TSTP Solution File: SET711+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET711+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 15:26:05 EDT 2023
% Result : Theorem 15.16s 2.82s
% Output : Proof 17.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET711+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n006.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 : Sat Aug 26 13:01:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 ________ _____
% 0.20/0.56 ___ __ \_________(_)________________________________
% 0.20/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.56
% 0.20/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.56 (2023-06-19)
% 0.20/0.56
% 0.20/0.56 (c) Philipp Rümmer, 2009-2023
% 0.20/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.56 Amanda Stjerna.
% 0.20/0.56 Free software under BSD-3-Clause.
% 0.20/0.56
% 0.20/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.56
% 0.20/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.58 Running up to 7 provers in parallel.
% 0.20/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.22/1.13 Prover 1: Preprocessing ...
% 3.22/1.13 Prover 4: Preprocessing ...
% 3.52/1.17 Prover 5: Preprocessing ...
% 3.52/1.17 Prover 2: Preprocessing ...
% 3.52/1.17 Prover 6: Preprocessing ...
% 3.52/1.17 Prover 3: Preprocessing ...
% 3.52/1.17 Prover 0: Preprocessing ...
% 8.53/1.95 Prover 5: Proving ...
% 8.53/1.96 Prover 2: Proving ...
% 8.53/2.01 Prover 6: Proving ...
% 9.72/2.09 Prover 1: Constructing countermodel ...
% 9.72/2.09 Prover 3: Constructing countermodel ...
% 11.78/2.30 Prover 3: gave up
% 11.78/2.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.10/2.37 Prover 7: Preprocessing ...
% 12.99/2.52 Prover 7: Warning: ignoring some quantifiers
% 13.74/2.57 Prover 4: Constructing countermodel ...
% 13.74/2.57 Prover 7: Constructing countermodel ...
% 13.74/2.57 Prover 1: gave up
% 13.74/2.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.74/2.59 Prover 0: Proving ...
% 14.03/2.64 Prover 8: Preprocessing ...
% 15.16/2.82 Prover 0: proved (2231ms)
% 15.16/2.82
% 15.16/2.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.16/2.82
% 15.68/2.84 Prover 5: stopped
% 15.68/2.84 Prover 2: stopped
% 15.68/2.84 Prover 6: stopped
% 15.68/2.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.68/2.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.68/2.86 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.68/2.86 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 15.68/2.86 Prover 4: Found proof (size 63)
% 15.68/2.86 Prover 4: proved (2270ms)
% 15.68/2.86 Prover 7: stopped
% 15.96/2.89 Prover 11: Preprocessing ...
% 15.96/2.90 Prover 10: Preprocessing ...
% 15.96/2.92 Prover 13: Preprocessing ...
% 15.96/2.92 Prover 16: Preprocessing ...
% 15.96/2.94 Prover 8: Warning: ignoring some quantifiers
% 15.96/2.94 Prover 10: stopped
% 16.81/2.98 Prover 8: Constructing countermodel ...
% 16.81/2.99 Prover 16: stopped
% 16.81/2.99 Prover 8: stopped
% 16.81/2.99 Prover 13: stopped
% 16.81/3.01 Prover 11: stopped
% 16.81/3.01
% 16.81/3.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.81/3.01
% 16.81/3.02 % SZS output start Proof for theBenchmark
% 16.81/3.03 Assumptions after simplification:
% 16.81/3.03 ---------------------------------
% 16.81/3.03
% 16.81/3.03 (equal_maps)
% 17.22/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.22/3.06 $i] : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~
% 17.22/3.06 (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ $i(v6) | ~ $i(v5)
% 17.22/3.06 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] :
% 17.22/3.06 ? [v8: any] : ? [v9: any] : (member(v6, v3) = v9 & member(v5, v3) = v8 &
% 17.22/3.06 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & !
% 17.22/3.06 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 17.22/3.06 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1,
% 17.22/3.06 v4, v6) = 0) | ~ (member(v5, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~
% 17.22/3.06 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ?
% 17.22/3.06 [v8: any] : ? [v9: any] : (apply(v0, v4, v5) = v9 & member(v6, v3) = v8 &
% 17.22/3.06 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & !
% 17.22/3.06 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 17.22/3.06 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0,
% 17.22/3.06 v4, v5) = 0) | ~ (member(v6, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~
% 17.22/3.06 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ?
% 17.22/3.06 [v8: any] : ? [v9: any] : (apply(v1, v4, v6) = v9 & member(v5, v3) = v8 &
% 17.22/3.06 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & !
% 17.22/3.06 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 17.22/3.06 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~
% 17.22/3.06 (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) |
% 17.22/3.06 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 17.22/3.06 $i(v0) | ? [v7: any] : ? [v8: any] : (apply(v1, v4, v6) = v8 & apply(v0,
% 17.22/3.06 v4, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1: $i]
% 17.22/3.06 : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (equal_maps(v0, v1,
% 17.22/3.06 v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 17.22/3.06 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 &
% 17.22/3.06 apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 &
% 17.22/3.06 member(v5, v2) = 0 & $i(v7) & $i(v6) & $i(v5)))
% 17.22/3.06
% 17.22/3.06 (injective)
% 17.22/3.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.22/3.07 $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0)
% 17.22/3.07 | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 17.22/3.07 | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 17.22/3.07 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 =
% 17.22/3.07 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 17.22/3.07 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~
% 17.22/3.07 (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3,
% 17.22/3.07 v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 17.22/3.07 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v5) =
% 17.22/3.07 v8 & member(v5, v2) = v7 & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 =
% 17.22/3.07 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.22/3.07 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) =
% 17.22/3.07 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ~ $i(v5) | ~
% 17.22/3.07 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 17.22/3.07 [v7: any] : ? [v8: any] : (apply(v0, v4, v5) = v8 & member(v5, v2) = v7 &
% 17.22/3.07 member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & !
% 17.22/3.07 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 17.22/3.07 : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~
% 17.22/3.07 (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 17.22/3.07 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 17.22/3.07 (apply(v0, v4, v5) = v7 & apply(v0, v3, v5) = v6 & ( ~ (v7 = 0) | ~ (v6 =
% 17.22/3.07 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 17.22/3.07 0 | ~ (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 17.22/3.07 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0
% 17.22/3.07 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 &
% 17.22/3.07 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4)))
% 17.22/3.07
% 17.22/3.07 (inverse_predicate)
% 17.22/3.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.22/3.07 $i] : ! [v6: any] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~
% 17.22/3.07 (apply(v1, v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 17.22/3.07 ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9: any] :
% 17.22/3.07 (apply(v0, v5, v4) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~
% 17.22/3.07 (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 =
% 17.22/3.07 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 17.22/3.07 [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ (inverse_predicate(v0, v1, v2, v3)
% 17.22/3.07 = 0) | ~ (apply(v0, v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 17.22/3.07 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9:
% 17.22/3.07 any] : (apply(v1, v4, v5) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7
% 17.22/3.07 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9
% 17.22/3.07 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 17.22/3.07 ! [v4: int] : (v4 = 0 | ~ (inverse_predicate(v0, v1, v2, v3) = v4) | ~
% 17.22/3.07 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ?
% 17.22/3.07 [v7: any] : ? [v8: any] : (apply(v1, v5, v6) = v7 & apply(v0, v6, v5) = v8
% 17.22/3.07 & member(v6, v3) = 0 & member(v5, v2) = 0 & $i(v6) & $i(v5) & ( ~ (v8 = 0)
% 17.22/3.07 | ~ (v7 = 0)) & (v8 = 0 | v7 = 0)))
% 17.22/3.07
% 17.22/3.07 (one_to_one)
% 17.22/3.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 17.22/3.07 (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 17.22/3.07 any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 & injective(v0, v1, v2)
% 17.22/3.07 = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.22/3.07 $i] : ! [v3: any] : ( ~ (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~
% 17.22/3.07 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) =
% 17.22/3.07 v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & !
% 17.22/3.07 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (injective(v0, v1,
% 17.22/3.07 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 17.22/3.07 any] : (one_to_one(v0, v1, v2) = v4 & surjective(v0, v1, v2) = v5 & ( ~
% 17.22/3.07 (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.22/3.07 $i] : ( ~ (one_to_one(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.22/3.07 (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0: $i] : !
% 17.22/3.07 [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ $i(v2) | ~
% 17.22/3.07 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) =
% 17.22/3.07 v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] :
% 17.22/3.07 ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~
% 17.22/3.07 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) =
% 17.22/3.08 v4 & surjective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 17.22/3.08
% 17.22/3.08 (thII03a)
% 17.22/3.08 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 17.22/3.08 int] : ( ~ (v5 = 0) & inverse_predicate(v2, v0, v3, v4) = 0 &
% 17.22/3.08 inverse_predicate(v1, v0, v3, v4) = 0 & one_to_one(v0, v3, v4) = 0 &
% 17.22/3.08 equal_maps(v1, v2, v4, v3) = v5 & maps(v0, v3, v4) = 0 & $i(v4) & $i(v3) &
% 17.22/3.08 $i(v2) & $i(v1) & $i(v0))
% 17.22/3.08
% 17.22/3.08 (function-axioms)
% 17.22/3.08 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 17.22/3.08 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 17.22/3.08 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 17.22/3.08 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 17.22/3.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.22/3.08 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 17.22/3.08 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 17.22/3.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.22/3.08 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 17.22/3.08 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 17.22/3.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.22/3.08 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 17.22/3.08 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 17.22/3.08 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 17.22/3.08 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 17.22/3.08 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 17.22/3.08 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.22/3.08 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 17.22/3.08 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 17.22/3.08 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.22/3.08 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 17.22/3.08 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 17.22/3.08 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 17.22/3.08 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.22/3.08 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 17.22/3.08 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.22/3.08 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 17.22/3.08 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 17.22/3.08 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 17.22/3.08 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 17.22/3.08 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.22/3.08 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 17.22/3.08 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.22/3.08 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 17.22/3.08 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 17.22/3.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.22/3.08 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 17.22/3.08 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 17.22/3.08 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 17.22/3.08 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.22/3.08 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 17.22/3.08 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.22/3.08 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 17.22/3.08 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 17.22/3.08 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 17.22/3.09 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.22/3.09 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 17.22/3.09 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.22/3.09 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 17.22/3.09 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 17.22/3.09 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 17.22/3.09 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 17.22/3.09 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 17.22/3.09 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 17.22/3.09 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.22/3.09 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 17.22/3.09 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 17.22/3.09 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.22/3.09 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 17.22/3.09 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 17.22/3.09 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 17.22/3.09 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 17.22/3.09 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 17.22/3.09 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 17.22/3.09 (power_set(v2) = v0))
% 17.22/3.09
% 17.22/3.09 Further assumptions not needed in the proof:
% 17.22/3.09 --------------------------------------------
% 17.22/3.09 compose_function, compose_predicate, decreasing_function, difference, empty_set,
% 17.22/3.09 equal_set, identity, image2, image3, increasing_function, intersection,
% 17.22/3.09 inverse_function, inverse_image2, inverse_image3, isomorphism, maps, power_set,
% 17.22/3.09 product, singleton, subset, sum, surjective, union, unordered_pair
% 17.22/3.09
% 17.22/3.09 Those formulas are unsatisfiable:
% 17.22/3.09 ---------------------------------
% 17.22/3.09
% 17.22/3.09 Begin of proof
% 17.22/3.09 |
% 17.22/3.09 | ALPHA: (equal_maps) implies:
% 17.22/3.09 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 17.22/3.09 | (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2)
% 17.22/3.09 | | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (
% 17.22/3.09 | ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 &
% 17.22/3.09 | member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0 &
% 17.22/3.09 | $i(v7) & $i(v6) & $i(v5)))
% 17.22/3.09 |
% 17.22/3.09 | ALPHA: (injective) implies:
% 17.22/3.09 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.22/3.09 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5,
% 17.22/3.09 | v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~
% 17.22/3.09 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.22/3.09 | ? [v6: any] : ? [v7: any] : (apply(v0, v4, v5) = v7 & apply(v0, v3,
% 17.22/3.09 | v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 17.22/3.09 |
% 17.22/3.09 | ALPHA: (one_to_one) implies:
% 17.22/3.09 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (one_to_one(v0, v1, v2) =
% 17.22/3.09 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (surjective(v0, v1, v2) =
% 17.22/3.09 | 0 & injective(v0, v1, v2) = 0))
% 17.22/3.09 |
% 17.22/3.09 | ALPHA: (inverse_predicate) implies:
% 17.22/3.09 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.22/3.09 | ! [v5: $i] : ! [v6: any] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0)
% 17.22/3.09 | | ~ (apply(v0, v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 17.22/3.09 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : ?
% 17.22/3.09 | [v9: any] : (apply(v1, v4, v5) = v9 & member(v5, v3) = v8 &
% 17.22/3.09 | member(v4, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) |
% 17.22/3.09 | v6 = 0) & ( ~ (v6 = 0) | v9 = 0)))))
% 17.22/3.09 |
% 17.22/3.09 | ALPHA: (function-axioms) implies:
% 17.22/3.09 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.22/3.09 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 17.22/3.09 | = v0))
% 17.22/3.09 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.22/3.09 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 17.22/3.09 | (apply(v4, v3, v2) = v0))
% 17.22/3.09 |
% 17.22/3.09 | DELTA: instantiating (thII03a) with fresh symbols all_32_0, all_32_1,
% 17.22/3.09 | all_32_2, all_32_3, all_32_4, all_32_5 gives:
% 17.22/3.09 | (7) ~ (all_32_0 = 0) & inverse_predicate(all_32_3, all_32_5, all_32_2,
% 17.22/3.09 | all_32_1) = 0 & inverse_predicate(all_32_4, all_32_5, all_32_2,
% 17.22/3.10 | all_32_1) = 0 & one_to_one(all_32_5, all_32_2, all_32_1) = 0 &
% 17.22/3.10 | equal_maps(all_32_4, all_32_3, all_32_1, all_32_2) = all_32_0 &
% 17.22/3.10 | maps(all_32_5, all_32_2, all_32_1) = 0 & $i(all_32_1) & $i(all_32_2) &
% 17.22/3.10 | $i(all_32_3) & $i(all_32_4) & $i(all_32_5)
% 17.22/3.10 |
% 17.22/3.10 | ALPHA: (7) implies:
% 17.22/3.10 | (8) ~ (all_32_0 = 0)
% 17.22/3.10 | (9) $i(all_32_5)
% 17.22/3.10 | (10) $i(all_32_4)
% 17.22/3.10 | (11) $i(all_32_3)
% 17.22/3.10 | (12) $i(all_32_2)
% 17.22/3.10 | (13) $i(all_32_1)
% 17.22/3.10 | (14) equal_maps(all_32_4, all_32_3, all_32_1, all_32_2) = all_32_0
% 17.22/3.10 | (15) one_to_one(all_32_5, all_32_2, all_32_1) = 0
% 17.22/3.10 | (16) inverse_predicate(all_32_4, all_32_5, all_32_2, all_32_1) = 0
% 17.22/3.10 | (17) inverse_predicate(all_32_3, all_32_5, all_32_2, all_32_1) = 0
% 17.22/3.10 |
% 17.22/3.10 | GROUND_INST: instantiating (1) with all_32_4, all_32_3, all_32_1, all_32_2,
% 17.22/3.10 | all_32_0, simplifying with (10), (11), (12), (13), (14) gives:
% 17.22/3.10 | (18) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1)
% 17.22/3.10 | & apply(all_32_3, v0, v2) = 0 & apply(all_32_4, v0, v1) = 0 &
% 17.22/3.10 | member(v2, all_32_2) = 0 & member(v1, all_32_2) = 0 & member(v0,
% 17.22/3.10 | all_32_1) = 0 & $i(v2) & $i(v1) & $i(v0))
% 17.22/3.10 |
% 17.22/3.10 | GROUND_INST: instantiating (3) with all_32_5, all_32_2, all_32_1, simplifying
% 17.22/3.10 | with (9), (12), (13), (15) gives:
% 17.22/3.10 | (19) surjective(all_32_5, all_32_2, all_32_1) = 0 & injective(all_32_5,
% 17.22/3.10 | all_32_2, all_32_1) = 0
% 17.22/3.10 |
% 17.22/3.10 | ALPHA: (19) implies:
% 17.22/3.10 | (20) injective(all_32_5, all_32_2, all_32_1) = 0
% 17.22/3.10 |
% 17.22/3.10 | BETA: splitting (18) gives:
% 17.22/3.10 |
% 17.22/3.10 | Case 1:
% 17.22/3.10 | |
% 17.22/3.10 | | (21) all_32_0 = 0
% 17.22/3.10 | |
% 17.22/3.10 | | REDUCE: (8), (21) imply:
% 17.22/3.10 | | (22) $false
% 17.22/3.10 | |
% 17.22/3.10 | | CLOSE: (22) is inconsistent.
% 17.22/3.10 | |
% 17.22/3.10 | Case 2:
% 17.22/3.10 | |
% 17.22/3.10 | | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) &
% 17.22/3.10 | | apply(all_32_3, v0, v2) = 0 & apply(all_32_4, v0, v1) = 0 &
% 17.22/3.10 | | member(v2, all_32_2) = 0 & member(v1, all_32_2) = 0 & member(v0,
% 17.22/3.10 | | all_32_1) = 0 & $i(v2) & $i(v1) & $i(v0))
% 17.22/3.10 | |
% 17.22/3.10 | | DELTA: instantiating (23) with fresh symbols all_44_0, all_44_1, all_44_2
% 17.22/3.10 | | gives:
% 17.22/3.10 | | (24) ~ (all_44_0 = all_44_1) & apply(all_32_3, all_44_2, all_44_0) = 0 &
% 17.22/3.10 | | apply(all_32_4, all_44_2, all_44_1) = 0 & member(all_44_0, all_32_2)
% 17.22/3.10 | | = 0 & member(all_44_1, all_32_2) = 0 & member(all_44_2, all_32_1) =
% 17.22/3.10 | | 0 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2)
% 17.22/3.10 | |
% 17.22/3.10 | | ALPHA: (24) implies:
% 17.22/3.10 | | (25) ~ (all_44_0 = all_44_1)
% 17.22/3.10 | | (26) $i(all_44_2)
% 17.22/3.10 | | (27) $i(all_44_1)
% 17.22/3.11 | | (28) $i(all_44_0)
% 17.22/3.11 | | (29) member(all_44_2, all_32_1) = 0
% 17.22/3.11 | | (30) member(all_44_1, all_32_2) = 0
% 17.22/3.11 | | (31) member(all_44_0, all_32_2) = 0
% 17.22/3.11 | | (32) apply(all_32_4, all_44_2, all_44_1) = 0
% 17.22/3.11 | | (33) apply(all_32_3, all_44_2, all_44_0) = 0
% 17.22/3.11 | |
% 17.22/3.11 | | GROUND_INST: instantiating (4) with all_32_4, all_32_5, all_32_2, all_32_1,
% 17.22/3.11 | | all_44_1, all_44_2, 0, simplifying with (9), (10), (12), (13),
% 17.22/3.11 | | (16), (26), (27), (32) gives:
% 17.22/3.11 | | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_5,
% 17.22/3.11 | | all_44_1, all_44_2) = v2 & member(all_44_1, all_32_2) = v0 &
% 17.22/3.11 | | member(all_44_2, all_32_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2
% 17.22/3.11 | | = 0))
% 17.22/3.11 | |
% 17.22/3.11 | | GROUND_INST: instantiating (4) with all_32_3, all_32_5, all_32_2, all_32_1,
% 17.22/3.11 | | all_44_0, all_44_2, 0, simplifying with (9), (11), (12), (13),
% 17.22/3.11 | | (17), (26), (28), (33) gives:
% 17.22/3.11 | | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_5,
% 17.22/3.11 | | all_44_0, all_44_2) = v2 & member(all_44_0, all_32_2) = v0 &
% 17.22/3.11 | | member(all_44_2, all_32_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2
% 17.22/3.11 | | = 0))
% 17.22/3.11 | |
% 17.22/3.11 | | GROUND_INST: instantiating (2) with all_32_5, all_32_2, all_32_1, all_44_1,
% 17.22/3.11 | | all_44_0, all_44_2, simplifying with (9), (12), (13), (20),
% 17.22/3.11 | | (26), (27), (28), (29), (30), (31) gives:
% 17.22/3.11 | | (36) all_44_0 = all_44_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_5,
% 17.22/3.11 | | all_44_0, all_44_2) = v1 & apply(all_32_5, all_44_1, all_44_2) =
% 17.22/3.11 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 17.22/3.11 | |
% 17.22/3.11 | | GROUND_INST: instantiating (2) with all_32_5, all_32_2, all_32_1, all_44_0,
% 17.22/3.11 | | all_44_1, all_44_2, simplifying with (9), (12), (13), (20),
% 17.22/3.11 | | (26), (27), (28), (29), (30), (31) gives:
% 17.22/3.11 | | (37) all_44_0 = all_44_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_5,
% 17.22/3.11 | | all_44_0, all_44_2) = v0 & apply(all_32_5, all_44_1, all_44_2) =
% 17.22/3.11 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 17.22/3.11 | |
% 17.22/3.11 | | DELTA: instantiating (35) with fresh symbols all_57_0, all_57_1, all_57_2
% 17.22/3.11 | | gives:
% 17.22/3.11 | | (38) apply(all_32_5, all_44_0, all_44_2) = all_57_0 & member(all_44_0,
% 17.22/3.11 | | all_32_2) = all_57_2 & member(all_44_2, all_32_1) = all_57_1 & ( ~
% 17.22/3.11 | | (all_57_1 = 0) | ~ (all_57_2 = 0) | all_57_0 = 0)
% 17.22/3.11 | |
% 17.22/3.11 | | ALPHA: (38) implies:
% 17.22/3.11 | | (39) member(all_44_2, all_32_1) = all_57_1
% 17.22/3.11 | | (40) member(all_44_0, all_32_2) = all_57_2
% 17.22/3.11 | | (41) apply(all_32_5, all_44_0, all_44_2) = all_57_0
% 17.22/3.11 | | (42) ~ (all_57_1 = 0) | ~ (all_57_2 = 0) | all_57_0 = 0
% 17.22/3.11 | |
% 17.22/3.11 | | DELTA: instantiating (34) with fresh symbols all_59_0, all_59_1, all_59_2
% 17.22/3.11 | | gives:
% 17.22/3.12 | | (43) apply(all_32_5, all_44_1, all_44_2) = all_59_0 & member(all_44_1,
% 17.22/3.12 | | all_32_2) = all_59_2 & member(all_44_2, all_32_1) = all_59_1 & ( ~
% 17.22/3.12 | | (all_59_1 = 0) | ~ (all_59_2 = 0) | all_59_0 = 0)
% 17.22/3.12 | |
% 17.22/3.12 | | ALPHA: (43) implies:
% 17.22/3.12 | | (44) member(all_44_2, all_32_1) = all_59_1
% 17.22/3.12 | | (45) member(all_44_1, all_32_2) = all_59_2
% 17.22/3.12 | | (46) apply(all_32_5, all_44_1, all_44_2) = all_59_0
% 17.22/3.12 | | (47) ~ (all_59_1 = 0) | ~ (all_59_2 = 0) | all_59_0 = 0
% 17.22/3.12 | |
% 17.22/3.12 | | GROUND_INST: instantiating (5) with 0, all_59_1, all_32_1, all_44_2,
% 17.22/3.12 | | simplifying with (29), (44) gives:
% 17.22/3.12 | | (48) all_59_1 = 0
% 17.22/3.12 | |
% 17.22/3.12 | | GROUND_INST: instantiating (5) with all_57_1, all_59_1, all_32_1, all_44_2,
% 17.22/3.12 | | simplifying with (39), (44) gives:
% 17.22/3.12 | | (49) all_59_1 = all_57_1
% 17.22/3.12 | |
% 17.22/3.12 | | GROUND_INST: instantiating (5) with 0, all_59_2, all_32_2, all_44_1,
% 17.22/3.12 | | simplifying with (30), (45) gives:
% 17.22/3.12 | | (50) all_59_2 = 0
% 17.22/3.12 | |
% 17.22/3.12 | | GROUND_INST: instantiating (5) with 0, all_57_2, all_32_2, all_44_0,
% 17.22/3.12 | | simplifying with (31), (40) gives:
% 17.22/3.12 | | (51) all_57_2 = 0
% 17.22/3.12 | |
% 17.22/3.12 | | COMBINE_EQS: (48), (49) imply:
% 17.22/3.12 | | (52) all_57_1 = 0
% 17.22/3.12 | |
% 17.22/3.12 | | BETA: splitting (47) gives:
% 17.22/3.12 | |
% 17.22/3.12 | | Case 1:
% 17.22/3.12 | | |
% 17.22/3.12 | | | (53) ~ (all_59_1 = 0)
% 17.22/3.12 | | |
% 17.22/3.12 | | | REDUCE: (48), (53) imply:
% 17.22/3.12 | | | (54) $false
% 17.22/3.12 | | |
% 17.22/3.12 | | | CLOSE: (54) is inconsistent.
% 17.22/3.12 | | |
% 17.22/3.12 | | Case 2:
% 17.22/3.12 | | |
% 17.22/3.12 | | | (55) ~ (all_59_2 = 0) | all_59_0 = 0
% 17.22/3.12 | | |
% 17.22/3.12 | | | BETA: splitting (55) gives:
% 17.22/3.12 | | |
% 17.22/3.12 | | | Case 1:
% 17.22/3.12 | | | |
% 17.54/3.12 | | | | (56) ~ (all_59_2 = 0)
% 17.54/3.12 | | | |
% 17.54/3.12 | | | | REDUCE: (50), (56) imply:
% 17.54/3.12 | | | | (57) $false
% 17.54/3.12 | | | |
% 17.54/3.12 | | | | CLOSE: (57) is inconsistent.
% 17.54/3.12 | | | |
% 17.54/3.12 | | | Case 2:
% 17.54/3.12 | | | |
% 17.54/3.12 | | | | (58) all_59_0 = 0
% 17.54/3.12 | | | |
% 17.54/3.12 | | | | REDUCE: (46), (58) imply:
% 17.54/3.12 | | | | (59) apply(all_32_5, all_44_1, all_44_2) = 0
% 17.54/3.12 | | | |
% 17.54/3.12 | | | | BETA: splitting (37) gives:
% 17.54/3.12 | | | |
% 17.54/3.12 | | | | Case 1:
% 17.54/3.12 | | | | |
% 17.54/3.12 | | | | | (60) all_44_0 = all_44_1
% 17.54/3.12 | | | | |
% 17.54/3.12 | | | | | REDUCE: (25), (60) imply:
% 17.54/3.12 | | | | | (61) $false
% 17.54/3.12 | | | | |
% 17.54/3.12 | | | | | CLOSE: (61) is inconsistent.
% 17.54/3.12 | | | | |
% 17.54/3.12 | | | | Case 2:
% 17.54/3.12 | | | | |
% 17.54/3.12 | | | | | (62) ? [v0: any] : ? [v1: any] : (apply(all_32_5, all_44_0,
% 17.54/3.12 | | | | | all_44_2) = v0 & apply(all_32_5, all_44_1, all_44_2) = v1
% 17.54/3.12 | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 17.54/3.12 | | | | |
% 17.54/3.12 | | | | | DELTA: instantiating (62) with fresh symbols all_77_0, all_77_1 gives:
% 17.54/3.12 | | | | | (63) apply(all_32_5, all_44_0, all_44_2) = all_77_1 &
% 17.54/3.12 | | | | | apply(all_32_5, all_44_1, all_44_2) = all_77_0 & ( ~ (all_77_0
% 17.54/3.12 | | | | | = 0) | ~ (all_77_1 = 0))
% 17.54/3.12 | | | | |
% 17.54/3.12 | | | | | ALPHA: (63) implies:
% 17.54/3.12 | | | | | (64) apply(all_32_5, all_44_1, all_44_2) = all_77_0
% 17.54/3.12 | | | | |
% 17.54/3.12 | | | | | BETA: splitting (42) gives:
% 17.54/3.12 | | | | |
% 17.54/3.12 | | | | | Case 1:
% 17.54/3.12 | | | | | |
% 17.54/3.12 | | | | | | (65) ~ (all_57_1 = 0)
% 17.54/3.12 | | | | | |
% 17.54/3.12 | | | | | | REDUCE: (52), (65) imply:
% 17.54/3.12 | | | | | | (66) $false
% 17.54/3.12 | | | | | |
% 17.54/3.12 | | | | | | CLOSE: (66) is inconsistent.
% 17.54/3.12 | | | | | |
% 17.54/3.12 | | | | | Case 2:
% 17.54/3.12 | | | | | |
% 17.54/3.12 | | | | | | (67) ~ (all_57_2 = 0) | all_57_0 = 0
% 17.54/3.12 | | | | | |
% 17.54/3.12 | | | | | | BETA: splitting (67) gives:
% 17.54/3.12 | | | | | |
% 17.54/3.12 | | | | | | Case 1:
% 17.54/3.12 | | | | | | |
% 17.54/3.12 | | | | | | | (68) ~ (all_57_2 = 0)
% 17.54/3.12 | | | | | | |
% 17.54/3.12 | | | | | | | REDUCE: (51), (68) imply:
% 17.54/3.12 | | | | | | | (69) $false
% 17.54/3.12 | | | | | | |
% 17.54/3.12 | | | | | | | CLOSE: (69) is inconsistent.
% 17.54/3.12 | | | | | | |
% 17.54/3.12 | | | | | | Case 2:
% 17.54/3.12 | | | | | | |
% 17.54/3.12 | | | | | | | (70) all_57_0 = 0
% 17.54/3.12 | | | | | | |
% 17.54/3.12 | | | | | | | REDUCE: (41), (70) imply:
% 17.54/3.12 | | | | | | | (71) apply(all_32_5, all_44_0, all_44_2) = 0
% 17.54/3.12 | | | | | | |
% 17.54/3.12 | | | | | | | BETA: splitting (36) gives:
% 17.54/3.12 | | | | | | |
% 17.54/3.12 | | | | | | | Case 1:
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | (72) all_44_0 = all_44_1
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | REDUCE: (25), (72) imply:
% 17.54/3.12 | | | | | | | | (73) $false
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | CLOSE: (73) is inconsistent.
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | Case 2:
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | (74) ? [v0: any] : ? [v1: any] : (apply(all_32_5, all_44_0,
% 17.54/3.12 | | | | | | | | all_44_2) = v1 & apply(all_32_5, all_44_1, all_44_2)
% 17.54/3.12 | | | | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | DELTA: instantiating (74) with fresh symbols all_91_0, all_91_1
% 17.54/3.12 | | | | | | | | gives:
% 17.54/3.12 | | | | | | | | (75) apply(all_32_5, all_44_0, all_44_2) = all_91_0 &
% 17.54/3.12 | | | | | | | | apply(all_32_5, all_44_1, all_44_2) = all_91_1 & ( ~
% 17.54/3.12 | | | | | | | | (all_91_0 = 0) | ~ (all_91_1 = 0))
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | ALPHA: (75) implies:
% 17.54/3.12 | | | | | | | | (76) apply(all_32_5, all_44_1, all_44_2) = all_91_1
% 17.54/3.12 | | | | | | | | (77) apply(all_32_5, all_44_0, all_44_2) = all_91_0
% 17.54/3.12 | | | | | | | | (78) ~ (all_91_0 = 0) | ~ (all_91_1 = 0)
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | GROUND_INST: instantiating (6) with all_77_0, all_91_1,
% 17.54/3.12 | | | | | | | | all_44_2, all_44_1, all_32_5, simplifying with
% 17.54/3.12 | | | | | | | | (64), (76) gives:
% 17.54/3.12 | | | | | | | | (79) all_91_1 = all_77_0
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | GROUND_INST: instantiating (6) with 0, all_91_1, all_44_2,
% 17.54/3.12 | | | | | | | | all_44_1, all_32_5, simplifying with (59), (76)
% 17.54/3.12 | | | | | | | | gives:
% 17.54/3.12 | | | | | | | | (80) all_91_1 = 0
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | GROUND_INST: instantiating (6) with 0, all_91_0, all_44_2,
% 17.54/3.12 | | | | | | | | all_44_0, all_32_5, simplifying with (71), (77)
% 17.54/3.12 | | | | | | | | gives:
% 17.54/3.12 | | | | | | | | (81) all_91_0 = 0
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | COMBINE_EQS: (79), (80) imply:
% 17.54/3.12 | | | | | | | | (82) all_77_0 = 0
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | BETA: splitting (78) gives:
% 17.54/3.12 | | | | | | | |
% 17.54/3.12 | | | | | | | | Case 1:
% 17.54/3.12 | | | | | | | | |
% 17.54/3.13 | | | | | | | | | (83) ~ (all_91_0 = 0)
% 17.54/3.13 | | | | | | | | |
% 17.54/3.13 | | | | | | | | | REDUCE: (81), (83) imply:
% 17.54/3.13 | | | | | | | | | (84) $false
% 17.54/3.13 | | | | | | | | |
% 17.54/3.13 | | | | | | | | | CLOSE: (84) is inconsistent.
% 17.54/3.13 | | | | | | | | |
% 17.54/3.13 | | | | | | | | Case 2:
% 17.54/3.13 | | | | | | | | |
% 17.54/3.13 | | | | | | | | | (85) ~ (all_91_1 = 0)
% 17.54/3.13 | | | | | | | | |
% 17.54/3.13 | | | | | | | | | REDUCE: (80), (85) imply:
% 17.54/3.13 | | | | | | | | | (86) $false
% 17.54/3.13 | | | | | | | | |
% 17.54/3.13 | | | | | | | | | CLOSE: (86) is inconsistent.
% 17.54/3.13 | | | | | | | | |
% 17.54/3.13 | | | | | | | | End of split
% 17.54/3.13 | | | | | | | |
% 17.54/3.13 | | | | | | | End of split
% 17.54/3.13 | | | | | | |
% 17.54/3.13 | | | | | | End of split
% 17.54/3.13 | | | | | |
% 17.54/3.13 | | | | | End of split
% 17.54/3.13 | | | | |
% 17.54/3.13 | | | | End of split
% 17.54/3.13 | | | |
% 17.54/3.13 | | | End of split
% 17.54/3.13 | | |
% 17.54/3.13 | | End of split
% 17.54/3.13 | |
% 17.54/3.13 | End of split
% 17.54/3.13 |
% 17.54/3.13 End of proof
% 17.54/3.13 % SZS output end Proof for theBenchmark
% 17.54/3.13
% 17.54/3.13 2560ms
%------------------------------------------------------------------------------