TSTP Solution File: SWC422+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC422+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 : n012.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 20:51:22 EDT 2023
% Result : Theorem 25.05s 4.15s
% Output : Proof 34.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC422+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n012.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 17:43:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 7.44/1.70 Prover 4: Preprocessing ...
% 7.44/1.71 Prover 1: Preprocessing ...
% 7.44/1.71 Prover 5: Preprocessing ...
% 7.44/1.72 Prover 6: Preprocessing ...
% 7.44/1.72 Prover 0: Preprocessing ...
% 7.44/1.72 Prover 3: Preprocessing ...
% 7.44/1.73 Prover 2: Preprocessing ...
% 17.71/3.12 Prover 2: Proving ...
% 18.07/3.13 Prover 5: Constructing countermodel ...
% 18.20/3.18 Prover 6: Proving ...
% 18.20/3.19 Prover 1: Constructing countermodel ...
% 18.20/3.20 Prover 3: Constructing countermodel ...
% 23.42/3.87 Prover 4: Constructing countermodel ...
% 24.52/4.00 Prover 0: Proving ...
% 25.05/4.15 Prover 3: proved (3518ms)
% 25.05/4.15
% 25.05/4.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.05/4.15
% 25.05/4.16 Prover 5: stopped
% 25.05/4.16 Prover 2: stopped
% 25.05/4.16 Prover 6: stopped
% 25.05/4.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 25.05/4.17 Prover 0: proved (3531ms)
% 25.05/4.17
% 25.05/4.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.05/4.17
% 25.05/4.18 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.05/4.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.05/4.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 25.05/4.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 27.51/4.40 Prover 10: Preprocessing ...
% 27.75/4.43 Prover 7: Preprocessing ...
% 27.81/4.47 Prover 11: Preprocessing ...
% 27.81/4.47 Prover 8: Preprocessing ...
% 27.81/4.48 Prover 13: Preprocessing ...
% 28.91/4.66 Prover 7: Constructing countermodel ...
% 29.65/4.68 Prover 10: Constructing countermodel ...
% 29.83/4.72 Prover 13: Constructing countermodel ...
% 30.18/4.92 Prover 8: Warning: ignoring some quantifiers
% 30.18/4.93 Prover 8: Constructing countermodel ...
% 32.22/5.07 Prover 10: Found proof (size 20)
% 32.62/5.07 Prover 10: proved (907ms)
% 32.62/5.07 Prover 4: stopped
% 32.62/5.07 Prover 7: stopped
% 32.62/5.07 Prover 13: stopped
% 32.62/5.07 Prover 1: stopped
% 32.62/5.07 Prover 8: stopped
% 34.15/5.48 Prover 11: Constructing countermodel ...
% 34.15/5.51 Prover 11: stopped
% 34.15/5.51
% 34.15/5.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.15/5.51
% 34.15/5.51 % SZS output start Proof for theBenchmark
% 34.15/5.52 Assumptions after simplification:
% 34.15/5.52 ---------------------------------
% 34.15/5.52
% 34.15/5.52 (ax17)
% 34.15/5.53 $i(nil) & ssList(nil)
% 34.15/5.53
% 34.15/5.53 (ax58)
% 34.15/5.53 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 34.15/5.53 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 34.15/5.53
% 34.15/5.53 (co1)
% 34.15/5.57 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 34.15/5.58 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (cons(v2, nil) = v3 & app(v7, v4)
% 34.15/5.58 = v0 & app(v6, v3) = v7 & app(v5, v6) = v1 & app(v4, v3) = v5 & $i(v7) &
% 34.15/5.58 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v6) &
% 34.15/5.58 ssList(v4) & ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ! [v8:
% 34.15/5.58 $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 34.15/5.58 (cons(v8, nil) = v9) | ~ (app(v11, v12) = v1) | ~ (app(v10, v9) = v11) |
% 34.15/5.58 ~ $i(v12) | ~ $i(v10) | ~ $i(v8) | ~ ssList(v12) | ~ ssList(v10) | ~
% 34.15/5.58 ssItem(v8) | ? [v13: $i] : ? [v14: $i] : ( ~ (v14 = v0) & app(v13, v10)
% 34.15/5.58 = v14 & app(v12, v9) = v13 & $i(v14) & $i(v13))))
% 34.15/5.58
% 34.15/5.58 (function-axioms)
% 34.30/5.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 34.30/5.58 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 34.30/5.58 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 34.30/5.58 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 34.30/5.58 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 34.30/5.58 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 34.30/5.58
% 34.30/5.58 Further assumptions not needed in the proof:
% 34.30/5.58 --------------------------------------------
% 34.30/5.58 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 34.30/5.58 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 34.30/5.58 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45,
% 34.30/5.58 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57,
% 34.30/5.58 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 34.30/5.58 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 34.30/5.58 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 34.30/5.58 ax94, ax95
% 34.30/5.58
% 34.30/5.58 Those formulas are unsatisfiable:
% 34.30/5.58 ---------------------------------
% 34.30/5.58
% 34.30/5.58 Begin of proof
% 34.30/5.58 |
% 34.30/5.58 | ALPHA: (ax17) implies:
% 34.30/5.59 | (1) ssList(nil)
% 34.30/5.59 |
% 34.30/5.59 | ALPHA: (ax58) implies:
% 34.30/5.59 | (2) ~ ssList(nil) | segmentP(nil, nil)
% 34.30/5.59 |
% 34.30/5.59 | ALPHA: (co1) implies:
% 34.30/5.59 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 34.30/5.59 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (cons(v2, nil) = v3 & app(v7,
% 34.30/5.59 | v4) = v0 & app(v6, v3) = v7 & app(v5, v6) = v1 & app(v4, v3) = v5 &
% 34.30/5.59 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)
% 34.30/5.59 | & ssList(v6) & ssList(v4) & ssList(v1) & ssList(v0) & neq(v1, nil) &
% 34.30/5.59 | ssItem(v2) & ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i]
% 34.30/5.59 | : ! [v12: $i] : ( ~ (cons(v8, nil) = v9) | ~ (app(v11, v12) = v1) |
% 34.30/5.59 | ~ (app(v10, v9) = v11) | ~ $i(v12) | ~ $i(v10) | ~ $i(v8) | ~
% 34.30/5.59 | ssList(v12) | ~ ssList(v10) | ~ ssItem(v8) | ? [v13: $i] : ?
% 34.30/5.59 | [v14: $i] : ( ~ (v14 = v0) & app(v13, v10) = v14 & app(v12, v9) =
% 34.30/5.59 | v13 & $i(v14) & $i(v13))))
% 34.30/5.59 |
% 34.30/5.59 | ALPHA: (function-axioms) implies:
% 34.30/5.59 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 34.30/5.59 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 34.30/5.59 |
% 34.30/5.59 | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2,
% 34.30/5.59 | all_91_3, all_91_4, all_91_5, all_91_6, all_91_7 gives:
% 34.30/5.60 | (5) cons(all_91_5, nil) = all_91_4 & app(all_91_0, all_91_3) = all_91_7 &
% 34.30/5.60 | app(all_91_1, all_91_4) = all_91_0 & app(all_91_2, all_91_1) = all_91_6
% 34.30/5.60 | & app(all_91_3, all_91_4) = all_91_2 & $i(all_91_0) & $i(all_91_1) &
% 34.30/5.60 | $i(all_91_2) & $i(all_91_3) & $i(all_91_4) & $i(all_91_5) &
% 34.30/5.60 | $i(all_91_6) & $i(all_91_7) & ssList(all_91_1) & ssList(all_91_3) &
% 34.30/5.60 | ssList(all_91_6) & ssList(all_91_7) & neq(all_91_6, nil) &
% 34.30/5.60 | ssItem(all_91_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 34.30/5.60 | $i] : ! [v4: $i] : ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) =
% 34.30/5.60 | all_91_6) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 34.30/5.60 | $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: $i]
% 34.30/5.60 | : ? [v6: any] : ( ~ (v6 = all_91_7) & app(v5, v2) = v6 & app(v4, v1)
% 34.30/5.60 | = v5 & $i(v6) & $i(v5)))
% 34.30/5.60 |
% 34.30/5.60 | ALPHA: (5) implies:
% 34.30/5.60 | (6) ssItem(all_91_5)
% 34.30/5.60 | (7) ssList(all_91_3)
% 34.30/5.60 | (8) ssList(all_91_1)
% 34.30/5.60 | (9) $i(all_91_5)
% 34.30/5.60 | (10) $i(all_91_3)
% 34.30/5.60 | (11) $i(all_91_1)
% 34.30/5.60 | (12) app(all_91_3, all_91_4) = all_91_2
% 34.30/5.60 | (13) app(all_91_2, all_91_1) = all_91_6
% 34.30/5.60 | (14) app(all_91_1, all_91_4) = all_91_0
% 34.30/5.60 | (15) app(all_91_0, all_91_3) = all_91_7
% 34.30/5.60 | (16) cons(all_91_5, nil) = all_91_4
% 34.30/5.61 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 34.30/5.61 | ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) = all_91_6) | ~ (app(v2,
% 34.30/5.61 | v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v4) |
% 34.30/5.61 | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: $i] : ? [v6: any] : ( ~ (v6
% 34.30/5.61 | = all_91_7) & app(v5, v2) = v6 & app(v4, v1) = v5 & $i(v6) &
% 34.30/5.61 | $i(v5)))
% 34.30/5.61 |
% 34.30/5.61 | BETA: splitting (2) gives:
% 34.30/5.61 |
% 34.30/5.61 | Case 1:
% 34.30/5.61 | |
% 34.30/5.61 | | (18) ~ ssList(nil)
% 34.30/5.61 | |
% 34.30/5.61 | | PRED_UNIFY: (1), (18) imply:
% 34.30/5.61 | | (19) $false
% 34.30/5.61 | |
% 34.30/5.61 | | CLOSE: (19) is inconsistent.
% 34.30/5.61 | |
% 34.30/5.61 | Case 2:
% 34.30/5.61 | |
% 34.30/5.61 | |
% 34.30/5.61 | | GROUND_INST: instantiating (17) with all_91_5, all_91_4, all_91_3, all_91_2,
% 34.30/5.61 | | all_91_1, simplifying with (6), (7), (8), (9), (10), (11),
% 34.30/5.61 | | (12), (13), (16) gives:
% 34.30/5.61 | | (20) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_91_7) & app(v0, all_91_3)
% 34.30/5.61 | | = v1 & app(all_91_1, all_91_4) = v0 & $i(v1) & $i(v0))
% 34.30/5.61 | |
% 34.30/5.61 | | DELTA: instantiating (20) with fresh symbols all_116_0, all_116_1 gives:
% 34.30/5.61 | | (21) ~ (all_116_0 = all_91_7) & app(all_116_1, all_91_3) = all_116_0 &
% 34.30/5.61 | | app(all_91_1, all_91_4) = all_116_1 & $i(all_116_0) & $i(all_116_1)
% 34.30/5.61 | |
% 34.30/5.61 | | ALPHA: (21) implies:
% 34.30/5.61 | | (22) ~ (all_116_0 = all_91_7)
% 34.30/5.61 | | (23) app(all_91_1, all_91_4) = all_116_1
% 34.30/5.61 | | (24) app(all_116_1, all_91_3) = all_116_0
% 34.30/5.61 | |
% 34.30/5.61 | | GROUND_INST: instantiating (4) with all_91_0, all_116_1, all_91_4, all_91_1,
% 34.30/5.61 | | simplifying with (14), (23) gives:
% 34.30/5.61 | | (25) all_116_1 = all_91_0
% 34.30/5.61 | |
% 34.30/5.61 | | REDUCE: (24), (25) imply:
% 34.30/5.61 | | (26) app(all_91_0, all_91_3) = all_116_0
% 34.30/5.61 | |
% 34.30/5.61 | | GROUND_INST: instantiating (4) with all_91_7, all_116_0, all_91_3, all_91_0,
% 34.30/5.61 | | simplifying with (15), (26) gives:
% 34.30/5.61 | | (27) all_116_0 = all_91_7
% 34.30/5.61 | |
% 34.30/5.61 | | REDUCE: (22), (27) imply:
% 34.30/5.61 | | (28) $false
% 34.30/5.61 | |
% 34.30/5.61 | | CLOSE: (28) is inconsistent.
% 34.30/5.61 | |
% 34.30/5.61 | End of split
% 34.30/5.61 |
% 34.30/5.61 End of proof
% 34.30/5.61 % SZS output end Proof for theBenchmark
% 34.30/5.61
% 34.30/5.61 5004ms
%------------------------------------------------------------------------------