TSTP Solution File: SWC104+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC104+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 : n020.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 20:49:41 EDT 2023
% Result : Theorem 21.81s 3.59s
% Output : Proof 30.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC104+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 18:42:43 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.47/0.59 ________ _____
% 0.47/0.59 ___ __ \_________(_)________________________________
% 0.47/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.47/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.47/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.47/0.59
% 0.47/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.47/0.59 (2023-06-19)
% 0.47/0.59
% 0.47/0.59 (c) Philipp Rümmer, 2009-2023
% 0.47/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.47/0.59 Amanda Stjerna.
% 0.47/0.59 Free software under BSD-3-Clause.
% 0.47/0.59
% 0.47/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.47/0.59
% 0.47/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.47/0.60 Running up to 7 provers in parallel.
% 0.47/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.47/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.47/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.47/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.47/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.47/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.47/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.13/1.37 Prover 1: Preprocessing ...
% 5.13/1.37 Prover 4: Preprocessing ...
% 5.13/1.38 Prover 5: Preprocessing ...
% 5.13/1.38 Prover 6: Preprocessing ...
% 5.13/1.38 Prover 0: Preprocessing ...
% 5.13/1.38 Prover 3: Preprocessing ...
% 5.13/1.39 Prover 2: Preprocessing ...
% 14.51/2.62 Prover 2: Proving ...
% 14.63/2.64 Prover 1: Constructing countermodel ...
% 14.63/2.67 Prover 6: Proving ...
% 15.21/2.73 Prover 5: Constructing countermodel ...
% 15.66/2.80 Prover 3: Constructing countermodel ...
% 21.81/3.59 Prover 3: proved (2974ms)
% 21.81/3.59
% 21.81/3.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.81/3.59
% 21.81/3.60 Prover 5: stopped
% 21.81/3.60 Prover 2: stopped
% 21.81/3.61 Prover 6: stopped
% 21.81/3.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.81/3.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.81/3.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.81/3.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.17/3.65 Prover 0: Proving ...
% 22.17/3.66 Prover 0: stopped
% 22.17/3.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 22.43/3.75 Prover 4: Constructing countermodel ...
% 24.25/3.92 Prover 7: Preprocessing ...
% 24.25/3.94 Prover 13: Preprocessing ...
% 24.25/3.94 Prover 8: Preprocessing ...
% 24.25/3.95 Prover 10: Preprocessing ...
% 24.63/3.96 Prover 11: Preprocessing ...
% 25.64/4.12 Prover 7: Constructing countermodel ...
% 26.12/4.16 Prover 10: Constructing countermodel ...
% 26.59/4.28 Prover 13: Constructing countermodel ...
% 27.07/4.37 Prover 8: Warning: ignoring some quantifiers
% 27.07/4.39 Prover 7: Found proof (size 22)
% 27.07/4.39 Prover 7: proved (796ms)
% 27.07/4.39 Prover 1: stopped
% 27.07/4.39 Prover 4: stopped
% 27.07/4.39 Prover 10: stopped
% 27.07/4.39 Prover 8: Constructing countermodel ...
% 27.07/4.40 Prover 8: stopped
% 27.07/4.41 Prover 13: stopped
% 29.99/4.91 Prover 11: Constructing countermodel ...
% 29.99/4.93 Prover 11: stopped
% 29.99/4.93
% 29.99/4.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.99/4.93
% 29.99/4.94 % SZS output start Proof for theBenchmark
% 29.99/4.95 Assumptions after simplification:
% 29.99/4.95 ---------------------------------
% 29.99/4.95
% 29.99/4.95 (ax15)
% 29.99/4.96 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) |
% 29.99/4.96 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~
% 29.99/4.96 neq(v0, v0))
% 29.99/4.96
% 29.99/4.97 (ax17)
% 29.99/4.97 $i(nil) & ssList(nil)
% 29.99/4.97
% 29.99/4.97 (ax5)
% 29.99/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 29.99/5.00 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 29.99/5.00 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 29.99/5.00 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 29.99/5.00 v2) = v0 & $i(v2) & ssList(v2)))
% 29.99/5.00
% 29.99/5.00 (co1)
% 29.99/5.01 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2)
% 29.99/5.01 & $i(v1) & $i(v0) & totalorderedP(v0) & ssList(v2) & ssList(v1) & ssList(v0)
% 29.99/5.01 & neq(v1, nil) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 29.99/5.01 [v7: $i] : ! [v8: $i] : ( ~ (cons(v6, nil) = v7) | ~ (cons(v3, nil) = v4)
% 29.99/5.01 | ~ (app(v8, v7) = v0) | ~ (app(v4, v5) = v2) | ~ $i(v8) | ~ $i(v6) |
% 29.99/5.01 ~ $i(v5) | ~ $i(v3) | ~ leq(v6, v3) | ~ ssList(v8) | ~ ssList(v5) | ~
% 29.99/5.01 ssItem(v6) | ~ ssItem(v3)) & ( ~ (v0 = nil) | v1 = nil) & ( ~
% 29.99/5.01 frontsegP(v1, v0) | ~ neq(v0, nil)))
% 29.99/5.01
% 29.99/5.01 Further assumptions not needed in the proof:
% 29.99/5.01 --------------------------------------------
% 29.99/5.01 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 29.99/5.01 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 29.99/5.01 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46,
% 29.99/5.01 ax47, ax48, ax49, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59,
% 29.99/5.01 ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70,
% 29.99/5.01 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82,
% 29.99/5.01 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94,
% 29.99/5.01 ax95
% 29.99/5.01
% 29.99/5.01 Those formulas are unsatisfiable:
% 29.99/5.01 ---------------------------------
% 29.99/5.01
% 29.99/5.01 Begin of proof
% 30.33/5.01 |
% 30.33/5.01 | ALPHA: (ax5) implies:
% 30.33/5.01 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~
% 30.33/5.01 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~
% 30.33/5.01 | ssList(v0) | frontsegP(v0, v1))
% 30.33/5.01 |
% 30.33/5.01 | ALPHA: (ax15) implies:
% 30.33/5.01 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 30.33/5.01 | ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 30.33/5.01 |
% 30.33/5.01 | ALPHA: (ax17) implies:
% 30.33/5.01 | (3) ssList(nil)
% 30.33/5.01 |
% 30.33/5.01 | ALPHA: (co1) implies:
% 30.33/5.01 | (4) $i(nil)
% 30.33/5.02 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2) &
% 30.33/5.02 | $i(v1) & $i(v0) & totalorderedP(v0) & ssList(v2) & ssList(v1) &
% 30.33/5.02 | ssList(v0) & neq(v1, nil) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 30.33/5.02 | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v6, nil) = v7) |
% 30.33/5.02 | ~ (cons(v3, nil) = v4) | ~ (app(v8, v7) = v0) | ~ (app(v4, v5) =
% 30.33/5.02 | v2) | ~ $i(v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) | ~ leq(v6,
% 30.33/5.02 | v3) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v6) | ~
% 30.33/5.02 | ssItem(v3)) & ( ~ (v0 = nil) | v1 = nil) & ( ~ frontsegP(v1, v0) |
% 30.33/5.02 | ~ neq(v0, nil)))
% 30.33/5.02 |
% 30.33/5.02 | DELTA: instantiating (5) with fresh symbols all_91_0, all_91_1, all_91_2
% 30.33/5.02 | gives:
% 30.33/5.02 | (6) app(all_91_2, all_91_0) = all_91_1 & $i(all_91_0) & $i(all_91_1) &
% 30.33/5.02 | $i(all_91_2) & totalorderedP(all_91_2) & ssList(all_91_0) &
% 30.33/5.02 | ssList(all_91_1) & ssList(all_91_2) & neq(all_91_1, nil) & ! [v0: $i]
% 30.33/5.02 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 30.33/5.02 | ( ~ (cons(v3, nil) = v4) | ~ (cons(v0, nil) = v1) | ~ (app(v5, v4) =
% 30.33/5.02 | all_91_2) | ~ (app(v1, v2) = all_91_0) | ~ $i(v5) | ~ $i(v3) |
% 30.33/5.02 | ~ $i(v2) | ~ $i(v0) | ~ leq(v3, v0) | ~ ssList(v5) | ~ ssList(v2)
% 30.33/5.02 | | ~ ssItem(v3) | ~ ssItem(v0)) & ( ~ (all_91_2 = nil) | all_91_1 =
% 30.33/5.02 | nil) & ( ~ frontsegP(all_91_1, all_91_2) | ~ neq(all_91_2, nil))
% 30.33/5.02 |
% 30.33/5.02 | ALPHA: (6) implies:
% 30.33/5.02 | (7) neq(all_91_1, nil)
% 30.33/5.02 | (8) ssList(all_91_2)
% 30.33/5.02 | (9) ssList(all_91_1)
% 30.33/5.02 | (10) ssList(all_91_0)
% 30.33/5.02 | (11) $i(all_91_2)
% 30.33/5.02 | (12) $i(all_91_1)
% 30.33/5.02 | (13) $i(all_91_0)
% 30.33/5.02 | (14) app(all_91_2, all_91_0) = all_91_1
% 30.33/5.02 | (15) ~ frontsegP(all_91_1, all_91_2) | ~ neq(all_91_2, nil)
% 30.33/5.02 | (16) ~ (all_91_2 = nil) | all_91_1 = nil
% 30.33/5.02 |
% 30.33/5.02 | GROUND_INST: instantiating (2) with all_91_2, nil, simplifying with (3), (4),
% 30.33/5.02 | (8), (11) gives:
% 30.33/5.02 | (17) all_91_2 = nil | neq(all_91_2, nil)
% 30.33/5.02 |
% 30.33/5.02 | GROUND_INST: instantiating (1) with all_91_1, all_91_2, all_91_0, simplifying
% 30.33/5.02 | with (8), (9), (10), (11), (12), (13), (14) gives:
% 30.33/5.02 | (18) frontsegP(all_91_1, all_91_2)
% 30.33/5.02 |
% 30.33/5.02 | BETA: splitting (15) gives:
% 30.33/5.02 |
% 30.33/5.03 | Case 1:
% 30.33/5.03 | |
% 30.33/5.03 | | (19) ~ neq(all_91_2, nil)
% 30.33/5.03 | |
% 30.33/5.03 | | BETA: splitting (17) gives:
% 30.33/5.03 | |
% 30.33/5.03 | | Case 1:
% 30.33/5.03 | | |
% 30.33/5.03 | | | (20) neq(all_91_2, nil)
% 30.33/5.03 | | |
% 30.33/5.03 | | | PRED_UNIFY: (19), (20) imply:
% 30.33/5.03 | | | (21) $false
% 30.33/5.03 | | |
% 30.33/5.03 | | | CLOSE: (21) is inconsistent.
% 30.33/5.03 | | |
% 30.33/5.03 | | Case 2:
% 30.33/5.03 | | |
% 30.33/5.03 | | | (22) all_91_2 = nil
% 30.33/5.03 | | |
% 30.33/5.03 | | | REDUCE: (19), (22) imply:
% 30.33/5.03 | | | (23) ~ neq(nil, nil)
% 30.33/5.03 | | |
% 30.33/5.03 | | | BETA: splitting (16) gives:
% 30.33/5.03 | | |
% 30.33/5.03 | | | Case 1:
% 30.33/5.03 | | | |
% 30.33/5.03 | | | | (24) ~ (all_91_2 = nil)
% 30.33/5.03 | | | |
% 30.33/5.03 | | | | REDUCE: (22), (24) imply:
% 30.33/5.03 | | | | (25) $false
% 30.33/5.03 | | | |
% 30.33/5.03 | | | | CLOSE: (25) is inconsistent.
% 30.33/5.03 | | | |
% 30.33/5.03 | | | Case 2:
% 30.33/5.03 | | | |
% 30.33/5.03 | | | | (26) all_91_1 = nil
% 30.33/5.03 | | | |
% 30.33/5.03 | | | | REDUCE: (7), (26) imply:
% 30.33/5.03 | | | | (27) neq(nil, nil)
% 30.33/5.03 | | | |
% 30.33/5.03 | | | | PRED_UNIFY: (23), (27) imply:
% 30.33/5.03 | | | | (28) $false
% 30.33/5.03 | | | |
% 30.33/5.03 | | | | CLOSE: (28) is inconsistent.
% 30.33/5.03 | | | |
% 30.33/5.03 | | | End of split
% 30.33/5.03 | | |
% 30.33/5.03 | | End of split
% 30.33/5.03 | |
% 30.33/5.03 | Case 2:
% 30.33/5.03 | |
% 30.33/5.03 | | (29) ~ frontsegP(all_91_1, all_91_2)
% 30.33/5.03 | |
% 30.33/5.03 | | PRED_UNIFY: (18), (29) imply:
% 30.33/5.03 | | (30) $false
% 30.33/5.03 | |
% 30.33/5.03 | | CLOSE: (30) is inconsistent.
% 30.33/5.03 | |
% 30.33/5.03 | End of split
% 30.33/5.03 |
% 30.33/5.03 End of proof
% 30.33/5.03 % SZS output end Proof for theBenchmark
% 30.33/5.03
% 30.33/5.03 4437ms
%------------------------------------------------------------------------------