TSTP Solution File: SWC380+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC380+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 : n006.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 20:51:08 EDT 2023
% Result : Theorem 39.92s 6.14s
% Output : Proof 75.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC380+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 15:03:06 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.65 Running up to 7 provers in parallel.
% 0.62/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.62/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.62/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.62/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.62/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.62/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.62/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.36/1.63 Prover 1: Preprocessing ...
% 6.36/1.63 Prover 4: Preprocessing ...
% 6.72/1.68 Prover 0: Preprocessing ...
% 6.72/1.68 Prover 2: Preprocessing ...
% 6.72/1.68 Prover 6: Preprocessing ...
% 6.72/1.68 Prover 3: Preprocessing ...
% 6.72/1.68 Prover 5: Preprocessing ...
% 22.29/3.78 Prover 2: Proving ...
% 22.29/3.78 Prover 1: Constructing countermodel ...
% 22.29/3.78 Prover 3: Constructing countermodel ...
% 22.29/3.79 Prover 5: Constructing countermodel ...
% 22.29/3.79 Prover 6: Proving ...
% 31.13/4.97 Prover 4: Constructing countermodel ...
% 32.30/5.15 Prover 0: Proving ...
% 39.92/6.13 Prover 3: proved (5467ms)
% 39.92/6.14
% 39.92/6.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.92/6.14
% 39.92/6.14 Prover 5: stopped
% 39.92/6.15 Prover 2: stopped
% 40.53/6.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 40.53/6.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 40.53/6.17 Prover 6: stopped
% 40.53/6.17 Prover 0: stopped
% 40.53/6.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 40.53/6.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 40.64/6.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 42.91/6.52 Prover 8: Preprocessing ...
% 42.91/6.59 Prover 10: Preprocessing ...
% 43.93/6.64 Prover 7: Preprocessing ...
% 43.93/6.65 Prover 11: Preprocessing ...
% 44.59/6.75 Prover 13: Preprocessing ...
% 46.91/7.04 Prover 7: Constructing countermodel ...
% 46.91/7.06 Prover 10: Constructing countermodel ...
% 47.53/7.10 Prover 8: Warning: ignoring some quantifiers
% 47.53/7.12 Prover 8: Constructing countermodel ...
% 49.23/7.35 Prover 13: Constructing countermodel ...
% 58.62/8.66 Prover 11: Constructing countermodel ...
% 74.98/10.67 Prover 10: Found proof (size 35)
% 74.98/10.67 Prover 10: proved (4499ms)
% 74.98/10.67 Prover 13: stopped
% 74.98/10.67 Prover 7: stopped
% 74.98/10.67 Prover 8: stopped
% 74.98/10.67 Prover 11: stopped
% 74.98/10.67 Prover 1: stopped
% 74.98/10.67 Prover 4: stopped
% 74.98/10.67
% 74.98/10.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 74.98/10.67
% 74.98/10.68 % SZS output start Proof for theBenchmark
% 74.98/10.68 Assumptions after simplification:
% 74.98/10.68 ---------------------------------
% 74.98/10.68
% 74.98/10.68 (ax1)
% 74.98/10.69 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) |
% 74.98/10.69 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) |
% 74.98/10.69 ~ ssItem(v0))
% 74.98/10.69
% 74.98/10.69 (ax17)
% 74.98/10.70 $i(nil) & ssList(nil)
% 74.98/10.70
% 74.98/10.70 (ax2)
% 74.98/10.70 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) &
% 74.98/10.70 ssItem(v0))
% 74.98/10.70
% 74.98/10.70 (ax23)
% 75.25/10.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1)
% 75.25/10.74 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1)
% 75.25/10.74
% 75.25/10.74 (ax25)
% 75.25/10.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1)
% 75.25/10.74 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0)
% 75.25/10.74
% 75.25/10.74 (ax37)
% 75.25/10.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 75.25/10.74 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v3, v0)
% 75.25/10.74 | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0)) & ! [v0:
% 75.25/10.74 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, v2) = v3) | ~
% 75.25/10.74 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v2, v0) | ~ ssList(v2) | ~
% 75.25/10.74 ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0: $i] : ! [v1: $i] :
% 75.25/10.74 ! [v2: $i] : ( ~ (cons(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) |
% 75.25/10.74 ~ ssItem(v0) | memberP(v2, v0))
% 75.25/10.74
% 75.25/10.74 (ax58)
% 75.25/10.75 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 75.25/10.75 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 75.25/10.75
% 75.25/10.75 (ax77)
% 75.43/10.75 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (tl(v0) = v1) | ~ $i(v0) | ~
% 75.43/10.75 ssList(v0) | ? [v2: $i] : (hd(v0) = v2 & $i(v2) & ! [v3: $i] : (v3 = v0 |
% 75.43/10.75 v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ $i(v3) | ~ ssList(v3) | ?
% 75.43/10.75 [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 & $i(v4)))))
% 75.43/10.75
% 75.43/10.75 (ax81)
% 75.43/10.75 $i(nil) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 75.43/10.75 (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 75.43/10.75 ssList(v0) | ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3)))
% 75.43/10.75
% 75.43/10.75 (co1)
% 75.43/10.76 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (cons(v2,
% 75.43/10.76 nil) = v0 & app(v0, v3) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 75.43/10.76 ssList(v3) & ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ! [v4:
% 75.43/10.76 $i] : ( ~ (cons(v4, nil) = v0) | ~ $i(v4) | ~ memberP(v1, v4) | ~
% 75.43/10.76 ssItem(v4)))
% 75.43/10.76
% 75.43/10.76 (function-axioms)
% 75.43/10.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 75.43/10.76 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 75.43/10.76 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 75.43/10.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 75.43/10.76 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 75.43/10.76 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 75.43/10.76
% 75.43/10.76 Further assumptions not needed in the proof:
% 75.43/10.76 --------------------------------------------
% 75.43/10.76 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax20, ax21, ax22, ax24,
% 75.43/10.76 ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax38,
% 75.43/10.76 ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5,
% 75.43/10.76 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6, ax60, ax61, ax62,
% 75.43/10.76 ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax72, ax73, ax74,
% 75.43/10.76 ax75, ax76, ax78, ax79, ax8, ax80, ax82, ax83, ax84, ax85, ax86, ax87, ax88,
% 75.43/10.76 ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 75.43/10.76
% 75.43/10.76 Those formulas are unsatisfiable:
% 75.43/10.76 ---------------------------------
% 75.43/10.76
% 75.43/10.76 Begin of proof
% 75.43/10.76 |
% 75.43/10.76 | ALPHA: (ax1) implies:
% 75.43/10.77 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 75.43/10.77 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1))
% 75.43/10.77 |
% 75.43/10.77 | ALPHA: (ax17) implies:
% 75.43/10.77 | (2) ssList(nil)
% 75.43/10.77 |
% 75.43/10.77 | ALPHA: (ax37) implies:
% 75.43/10.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) = v2) | ~
% 75.43/10.77 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0))
% 75.43/10.77 |
% 75.43/10.77 | ALPHA: (ax58) implies:
% 75.43/10.77 | (4) ~ ssList(nil) | segmentP(nil, nil)
% 75.43/10.77 |
% 75.43/10.77 | ALPHA: (ax77) implies:
% 75.43/10.77 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (tl(v0) = v1) | ~ $i(v0) | ~
% 75.43/10.77 | ssList(v0) | ? [v2: $i] : (hd(v0) = v2 & $i(v2) & ! [v3: $i] : (v3
% 75.43/10.77 | = v0 | v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ $i(v3) | ~
% 75.43/10.77 | ssList(v3) | ? [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 &
% 75.43/10.77 | $i(v4)))))
% 75.43/10.77 |
% 75.43/10.77 | ALPHA: (ax81) implies:
% 75.43/10.77 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1,
% 75.43/10.77 | nil) = v2) | ~ (app(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 75.43/10.77 | ssList(v0) | ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3)))
% 75.43/10.77 |
% 75.43/10.77 | ALPHA: (co1) implies:
% 75.43/10.78 | (7) $i(nil)
% 75.43/10.78 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (cons(v2, nil)
% 75.43/10.78 | = v0 & app(v0, v3) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 75.43/10.78 | ssList(v3) & ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & !
% 75.43/10.78 | [v4: $i] : ( ~ (cons(v4, nil) = v0) | ~ $i(v4) | ~ memberP(v1, v4)
% 75.43/10.78 | | ~ ssItem(v4)))
% 75.43/10.78 |
% 75.43/10.78 | ALPHA: (function-axioms) implies:
% 75.43/10.78 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (hd(v2) = v1) |
% 75.43/10.78 | ~ (hd(v2) = v0))
% 75.43/10.78 |
% 75.43/10.78 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives:
% 75.43/10.78 | (10) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) &
% 75.43/10.78 | ssItem(all_89_0) & ssItem(all_89_1)
% 75.43/10.78 |
% 75.43/10.78 | ALPHA: (10) implies:
% 75.43/10.78 | (11) ~ (all_89_0 = all_89_1)
% 75.43/10.78 | (12) ssItem(all_89_1)
% 75.43/10.78 | (13) ssItem(all_89_0)
% 75.43/10.78 | (14) $i(all_89_1)
% 75.43/10.78 | (15) $i(all_89_0)
% 75.43/10.78 |
% 75.43/10.78 | DELTA: instantiating (8) with fresh symbols all_91_0, all_91_1, all_91_2,
% 75.43/10.78 | all_91_3 gives:
% 75.43/10.79 | (16) cons(all_91_1, nil) = all_91_3 & app(all_91_3, all_91_0) = all_91_2 &
% 75.43/10.79 | $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 75.43/10.79 | ssList(all_91_0) & ssList(all_91_2) & ssList(all_91_3) & neq(all_91_2,
% 75.43/10.79 | nil) & ssItem(all_91_1) & ! [v0: $i] : ( ~ (cons(v0, nil) =
% 75.43/10.79 | all_91_3) | ~ $i(v0) | ~ memberP(all_91_2, v0) | ~ ssItem(v0))
% 75.43/10.79 |
% 75.43/10.79 | ALPHA: (16) implies:
% 75.43/10.79 | (17) ssItem(all_91_1)
% 75.43/10.79 | (18) ssList(all_91_3)
% 75.43/10.79 | (19) ssList(all_91_0)
% 75.43/10.79 | (20) $i(all_91_3)
% 75.43/10.79 | (21) $i(all_91_1)
% 75.43/10.79 | (22) $i(all_91_0)
% 75.43/10.79 | (23) app(all_91_3, all_91_0) = all_91_2
% 75.43/10.79 | (24) cons(all_91_1, nil) = all_91_3
% 75.43/10.79 | (25) ! [v0: $i] : ( ~ (cons(v0, nil) = all_91_3) | ~ $i(v0) | ~
% 75.43/10.79 | memberP(all_91_2, v0) | ~ ssItem(v0))
% 75.43/10.79 |
% 75.43/10.79 | BETA: splitting (4) gives:
% 75.43/10.79 |
% 75.43/10.79 | Case 1:
% 75.43/10.79 | |
% 75.43/10.79 | | (26) ~ ssList(nil)
% 75.43/10.79 | |
% 75.43/10.79 | | PRED_UNIFY: (2), (26) imply:
% 75.43/10.79 | | (27) $false
% 75.43/10.79 | |
% 75.43/10.79 | | CLOSE: (27) is inconsistent.
% 75.43/10.79 | |
% 75.43/10.79 | Case 2:
% 75.43/10.79 | |
% 75.43/10.79 | |
% 75.43/10.79 | | GROUND_INST: instantiating (1) with all_89_1, all_89_0, simplifying with
% 75.43/10.79 | | (12), (13), (14), (15) gives:
% 75.43/10.79 | | (28) all_89_0 = all_89_1 | neq(all_89_1, all_89_0)
% 75.43/10.79 | |
% 75.43/10.80 | | GROUND_INST: instantiating (ax25) with nil, all_91_1, all_91_3, simplifying
% 75.43/10.80 | | with (2), (7), (17), (21), (24) gives:
% 75.43/10.80 | | (29) tl(all_91_3) = nil
% 75.43/10.80 | |
% 75.43/10.80 | | GROUND_INST: instantiating (ax23) with nil, all_91_1, all_91_3, simplifying
% 75.43/10.80 | | with (2), (7), (17), (21), (24) gives:
% 75.43/10.80 | | (30) hd(all_91_3) = all_91_1
% 75.43/10.80 | |
% 75.43/10.80 | | GROUND_INST: instantiating (6) with all_91_0, all_91_1, all_91_3, all_91_2,
% 75.43/10.80 | | simplifying with (17), (19), (21), (22), (23), (24) gives:
% 75.43/10.80 | | (31) cons(all_91_1, all_91_0) = all_91_2 & $i(all_91_2)
% 75.43/10.80 | |
% 75.43/10.80 | | ALPHA: (31) implies:
% 75.43/10.80 | | (32) cons(all_91_1, all_91_0) = all_91_2
% 75.43/10.80 | |
% 75.43/10.80 | | BETA: splitting (28) gives:
% 75.43/10.80 | |
% 75.43/10.80 | | Case 1:
% 75.43/10.80 | | |
% 75.43/10.80 | | |
% 75.43/10.80 | | | GROUND_INST: instantiating (3) with all_91_1, all_91_0, all_91_2,
% 75.43/10.80 | | | simplifying with (17), (19), (21), (22), (32) gives:
% 75.43/10.80 | | | (33) memberP(all_91_2, all_91_1)
% 75.43/10.80 | | |
% 75.43/10.80 | | | GROUND_INST: instantiating (5) with all_91_3, nil, simplifying with (18),
% 75.43/10.80 | | | (20), (29) gives:
% 75.43/10.80 | | | (34) ? [v0: $i] : (hd(all_91_3) = v0 & $i(v0) & ! [v1: any] : (v1 =
% 75.43/10.80 | | | all_91_3 | v1 = nil | all_91_3 = nil | ~ (tl(v1) = nil) | ~
% 75.43/10.80 | | | $i(v1) | ~ ssList(v1) | ? [v2: $i] : ( ~ (v2 = v0) & hd(v1)
% 75.43/10.80 | | | = v2 & $i(v2))))
% 75.43/10.80 | | |
% 75.43/10.80 | | | DELTA: instantiating (34) with fresh symbol all_180_0 gives:
% 75.43/10.81 | | | (35) hd(all_91_3) = all_180_0 & $i(all_180_0) & ! [v0: any] : (v0 =
% 75.43/10.81 | | | all_91_3 | v0 = nil | all_91_3 = nil | ~ (tl(v0) = nil) | ~
% 75.43/10.81 | | | $i(v0) | ~ ssList(v0) | ? [v1: any] : ( ~ (v1 = all_180_0) &
% 75.43/10.81 | | | hd(v0) = v1 & $i(v1)))
% 75.43/10.81 | | |
% 75.43/10.81 | | | ALPHA: (35) implies:
% 75.43/10.81 | | | (36) $i(all_180_0)
% 75.43/10.81 | | | (37) hd(all_91_3) = all_180_0
% 75.43/10.81 | | |
% 75.43/10.81 | | | GROUND_INST: instantiating (9) with all_91_1, all_180_0, all_91_3,
% 75.43/10.81 | | | simplifying with (30), (37) gives:
% 75.43/10.81 | | | (38) all_180_0 = all_91_1
% 75.43/10.81 | | |
% 75.43/10.81 | | | GROUND_INST: instantiating (25) with all_91_1, simplifying with (17),
% 75.43/10.81 | | | (21), (24), (33) gives:
% 75.43/10.81 | | | (39) $false
% 75.43/10.81 | | |
% 75.43/10.81 | | | CLOSE: (39) is inconsistent.
% 75.43/10.81 | | |
% 75.43/10.81 | | Case 2:
% 75.43/10.81 | | |
% 75.43/10.81 | | | (40) all_89_0 = all_89_1
% 75.43/10.81 | | |
% 75.43/10.81 | | | REDUCE: (11), (40) imply:
% 75.43/10.81 | | | (41) $false
% 75.43/10.81 | | |
% 75.43/10.81 | | | CLOSE: (41) is inconsistent.
% 75.43/10.81 | | |
% 75.43/10.81 | | End of split
% 75.43/10.81 | |
% 75.43/10.81 | End of split
% 75.43/10.81 |
% 75.43/10.81 End of proof
% 75.43/10.81 % SZS output end Proof for theBenchmark
% 75.43/10.81
% 75.43/10.81 10177ms
%------------------------------------------------------------------------------