TSTP Solution File: SWC007+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC007+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 20:49:08 EDT 2023
% Result : Theorem 25.03s 4.23s
% Output : Proof 47.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC007+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.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 15:01:08 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.69 ________ _____
% 0.19/0.69 ___ __ \_________(_)________________________________
% 0.19/0.69 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.69 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.69 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.69
% 0.19/0.69 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.69 (2023-06-19)
% 0.19/0.69
% 0.19/0.69 (c) Philipp Rümmer, 2009-2023
% 0.19/0.69 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.69 Amanda Stjerna.
% 0.19/0.69 Free software under BSD-3-Clause.
% 0.19/0.69
% 0.19/0.69 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.69
% 0.19/0.69 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.70 Running up to 7 provers in parallel.
% 0.19/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.71/1.50 Prover 1: Preprocessing ...
% 4.71/1.50 Prover 4: Preprocessing ...
% 5.27/1.54 Prover 5: Preprocessing ...
% 5.27/1.54 Prover 3: Preprocessing ...
% 5.27/1.54 Prover 6: Preprocessing ...
% 5.27/1.54 Prover 0: Preprocessing ...
% 5.27/1.54 Prover 2: Preprocessing ...
% 14.43/2.77 Prover 2: Proving ...
% 14.43/2.80 Prover 5: Constructing countermodel ...
% 14.99/2.84 Prover 1: Constructing countermodel ...
% 15.49/2.88 Prover 3: Constructing countermodel ...
% 15.49/2.90 Prover 6: Proving ...
% 20.40/3.57 Prover 4: Constructing countermodel ...
% 21.41/3.69 Prover 0: Proving ...
% 25.03/4.23 Prover 2: proved (3517ms)
% 25.03/4.23
% 25.03/4.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.03/4.23
% 25.03/4.23 Prover 5: stopped
% 25.03/4.23 Prover 3: stopped
% 25.81/4.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 25.81/4.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.81/4.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.81/4.26 Prover 6: stopped
% 25.81/4.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 25.81/4.27 Prover 0: stopped
% 25.81/4.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.74/4.45 Prover 8: Preprocessing ...
% 27.54/4.49 Prover 7: Preprocessing ...
% 27.54/4.49 Prover 10: Preprocessing ...
% 27.85/4.52 Prover 11: Preprocessing ...
% 28.15/4.56 Prover 13: Preprocessing ...
% 29.41/4.73 Prover 10: Constructing countermodel ...
% 29.89/4.80 Prover 7: Constructing countermodel ...
% 30.77/4.91 Prover 8: Warning: ignoring some quantifiers
% 31.09/4.92 Prover 8: Constructing countermodel ...
% 31.24/4.99 Prover 13: Constructing countermodel ...
% 38.48/5.87 Prover 11: Constructing countermodel ...
% 46.78/6.94 Prover 10: Found proof (size 161)
% 46.78/6.94 Prover 10: proved (2695ms)
% 46.78/6.94 Prover 8: stopped
% 46.78/6.94 Prover 1: stopped
% 46.78/6.94 Prover 7: stopped
% 46.78/6.94 Prover 11: stopped
% 46.78/6.94 Prover 4: stopped
% 46.78/6.94 Prover 13: stopped
% 46.78/6.94
% 46.78/6.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.78/6.94
% 46.93/6.97 % SZS output start Proof for theBenchmark
% 46.93/6.98 Assumptions after simplification:
% 46.93/6.98 ---------------------------------
% 46.93/6.98
% 46.93/6.98 (ax1)
% 46.93/6.98 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) |
% 46.93/6.98 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) |
% 46.93/6.98 ~ ssItem(v0))
% 46.93/6.98
% 46.93/6.98 (ax2)
% 46.93/6.98 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) &
% 46.93/6.98 ssItem(v0))
% 46.93/6.99
% 46.93/6.99 (ax26)
% 46.93/7.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) |
% 46.93/7.00 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 46.93/7.00
% 46.93/7.00 (ax28)
% 46.93/7.00 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 46.93/7.01 $i(v0) | ~ ssList(v0))
% 46.93/7.01
% 46.93/7.01 (ax42)
% 46.93/7.01 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0))
% 46.93/7.01
% 46.93/7.01 (ax45)
% 46.93/7.01 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 46.93/7.01
% 46.93/7.01 (ax46)
% 46.93/7.01 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 46.93/7.01 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 46.93/7.01
% 46.93/7.01 (ax5)
% 46.93/7.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 46.93/7.01 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 46.93/7.01 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 46.93/7.01 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 46.93/7.01 v2) = v0 & $i(v2) & ssList(v2)))
% 46.93/7.01
% 46.93/7.01 (ax51)
% 46.93/7.01 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 46.93/7.01
% 46.93/7.01 (ax52)
% 46.93/7.01 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~
% 46.93/7.01 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 46.93/7.01
% 46.93/7.01 (ax58)
% 46.93/7.01 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 46.93/7.01 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 46.93/7.01
% 46.93/7.01 (ax6)
% 46.93/7.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 46.93/7.01 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 46.93/7.01 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 46.93/7.01 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 46.93/7.01 v1) = v0 & $i(v2) & ssList(v2)))
% 46.93/7.01
% 46.93/7.01 (ax7)
% 46.93/7.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 46.93/7.02 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 46.93/7.02 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 46.93/7.02 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 46.93/7.02 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 46.93/7.02 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 46.93/7.02 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 46.93/7.02
% 46.93/7.02 (ax80)
% 46.93/7.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v1,
% 46.93/7.02 v3) = v2) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 46.93/7.02 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 46.93/7.02
% 46.93/7.02 (ax82)
% 46.93/7.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 46.93/7.02 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 46.93/7.02 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 46.93/7.02 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 46.93/7.02
% 46.93/7.02 (ax83)
% 46.93/7.02 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 46.93/7.02 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 46.93/7.02 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 46.93/7.02 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 46.93/7.02 v0) | ~ ssList(nil))
% 46.93/7.02
% 46.93/7.02 (ax84)
% 47.24/7.02 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 47.24/7.02 $i(v0) | ~ ssList(v0))
% 47.24/7.02
% 47.24/7.02 (co1)
% 47.24/7.02 $i(nil) & ? [v0: $i] : ($i(v0) & ssList(v0) & ssList(nil) & ! [v1: $i] : !
% 47.24/7.02 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (app(v3, v4) = v0) | ~ (app(v1,
% 47.24/7.02 v2) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ ssList(v4) | ~
% 47.24/7.02 ssList(v2) | ~ ssList(v1) | ? [v5: $i] : ( ~ (v5 = nil) & app(v1, v4) =
% 47.24/7.02 v5 & $i(v5))))
% 47.24/7.02
% 47.24/7.02 (function-axioms)
% 47.24/7.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 47.24/7.02 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 47.24/7.02 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 47.24/7.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 47.24/7.02 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 47.24/7.02 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 47.24/7.02
% 47.24/7.02 Further assumptions not needed in the proof:
% 47.24/7.02 --------------------------------------------
% 47.24/7.02 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax21, ax22,
% 47.24/7.02 ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36,
% 47.24/7.02 ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax47, ax48, ax49, ax50, ax53,
% 47.24/7.02 ax54, ax55, ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67,
% 47.24/7.02 ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8,
% 47.24/7.02 ax81, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 47.24/7.02
% 47.24/7.02 Those formulas are unsatisfiable:
% 47.24/7.02 ---------------------------------
% 47.24/7.02
% 47.24/7.02 Begin of proof
% 47.24/7.02 |
% 47.24/7.03 | ALPHA: (ax1) implies:
% 47.24/7.03 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 47.24/7.03 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1))
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (ax5) implies:
% 47.24/7.03 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 47.24/7.03 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 47.24/7.03 | v0 & $i(v2) & ssList(v2)))
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (ax6) implies:
% 47.24/7.03 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 47.24/7.03 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 47.24/7.03 | v0 & $i(v2) & ssList(v2)))
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (ax7) implies:
% 47.24/7.03 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0,
% 47.24/7.03 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] :
% 47.24/7.03 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) &
% 47.24/7.03 | $i(v2) & ssList(v4) & ssList(v2)))
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (ax28) implies:
% 47.24/7.03 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 47.24/7.03 | $i(v0) | ~ ssList(v0))
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (ax45) implies:
% 47.24/7.03 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (ax46) implies:
% 47.24/7.03 | (7) ~ ssList(nil) | frontsegP(nil, nil)
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (ax51) implies:
% 47.24/7.03 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (ax52) implies:
% 47.24/7.03 | (9) ~ ssList(nil) | rearsegP(nil, nil)
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (ax58) implies:
% 47.24/7.03 | (10) ~ ssList(nil) | segmentP(nil, nil)
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (ax83) implies:
% 47.24/7.03 | (11) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 47.24/7.03 | (12) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~
% 47.24/7.03 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 47.24/7.03 | (13) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 47.24/7.03 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (ax84) implies:
% 47.24/7.03 | (14) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 47.24/7.03 | $i(v0) | ~ ssList(v0))
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (co1) implies:
% 47.24/7.03 | (15) $i(nil)
% 47.24/7.03 | (16) ? [v0: $i] : ($i(v0) & ssList(v0) & ssList(nil) & ! [v1: $i] : !
% 47.24/7.03 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (app(v3, v4) = v0) | ~
% 47.24/7.03 | (app(v1, v2) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~
% 47.24/7.03 | ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ? [v5: $i] : ( ~ (v5
% 47.24/7.03 | = nil) & app(v1, v4) = v5 & $i(v5))))
% 47.24/7.03 |
% 47.24/7.03 | ALPHA: (function-axioms) implies:
% 47.24/7.04 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 47.24/7.04 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 47.24/7.04 |
% 47.24/7.04 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives:
% 47.24/7.04 | (18) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) &
% 47.24/7.04 | ssItem(all_89_0) & ssItem(all_89_1)
% 47.24/7.04 |
% 47.24/7.04 | ALPHA: (18) implies:
% 47.24/7.04 | (19) ~ (all_89_0 = all_89_1)
% 47.24/7.04 | (20) ssItem(all_89_1)
% 47.24/7.04 | (21) ssItem(all_89_0)
% 47.24/7.04 | (22) $i(all_89_1)
% 47.24/7.04 | (23) $i(all_89_0)
% 47.24/7.04 |
% 47.24/7.04 | DELTA: instantiating (16) with fresh symbol all_91_0 gives:
% 47.24/7.04 | (24) $i(all_91_0) & ssList(all_91_0) & ssList(nil) & ! [v0: $i] : ! [v1:
% 47.24/7.04 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2, v3) = all_91_0) | ~
% 47.24/7.04 | (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 47.24/7.04 | ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v4: $i] : ( ~ (v4 =
% 47.24/7.04 | nil) & app(v0, v3) = v4 & $i(v4)))
% 47.24/7.04 |
% 47.24/7.04 | ALPHA: (24) implies:
% 47.24/7.04 | (25) ssList(nil)
% 47.24/7.04 | (26) ssList(all_91_0)
% 47.24/7.04 | (27) $i(all_91_0)
% 47.24/7.04 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2,
% 47.24/7.04 | v3) = all_91_0) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1)
% 47.24/7.04 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ?
% 47.24/7.04 | [v4: $i] : ( ~ (v4 = nil) & app(v0, v3) = v4 & $i(v4)))
% 47.24/7.04 |
% 47.24/7.04 | BETA: splitting (7) gives:
% 47.24/7.04 |
% 47.24/7.04 | Case 1:
% 47.24/7.04 | |
% 47.24/7.04 | | (29) ~ ssList(nil)
% 47.24/7.04 | |
% 47.24/7.04 | | PRED_UNIFY: (25), (29) imply:
% 47.24/7.04 | | (30) $false
% 47.24/7.04 | |
% 47.24/7.04 | | CLOSE: (30) is inconsistent.
% 47.24/7.04 | |
% 47.24/7.04 | Case 2:
% 47.24/7.04 | |
% 47.24/7.04 | | (31) frontsegP(nil, nil)
% 47.24/7.04 | |
% 47.24/7.04 | | BETA: splitting (9) gives:
% 47.24/7.04 | |
% 47.24/7.04 | | Case 1:
% 47.24/7.04 | | |
% 47.24/7.04 | | | (32) ~ ssList(nil)
% 47.24/7.04 | | |
% 47.24/7.04 | | | PRED_UNIFY: (25), (32) imply:
% 47.24/7.04 | | | (33) $false
% 47.24/7.04 | | |
% 47.24/7.04 | | | CLOSE: (33) is inconsistent.
% 47.24/7.04 | | |
% 47.24/7.04 | | Case 2:
% 47.24/7.04 | | |
% 47.24/7.04 | | | (34) rearsegP(nil, nil)
% 47.24/7.04 | | |
% 47.24/7.04 | | | BETA: splitting (10) gives:
% 47.24/7.04 | | |
% 47.24/7.04 | | | Case 1:
% 47.24/7.04 | | | |
% 47.24/7.04 | | | | (35) ~ ssList(nil)
% 47.24/7.04 | | | |
% 47.24/7.04 | | | | PRED_UNIFY: (25), (35) imply:
% 47.24/7.04 | | | | (36) $false
% 47.24/7.04 | | | |
% 47.24/7.04 | | | | CLOSE: (36) is inconsistent.
% 47.24/7.04 | | | |
% 47.24/7.04 | | | Case 2:
% 47.24/7.04 | | | |
% 47.24/7.04 | | | | (37) segmentP(nil, nil)
% 47.24/7.04 | | | |
% 47.24/7.04 | | | | GROUND_INST: instantiating (1) with all_89_1, all_89_0, simplifying with
% 47.24/7.04 | | | | (20), (21), (22), (23) gives:
% 47.24/7.04 | | | | (38) all_89_0 = all_89_1 | neq(all_89_1, all_89_0)
% 47.24/7.04 | | | |
% 47.24/7.04 | | | | GROUND_INST: instantiating (8) with all_91_0, simplifying with (26),
% 47.24/7.04 | | | | (27) gives:
% 47.24/7.04 | | | | (39) rearsegP(all_91_0, nil)
% 47.24/7.04 | | | |
% 47.24/7.04 | | | | GROUND_INST: instantiating (ax42) with all_91_0, simplifying with (26),
% 47.24/7.04 | | | | (27) gives:
% 47.24/7.04 | | | | (40) frontsegP(all_91_0, all_91_0)
% 47.24/7.04 | | | |
% 47.24/7.04 | | | | GROUND_INST: instantiating (6) with all_91_0, simplifying with (26),
% 47.24/7.04 | | | | (27) gives:
% 47.24/7.04 | | | | (41) frontsegP(all_91_0, nil)
% 47.24/7.04 | | | |
% 47.24/7.05 | | | | GROUND_INST: instantiating (2) with nil, nil, simplifying with (15),
% 47.24/7.05 | | | | (25), (31) gives:
% 47.24/7.05 | | | | (42) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 47.24/7.05 | | | |
% 47.24/7.05 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (15),
% 47.24/7.05 | | | | (25), (34) gives:
% 47.24/7.05 | | | | (43) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0))
% 47.24/7.05 | | | |
% 47.24/7.05 | | | | GROUND_INST: instantiating (4) with nil, nil, simplifying with (15),
% 47.24/7.05 | | | | (25), (37) gives:
% 47.24/7.05 | | | | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil &
% 47.24/7.05 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) &
% 47.24/7.05 | | | | ssList(v0))
% 47.24/7.05 | | | |
% 47.24/7.05 | | | | DELTA: instantiating (43) with fresh symbol all_112_0 gives:
% 47.24/7.05 | | | | (45) app(all_112_0, nil) = nil & $i(all_112_0) & ssList(all_112_0)
% 47.24/7.05 | | | |
% 47.24/7.05 | | | | ALPHA: (45) implies:
% 47.24/7.05 | | | | (46) ssList(all_112_0)
% 47.24/7.05 | | | | (47) $i(all_112_0)
% 47.24/7.05 | | | | (48) app(all_112_0, nil) = nil
% 47.24/7.05 | | | |
% 47.24/7.05 | | | | DELTA: instantiating (42) with fresh symbol all_114_0 gives:
% 47.24/7.05 | | | | (49) app(nil, all_114_0) = nil & $i(all_114_0) & ssList(all_114_0)
% 47.24/7.05 | | | |
% 47.24/7.05 | | | | ALPHA: (49) implies:
% 47.24/7.05 | | | | (50) ssList(all_114_0)
% 47.24/7.05 | | | | (51) $i(all_114_0)
% 47.24/7.05 | | | | (52) app(nil, all_114_0) = nil
% 47.24/7.05 | | | |
% 47.24/7.05 | | | | DELTA: instantiating (44) with fresh symbols all_116_0, all_116_1,
% 47.24/7.05 | | | | all_116_2 gives:
% 47.24/7.05 | | | | (53) app(all_116_1, all_116_0) = nil & app(all_116_2, nil) =
% 47.24/7.05 | | | | all_116_1 & $i(all_116_0) & $i(all_116_1) & $i(all_116_2) &
% 47.24/7.05 | | | | ssList(all_116_0) & ssList(all_116_2)
% 47.24/7.05 | | | |
% 47.24/7.05 | | | | ALPHA: (53) implies:
% 47.24/7.05 | | | | (54) ssList(all_116_2)
% 47.24/7.05 | | | | (55) ssList(all_116_0)
% 47.24/7.05 | | | | (56) $i(all_116_2)
% 47.24/7.05 | | | | (57) $i(all_116_1)
% 47.24/7.05 | | | | (58) $i(all_116_0)
% 47.24/7.05 | | | | (59) app(all_116_2, nil) = all_116_1
% 47.24/7.05 | | | | (60) app(all_116_1, all_116_0) = nil
% 47.24/7.05 | | | |
% 47.24/7.05 | | | | BETA: splitting (38) gives:
% 47.24/7.05 | | | |
% 47.24/7.05 | | | | Case 1:
% 47.24/7.05 | | | | |
% 47.24/7.05 | | | | |
% 47.24/7.05 | | | | | GROUND_INST: instantiating (2) with all_91_0, nil, simplifying with
% 47.24/7.05 | | | | | (15), (25), (26), (27), (41) gives:
% 47.24/7.05 | | | | | (61) ? [v0: $i] : (app(nil, v0) = all_91_0 & $i(v0) & ssList(v0))
% 47.24/7.05 | | | | |
% 47.24/7.05 | | | | | GROUND_INST: instantiating (2) with all_91_0, all_91_0, simplifying
% 47.24/7.05 | | | | | with (26), (27), (40) gives:
% 47.24/7.05 | | | | | (62) ? [v0: $i] : (app(all_91_0, v0) = all_91_0 & $i(v0) &
% 47.24/7.05 | | | | | ssList(v0))
% 47.24/7.05 | | | | |
% 47.24/7.05 | | | | | GROUND_INST: instantiating (3) with all_91_0, nil, simplifying with
% 47.24/7.05 | | | | | (15), (25), (26), (27), (39) gives:
% 47.24/7.05 | | | | | (63) ? [v0: $i] : (app(v0, nil) = all_91_0 & $i(v0) & ssList(v0))
% 47.24/7.05 | | | | |
% 47.24/7.06 | | | | | GROUND_INST: instantiating (ax82) with nil, all_114_0, nil, all_114_0,
% 47.24/7.06 | | | | | nil, simplifying with (15), (25), (50), (51), (52) gives:
% 47.24/7.06 | | | | | (64) ? [v0: $i] : (app(all_114_0, all_114_0) = v0 & app(nil, v0) =
% 47.24/7.06 | | | | | nil & $i(v0))
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | GROUND_INST: instantiating (5) with all_114_0, nil, simplifying with
% 47.24/7.06 | | | | | (50), (51), (52) gives:
% 47.24/7.06 | | | | | (65) all_114_0 = nil
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | GROUND_INST: instantiating (14) with all_112_0, nil, simplifying with
% 47.24/7.06 | | | | | (46), (47), (48) gives:
% 47.24/7.06 | | | | | (66) all_112_0 = nil
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | GROUND_INST: instantiating (ax26) with all_116_2, nil, all_116_1,
% 47.24/7.06 | | | | | simplifying with (15), (25), (54), (56), (59) gives:
% 47.24/7.06 | | | | | (67) ssList(all_116_1)
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | GROUND_INST: instantiating (14) with all_116_2, all_116_1, simplifying
% 47.24/7.06 | | | | | with (54), (56), (59) gives:
% 47.24/7.06 | | | | | (68) all_116_1 = all_116_2
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | GROUND_INST: instantiating (ax82) with all_116_2, nil, all_116_1,
% 47.24/7.06 | | | | | all_116_0, nil, simplifying with (15), (25), (54), (55),
% 47.24/7.06 | | | | | (56), (58), (59), (60) gives:
% 47.24/7.06 | | | | | (69) ? [v0: $i] : (app(all_116_2, v0) = nil & app(nil, all_116_0)
% 47.24/7.06 | | | | | = v0 & $i(v0))
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | DELTA: instantiating (69) with fresh symbol all_132_0 gives:
% 47.24/7.06 | | | | | (70) app(all_116_2, all_132_0) = nil & app(nil, all_116_0) =
% 47.24/7.06 | | | | | all_132_0 & $i(all_132_0)
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | ALPHA: (70) implies:
% 47.24/7.06 | | | | | (71) app(nil, all_116_0) = all_132_0
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | DELTA: instantiating (63) with fresh symbol all_136_0 gives:
% 47.24/7.06 | | | | | (72) app(all_136_0, nil) = all_91_0 & $i(all_136_0) &
% 47.24/7.06 | | | | | ssList(all_136_0)
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | ALPHA: (72) implies:
% 47.24/7.06 | | | | | (73) ssList(all_136_0)
% 47.24/7.06 | | | | | (74) $i(all_136_0)
% 47.24/7.06 | | | | | (75) app(all_136_0, nil) = all_91_0
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | DELTA: instantiating (62) with fresh symbol all_138_0 gives:
% 47.24/7.06 | | | | | (76) app(all_91_0, all_138_0) = all_91_0 & $i(all_138_0) &
% 47.24/7.06 | | | | | ssList(all_138_0)
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | ALPHA: (76) implies:
% 47.24/7.06 | | | | | (77) ssList(all_138_0)
% 47.24/7.06 | | | | | (78) $i(all_138_0)
% 47.24/7.06 | | | | | (79) app(all_91_0, all_138_0) = all_91_0
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | DELTA: instantiating (64) with fresh symbol all_140_0 gives:
% 47.24/7.06 | | | | | (80) app(all_114_0, all_114_0) = all_140_0 & app(nil, all_140_0) =
% 47.24/7.06 | | | | | nil & $i(all_140_0)
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | ALPHA: (80) implies:
% 47.24/7.06 | | | | | (81) $i(all_140_0)
% 47.24/7.06 | | | | | (82) app(all_114_0, all_114_0) = all_140_0
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | DELTA: instantiating (61) with fresh symbol all_142_0 gives:
% 47.24/7.06 | | | | | (83) app(nil, all_142_0) = all_91_0 & $i(all_142_0) &
% 47.24/7.06 | | | | | ssList(all_142_0)
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | ALPHA: (83) implies:
% 47.24/7.06 | | | | | (84) ssList(all_142_0)
% 47.24/7.06 | | | | | (85) $i(all_142_0)
% 47.24/7.06 | | | | | (86) app(nil, all_142_0) = all_91_0
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | REDUCE: (60), (68) imply:
% 47.24/7.06 | | | | | (87) app(all_116_2, all_116_0) = nil
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | REDUCE: (65), (82) imply:
% 47.24/7.06 | | | | | (88) app(nil, nil) = all_140_0
% 47.24/7.06 | | | | |
% 47.24/7.06 | | | | | GROUND_INST: instantiating (11) with all_140_0, simplifying with (25),
% 47.24/7.06 | | | | | (88) gives:
% 47.45/7.06 | | | | | (89) all_140_0 = nil
% 47.45/7.06 | | | | |
% 47.45/7.06 | | | | | REDUCE: (88), (89) imply:
% 47.45/7.06 | | | | | (90) app(nil, nil) = nil
% 47.45/7.06 | | | | |
% 47.45/7.06 | | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_116_0,
% 47.45/7.06 | | | | | all_132_0, simplifying with (15), (25), (55), (58), (71),
% 47.45/7.06 | | | | | (90) gives:
% 47.45/7.06 | | | | | (91) ? [v0: $i] : (app(nil, v0) = all_132_0 & app(nil, all_116_0)
% 47.45/7.06 | | | | | = v0 & $i(v0) & $i(all_132_0))
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (5) with all_116_0, all_132_0, simplifying
% 47.45/7.07 | | | | | with (55), (58), (71) gives:
% 47.45/7.07 | | | | | (92) all_132_0 = all_116_0
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_142_0,
% 47.45/7.07 | | | | | all_91_0, simplifying with (15), (25), (84), (85), (86),
% 47.45/7.07 | | | | | (90) gives:
% 47.45/7.07 | | | | | (93) ? [v0: $i] : (app(nil, v0) = all_91_0 & app(nil, all_142_0) =
% 47.45/7.07 | | | | | v0 & $i(v0) & $i(all_91_0))
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (28) with nil, nil, nil, all_142_0,
% 47.45/7.07 | | | | | simplifying with (15), (25), (84), (85), (86), (90)
% 47.45/7.07 | | | | | gives:
% 47.45/7.07 | | | | | (94) ? [v0: $i] : ( ~ (v0 = nil) & app(nil, all_142_0) = v0 &
% 47.45/7.07 | | | | | $i(v0))
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (5) with all_142_0, all_91_0, simplifying
% 47.45/7.07 | | | | | with (84), (85), (86) gives:
% 47.45/7.07 | | | | | (95) all_142_0 = all_91_0
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (28) with all_91_0, all_138_0, all_91_0,
% 47.45/7.07 | | | | | all_138_0, simplifying with (26), (27), (77), (78), (79)
% 47.45/7.07 | | | | | gives:
% 47.45/7.07 | | | | | (96) ? [v0: $i] : ( ~ (v0 = nil) & app(all_91_0, all_138_0) = v0 &
% 47.45/7.07 | | | | | $i(v0))
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (ax82) with nil, all_142_0, all_91_0,
% 47.45/7.07 | | | | | all_138_0, all_91_0, simplifying with (15), (25), (77),
% 47.45/7.07 | | | | | (78), (79), (84), (85), (86) gives:
% 47.45/7.07 | | | | | (97) ? [v0: $i] : (app(all_142_0, all_138_0) = v0 & app(nil, v0) =
% 47.45/7.07 | | | | | all_91_0 & $i(v0) & $i(all_91_0))
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (28) with nil, all_142_0, all_91_0,
% 47.45/7.07 | | | | | all_138_0, simplifying with (15), (25), (77), (78), (79),
% 47.45/7.07 | | | | | (84), (85), (86) gives:
% 47.45/7.07 | | | | | (98) ? [v0: $i] : ( ~ (v0 = nil) & app(nil, all_138_0) = v0 &
% 47.45/7.07 | | | | | $i(v0))
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil,
% 47.45/7.07 | | | | | all_142_0, all_91_0, simplifying with (54), (55), (56),
% 47.45/7.07 | | | | | (58), (84), (85), (86), (87) gives:
% 47.45/7.07 | | | | | (99) ? [v0: $i] : (app(all_116_0, all_142_0) = v0 & app(all_116_2,
% 47.45/7.07 | | | | | v0) = all_91_0 & $i(v0) & $i(all_91_0))
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (28) with all_116_2, all_116_0, nil,
% 47.45/7.07 | | | | | all_142_0, simplifying with (54), (55), (56), (58), (84),
% 47.45/7.07 | | | | | (85), (86), (87) gives:
% 47.45/7.07 | | | | | (100) ? [v0: $i] : ( ~ (v0 = nil) & app(all_116_2, all_142_0) = v0
% 47.45/7.07 | | | | | & $i(v0))
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil,
% 47.45/7.07 | | | | | all_116_0, all_132_0, simplifying with (54), (55), (56),
% 47.45/7.07 | | | | | (58), (71), (87) gives:
% 47.45/7.07 | | | | | (101) ? [v0: $i] : (app(all_116_0, all_116_0) = v0 &
% 47.45/7.07 | | | | | app(all_116_2, v0) = all_132_0 & $i(v0) & $i(all_132_0))
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil, nil,
% 47.45/7.07 | | | | | nil, simplifying with (15), (25), (54), (55), (56), (58),
% 47.45/7.07 | | | | | (87), (90) gives:
% 47.45/7.07 | | | | | (102) ? [v0: $i] : (app(all_116_0, nil) = v0 & app(all_116_2, v0)
% 47.45/7.07 | | | | | = nil & $i(v0))
% 47.45/7.07 | | | | |
% 47.45/7.07 | | | | | GROUND_INST: instantiating (13) with all_116_2, all_116_0, simplifying
% 47.45/7.07 | | | | | with (54), (55), (56), (58), (87) gives:
% 47.45/7.08 | | | | | (103) all_116_0 = nil
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | GROUND_INST: instantiating (12) with all_116_2, all_116_0, simplifying
% 47.45/7.08 | | | | | with (54), (55), (56), (58), (87) gives:
% 47.45/7.08 | | | | | (104) all_116_2 = nil
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | GROUND_INST: instantiating (ax82) with all_136_0, nil, all_91_0,
% 47.45/7.08 | | | | | all_138_0, all_91_0, simplifying with (15), (25), (73),
% 47.45/7.08 | | | | | (74), (75), (77), (78), (79) gives:
% 47.45/7.08 | | | | | (105) ? [v0: $i] : (app(all_136_0, v0) = all_91_0 & app(nil,
% 47.45/7.08 | | | | | all_138_0) = v0 & $i(v0) & $i(all_91_0))
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | GROUND_INST: instantiating (28) with all_136_0, nil, all_91_0,
% 47.45/7.08 | | | | | all_138_0, simplifying with (15), (25), (73), (74), (75),
% 47.45/7.08 | | | | | (77), (78), (79) gives:
% 47.45/7.08 | | | | | (106) ? [v0: $i] : ( ~ (v0 = nil) & app(all_136_0, all_138_0) = v0
% 47.45/7.08 | | | | | & $i(v0))
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | GROUND_INST: instantiating (14) with all_136_0, all_91_0, simplifying
% 47.45/7.08 | | | | | with (73), (74), (75) gives:
% 47.45/7.08 | | | | | (107) all_136_0 = all_91_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | COMBINE_EQS: (92), (103) imply:
% 47.45/7.08 | | | | | (108) all_132_0 = nil
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (100) with fresh symbol all_158_0 gives:
% 47.45/7.08 | | | | | (109) ~ (all_158_0 = nil) & app(all_116_2, all_142_0) = all_158_0
% 47.45/7.08 | | | | | & $i(all_158_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (109) implies:
% 47.45/7.08 | | | | | (110) $i(all_158_0)
% 47.45/7.08 | | | | | (111) app(all_116_2, all_142_0) = all_158_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (98) with fresh symbol all_160_0 gives:
% 47.45/7.08 | | | | | (112) ~ (all_160_0 = nil) & app(nil, all_138_0) = all_160_0 &
% 47.45/7.08 | | | | | $i(all_160_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (112) implies:
% 47.45/7.08 | | | | | (113) ~ (all_160_0 = nil)
% 47.45/7.08 | | | | | (114) app(nil, all_138_0) = all_160_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (96) with fresh symbol all_162_0 gives:
% 47.45/7.08 | | | | | (115) ~ (all_162_0 = nil) & app(all_91_0, all_138_0) = all_162_0 &
% 47.45/7.08 | | | | | $i(all_162_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (115) implies:
% 47.45/7.08 | | | | | (116) app(all_91_0, all_138_0) = all_162_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (94) with fresh symbol all_170_0 gives:
% 47.45/7.08 | | | | | (117) ~ (all_170_0 = nil) & app(nil, all_142_0) = all_170_0 &
% 47.45/7.08 | | | | | $i(all_170_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (117) implies:
% 47.45/7.08 | | | | | (118) app(nil, all_142_0) = all_170_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (102) with fresh symbol all_172_0 gives:
% 47.45/7.08 | | | | | (119) app(all_116_0, nil) = all_172_0 & app(all_116_2, all_172_0) =
% 47.45/7.08 | | | | | nil & $i(all_172_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (119) implies:
% 47.45/7.08 | | | | | (120) $i(all_172_0)
% 47.45/7.08 | | | | | (121) app(all_116_0, nil) = all_172_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (106) with fresh symbol all_186_0 gives:
% 47.45/7.08 | | | | | (122) ~ (all_186_0 = nil) & app(all_136_0, all_138_0) = all_186_0
% 47.45/7.08 | | | | | & $i(all_186_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (122) implies:
% 47.45/7.08 | | | | | (123) app(all_136_0, all_138_0) = all_186_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (93) with fresh symbol all_196_0 gives:
% 47.45/7.08 | | | | | (124) app(nil, all_196_0) = all_91_0 & app(nil, all_142_0) =
% 47.45/7.08 | | | | | all_196_0 & $i(all_196_0) & $i(all_91_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (124) implies:
% 47.45/7.08 | | | | | (125) app(nil, all_142_0) = all_196_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (91) with fresh symbol all_198_0 gives:
% 47.45/7.08 | | | | | (126) app(nil, all_198_0) = all_132_0 & app(nil, all_116_0) =
% 47.45/7.08 | | | | | all_198_0 & $i(all_198_0) & $i(all_132_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (126) implies:
% 47.45/7.08 | | | | | (127) app(nil, all_116_0) = all_198_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (99) with fresh symbol all_200_0 gives:
% 47.45/7.08 | | | | | (128) app(all_116_0, all_142_0) = all_200_0 & app(all_116_2,
% 47.45/7.08 | | | | | all_200_0) = all_91_0 & $i(all_200_0) & $i(all_91_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (128) implies:
% 47.45/7.08 | | | | | (129) app(all_116_0, all_142_0) = all_200_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (101) with fresh symbol all_202_0 gives:
% 47.45/7.08 | | | | | (130) app(all_116_0, all_116_0) = all_202_0 & app(all_116_2,
% 47.45/7.08 | | | | | all_202_0) = all_132_0 & $i(all_202_0) & $i(all_132_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (130) implies:
% 47.45/7.08 | | | | | (131) app(all_116_0, all_116_0) = all_202_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (97) with fresh symbol all_206_0 gives:
% 47.45/7.08 | | | | | (132) app(all_142_0, all_138_0) = all_206_0 & app(nil, all_206_0) =
% 47.45/7.08 | | | | | all_91_0 & $i(all_206_0) & $i(all_91_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (132) implies:
% 47.45/7.08 | | | | | (133) app(all_142_0, all_138_0) = all_206_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | DELTA: instantiating (105) with fresh symbol all_208_0 gives:
% 47.45/7.08 | | | | | (134) app(all_136_0, all_208_0) = all_91_0 & app(nil, all_138_0) =
% 47.45/7.08 | | | | | all_208_0 & $i(all_208_0) & $i(all_91_0)
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | ALPHA: (134) implies:
% 47.45/7.08 | | | | | (135) app(nil, all_138_0) = all_208_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | REDUCE: (95), (133) imply:
% 47.45/7.08 | | | | | (136) app(all_91_0, all_138_0) = all_206_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | REDUCE: (107), (123) imply:
% 47.45/7.08 | | | | | (137) app(all_91_0, all_138_0) = all_186_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | REDUCE: (75), (107) imply:
% 47.45/7.08 | | | | | (138) app(all_91_0, nil) = all_91_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | REDUCE: (95), (103), (129) imply:
% 47.45/7.08 | | | | | (139) app(nil, all_91_0) = all_200_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | REDUCE: (103), (131) imply:
% 47.45/7.08 | | | | | (140) app(nil, nil) = all_202_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | REDUCE: (103), (121) imply:
% 47.45/7.08 | | | | | (141) app(nil, nil) = all_172_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | REDUCE: (95), (104), (111) imply:
% 47.45/7.08 | | | | | (142) app(nil, all_91_0) = all_158_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | REDUCE: (95), (125) imply:
% 47.45/7.08 | | | | | (143) app(nil, all_91_0) = all_196_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | REDUCE: (95), (118) imply:
% 47.45/7.08 | | | | | (144) app(nil, all_91_0) = all_170_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | REDUCE: (86), (95) imply:
% 47.45/7.08 | | | | | (145) app(nil, all_91_0) = all_91_0
% 47.45/7.08 | | | | |
% 47.45/7.08 | | | | | REDUCE: (103), (127) imply:
% 47.45/7.08 | | | | | (146) app(nil, nil) = all_198_0
% 47.45/7.08 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (17) with nil, all_202_0, nil, nil,
% 47.45/7.09 | | | | | simplifying with (90), (140) gives:
% 47.45/7.09 | | | | | (147) all_202_0 = nil
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (17) with all_198_0, all_202_0, nil, nil,
% 47.45/7.09 | | | | | simplifying with (140), (146) gives:
% 47.45/7.09 | | | | | (148) all_202_0 = all_198_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (17) with all_172_0, all_202_0, nil, nil,
% 47.45/7.09 | | | | | simplifying with (140), (141) gives:
% 47.45/7.09 | | | | | (149) all_202_0 = all_172_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (17) with all_91_0, all_170_0, all_91_0,
% 47.45/7.09 | | | | | nil, simplifying with (144), (145) gives:
% 47.45/7.09 | | | | | (150) all_170_0 = all_91_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (17) with all_196_0, all_200_0, all_91_0,
% 47.45/7.09 | | | | | nil, simplifying with (139), (143) gives:
% 47.45/7.09 | | | | | (151) all_200_0 = all_196_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (17) with all_170_0, all_200_0, all_91_0,
% 47.45/7.09 | | | | | nil, simplifying with (139), (144) gives:
% 47.45/7.09 | | | | | (152) all_200_0 = all_170_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (17) with all_158_0, all_200_0, all_91_0,
% 47.45/7.09 | | | | | nil, simplifying with (139), (142) gives:
% 47.45/7.09 | | | | | (153) all_200_0 = all_158_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (17) with all_160_0, all_208_0, all_138_0,
% 47.45/7.09 | | | | | nil, simplifying with (114), (135) gives:
% 47.45/7.09 | | | | | (154) all_208_0 = all_160_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (17) with all_91_0, all_186_0, all_138_0,
% 47.45/7.09 | | | | | all_91_0, simplifying with (79), (137) gives:
% 47.45/7.09 | | | | | (155) all_186_0 = all_91_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (17) with all_186_0, all_206_0, all_138_0,
% 47.45/7.09 | | | | | all_91_0, simplifying with (136), (137) gives:
% 47.45/7.09 | | | | | (156) all_206_0 = all_186_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (17) with all_162_0, all_206_0, all_138_0,
% 47.45/7.09 | | | | | all_91_0, simplifying with (116), (136) gives:
% 47.45/7.09 | | | | | (157) all_206_0 = all_162_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | COMBINE_EQS: (156), (157) imply:
% 47.45/7.09 | | | | | (158) all_186_0 = all_162_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | SIMP: (158) implies:
% 47.45/7.09 | | | | | (159) all_186_0 = all_162_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | COMBINE_EQS: (147), (148) imply:
% 47.45/7.09 | | | | | (160) all_198_0 = nil
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | COMBINE_EQS: (148), (149) imply:
% 47.45/7.09 | | | | | (161) all_198_0 = all_172_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | COMBINE_EQS: (151), (153) imply:
% 47.45/7.09 | | | | | (162) all_196_0 = all_158_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | COMBINE_EQS: (151), (152) imply:
% 47.45/7.09 | | | | | (163) all_196_0 = all_170_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | COMBINE_EQS: (160), (161) imply:
% 47.45/7.09 | | | | | (164) all_172_0 = nil
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | COMBINE_EQS: (162), (163) imply:
% 47.45/7.09 | | | | | (165) all_170_0 = all_158_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | SIMP: (165) implies:
% 47.45/7.09 | | | | | (166) all_170_0 = all_158_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | COMBINE_EQS: (155), (159) imply:
% 47.45/7.09 | | | | | (167) all_162_0 = all_91_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | COMBINE_EQS: (150), (166) imply:
% 47.45/7.09 | | | | | (168) all_158_0 = all_91_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (5) with all_138_0, all_160_0, simplifying
% 47.45/7.09 | | | | | with (77), (78), (114) gives:
% 47.45/7.09 | | | | | (169) all_160_0 = all_138_0
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | GROUND_INST: instantiating (ax80) with nil, all_91_0, all_91_0,
% 47.45/7.09 | | | | | all_138_0, simplifying with (15), (25), (26), (27), (77),
% 47.45/7.09 | | | | | (78), (79), (138) gives:
% 47.45/7.09 | | | | | (170) all_138_0 = nil
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | COMBINE_EQS: (169), (170) imply:
% 47.45/7.09 | | | | | (171) all_160_0 = nil
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | REDUCE: (113), (171) imply:
% 47.45/7.09 | | | | | (172) $false
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | CLOSE: (172) is inconsistent.
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | Case 2:
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | (173) all_89_0 = all_89_1
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | REDUCE: (19), (173) imply:
% 47.45/7.09 | | | | | (174) $false
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | | CLOSE: (174) is inconsistent.
% 47.45/7.09 | | | | |
% 47.45/7.09 | | | | End of split
% 47.45/7.09 | | | |
% 47.45/7.09 | | | End of split
% 47.45/7.09 | | |
% 47.45/7.09 | | End of split
% 47.45/7.09 | |
% 47.45/7.09 | End of split
% 47.45/7.09 |
% 47.45/7.09 End of proof
% 47.45/7.09 % SZS output end Proof for theBenchmark
% 47.45/7.09
% 47.45/7.09 6401ms
%------------------------------------------------------------------------------