TSTP Solution File: SWC010+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC010+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 : n008.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 20:49:09 EDT 2023
% Result : Theorem 22.87s 3.88s
% Output : Proof 33.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC010+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 18:02:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.60/1.45 Prover 1: Preprocessing ...
% 4.60/1.45 Prover 4: Preprocessing ...
% 4.60/1.49 Prover 3: Preprocessing ...
% 4.60/1.49 Prover 6: Preprocessing ...
% 4.60/1.49 Prover 5: Preprocessing ...
% 4.60/1.49 Prover 0: Preprocessing ...
% 4.60/1.49 Prover 2: Preprocessing ...
% 14.23/2.70 Prover 2: Proving ...
% 14.23/2.74 Prover 5: Constructing countermodel ...
% 14.23/2.75 Prover 1: Constructing countermodel ...
% 14.82/2.79 Prover 6: Proving ...
% 14.82/2.88 Prover 3: Constructing countermodel ...
% 21.52/3.66 Prover 4: Constructing countermodel ...
% 22.87/3.85 Prover 0: Proving ...
% 22.87/3.87 Prover 3: proved (3216ms)
% 22.87/3.88
% 22.87/3.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.87/3.88
% 22.87/3.89 Prover 5: stopped
% 22.87/3.89 Prover 2: stopped
% 22.87/3.89 Prover 6: stopped
% 22.87/3.89 Prover 0: stopped
% 23.20/3.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.20/3.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 23.20/3.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.20/3.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.20/3.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 23.98/4.15 Prover 11: Preprocessing ...
% 24.90/4.20 Prover 10: Preprocessing ...
% 24.90/4.21 Prover 7: Preprocessing ...
% 24.90/4.22 Prover 13: Preprocessing ...
% 24.90/4.22 Prover 8: Preprocessing ...
% 27.26/4.45 Prover 10: Constructing countermodel ...
% 27.26/4.46 Prover 7: Constructing countermodel ...
% 27.26/4.53 Prover 13: Constructing countermodel ...
% 28.80/4.66 Prover 8: Warning: ignoring some quantifiers
% 28.80/4.67 Prover 8: Constructing countermodel ...
% 29.19/4.80 Prover 10: Found proof (size 18)
% 29.19/4.80 Prover 10: proved (887ms)
% 29.19/4.80 Prover 13: stopped
% 29.19/4.80 Prover 7: stopped
% 29.19/4.80 Prover 4: stopped
% 29.19/4.80 Prover 8: stopped
% 29.19/4.81 Prover 1: stopped
% 32.38/5.54 Prover 11: Constructing countermodel ...
% 32.38/5.58 Prover 11: stopped
% 32.38/5.58
% 32.38/5.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.38/5.59
% 32.38/5.59 % SZS output start Proof for theBenchmark
% 32.38/5.60 Assumptions after simplification:
% 32.38/5.60 ---------------------------------
% 32.38/5.60
% 32.38/5.60 (ax17)
% 32.38/5.61 $i(nil) & ssList(nil)
% 32.38/5.61
% 32.38/5.61 (ax58)
% 32.38/5.61 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 32.38/5.61 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 32.38/5.62
% 32.38/5.62 (co1)
% 33.02/5.66 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 33.02/5.66 : ? [v5: $i] : ? [v6: $i] : (cons(v2, nil) = v3 & app(v5, v6) = v1 & app(v4,
% 33.02/5.66 v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 33.02/5.66 $i(v1) & $i(v0) & ssList(v6) & ssList(v4) & ssList(v1) & ssList(v0) &
% 33.02/5.66 neq(v1, nil) & ssItem(v2) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 33.02/5.66 [v10: $i] : ! [v11: $i] : ( ~ (cons(v7, nil) = v8) | ~ (app(v10, v11) =
% 33.02/5.66 v1) | ~ (app(v9, v8) = v10) | ~ $i(v11) | ~ $i(v9) | ~ $i(v7) | ~
% 33.02/5.66 ssList(v11) | ~ ssList(v9) | ~ ssItem(v7) | ? [v12: $i] : ( ~ (v12 =
% 33.02/5.66 v0) & app(v9, v11) = v12 & $i(v12))) & ! [v7: $i] : (v7 = v2 | ~
% 33.02/5.66 $i(v7) | ~ geq(v7, v2) | ~ memberP(v1, v7) | ~ ssItem(v7)))
% 33.02/5.66
% 33.02/5.66 (function-axioms)
% 33.02/5.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.02/5.67 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 33.02/5.67 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 33.02/5.67 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 33.02/5.67 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 33.02/5.67 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 33.02/5.67
% 33.02/5.67 Further assumptions not needed in the proof:
% 33.02/5.67 --------------------------------------------
% 33.02/5.67 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 33.02/5.67 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 33.02/5.67 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45,
% 33.02/5.67 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57,
% 33.02/5.67 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 33.02/5.67 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 33.02/5.67 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 33.02/5.67 ax94, ax95
% 33.02/5.67
% 33.02/5.67 Those formulas are unsatisfiable:
% 33.02/5.67 ---------------------------------
% 33.02/5.67
% 33.02/5.67 Begin of proof
% 33.02/5.67 |
% 33.02/5.67 | ALPHA: (ax17) implies:
% 33.02/5.67 | (1) ssList(nil)
% 33.02/5.67 |
% 33.02/5.67 | ALPHA: (ax58) implies:
% 33.02/5.68 | (2) ~ ssList(nil) | segmentP(nil, nil)
% 33.02/5.68 |
% 33.02/5.68 | ALPHA: (co1) implies:
% 33.02/5.68 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 33.02/5.68 | ? [v5: $i] : ? [v6: $i] : (cons(v2, nil) = v3 & app(v5, v6) = v1 &
% 33.02/5.68 | app(v4, v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) &
% 33.02/5.68 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v6) & ssList(v4) &
% 33.02/5.68 | ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ! [v7: $i] :
% 33.02/5.68 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 33.02/5.68 | (cons(v7, nil) = v8) | ~ (app(v10, v11) = v1) | ~ (app(v9, v8) =
% 33.02/5.68 | v10) | ~ $i(v11) | ~ $i(v9) | ~ $i(v7) | ~ ssList(v11) | ~
% 33.02/5.68 | ssList(v9) | ~ ssItem(v7) | ? [v12: $i] : ( ~ (v12 = v0) &
% 33.02/5.68 | app(v9, v11) = v12 & $i(v12))) & ! [v7: $i] : (v7 = v2 | ~
% 33.02/5.68 | $i(v7) | ~ geq(v7, v2) | ~ memberP(v1, v7) | ~ ssItem(v7)))
% 33.02/5.68 |
% 33.02/5.68 | ALPHA: (function-axioms) implies:
% 33.02/5.68 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.02/5.68 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 33.02/5.68 |
% 33.02/5.69 | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2,
% 33.02/5.69 | all_91_3, all_91_4, all_91_5, all_91_6 gives:
% 33.02/5.69 | (5) cons(all_91_4, nil) = all_91_3 & app(all_91_1, all_91_0) = all_91_5 &
% 33.02/5.69 | app(all_91_2, all_91_0) = all_91_6 & app(all_91_2, all_91_3) = all_91_1
% 33.02/5.69 | & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 33.02/5.69 | $i(all_91_4) & $i(all_91_5) & $i(all_91_6) & ssList(all_91_0) &
% 33.02/5.69 | ssList(all_91_2) & ssList(all_91_5) & ssList(all_91_6) & neq(all_91_5,
% 33.02/5.69 | nil) & ssItem(all_91_4) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 33.02/5.69 | ! [v3: $i] : ! [v4: $i] : ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) =
% 33.02/5.69 | all_91_5) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 33.02/5.69 | $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: any]
% 33.02/5.69 | : ( ~ (v5 = all_91_6) & app(v2, v4) = v5 & $i(v5))) & ! [v0: any] :
% 33.02/5.69 | (v0 = all_91_4 | ~ $i(v0) | ~ geq(v0, all_91_4) | ~
% 33.02/5.69 | memberP(all_91_5, v0) | ~ ssItem(v0))
% 33.02/5.69 |
% 33.02/5.69 | ALPHA: (5) implies:
% 33.02/5.70 | (6) ssItem(all_91_4)
% 33.02/5.70 | (7) ssList(all_91_2)
% 33.02/5.70 | (8) ssList(all_91_0)
% 33.02/5.70 | (9) $i(all_91_4)
% 33.02/5.70 | (10) $i(all_91_2)
% 33.02/5.70 | (11) $i(all_91_0)
% 33.02/5.70 | (12) app(all_91_2, all_91_3) = all_91_1
% 33.02/5.70 | (13) app(all_91_2, all_91_0) = all_91_6
% 33.02/5.70 | (14) app(all_91_1, all_91_0) = all_91_5
% 33.02/5.70 | (15) cons(all_91_4, nil) = all_91_3
% 33.02/5.70 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 33.02/5.70 | ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) = all_91_5) | ~ (app(v2,
% 33.02/5.70 | v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v4) |
% 33.02/5.70 | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: any] : ( ~ (v5 = all_91_6) &
% 33.02/5.70 | app(v2, v4) = v5 & $i(v5)))
% 33.02/5.70 |
% 33.02/5.70 | BETA: splitting (2) gives:
% 33.02/5.70 |
% 33.02/5.70 | Case 1:
% 33.02/5.70 | |
% 33.02/5.70 | | (17) ~ ssList(nil)
% 33.02/5.70 | |
% 33.02/5.70 | | PRED_UNIFY: (1), (17) imply:
% 33.02/5.70 | | (18) $false
% 33.02/5.70 | |
% 33.02/5.70 | | CLOSE: (18) is inconsistent.
% 33.02/5.70 | |
% 33.02/5.71 | Case 2:
% 33.02/5.71 | |
% 33.02/5.71 | |
% 33.02/5.71 | | GROUND_INST: instantiating (16) with all_91_4, all_91_3, all_91_2, all_91_1,
% 33.02/5.71 | | all_91_0, simplifying with (6), (7), (8), (9), (10), (11),
% 33.02/5.71 | | (12), (14), (15) gives:
% 33.02/5.71 | | (19) ? [v0: any] : ( ~ (v0 = all_91_6) & app(all_91_2, all_91_0) = v0 &
% 33.02/5.71 | | $i(v0))
% 33.02/5.71 | |
% 33.02/5.71 | | DELTA: instantiating (19) with fresh symbol all_112_0 gives:
% 33.02/5.71 | | (20) ~ (all_112_0 = all_91_6) & app(all_91_2, all_91_0) = all_112_0 &
% 33.02/5.71 | | $i(all_112_0)
% 33.02/5.71 | |
% 33.02/5.71 | | ALPHA: (20) implies:
% 33.02/5.71 | | (21) ~ (all_112_0 = all_91_6)
% 33.02/5.71 | | (22) app(all_91_2, all_91_0) = all_112_0
% 33.02/5.71 | |
% 33.02/5.71 | | GROUND_INST: instantiating (4) with all_91_6, all_112_0, all_91_0, all_91_2,
% 33.02/5.71 | | simplifying with (13), (22) gives:
% 33.02/5.71 | | (23) all_112_0 = all_91_6
% 33.02/5.71 | |
% 33.02/5.71 | | REDUCE: (21), (23) imply:
% 33.02/5.71 | | (24) $false
% 33.02/5.71 | |
% 33.02/5.71 | | CLOSE: (24) is inconsistent.
% 33.02/5.71 | |
% 33.02/5.71 | End of split
% 33.02/5.71 |
% 33.02/5.71 End of proof
% 33.02/5.71 % SZS output end Proof for theBenchmark
% 33.02/5.71
% 33.02/5.71 5086ms
%------------------------------------------------------------------------------