(nil)
% 52.30/10.50
% 52.30/10.50 (ax4)
% 52.30/10.51 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) |
% 52.30/10.51 ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) & ! [v0: $i] : (
% 52.30/10.51 ~ $i(v0) | ~ singletonP(v0) | ~ ssList(v0) | ? [v1: $i] : (cons(v1, nil)
% 52.30/10.51 = v0 & $i(v1) & ssItem(v1)))
% 52.30/10.51
% 52.30/10.51 (ax46)
% 52.30/10.51 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 52.30/10.51 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 52.30/10.51
% 52.30/10.51 (ax5)
% 52.30/10.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 52.30/10.51 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 52.30/10.51 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 52.30/10.51 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 52.30/10.51 v2) = v0 & $i(v2) & ssList(v2)))
% 52.30/10.51
% 52.30/10.51 (ax52)
% 52.30/10.51 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~
% 52.30/10.51 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 52.30/10.51
% 52.30/10.51 (ax54)
% 52.30/10.51 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ segmentP(v1,
% 52.30/10.51 v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 52.30/10.51
% 52.30/10.51 (ax57)
% 52.30/10.51 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil))
% 52.30/10.51
% 52.30/10.51 (ax58)
% 52.30/10.52 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 52.30/10.52 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 52.30/10.52
% 52.30/10.52 (ax6)
% 52.30/10.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 52.30/10.52 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 52.30/10.52 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 52.30/10.52 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 52.30/10.52 v1) = v0 & $i(v2) & ssList(v2)))
% 52.30/10.52
% 52.30/10.52 (ax7)
% 52.30/10.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 52.30/10.52 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 52.30/10.52 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 52.30/10.52 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 52.30/10.52 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 52.30/10.52 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 52.30/10.52 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 52.30/10.52
% 52.30/10.52 (ax82)
% 52.30/10.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 52.30/10.52 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 52.30/10.52 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 52.30/10.52 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 52.30/10.52
% 52.30/10.52 (ax83)
% 52.30/10.52 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 52.30/10.52 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 52.30/10.52 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 52.30/10.52 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 52.30/10.52 v0) | ~ ssList(nil))
% 52.30/10.52
% 52.30/10.53 (ax84)
% 52.30/10.53 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 52.30/10.53 $i(v0) | ~ ssList(v0))
% 52.30/10.53
% 52.30/10.53 (co1)
% 52.30/10.53 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 52.30/10.53 : ? [v5: $i] : (cons(v1, nil) = v2 & app(v4, v5) = nil & app(v3, v2) = v4 &
% 52.30/10.53 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v5) &
% 52.30/10.53 ssList(v3) & ssList(v0) & ssList(nil) & ssItem(v1) & (memberP(v5, v1) |
% 52.30/10.53 memberP(v3, v1)))
% 52.30/10.53
% 52.30/10.53 (function-axioms)
% 52.30/10.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 52.30/10.53 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 52.30/10.53 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 52.30/10.53 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 52.30/10.53 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 52.30/10.53 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 52.30/10.53
% 52.30/10.53 Further assumptions not needed in the proof:
% 52.30/10.53 --------------------------------------------
% 52.30/10.53 ax10, ax11, ax12, ax13, ax14, ax15, ax17, ax18, ax19, ax20, ax21, ax22, ax23,
% 52.30/10.53 ax24, ax25, ax26, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37,
% 52.30/10.53 ax38, ax40, ax41, ax42, ax43, ax44, ax45, ax47, ax48, ax49, ax50, ax51, ax53,
% 52.30/10.53 ax55, ax56, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69,
% 52.30/10.53 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 52.30/10.53 ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 52.30/10.53
% 52.30/10.53 Those formulas are unsatisfiable:
% 52.30/10.53 ---------------------------------
% 52.30/10.53
% 52.30/10.53 Begin of proof
% 52.30/10.53 |
% 52.30/10.53 | ALPHA: (ax1) implies:
% 52.30/10.53 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 52.30/10.53 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1))
% 52.30/10.53 |
% 52.30/10.53 | ALPHA: (ax4) implies:
% 52.30/10.53 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) | ~
% 52.30/10.53 | $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0))
% 52.30/10.53 |
% 52.30/10.53 | ALPHA: (ax5) implies:
% 52.30/10.53 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 52.30/10.53 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 52.30/10.53 | v0 & $i(v2) & ssList(v2)))
% 52.30/10.53 |
% 52.30/10.53 | ALPHA: (ax6) implies:
% 52.30/10.54 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 52.30/10.54 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 52.30/10.54 | v0 & $i(v2) & ssList(v2)))
% 52.30/10.54 |
% 52.30/10.54 | ALPHA: (ax7) implies:
% 52.30/10.54 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 52.30/10.54 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2)
% 52.30/10.54 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~
% 52.30/10.54 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 52.30/10.54 |
% 52.30/10.54 | ALPHA: (ax28) implies:
% 52.30/10.54 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 52.30/10.54 | $i(v0) | ~ ssList(v0))
% 52.30/10.54 |
% 52.30/10.54 | ALPHA: (ax39) implies:
% 52.30/10.54 | (7) ~ singletonP(nil)
% 52.30/10.54 |
% 52.30/10.54 | ALPHA: (ax46) implies:
% 52.30/10.54 | (8) ~ ssList(nil) | frontsegP(nil, nil)
% 52.30/10.54 |
% 52.30/10.54 | ALPHA: (ax52) implies:
% 52.30/10.54 | (9) ~ ssList(nil) | rearsegP(nil, nil)
% 52.30/10.54 |
% 52.30/10.54 | ALPHA: (ax57) implies:
% 52.30/10.54 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil))
% 52.30/10.54 |
% 52.30/10.54 | ALPHA: (ax58) implies:
% 52.30/10.54 | (11) ~ ssList(nil) | segmentP(nil, nil)
% 52.30/10.54 |
% 52.30/10.54 | ALPHA: (ax83) implies:
% 52.30/10.54 | (12) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 52.30/10.54 |
% 52.30/10.54 | ALPHA: (ax84) implies:
% 52.30/10.54 | (13) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 52.30/10.54 | $i(v0) | ~ ssList(v0))
% 52.30/10.54 |
% 52.30/10.54 | ALPHA: (co1) implies:
% 52.30/10.54 | (14) $i(nil)
% 52.30/10.54 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 52.30/10.54 | ? [v5: $i] : (cons(v1, nil) = v2 & app(v4, v5) = nil & app(v3, v2) =
% 52.30/10.54 | v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 52.30/10.54 | ssList(v5) & ssList(v3) & ssList(v0) & ssList(nil) & ssItem(v1) &
% 52.30/10.54 | (memberP(v5, v1) | memberP(v3, v1)))
% 52.30/10.54 |
% 52.30/10.54 | ALPHA: (function-axioms) implies:
% 52.30/10.54 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 52.30/10.54 | (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 52.30/10.54 |
% 52.30/10.54 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives:
% 52.30/10.55 | (17) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) &
% 52.30/10.55 | ssItem(all_89_0) & ssItem(all_89_1)
% 52.30/10.55 |
% 52.30/10.55 | ALPHA: (17) implies:
% 52.30/10.55 | (18) ~ (all_89_0 = all_89_1)
% 52.30/10.55 | (19) ssItem(all_89_1)
% 52.30/10.55 | (20) ssItem(all_89_0)
% 52.30/10.55 | (21) $i(all_89_1)
% 52.30/10.55 | (22) $i(all_89_0)
% 52.30/10.55 |
% 52.30/10.55 | DELTA: instantiating (15) with fresh symbols all_91_0, all_91_1, all_91_2,
% 52.30/10.55 | all_91_3, all_91_4, all_91_5 gives:
% 52.30/10.55 | (23) cons(all_91_4, nil) = all_91_3 & app(all_91_1, all_91_0) = nil &
% 52.30/10.55 | app(all_91_2, all_91_3) = all_91_1 & $i(all_91_0) & $i(all_91_1) &
% 52.30/10.55 | $i(all_91_2) & $i(all_91_3) & $i(all_91_4) & $i(all_91_5) &
% 52.30/10.55 | ssList(all_91_0) & ssList(all_91_2) & ssList(all_91_5) & ssList(nil) &
% 52.30/10.55 | ssItem(all_91_4) & (memberP(all_91_0, all_91_4) | memberP(all_91_2,
% 52.30/10.55 | all_91_4))
% 52.30/10.55 |
% 52.30/10.55 | ALPHA: (23) implies:
% 52.30/10.55 | (24) ssItem(all_91_4)
% 52.30/10.55 | (25) ssList(nil)
% 52.30/10.55 | (26) ssList(all_91_2)
% 52.30/10.55 | (27) ssList(all_91_0)
% 52.30/10.55 | (28) $i(all_91_4)
% 52.30/10.55 | (29) $i(all_91_3)
% 52.30/10.55 | (30) $i(all_91_2)
% 52.30/10.55 | (31) $i(all_91_0)
% 52.30/10.55 | (32) app(all_91_2, all_91_3) = all_91_1
% 52.30/10.55 | (33) app(all_91_1, all_91_0) = nil
% 52.30/10.55 | (34) cons(all_91_4, nil) = all_91_3
% 52.30/10.55 |
% 52.30/10.55 | BETA: splitting (9) gives:
% 52.30/10.55 |
% 52.30/10.55 | Case 1:
% 52.30/10.55 | |
% 52.30/10.55 | | (35) ~ ssList(nil)
% 52.30/10.55 | |
% 52.30/10.55 | | PRED_UNIFY: (25), (35) imply:
% 52.30/10.55 | | (36) $false
% 52.30/10.55 | |
% 52.30/10.55 | | CLOSE: (36) is inconsistent.
% 52.30/10.55 | |
% 52.30/10.55 | Case 2:
% 52.30/10.55 | |
% 52.30/10.55 | | (37) rearsegP(nil, nil)
% 52.30/10.55 | |
% 52.30/10.55 | | BETA: splitting (8) gives:
% 52.30/10.55 | |
% 52.30/10.55 | | Case 1:
% 52.30/10.55 | | |
% 52.30/10.55 | | | (38) ~ ssList(nil)
% 52.30/10.55 | | |
% 52.30/10.55 | | | PRED_UNIFY: (25), (38) imply:
% 52.30/10.55 | | | (39) $false
% 52.30/10.55 | | |
% 52.30/10.55 | | | CLOSE: (39) is inconsistent.
% 52.30/10.55 | | |
% 52.30/10.55 | | Case 2:
% 52.30/10.55 | | |
% 52.30/10.55 | | | (40) frontsegP(nil, nil)
% 52.30/10.55 | | |
% 52.30/10.55 | | | BETA: splitting (11) gives:
% 52.30/10.55 | | |
% 52.30/10.55 | | | Case 1:
% 52.30/10.55 | | | |
% 52.30/10.55 | | | | (41) ~ ssList(nil)
% 52.30/10.55 | | | |
% 52.30/10.55 | | | | PRED_UNIFY: (25), (41) imply:
% 52.30/10.55 | | | | (42) $false
% 52.30/10.55 | | | |
% 52.30/10.55 | | | | CLOSE: (42) is inconsistent.
% 52.30/10.55 | | | |
% 52.30/10.55 | | | Case 2:
% 52.30/10.55 | | | |
% 52.30/10.55 | | | |
% 52.30/10.56 | | | | GROUND_INST: instantiating (1) with all_89_0, all_89_1, simplifying with
% 52.30/10.56 | | | | (19), (20), (21), (22) gives:
% 52.30/10.56 | | | | (43) all_89_0 = all_89_1 | neq(all_89_0, all_89_1)
% 52.30/10.56 | | | |
% 52.30/10.56 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (14),
% 52.30/10.56 | | | | (25), (40) gives:
% 52.30/10.56 | | | | (44) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 52.30/10.56 | | | |
% 52.30/10.56 | | | | GROUND_INST: instantiating (4) with nil, nil, simplifying with (14),
% 52.30/10.56 | | | | (25), (37) gives:
% 52.30/10.56 | | | | (45) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0))
% 52.30/10.56 | | | |
% 52.30/10.56 | | | | GROUND_INST: instantiating (ax16) with nil, all_91_4, all_91_3,
% 52.30/10.56 | | | | simplifying with (14), (24), (25), (28), (34) gives:
% 52.30/10.56 | | | | (46) ssList(all_91_3)
% 52.30/10.56 | | | |
% 52.30/10.56 | | | | DELTA: instantiating (45) with fresh symbol all_111_0 gives:
% 52.30/10.56 | | | | (47) app(all_111_0, nil) = nil & $i(all_111_0) & ssList(all_111_0)
% 52.30/10.56 | | | |
% 52.30/10.56 | | | | ALPHA: (47) implies:
% 52.30/10.56 | | | | (48) ssList(all_111_0)
% 52.30/10.56 | | | | (49) $i(all_111_0)
% 52.30/10.56 | | | | (50) app(all_111_0, nil) = nil
% 52.30/10.56 | | | |
% 52.30/10.56 | | | | DELTA: instantiating (44) with fresh symbol all_113_0 gives:
% 52.30/10.56 | | | | (51) app(nil, all_113_0) = nil & $i(all_113_0) & ssList(all_113_0)
% 52.30/10.56 | | | |
% 52.30/10.56 | | | | ALPHA: (51) implies:
% 52.30/10.56 | | | | (52) ssList(all_113_0)
% 52.30/10.56 | | | | (53) $i(all_113_0)
% 52.30/10.56 | | | | (54) app(nil, all_113_0) = nil
% 52.30/10.56 | | | |
% 52.30/10.56 | | | | BETA: splitting (43) gives:
% 52.30/10.56 | | | |
% 52.30/10.56 | | | | Case 1:
% 52.30/10.56 | | | | |
% 52.30/10.56 | | | | |
% 52.30/10.56 | | | | | GROUND_INST: instantiating (2) with all_91_3, all_91_4, simplifying
% 52.30/10.56 | | | | | with (24), (28), (29), (34), (46) gives:
% 52.30/10.56 | | | | | (55) singletonP(all_91_3)
% 52.30/10.56 | | | | |
% 52.62/10.56 | | | | | GROUND_INST: instantiating (5) with nil, all_91_3, all_91_2, all_91_1,
% 52.62/10.56 | | | | | all_91_0, simplifying with (14), (25), (26), (27), (29),
% 52.62/10.56 | | | | | (30), (31), (32), (33), (46) gives:
% 52.62/10.56 | | | | | (56) segmentP(nil, all_91_3)
% 52.62/10.56 | | | | |
% 52.62/10.56 | | | | | GROUND_INST: instantiating (10) with all_91_3, simplifying with (29),
% 52.62/10.56 | | | | | (46) gives:
% 52.62/10.56 | | | | | (57) segmentP(all_91_3, nil)
% 52.62/10.56 | | | | |
% 52.62/10.57 | | | | | GROUND_INST: instantiating (ax27) with all_113_0, nil, nil, all_91_4,
% 52.62/10.57 | | | | | all_91_3, simplifying with (14), (24), (25), (28), (34),
% 52.63/10.57 | | | | | (52), (53), (54) gives:
% 52.63/10.57 | | | | | (58) ? [v0: $i] : (cons(all_91_4, nil) = v0 & app(v0, all_113_0) =
% 52.63/10.57 | | | | | all_91_3 & $i(v0) & $i(all_91_3))
% 52.63/10.57 | | | | |
% 52.63/10.57 | | | | | GROUND_INST: instantiating (ax82) with nil, all_113_0, nil, all_113_0,
% 52.63/10.57 | | | | | nil, simplifying with (14), (25), (52), (53), (54) gives:
% 52.63/10.58 | | | | | (59) ? [v0: $i] : (app(all_113_0, all_113_0) = v0 & app(nil, v0) =
% 52.63/10.58 | | | | | nil & $i(v0))
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | GROUND_INST: instantiating (6) with all_113_0, nil, simplifying with
% 52.63/10.58 | | | | | (52), (53), (54) gives:
% 52.63/10.58 | | | | | (60) all_113_0 = nil
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | GROUND_INST: instantiating (ax27) with nil, all_111_0, nil, all_91_4,
% 52.63/10.58 | | | | | all_91_3, simplifying with (14), (24), (25), (28), (34),
% 52.63/10.58 | | | | | (48), (49), (50) gives:
% 52.63/10.58 | | | | | (61) ? [v0: $i] : (cons(all_91_4, all_111_0) = v0 & app(v0, nil) =
% 52.63/10.58 | | | | | all_91_3 & $i(v0) & $i(all_91_3))
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | GROUND_INST: instantiating (13) with all_111_0, nil, simplifying with
% 52.63/10.58 | | | | | (48), (49), (50) gives:
% 52.63/10.58 | | | | | (62) all_111_0 = nil
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | DELTA: instantiating (59) with fresh symbol all_159_0 gives:
% 52.63/10.58 | | | | | (63) app(all_113_0, all_113_0) = all_159_0 & app(nil, all_159_0) =
% 52.63/10.58 | | | | | nil & $i(all_159_0)
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | ALPHA: (63) implies:
% 52.63/10.58 | | | | | (64) $i(all_159_0)
% 52.63/10.58 | | | | | (65) app(all_113_0, all_113_0) = all_159_0
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | DELTA: instantiating (61) with fresh symbol all_161_0 gives:
% 52.63/10.58 | | | | | (66) cons(all_91_4, all_111_0) = all_161_0 & app(all_161_0, nil) =
% 52.63/10.58 | | | | | all_91_3 & $i(all_161_0) & $i(all_91_3)
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | ALPHA: (66) implies:
% 52.63/10.58 | | | | | (67) $i(all_161_0)
% 52.63/10.58 | | | | | (68) cons(all_91_4, all_111_0) = all_161_0
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | DELTA: instantiating (58) with fresh symbol all_163_0 gives:
% 52.63/10.58 | | | | | (69) cons(all_91_4, nil) = all_163_0 & app(all_163_0, all_113_0) =
% 52.63/10.58 | | | | | all_91_3 & $i(all_163_0) & $i(all_91_3)
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | ALPHA: (69) implies:
% 52.63/10.58 | | | | | (70) cons(all_91_4, nil) = all_163_0
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | REDUCE: (62), (68) imply:
% 52.63/10.58 | | | | | (71) cons(all_91_4, nil) = all_161_0
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | REDUCE: (60), (65) imply:
% 52.63/10.58 | | | | | (72) app(nil, nil) = all_159_0
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | GROUND_INST: instantiating (12) with all_159_0, simplifying with (25),
% 52.63/10.58 | | | | | (72) gives:
% 52.63/10.58 | | | | | (73) all_159_0 = nil
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | GROUND_INST: instantiating (16) with all_91_3, all_163_0, nil,
% 52.63/10.58 | | | | | all_91_4, simplifying with (34), (70) gives:
% 52.63/10.58 | | | | | (74) all_163_0 = all_91_3
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | GROUND_INST: instantiating (16) with all_161_0, all_163_0, nil,
% 52.63/10.58 | | | | | all_91_4, simplifying with (70), (71) gives:
% 52.63/10.58 | | | | | (75) all_163_0 = all_161_0
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | COMBINE_EQS: (74), (75) imply:
% 52.63/10.58 | | | | | (76) all_161_0 = all_91_3
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | GROUND_INST: instantiating (ax54) with nil, all_91_3, simplifying with
% 52.63/10.58 | | | | | (14), (25), (29), (46), (56), (57) gives:
% 52.63/10.58 | | | | | (77) all_91_3 = nil
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | REDUCE: (55), (77) imply:
% 52.63/10.58 | | | | | (78) singletonP(nil)
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | PRED_UNIFY: (7), (78) imply:
% 52.63/10.58 | | | | | (79) $false
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | CLOSE: (79) is inconsistent.
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | Case 2:
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | (80) all_89_0 = all_89_1
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | REDUCE: (18), (80) imply:
% 52.63/10.58 | | | | | (81) $false
% 52.63/10.58 | | | | |
% 52.63/10.58 | | | | | CLOSE: (81) is inconsistent.
% 52.63/10.59 | | | | |
% 52.63/10.59 | | | | End of split
% 52.63/10.59 | | | |
% 52.63/10.59 | | | End of split
% 52.63/10.59 | | |
% 52.63/10.59 | | End of split
% 52.63/10.59 | |
% 52.63/10.59 | End of split
% 52.63/10.59 |
% 52.63/10.59 End of proof
% 52.63/10.59 % SZS output end Proof for theBenchmark
% 52.63/10.59
% 52.63/10.59 9958ms
%------------------------------------------------------------------------------