TSTP Solution File: LCL658+1.001 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL658+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n021.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 08:12:09 EDT 2023
% Result : Theorem 14.31s 2.93s
% Output : Proof 18.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL658+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.18/0.35 % Computer : n021.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 24 17:45:40 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.53/1.09 Prover 4: Preprocessing ...
% 2.53/1.09 Prover 1: Preprocessing ...
% 2.86/1.15 Prover 0: Preprocessing ...
% 2.86/1.15 Prover 3: Preprocessing ...
% 2.86/1.15 Prover 5: Preprocessing ...
% 2.86/1.15 Prover 6: Preprocessing ...
% 2.86/1.15 Prover 2: Preprocessing ...
% 4.24/1.44 Prover 2: Proving ...
% 4.24/1.46 Prover 5: Proving ...
% 5.69/1.60 Prover 6: Proving ...
% 5.69/1.63 Prover 3: Constructing countermodel ...
% 5.69/1.64 Prover 1: Constructing countermodel ...
% 11.01/2.41 Prover 0: Proving ...
% 11.45/2.55 Prover 4: Constructing countermodel ...
% 14.31/2.93 Prover 5: proved (2271ms)
% 14.31/2.93
% 14.31/2.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.31/2.93
% 14.31/2.93 Prover 3: stopped
% 14.31/2.93 Prover 6: stopped
% 14.31/2.94 Prover 0: stopped
% 14.31/2.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.31/2.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.31/2.95 Prover 2: stopped
% 14.31/2.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.31/2.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.31/2.95 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.88/2.97 Prover 8: Preprocessing ...
% 14.99/2.99 Prover 7: Preprocessing ...
% 14.99/2.99 Prover 10: Preprocessing ...
% 14.99/3.00 Prover 13: Preprocessing ...
% 14.99/3.01 Prover 11: Preprocessing ...
% 15.25/3.02 Prover 7: Warning: ignoring some quantifiers
% 15.25/3.03 Prover 7: Constructing countermodel ...
% 15.25/3.03 Prover 10: Warning: ignoring some quantifiers
% 15.25/3.03 Prover 10: Constructing countermodel ...
% 15.38/3.08 Prover 13: Warning: ignoring some quantifiers
% 15.38/3.08 Prover 13: Constructing countermodel ...
% 15.38/3.10 Prover 8: Warning: ignoring some quantifiers
% 15.38/3.10 Prover 8: Constructing countermodel ...
% 17.06/3.38 Prover 10: Found proof (size 44)
% 17.06/3.39 Prover 10: proved (448ms)
% 17.06/3.39 Prover 8: stopped
% 17.06/3.39 Prover 4: stopped
% 17.06/3.39 Prover 13: stopped
% 17.06/3.39 Prover 1: stopped
% 17.06/3.39 Prover 7: stopped
% 18.05/3.51 Prover 11: Constructing countermodel ...
% 18.05/3.52 Prover 11: stopped
% 18.05/3.52
% 18.05/3.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.05/3.52
% 18.05/3.52 % SZS output start Proof for theBenchmark
% 18.05/3.52 Assumptions after simplification:
% 18.05/3.52 ---------------------------------
% 18.05/3.52
% 18.05/3.52 (main)
% 18.42/3.54 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) &
% 18.42/3.54 $i(v1) & $i(v0) & r1(v1, v3) & r1(v1, v2) & r1(v0, v1) & ~ p1(v3) & ! [v4:
% 18.42/3.54 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) |
% 18.42/3.54 ~ $i(v5) | ~ $i(v4) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 18.42/3.54 r1(v0, v4) | p1(v7) | ? [v8: $i] : ($i(v8) & r1(v5, v8) & ~ p1(v8))) &
% 18.42/3.54 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4)
% 18.42/3.54 | ~ p1(v4) | ~ r1(v4, v6) | ~ r1(v4, v5) | ~ r1(v0, v4) | p1(v6) | ?
% 18.42/3.54 [v7: $i] : ? [v8: $i] : ($i(v8) & $i(v7) & ((p1(v7) & r1(v7, v8) & r1(v5,
% 18.42/3.54 v7) & ~ p1(v8)) | (p1(v7) & r1(v7, v8) & r1(v4, v7) & ~ p1(v8) &
% 18.42/3.54 ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10)
% 18.42/3.54 | ~ $i(v9) | ~ p1(v10) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~
% 18.42/3.54 r1(v7, v9) | p1(v11) | p1(v9)) & ! [v9: $i] : ! [v10: $i] : !
% 18.42/3.54 [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ p1(v10) | ~
% 18.42/3.54 r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v7, v9) | p1(v11) | ? [v12:
% 18.42/3.54 $i] : ($i(v12) & r1(v9, v12) & ~ p1(v12))))))) & ! [v4: $i] :
% 18.42/3.54 ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ r1(v5,
% 18.42/3.54 v6) | ~ r1(v4, v5) | ~ r1(v0, v4) | p1(v6) | ? [v7: $i] : ? [v8: $i]
% 18.42/3.54 : ($i(v8) & $i(v7) & ((p1(v7) & r1(v7, v8) & r1(v6, v7) & ~ p1(v8)) |
% 18.42/3.54 (r1(v4, v7) & ~ p1(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) |
% 18.42/3.54 ~ $i(v9) | ~ p1(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) |
% 18.42/3.54 p1(v10)))))) & ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4)
% 18.42/3.54 | ~ r1(v4, v5) | ~ r1(v0, v4) | p1(v4) | ? [v6: $i] : ($i(v6) &
% 18.42/3.54 ((r1(v5, v6) & ~ p1(v6)) | (r1(v4, v6) & ~ p1(v6) & ! [v7: $i] : !
% 18.42/3.54 [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p1(v7) | ~ r1(v7, v8) | ~
% 18.42/3.54 r1(v6, v7) | p1(v8)))))) & ! [v4: $i] : ( ~ $i(v4) | ~ r1(v2,
% 18.42/3.54 v4) | p1(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ r1(v1, v4) | p1(v4) | ?
% 18.42/3.54 [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & p1(v5) & r1(v5, v6) & r1(v4,
% 18.42/3.54 v5) & ~ p1(v6))))
% 18.42/3.54
% 18.42/3.54 Further assumptions not needed in the proof:
% 18.42/3.54 --------------------------------------------
% 18.42/3.54 reflexivity
% 18.42/3.54
% 18.42/3.54 Those formulas are unsatisfiable:
% 18.42/3.54 ---------------------------------
% 18.42/3.54
% 18.42/3.54 Begin of proof
% 18.42/3.54 |
% 18.42/3.54 | DELTA: instantiating (main) with fresh symbols all_3_0, all_3_1, all_3_2,
% 18.42/3.54 | all_3_3 gives:
% 18.42/3.55 | (1) $i(all_3_0) & $i(all_3_1) & $i(all_3_2) & $i(all_3_3) & r1(all_3_2,
% 18.42/3.55 | all_3_0) & r1(all_3_2, all_3_1) & r1(all_3_3, all_3_2) & ~
% 18.42/3.55 | p1(all_3_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 18.42/3.55 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~
% 18.42/3.55 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_3, v0) | p1(v3) | ? [v4:
% 18.42/3.55 | $i] : ($i(v4) & r1(v1, v4) & ~ p1(v4))) & ! [v0: $i] : ! [v1:
% 18.42/3.55 | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) |
% 18.42/3.55 | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_3_3, v0) | p1(v2) | ? [v3:
% 18.42/3.55 | $i] : ? [v4: $i] : ($i(v4) & $i(v3) & ((p1(v3) & r1(v3, v4) &
% 18.42/3.55 | r1(v1, v3) & ~ p1(v4)) | (p1(v3) & r1(v3, v4) & r1(v0, v3) &
% 18.42/3.55 | ~ p1(v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7)
% 18.42/3.55 | | ~ $i(v6) | ~ $i(v5) | ~ p1(v6) | ~ r1(v6, v7) | ~
% 18.42/3.55 | r1(v5, v6) | ~ r1(v3, v5) | p1(v7) | p1(v5)) & ! [v5: $i] :
% 18.42/3.55 | ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5)
% 18.42/3.55 | | ~ p1(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v3, v5) |
% 18.42/3.55 | p1(v7) | ? [v8: $i] : ($i(v8) & r1(v5, v8) & ~ p1(v8)))))))
% 18.42/3.55 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 18.42/3.55 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_3, v0) | p1(v2)
% 18.42/3.55 | | ? [v3: $i] : ? [v4: $i] : ($i(v4) & $i(v3) & ((p1(v3) & r1(v3,
% 18.42/3.55 | v4) & r1(v2, v3) & ~ p1(v4)) | (r1(v0, v3) & ~ p1(v3) & !
% 18.42/3.55 | [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ p1(v5) |
% 18.42/3.55 | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v6)))))) & ! [v0: $i] : !
% 18.42/3.55 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_3_3, v0)
% 18.42/3.55 | | p1(v0) | ? [v2: $i] : ($i(v2) & ((r1(v1, v2) & ~ p1(v2)) |
% 18.42/3.55 | (r1(v0, v2) & ~ p1(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4)
% 18.42/3.55 | | ~ $i(v3) | ~ p1(v3) | ~ r1(v3, v4) | ~ r1(v2, v3) |
% 18.42/3.55 | p1(v4)))))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_1, v0) |
% 18.42/3.55 | p1(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2, v0) | p1(v0) | ?
% 18.42/3.55 | [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) &
% 18.42/3.55 | r1(v0, v1) & ~ p1(v2)))
% 18.42/3.55 |
% 18.42/3.55 | ALPHA: (1) implies:
% 18.42/3.55 | (2) ~ p1(all_3_0)
% 18.42/3.55 | (3) r1(all_3_3, all_3_2)
% 18.42/3.55 | (4) r1(all_3_2, all_3_1)
% 18.42/3.55 | (5) r1(all_3_2, all_3_0)
% 18.42/3.55 | (6) $i(all_3_2)
% 18.42/3.55 | (7) $i(all_3_1)
% 18.42/3.55 | (8) $i(all_3_0)
% 18.42/3.55 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2, v0) | p1(v0) | ? [v1: $i] :
% 18.42/3.55 | ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) & r1(v0, v1) & ~
% 18.42/3.55 | p1(v2)))
% 18.42/3.55 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_1, v0) | p1(v0))
% 18.42/3.55 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) |
% 18.42/3.55 | ~ r1(all_3_3, v0) | p1(v0) | ? [v2: $i] : ($i(v2) & ((r1(v1, v2) &
% 18.42/3.55 | ~ p1(v2)) | (r1(v0, v2) & ~ p1(v2) & ! [v3: $i] : ! [v4:
% 18.42/3.55 | $i] : ( ~ $i(v4) | ~ $i(v3) | ~ p1(v3) | ~ r1(v3, v4) |
% 18.42/3.55 | ~ r1(v2, v3) | p1(v4))))))
% 18.42/3.55 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 18.42/3.55 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_3, v0) | p1(v2)
% 18.42/3.55 | | ? [v3: $i] : ? [v4: $i] : ($i(v4) & $i(v3) & ((p1(v3) & r1(v3,
% 18.42/3.56 | v4) & r1(v2, v3) & ~ p1(v4)) | (r1(v0, v3) & ~ p1(v3) & !
% 18.42/3.56 | [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ p1(v5) |
% 18.42/3.56 | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v6))))))
% 18.42/3.56 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 18.42/3.56 | $i(v0) | ~ p1(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_3_3,
% 18.42/3.56 | v0) | p1(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v4) & $i(v3) &
% 18.42/3.56 | ((p1(v3) & r1(v3, v4) & r1(v1, v3) & ~ p1(v4)) | (p1(v3) & r1(v3,
% 18.42/3.56 | v4) & r1(v0, v3) & ~ p1(v4) & ! [v5: $i] : ! [v6: $i] :
% 18.42/3.56 | ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ p1(v6) |
% 18.42/3.56 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v7) |
% 18.42/3.56 | p1(v5)) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 18.42/3.56 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ p1(v6) | ~ r1(v6, v7) |
% 18.42/3.56 | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v7) | ? [v8: $i] :
% 18.42/3.56 | ($i(v8) & r1(v5, v8) & ~ p1(v8)))))))
% 18.42/3.56 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) |
% 18.42/3.56 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) |
% 18.42/3.56 | ~ r1(v0, v1) | ~ r1(all_3_3, v0) | p1(v3) | ? [v4: $i] : ($i(v4) &
% 18.42/3.56 | r1(v1, v4) & ~ p1(v4)))
% 18.42/3.56 |
% 18.42/3.56 | GROUND_INST: instantiating (11) with all_3_2, all_3_1, simplifying with (3),
% 18.42/3.56 | (4), (6), (7) gives:
% 18.42/3.56 | (15) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) |
% 18.42/3.56 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 18.42/3.56 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1)
% 18.42/3.56 | | p1(v2)))))
% 18.42/3.56 |
% 18.42/3.56 | BETA: splitting (15) gives:
% 18.42/3.56 |
% 18.42/3.56 | Case 1:
% 18.42/3.56 | |
% 18.42/3.56 | | (16) p1(all_3_2)
% 18.42/3.56 | |
% 18.42/3.56 | | GROUND_INST: instantiating (13) with all_3_2, all_3_1, all_3_0, simplifying
% 18.42/3.56 | | with (2), (3), (4), (5), (6), (7), (8), (16) gives:
% 18.42/3.56 | | (17) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0, v1)
% 18.42/3.56 | | & r1(all_3_1, v0) & ~ p1(v1)) | (p1(v0) & r1(v0, v1) &
% 18.42/3.56 | | r1(all_3_2, v0) & ~ p1(v1) & ! [v2: $i] : ! [v3: $i] : !
% 18.42/3.56 | | [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~
% 18.42/3.56 | | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) |
% 18.42/3.56 | | p1(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 18.42/3.56 | | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~ r1(v3, v4) |
% 18.42/3.56 | | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | ? [v5: $i] :
% 18.42/3.56 | | ($i(v5) & r1(v2, v5) & ~ p1(v5))))))
% 18.42/3.56 | |
% 18.42/3.56 | | DELTA: instantiating (17) with fresh symbols all_46_0, all_46_1 gives:
% 18.42/3.57 | | (18) $i(all_46_0) & $i(all_46_1) & ((p1(all_46_1) & r1(all_46_1,
% 18.42/3.57 | | all_46_0) & r1(all_3_1, all_46_1) & ~ p1(all_46_0)) |
% 18.42/3.57 | | (p1(all_46_1) & r1(all_46_1, all_46_0) & r1(all_3_2, all_46_1) &
% 18.42/3.57 | | ~ p1(all_46_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 18.42/3.57 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) |
% 18.42/3.57 | | ~ r1(v0, v1) | ~ r1(all_46_1, v0) | p1(v2) | p1(v0)) & !
% 18.42/3.57 | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) |
% 18.42/3.57 | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 18.42/3.57 | | r1(all_46_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, v3)
% 18.42/3.57 | | & ~ p1(v3)))))
% 18.42/3.57 | |
% 18.42/3.57 | | ALPHA: (18) implies:
% 18.42/3.57 | | (19) $i(all_46_1)
% 18.42/3.57 | | (20) $i(all_46_0)
% 18.42/3.57 | | (21) (p1(all_46_1) & r1(all_46_1, all_46_0) & r1(all_3_1, all_46_1) & ~
% 18.42/3.57 | | p1(all_46_0)) | (p1(all_46_1) & r1(all_46_1, all_46_0) &
% 18.42/3.57 | | r1(all_3_2, all_46_1) & ~ p1(all_46_0) & ! [v0: $i] : ! [v1:
% 18.42/3.57 | | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 18.42/3.57 | | p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_46_1, v0) |
% 18.42/3.57 | | p1(v2) | p1(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 18.42/3.57 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~
% 18.42/3.57 | | r1(v0, v1) | ~ r1(all_46_1, v0) | p1(v2) | ? [v3: $i] :
% 18.42/3.57 | | ($i(v3) & r1(v0, v3) & ~ p1(v3))))
% 18.42/3.57 | |
% 18.42/3.57 | | BETA: splitting (21) gives:
% 18.42/3.57 | |
% 18.42/3.57 | | Case 1:
% 18.42/3.57 | | |
% 18.42/3.57 | | | (22) p1(all_46_1) & r1(all_46_1, all_46_0) & r1(all_3_1, all_46_1) & ~
% 18.42/3.57 | | | p1(all_46_0)
% 18.42/3.57 | | |
% 18.42/3.57 | | | ALPHA: (22) implies:
% 18.42/3.57 | | | (23) ~ p1(all_46_0)
% 18.42/3.57 | | | (24) r1(all_3_1, all_46_1)
% 18.42/3.57 | | | (25) r1(all_46_1, all_46_0)
% 18.42/3.57 | | |
% 18.42/3.57 | | | GROUND_INST: instantiating (14) with all_3_2, all_3_1, all_46_1, all_46_0,
% 18.42/3.57 | | | simplifying with (3), (4), (6), (7), (19), (20), (23), (24),
% 18.42/3.57 | | | (25) gives:
% 18.42/3.57 | | | (26) ? [v0: $i] : ($i(v0) & r1(all_3_1, v0) & ~ p1(v0))
% 18.42/3.57 | | |
% 18.42/3.57 | | | DELTA: instantiating (26) with fresh symbol all_76_0 gives:
% 18.42/3.57 | | | (27) $i(all_76_0) & r1(all_3_1, all_76_0) & ~ p1(all_76_0)
% 18.42/3.57 | | |
% 18.42/3.57 | | | ALPHA: (27) implies:
% 18.42/3.57 | | | (28) ~ p1(all_76_0)
% 18.42/3.57 | | | (29) r1(all_3_1, all_76_0)
% 18.42/3.57 | | | (30) $i(all_76_0)
% 18.42/3.57 | | |
% 18.42/3.57 | | | GROUND_INST: instantiating (10) with all_76_0, simplifying with (28),
% 18.42/3.57 | | | (29), (30) gives:
% 18.42/3.57 | | | (31) $false
% 18.42/3.57 | | |
% 18.42/3.57 | | | CLOSE: (31) is inconsistent.
% 18.42/3.57 | | |
% 18.42/3.57 | | Case 2:
% 18.42/3.57 | | |
% 18.42/3.58 | | | (32) p1(all_46_1) & r1(all_46_1, all_46_0) & r1(all_3_2, all_46_1) & ~
% 18.42/3.58 | | | p1(all_46_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 18.42/3.58 | | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~
% 18.42/3.58 | | | r1(v0, v1) | ~ r1(all_46_1, v0) | p1(v2) | p1(v0)) & ! [v0:
% 18.42/3.58 | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 18.42/3.58 | | | $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 18.42/3.58 | | | r1(all_46_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, v3) &
% 18.42/3.58 | | | ~ p1(v3)))
% 18.63/3.58 | | |
% 18.63/3.58 | | | ALPHA: (32) implies:
% 18.63/3.58 | | | (33) ~ p1(all_46_0)
% 18.63/3.58 | | | (34) r1(all_3_2, all_46_1)
% 18.63/3.58 | | | (35) r1(all_46_1, all_46_0)
% 18.63/3.58 | | | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) |
% 18.63/3.58 | | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 18.63/3.58 | | | r1(all_46_1, v0) | p1(v2) | p1(v0))
% 18.63/3.58 | | |
% 18.63/3.58 | | | GROUND_INST: instantiating (12) with all_3_2, all_46_1, all_46_0,
% 18.63/3.58 | | | simplifying with (3), (6), (19), (20), (33), (34), (35)
% 18.63/3.58 | | | gives:
% 18.63/3.58 | | | (37) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0,
% 18.63/3.58 | | | v1) & r1(all_46_0, v0) & ~ p1(v1)) | (r1(all_3_2, v0) &
% 18.63/3.58 | | | ~ p1(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 18.63/3.58 | | | $i(v2) | ~ p1(v2) | ~ r1(v2, v3) | ~ r1(v0, v2) |
% 18.63/3.58 | | | p1(v3)))))
% 18.63/3.58 | | |
% 18.63/3.58 | | | DELTA: instantiating (37) with fresh symbols all_77_0, all_77_1 gives:
% 18.63/3.58 | | | (38) $i(all_77_0) & $i(all_77_1) & ((p1(all_77_1) & r1(all_77_1,
% 18.63/3.58 | | | all_77_0) & r1(all_46_0, all_77_1) & ~ p1(all_77_0)) |
% 18.63/3.58 | | | (r1(all_3_2, all_77_1) & ~ p1(all_77_1) & ! [v0: $i] : ! [v1:
% 18.63/3.58 | | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) |
% 18.63/3.58 | | | ~ r1(all_77_1, v0) | p1(v1))))
% 18.63/3.58 | | |
% 18.63/3.58 | | | ALPHA: (38) implies:
% 18.63/3.58 | | | (39) $i(all_77_1)
% 18.63/3.58 | | | (40) $i(all_77_0)
% 18.63/3.58 | | | (41) (p1(all_77_1) & r1(all_77_1, all_77_0) & r1(all_46_0, all_77_1) &
% 18.63/3.58 | | | ~ p1(all_77_0)) | (r1(all_3_2, all_77_1) & ~ p1(all_77_1) & !
% 18.63/3.58 | | | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~
% 18.63/3.58 | | | r1(v0, v1) | ~ r1(all_77_1, v0) | p1(v1)))
% 18.63/3.58 | | |
% 18.63/3.58 | | | BETA: splitting (41) gives:
% 18.63/3.58 | | |
% 18.63/3.58 | | | Case 1:
% 18.63/3.58 | | | |
% 18.63/3.58 | | | | (42) p1(all_77_1) & r1(all_77_1, all_77_0) & r1(all_46_0, all_77_1) &
% 18.63/3.58 | | | | ~ p1(all_77_0)
% 18.63/3.58 | | | |
% 18.63/3.58 | | | | ALPHA: (42) implies:
% 18.63/3.58 | | | | (43) ~ p1(all_77_0)
% 18.63/3.58 | | | | (44) r1(all_46_0, all_77_1)
% 18.63/3.58 | | | | (45) r1(all_77_1, all_77_0)
% 18.63/3.58 | | | | (46) p1(all_77_1)
% 18.63/3.58 | | | |
% 18.63/3.59 | | | | GROUND_INST: instantiating (36) with all_46_0, all_77_1, all_77_0,
% 18.63/3.59 | | | | simplifying with (20), (33), (35), (39), (40), (43), (44),
% 18.63/3.59 | | | | (45), (46) gives:
% 18.63/3.59 | | | | (47) $false
% 18.63/3.59 | | | |
% 18.63/3.59 | | | | CLOSE: (47) is inconsistent.
% 18.63/3.59 | | | |
% 18.63/3.59 | | | Case 2:
% 18.63/3.59 | | | |
% 18.63/3.59 | | | | (48) r1(all_3_2, all_77_1) & ~ p1(all_77_1) & ! [v0: $i] : ! [v1:
% 18.63/3.59 | | | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~
% 18.63/3.59 | | | | r1(all_77_1, v0) | p1(v1))
% 18.63/3.59 | | | |
% 18.63/3.59 | | | | ALPHA: (48) implies:
% 18.63/3.59 | | | | (49) ~ p1(all_77_1)
% 18.63/3.59 | | | | (50) r1(all_3_2, all_77_1)
% 18.63/3.59 | | | | (51) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) |
% 18.63/3.59 | | | | ~ r1(v0, v1) | ~ r1(all_77_1, v0) | p1(v1))
% 18.63/3.59 | | | |
% 18.63/3.59 | | | | GROUND_INST: instantiating (9) with all_77_1, simplifying with (39),
% 18.63/3.59 | | | | (49), (50) gives:
% 18.63/3.59 | | | | (52) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0,
% 18.63/3.59 | | | | v1) & r1(all_77_1, v0) & ~ p1(v1))
% 18.63/3.59 | | | |
% 18.63/3.59 | | | | DELTA: instantiating (52) with fresh symbols all_115_0, all_115_1 gives:
% 18.63/3.59 | | | | (53) $i(all_115_0) & $i(all_115_1) & p1(all_115_1) & r1(all_115_1,
% 18.63/3.59 | | | | all_115_0) & r1(all_77_1, all_115_1) & ~ p1(all_115_0)
% 18.63/3.59 | | | |
% 18.63/3.59 | | | | ALPHA: (53) implies:
% 18.63/3.59 | | | | (54) ~ p1(all_115_0)
% 18.63/3.59 | | | | (55) r1(all_77_1, all_115_1)
% 18.63/3.59 | | | | (56) r1(all_115_1, all_115_0)
% 18.63/3.59 | | | | (57) p1(all_115_1)
% 18.63/3.59 | | | | (58) $i(all_115_1)
% 18.63/3.59 | | | | (59) $i(all_115_0)
% 18.63/3.59 | | | |
% 18.63/3.59 | | | | GROUND_INST: instantiating (51) with all_115_1, all_115_0, simplifying
% 18.63/3.59 | | | | with (54), (55), (56), (57), (58), (59) gives:
% 18.63/3.59 | | | | (60) $false
% 18.63/3.59 | | | |
% 18.63/3.59 | | | | CLOSE: (60) is inconsistent.
% 18.63/3.59 | | | |
% 18.63/3.59 | | | End of split
% 18.63/3.59 | | |
% 18.63/3.59 | | End of split
% 18.63/3.59 | |
% 18.63/3.59 | Case 2:
% 18.63/3.59 | |
% 18.63/3.59 | | (61) ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) |
% 18.63/3.59 | | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 18.63/3.59 | | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0,
% 18.63/3.59 | | v1) | p1(v2)))))
% 18.63/3.59 | |
% 18.63/3.59 | | DELTA: instantiating (61) with fresh symbol all_41_0 gives:
% 18.63/3.59 | | (62) $i(all_41_0) & ((r1(all_3_1, all_41_0) & ~ p1(all_41_0)) |
% 18.63/3.59 | | (r1(all_3_2, all_41_0) & ~ p1(all_41_0) & ! [v0: $i] : ! [v1:
% 18.63/3.59 | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~
% 18.63/3.59 | | r1(all_41_0, v0) | p1(v1))))
% 18.63/3.59 | |
% 18.63/3.59 | | ALPHA: (62) implies:
% 18.63/3.59 | | (63) $i(all_41_0)
% 18.63/3.59 | | (64) (r1(all_3_1, all_41_0) & ~ p1(all_41_0)) | (r1(all_3_2, all_41_0) &
% 18.63/3.59 | | ~ p1(all_41_0) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 18.63/3.59 | | $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_41_0, v0) |
% 18.63/3.59 | | p1(v1)))
% 18.63/3.59 | |
% 18.63/3.59 | | BETA: splitting (64) gives:
% 18.63/3.59 | |
% 18.63/3.59 | | Case 1:
% 18.63/3.59 | | |
% 18.63/3.59 | | | (65) r1(all_3_1, all_41_0) & ~ p1(all_41_0)
% 18.63/3.59 | | |
% 18.63/3.59 | | | ALPHA: (65) implies:
% 18.63/3.59 | | | (66) ~ p1(all_41_0)
% 18.63/3.59 | | | (67) r1(all_3_1, all_41_0)
% 18.63/3.59 | | |
% 18.63/3.59 | | | GROUND_INST: instantiating (10) with all_41_0, simplifying with (63),
% 18.63/3.59 | | | (66), (67) gives:
% 18.63/3.59 | | | (68) $false
% 18.63/3.59 | | |
% 18.63/3.59 | | | CLOSE: (68) is inconsistent.
% 18.63/3.59 | | |
% 18.63/3.59 | | Case 2:
% 18.63/3.59 | | |
% 18.63/3.60 | | | (69) r1(all_3_2, all_41_0) & ~ p1(all_41_0) & ! [v0: $i] : ! [v1:
% 18.63/3.60 | | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~
% 18.63/3.60 | | | r1(all_41_0, v0) | p1(v1))
% 18.63/3.60 | | |
% 18.63/3.60 | | | ALPHA: (69) implies:
% 18.63/3.60 | | | (70) ~ p1(all_41_0)
% 18.63/3.60 | | | (71) r1(all_3_2, all_41_0)
% 18.63/3.60 | | | (72) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) |
% 18.63/3.60 | | | ~ r1(v0, v1) | ~ r1(all_41_0, v0) | p1(v1))
% 18.63/3.60 | | |
% 18.63/3.60 | | | GROUND_INST: instantiating (9) with all_41_0, simplifying with (63), (70),
% 18.63/3.60 | | | (71) gives:
% 18.63/3.60 | | | (73) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0, v1)
% 18.63/3.60 | | | & r1(all_41_0, v0) & ~ p1(v1))
% 18.63/3.60 | | |
% 18.63/3.60 | | | DELTA: instantiating (73) with fresh symbols all_76_0, all_76_1 gives:
% 18.63/3.60 | | | (74) $i(all_76_0) & $i(all_76_1) & p1(all_76_1) & r1(all_76_1,
% 18.63/3.60 | | | all_76_0) & r1(all_41_0, all_76_1) & ~ p1(all_76_0)
% 18.63/3.60 | | |
% 18.63/3.60 | | | ALPHA: (74) implies:
% 18.63/3.60 | | | (75) ~ p1(all_76_0)
% 18.63/3.60 | | | (76) r1(all_41_0, all_76_1)
% 18.63/3.60 | | | (77) r1(all_76_1, all_76_0)
% 18.63/3.60 | | | (78) p1(all_76_1)
% 18.63/3.60 | | | (79) $i(all_76_1)
% 18.63/3.60 | | | (80) $i(all_76_0)
% 18.63/3.60 | | |
% 18.63/3.60 | | | GROUND_INST: instantiating (72) with all_76_1, all_76_0, simplifying with
% 18.63/3.60 | | | (75), (76), (77), (78), (79), (80) gives:
% 18.63/3.60 | | | (81) $false
% 18.63/3.60 | | |
% 18.63/3.60 | | | CLOSE: (81) is inconsistent.
% 18.63/3.60 | | |
% 18.63/3.60 | | End of split
% 18.63/3.60 | |
% 18.63/3.60 | End of split
% 18.63/3.60 |
% 18.63/3.60 End of proof
% 18.63/3.60 % SZS output end Proof for theBenchmark
% 18.63/3.60
% 18.63/3.60 2978ms
%------------------------------------------------------------------------------