TSTP Solution File: SET713+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET713+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 : n015.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 15:26:06 EDT 2023
% Result : Theorem 24.89s 4.15s
% Output : Proof 25.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET713+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.35 % Computer : n015.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sat Aug 26 09:43:22 EDT 2023
% 0.20/0.35 % 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 ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 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 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 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
% 4.03/1.29 Prover 4: Preprocessing ...
% 4.03/1.29 Prover 1: Preprocessing ...
% 4.52/1.34 Prover 2: Preprocessing ...
% 4.52/1.34 Prover 3: Preprocessing ...
% 4.52/1.34 Prover 6: Preprocessing ...
% 4.52/1.34 Prover 5: Preprocessing ...
% 4.52/1.34 Prover 0: Preprocessing ...
% 12.49/2.48 Prover 5: Proving ...
% 12.84/2.51 Prover 2: Proving ...
% 13.22/2.59 Prover 1: Constructing countermodel ...
% 13.22/2.60 Prover 6: Proving ...
% 13.97/2.66 Prover 3: Constructing countermodel ...
% 13.97/2.72 Prover 3: gave up
% 13.97/2.73 Prover 1: gave up
% 13.97/2.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.97/2.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.42/2.85 Prover 8: Preprocessing ...
% 15.42/2.85 Prover 7: Preprocessing ...
% 16.94/3.07 Prover 7: Warning: ignoring some quantifiers
% 17.35/3.12 Prover 7: Constructing countermodel ...
% 17.65/3.19 Prover 4: Constructing countermodel ...
% 18.25/3.27 Prover 8: Warning: ignoring some quantifiers
% 18.62/3.34 Prover 8: Constructing countermodel ...
% 19.81/3.49 Prover 0: Proving ...
% 20.44/3.54 Prover 8: gave up
% 20.44/3.54 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 20.44/3.59 Prover 9: Preprocessing ...
% 24.47/4.12 Prover 4: Found proof (size 100)
% 24.47/4.12 Prover 4: proved (3480ms)
% 24.47/4.12 Prover 7: stopped
% 24.47/4.12 Prover 6: stopped
% 24.47/4.12 Prover 5: stopped
% 24.47/4.12 Prover 2: stopped
% 24.47/4.13 Prover 9: Constructing countermodel ...
% 24.47/4.14 Prover 0: stopped
% 24.89/4.14 Prover 9: stopped
% 24.89/4.15
% 24.89/4.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.89/4.15
% 24.96/4.16 % SZS output start Proof for theBenchmark
% 24.96/4.17 Assumptions after simplification:
% 24.96/4.17 ---------------------------------
% 24.96/4.17
% 24.96/4.17 (injective)
% 25.23/4.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 25.23/4.23 $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0)
% 25.23/4.23 | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 25.23/4.23 | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 25.23/4.23 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 =
% 25.23/4.23 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 25.23/4.23 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~
% 25.23/4.23 (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3,
% 25.23/4.23 v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 25.23/4.23 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v5) =
% 25.23/4.23 v8 & member(v5, v2) = v7 & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 =
% 25.23/4.23 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 25.23/4.23 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) =
% 25.23/4.23 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ~ $i(v5) | ~
% 25.23/4.23 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 25.23/4.23 [v7: any] : ? [v8: any] : (apply(v0, v4, v5) = v8 & member(v5, v2) = v7 &
% 25.23/4.23 member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & !
% 25.23/4.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 25.23/4.23 : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~
% 25.23/4.24 (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 25.23/4.24 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 25.23/4.24 (apply(v0, v4, v5) = v7 & apply(v0, v3, v5) = v6 & ( ~ (v7 = 0) | ~ (v6 =
% 25.23/4.24 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 25.23/4.24 0 | ~ (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 25.23/4.24 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0
% 25.23/4.24 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 &
% 25.23/4.24 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4)))
% 25.23/4.24
% 25.23/4.24 (inverse_function)
% 25.23/4.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 25.23/4.24 $i] : ! [v6: any] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5,
% 25.23/4.24 v4, v3) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 25.23/4.24 $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) =
% 25.23/4.24 v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 =
% 25.23/4.24 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0)))))
% 25.23/4.24
% 25.23/4.24 (maps)
% 25.45/4.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 25.45/4.26 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~
% 25.45/4.26 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 25.45/4.26 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 25.45/4.26 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 =
% 25.45/4.26 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 25.45/4.26 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0,
% 25.45/4.26 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~
% 25.45/4.26 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 25.45/4.26 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5,
% 25.45/4.26 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 =
% 25.45/4.26 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 25.45/4.26 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0,
% 25.45/4.26 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 25.45/4.26 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 25.45/4.26 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1)
% 25.45/4.26 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1:
% 25.45/4.26 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 25.45/4.26 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) |
% 25.45/4.26 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 25.45/4.26 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 &
% 25.45/4.26 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : !
% 25.45/4.26 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) |
% 25.45/4.26 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 25.45/4.26 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int]
% 25.45/4.26 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13
% 25.45/4.26 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) =
% 25.45/4.26 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2)
% 25.45/4.26 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) |
% 25.45/4.26 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 =
% 25.45/4.26 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4,
% 25.45/4.26 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5,
% 25.45/4.26 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 25.45/4.26 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0)
% 25.45/4.26 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0,
% 25.45/4.26 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4)))
% 25.45/4.26
% 25.45/4.26 (one_to_one)
% 25.45/4.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 25.45/4.27 (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 25.45/4.27 any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 & injective(v0, v1, v2)
% 25.45/4.27 = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 25.45/4.27 $i] : ! [v3: any] : ( ~ (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~
% 25.45/4.27 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) =
% 25.45/4.27 v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & !
% 25.45/4.27 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (injective(v0, v1,
% 25.45/4.27 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 25.45/4.27 any] : (one_to_one(v0, v1, v2) = v4 & surjective(v0, v1, v2) = v5 & ( ~
% 25.45/4.27 (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 25.45/4.27 $i] : ( ~ (one_to_one(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 25.45/4.27 (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0: $i] : !
% 25.45/4.27 [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ $i(v2) | ~
% 25.45/4.27 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) =
% 25.45/4.27 v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] :
% 25.45/4.27 ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~
% 25.45/4.27 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) =
% 25.45/4.27 v4 & surjective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 25.45/4.27
% 25.45/4.27 (surjective)
% 25.45/4.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 25.45/4.27 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 25.45/4.27 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4)
% 25.45/4.27 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))
% 25.45/4.27 & ! [v5: $i] : ( ~ (member(v5, v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~
% 25.45/4.27 (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0: $i] : ! [v1: $i] : !
% 25.45/4.27 [v2: $i] : ! [v3: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2)
% 25.45/4.27 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 25.45/4.27 (apply(v0, v4, v3) = 0 & member(v4, v1) = 0 & $i(v4)))
% 25.45/4.27
% 25.45/4.27 (thII04)
% 25.45/4.27 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 25.45/4.27 = 0) & inverse_function(v0, v1, v2) = v3 & one_to_one(v3, v2, v1) = v4 &
% 25.45/4.27 one_to_one(v0, v1, v2) = 0 & maps(v0, v1, v2) = 0 & $i(v3) & $i(v2) & $i(v1)
% 25.45/4.27 & $i(v0))
% 25.45/4.27
% 25.45/4.27 (function-axioms)
% 25.45/4.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 25.45/4.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 25.45/4.29 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 25.45/4.29 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 25.45/4.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 25.45/4.29 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 25.45/4.29 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 25.45/4.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 25.45/4.29 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 25.45/4.29 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 25.45/4.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 25.45/4.29 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 25.45/4.29 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 25.45/4.29 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 25.45/4.29 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 25.45/4.29 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 25.45/4.29 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 25.45/4.29 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 25.45/4.29 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 25.45/4.29 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 25.45/4.29 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 25.45/4.29 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 25.45/4.29 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 25.45/4.29 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 25.45/4.29 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 25.45/4.29 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 25.45/4.29 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 25.45/4.29 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 25.45/4.29 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 25.45/4.29 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 25.45/4.29 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 25.45/4.29 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 25.45/4.29 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 25.45/4.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 25.45/4.29 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 25.45/4.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 25.45/4.29 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 25.45/4.29 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 25.45/4.29 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 25.45/4.29 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 25.45/4.29 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 25.45/4.29 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 25.45/4.29 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 25.45/4.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 25.45/4.30 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 25.45/4.30 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.45/4.30 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 25.45/4.30 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.45/4.30 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 25.45/4.30 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 25.45/4.30 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 25.45/4.30 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 25.45/4.30 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 25.45/4.30 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 25.45/4.30 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 25.45/4.30 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 25.45/4.30 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 25.45/4.30 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.45/4.30 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 25.45/4.30 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 25.45/4.30 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 25.45/4.30 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 25.45/4.30 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 25.45/4.30 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 25.45/4.30 (power_set(v2) = v0))
% 25.45/4.30
% 25.45/4.30 Further assumptions not needed in the proof:
% 25.45/4.30 --------------------------------------------
% 25.45/4.30 compose_function, compose_predicate, decreasing_function, difference, empty_set,
% 25.45/4.30 equal_maps, equal_set, identity, image2, image3, increasing_function,
% 25.45/4.30 intersection, inverse_image2, inverse_image3, inverse_predicate, isomorphism,
% 25.45/4.30 power_set, product, singleton, subset, sum, union, unordered_pair
% 25.45/4.30
% 25.45/4.30 Those formulas are unsatisfiable:
% 25.45/4.30 ---------------------------------
% 25.45/4.30
% 25.45/4.30 Begin of proof
% 25.45/4.30 |
% 25.45/4.30 | ALPHA: (maps) implies:
% 25.45/4.30 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0,
% 25.45/4.30 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) |
% 25.45/4.30 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 &
% 25.45/4.30 | member(v4, v2) = 0 & $i(v4)))
% 25.45/4.31 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 25.45/4.31 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2)
% 25.45/4.31 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~
% 25.45/4.31 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 25.45/4.31 | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3,
% 25.45/4.31 | v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 25.45/4.31 |
% 25.45/4.31 | ALPHA: (injective) implies:
% 25.45/4.31 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 25.45/4.31 | (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 25.45/4.31 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5,
% 25.45/4.31 | v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5,
% 25.45/4.31 | v1) = 0 & member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4)))
% 25.45/4.31 |
% 25.45/4.31 | ALPHA: (surjective) implies:
% 25.45/4.31 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 25.45/4.31 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 25.45/4.31 | ? [v4: $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~
% 25.45/4.31 | (apply(v0, v5, v4) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0)
% 25.45/4.31 | & member(v5, v1) = v6)) & ! [v5: $i] : ( ~ (member(v5, v1) =
% 25.45/4.31 | 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & apply(v0, v5,
% 25.45/4.31 | v4) = v6))))
% 25.45/4.31 |
% 25.45/4.31 | ALPHA: (one_to_one) implies:
% 25.45/4.31 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 25.45/4.31 | (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 25.45/4.31 | ? [v4: any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 &
% 25.45/4.32 | injective(v0, v1, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 25.45/4.32 |
% 25.45/4.32 | ALPHA: (function-axioms) implies:
% 25.45/4.32 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 25.45/4.32 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 25.45/4.32 | = v0))
% 25.45/4.32 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 25.45/4.32 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 25.45/4.32 | (apply(v4, v3, v2) = v0))
% 25.45/4.32 |
% 25.45/4.32 | DELTA: instantiating (thII04) with fresh symbols all_32_0, all_32_1, all_32_2,
% 25.45/4.32 | all_32_3, all_32_4 gives:
% 25.45/4.32 | (8) ~ (all_32_0 = 0) & inverse_function(all_32_4, all_32_3, all_32_2) =
% 25.45/4.32 | all_32_1 & one_to_one(all_32_1, all_32_2, all_32_3) = all_32_0 &
% 25.45/4.32 | one_to_one(all_32_4, all_32_3, all_32_2) = 0 & maps(all_32_4, all_32_3,
% 25.45/4.32 | all_32_2) = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) &
% 25.45/4.32 | $i(all_32_4)
% 25.45/4.32 |
% 25.45/4.32 | ALPHA: (8) implies:
% 25.45/4.32 | (9) ~ (all_32_0 = 0)
% 25.45/4.32 | (10) $i(all_32_4)
% 25.45/4.32 | (11) $i(all_32_3)
% 25.45/4.32 | (12) $i(all_32_2)
% 25.45/4.32 | (13) $i(all_32_1)
% 25.45/4.32 | (14) maps(all_32_4, all_32_3, all_32_2) = 0
% 25.45/4.32 | (15) one_to_one(all_32_1, all_32_2, all_32_3) = all_32_0
% 25.45/4.32 | (16) inverse_function(all_32_4, all_32_3, all_32_2) = all_32_1
% 25.45/4.32 |
% 25.45/4.32 | GROUND_INST: instantiating (5) with all_32_1, all_32_2, all_32_3, all_32_0,
% 25.45/4.32 | simplifying with (11), (12), (13), (15) gives:
% 25.45/4.33 | (17) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (surjective(all_32_1,
% 25.45/4.33 | all_32_2, all_32_3) = v1 & injective(all_32_1, all_32_2, all_32_3)
% 25.45/4.33 | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 25.45/4.33 |
% 25.45/4.33 | BETA: splitting (17) gives:
% 25.45/4.33 |
% 25.45/4.33 | Case 1:
% 25.45/4.33 | |
% 25.45/4.33 | | (18) all_32_0 = 0
% 25.45/4.33 | |
% 25.45/4.33 | | REDUCE: (9), (18) imply:
% 25.45/4.33 | | (19) $false
% 25.45/4.33 | |
% 25.45/4.33 | | CLOSE: (19) is inconsistent.
% 25.45/4.33 | |
% 25.45/4.33 | Case 2:
% 25.45/4.33 | |
% 25.45/4.33 | | (20) ? [v0: any] : ? [v1: any] : (surjective(all_32_1, all_32_2,
% 25.45/4.33 | | all_32_3) = v1 & injective(all_32_1, all_32_2, all_32_3) = v0 &
% 25.45/4.33 | | ( ~ (v1 = 0) | ~ (v0 = 0)))
% 25.45/4.33 | |
% 25.45/4.33 | | DELTA: instantiating (20) with fresh symbols all_44_0, all_44_1 gives:
% 25.45/4.33 | | (21) surjective(all_32_1, all_32_2, all_32_3) = all_44_0 &
% 25.45/4.33 | | injective(all_32_1, all_32_2, all_32_3) = all_44_1 & ( ~ (all_44_0 =
% 25.45/4.33 | | 0) | ~ (all_44_1 = 0))
% 25.45/4.33 | |
% 25.45/4.33 | | ALPHA: (21) implies:
% 25.45/4.33 | | (22) injective(all_32_1, all_32_2, all_32_3) = all_44_1
% 25.45/4.33 | | (23) surjective(all_32_1, all_32_2, all_32_3) = all_44_0
% 25.45/4.33 | | (24) ~ (all_44_0 = 0) | ~ (all_44_1 = 0)
% 25.45/4.33 | |
% 25.45/4.33 | | GROUND_INST: instantiating (3) with all_32_1, all_32_2, all_32_3, all_44_1,
% 25.45/4.33 | | simplifying with (11), (12), (13), (22) gives:
% 25.45/4.33 | | (25) all_44_1 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 =
% 25.45/4.34 | | v0) & apply(all_32_1, v1, v2) = 0 & apply(all_32_1, v0, v2) = 0
% 25.45/4.34 | | & member(v2, all_32_3) = 0 & member(v1, all_32_2) = 0 & member(v0,
% 25.45/4.34 | | all_32_2) = 0 & $i(v2) & $i(v1) & $i(v0))
% 25.45/4.34 | |
% 25.45/4.34 | | GROUND_INST: instantiating (4) with all_32_1, all_32_2, all_32_3, all_44_0,
% 25.45/4.34 | | simplifying with (11), (12), (13), (23) gives:
% 25.45/4.34 | | (26) all_44_0 = 0 | ? [v0: $i] : (member(v0, all_32_3) = 0 & $i(v0) & !
% 25.45/4.34 | | [v1: $i] : ( ~ (apply(all_32_1, v1, v0) = 0) | ~ $i(v1) | ? [v2:
% 25.45/4.34 | | int] : ( ~ (v2 = 0) & member(v1, all_32_2) = v2)) & ! [v1:
% 25.45/4.34 | | $i] : ( ~ (member(v1, all_32_2) = 0) | ~ $i(v1) | ? [v2: int]
% 25.45/4.34 | | : ( ~ (v2 = 0) & apply(all_32_1, v1, v0) = v2)))
% 25.45/4.34 | |
% 25.45/4.34 | | BETA: splitting (24) gives:
% 25.45/4.34 | |
% 25.45/4.34 | | Case 1:
% 25.45/4.34 | | |
% 25.45/4.34 | | | (27) ~ (all_44_0 = 0)
% 25.45/4.34 | | |
% 25.45/4.34 | | | BETA: splitting (26) gives:
% 25.45/4.34 | | |
% 25.45/4.34 | | | Case 1:
% 25.45/4.34 | | | |
% 25.45/4.34 | | | | (28) all_44_0 = 0
% 25.45/4.34 | | | |
% 25.45/4.34 | | | | REDUCE: (27), (28) imply:
% 25.45/4.34 | | | | (29) $false
% 25.45/4.34 | | | |
% 25.45/4.34 | | | | CLOSE: (29) is inconsistent.
% 25.45/4.34 | | | |
% 25.45/4.34 | | | Case 2:
% 25.45/4.34 | | | |
% 25.45/4.34 | | | | (30) ? [v0: $i] : (member(v0, all_32_3) = 0 & $i(v0) & ! [v1: $i] :
% 25.45/4.34 | | | | ( ~ (apply(all_32_1, v1, v0) = 0) | ~ $i(v1) | ? [v2: int] :
% 25.45/4.34 | | | | ( ~ (v2 = 0) & member(v1, all_32_2) = v2)) & ! [v1: $i] : (
% 25.45/4.34 | | | | ~ (member(v1, all_32_2) = 0) | ~ $i(v1) | ? [v2: int] : (
% 25.45/4.34 | | | | ~ (v2 = 0) & apply(all_32_1, v1, v0) = v2)))
% 25.45/4.34 | | | |
% 25.45/4.34 | | | | DELTA: instantiating (30) with fresh symbol all_57_0 gives:
% 25.45/4.34 | | | | (31) member(all_57_0, all_32_3) = 0 & $i(all_57_0) & ! [v0: $i] : (
% 25.45/4.34 | | | | ~ (apply(all_32_1, v0, all_57_0) = 0) | ~ $i(v0) | ? [v1:
% 25.45/4.34 | | | | int] : ( ~ (v1 = 0) & member(v0, all_32_2) = v1)) & ! [v0:
% 25.45/4.34 | | | | $i] : ( ~ (member(v0, all_32_2) = 0) | ~ $i(v0) | ? [v1:
% 25.45/4.34 | | | | int] : ( ~ (v1 = 0) & apply(all_32_1, v0, all_57_0) = v1))
% 25.45/4.34 | | | |
% 25.45/4.34 | | | | ALPHA: (31) implies:
% 25.45/4.34 | | | | (32) $i(all_57_0)
% 25.45/4.34 | | | | (33) member(all_57_0, all_32_3) = 0
% 25.45/4.35 | | | | (34) ! [v0: $i] : ( ~ (member(v0, all_32_2) = 0) | ~ $i(v0) | ?
% 25.45/4.35 | | | | [v1: int] : ( ~ (v1 = 0) & apply(all_32_1, v0, all_57_0) =
% 25.45/4.35 | | | | v1))
% 25.45/4.35 | | | |
% 25.45/4.35 | | | | GROUND_INST: instantiating (1) with all_32_4, all_32_3, all_32_2,
% 25.45/4.35 | | | | all_57_0, simplifying with (10), (11), (12), (14), (32),
% 25.45/4.35 | | | | (33) gives:
% 25.45/4.35 | | | | (35) ? [v0: $i] : (apply(all_32_4, all_57_0, v0) = 0 & member(v0,
% 25.45/4.35 | | | | all_32_2) = 0 & $i(v0))
% 25.45/4.35 | | | |
% 25.45/4.35 | | | | DELTA: instantiating (35) with fresh symbol all_65_0 gives:
% 25.45/4.35 | | | | (36) apply(all_32_4, all_57_0, all_65_0) = 0 & member(all_65_0,
% 25.45/4.35 | | | | all_32_2) = 0 & $i(all_65_0)
% 25.45/4.35 | | | |
% 25.45/4.35 | | | | ALPHA: (36) implies:
% 25.45/4.35 | | | | (37) $i(all_65_0)
% 25.45/4.35 | | | | (38) member(all_65_0, all_32_2) = 0
% 25.45/4.35 | | | | (39) apply(all_32_4, all_57_0, all_65_0) = 0
% 25.45/4.35 | | | |
% 25.45/4.35 | | | | GROUND_INST: instantiating (34) with all_65_0, simplifying with (37),
% 25.45/4.35 | | | | (38) gives:
% 25.45/4.35 | | | | (40) ? [v0: int] : ( ~ (v0 = 0) & apply(all_32_1, all_65_0,
% 25.45/4.35 | | | | all_57_0) = v0)
% 25.45/4.35 | | | |
% 25.45/4.35 | | | | DELTA: instantiating (40) with fresh symbol all_72_0 gives:
% 25.45/4.35 | | | | (41) ~ (all_72_0 = 0) & apply(all_32_1, all_65_0, all_57_0) =
% 25.45/4.35 | | | | all_72_0
% 25.45/4.35 | | | |
% 25.45/4.35 | | | | ALPHA: (41) implies:
% 25.45/4.35 | | | | (42) ~ (all_72_0 = 0)
% 25.45/4.35 | | | | (43) apply(all_32_1, all_65_0, all_57_0) = all_72_0
% 25.45/4.35 | | | |
% 25.45/4.35 | | | | GROUND_INST: instantiating (inverse_function) with all_32_4, all_32_3,
% 25.45/4.35 | | | | all_32_2, all_57_0, all_65_0, all_32_1, all_72_0,
% 25.45/4.35 | | | | simplifying with (10), (11), (12), (16), (32), (37), (43)
% 25.45/4.35 | | | | gives:
% 25.45/4.35 | | | | (44) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_4,
% 25.45/4.35 | | | | all_57_0, all_65_0) = v2 & member(all_65_0, all_32_2) = v1 &
% 25.45/4.35 | | | | member(all_57_0, all_32_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 25.45/4.35 | | | | (( ~ (v2 = 0) | all_72_0 = 0) & ( ~ (all_72_0 = 0) | v2 =
% 25.45/4.36 | | | | 0))))
% 25.45/4.36 | | | |
% 25.45/4.36 | | | | DELTA: instantiating (44) with fresh symbols all_83_0, all_83_1,
% 25.45/4.36 | | | | all_83_2 gives:
% 25.45/4.36 | | | | (45) apply(all_32_4, all_57_0, all_65_0) = all_83_0 &
% 25.45/4.36 | | | | member(all_65_0, all_32_2) = all_83_1 & member(all_57_0,
% 25.45/4.36 | | | | all_32_3) = all_83_2 & ( ~ (all_83_1 = 0) | ~ (all_83_2 = 0)
% 25.45/4.36 | | | | | (( ~ (all_83_0 = 0) | all_72_0 = 0) & ( ~ (all_72_0 = 0) |
% 25.45/4.36 | | | | all_83_0 = 0)))
% 25.45/4.36 | | | |
% 25.45/4.36 | | | | ALPHA: (45) implies:
% 25.45/4.36 | | | | (46) member(all_57_0, all_32_3) = all_83_2
% 25.45/4.36 | | | | (47) member(all_65_0, all_32_2) = all_83_1
% 25.45/4.36 | | | | (48) apply(all_32_4, all_57_0, all_65_0) = all_83_0
% 25.45/4.36 | | | | (49) ~ (all_83_1 = 0) | ~ (all_83_2 = 0) | (( ~ (all_83_0 = 0) |
% 25.45/4.36 | | | | all_72_0 = 0) & ( ~ (all_72_0 = 0) | all_83_0 = 0))
% 25.45/4.36 | | | |
% 25.45/4.36 | | | | GROUND_INST: instantiating (6) with 0, all_83_2, all_32_3, all_57_0,
% 25.45/4.36 | | | | simplifying with (33), (46) gives:
% 25.45/4.36 | | | | (50) all_83_2 = 0
% 25.45/4.36 | | | |
% 25.45/4.36 | | | | GROUND_INST: instantiating (6) with 0, all_83_1, all_32_2, all_65_0,
% 25.45/4.36 | | | | simplifying with (38), (47) gives:
% 25.45/4.36 | | | | (51) all_83_1 = 0
% 25.45/4.36 | | | |
% 25.45/4.36 | | | | GROUND_INST: instantiating (7) with 0, all_83_0, all_65_0, all_57_0,
% 25.45/4.36 | | | | all_32_4, simplifying with (39), (48) gives:
% 25.45/4.36 | | | | (52) all_83_0 = 0
% 25.45/4.36 | | | |
% 25.45/4.36 | | | | BETA: splitting (49) gives:
% 25.45/4.36 | | | |
% 25.45/4.36 | | | | Case 1:
% 25.45/4.36 | | | | |
% 25.45/4.36 | | | | | (53) ~ (all_83_1 = 0)
% 25.45/4.36 | | | | |
% 25.45/4.36 | | | | | REDUCE: (51), (53) imply:
% 25.45/4.36 | | | | | (54) $false
% 25.45/4.36 | | | | |
% 25.45/4.36 | | | | | CLOSE: (54) is inconsistent.
% 25.45/4.36 | | | | |
% 25.45/4.36 | | | | Case 2:
% 25.45/4.36 | | | | |
% 25.45/4.36 | | | | | (55) ~ (all_83_2 = 0) | (( ~ (all_83_0 = 0) | all_72_0 = 0) & ( ~
% 25.45/4.36 | | | | | (all_72_0 = 0) | all_83_0 = 0))
% 25.45/4.36 | | | | |
% 25.45/4.36 | | | | | BETA: splitting (55) gives:
% 25.45/4.36 | | | | |
% 25.45/4.36 | | | | | Case 1:
% 25.45/4.36 | | | | | |
% 25.45/4.36 | | | | | | (56) ~ (all_83_2 = 0)
% 25.45/4.36 | | | | | |
% 25.45/4.36 | | | | | | REDUCE: (50), (56) imply:
% 25.45/4.36 | | | | | | (57) $false
% 25.45/4.36 | | | | | |
% 25.45/4.36 | | | | | | CLOSE: (57) is inconsistent.
% 25.45/4.36 | | | | | |
% 25.45/4.36 | | | | | Case 2:
% 25.45/4.36 | | | | | |
% 25.45/4.36 | | | | | | (58) ( ~ (all_83_0 = 0) | all_72_0 = 0) & ( ~ (all_72_0 = 0) |
% 25.45/4.36 | | | | | | all_83_0 = 0)
% 25.45/4.36 | | | | | |
% 25.45/4.36 | | | | | | ALPHA: (58) implies:
% 25.45/4.36 | | | | | | (59) ~ (all_83_0 = 0) | all_72_0 = 0
% 25.45/4.36 | | | | | |
% 25.45/4.36 | | | | | | BETA: splitting (59) gives:
% 25.45/4.36 | | | | | |
% 25.45/4.36 | | | | | | Case 1:
% 25.45/4.36 | | | | | | |
% 25.45/4.37 | | | | | | | (60) ~ (all_83_0 = 0)
% 25.45/4.37 | | | | | | |
% 25.45/4.37 | | | | | | | REDUCE: (52), (60) imply:
% 25.45/4.37 | | | | | | | (61) $false
% 25.45/4.37 | | | | | | |
% 25.45/4.37 | | | | | | | CLOSE: (61) is inconsistent.
% 25.45/4.37 | | | | | | |
% 25.45/4.37 | | | | | | Case 2:
% 25.45/4.37 | | | | | | |
% 25.45/4.37 | | | | | | | (62) all_72_0 = 0
% 25.45/4.37 | | | | | | |
% 25.45/4.37 | | | | | | | REDUCE: (42), (62) imply:
% 25.45/4.37 | | | | | | | (63) $false
% 25.45/4.37 | | | | | | |
% 25.45/4.37 | | | | | | | CLOSE: (63) is inconsistent.
% 25.45/4.37 | | | | | | |
% 25.45/4.37 | | | | | | End of split
% 25.45/4.37 | | | | | |
% 25.45/4.37 | | | | | End of split
% 25.45/4.37 | | | | |
% 25.45/4.37 | | | | End of split
% 25.45/4.37 | | | |
% 25.45/4.37 | | | End of split
% 25.45/4.37 | | |
% 25.45/4.37 | | Case 2:
% 25.45/4.37 | | |
% 25.45/4.37 | | | (64) ~ (all_44_1 = 0)
% 25.45/4.37 | | |
% 25.45/4.37 | | | BETA: splitting (25) gives:
% 25.45/4.37 | | |
% 25.45/4.37 | | | Case 1:
% 25.45/4.37 | | | |
% 25.45/4.37 | | | | (65) all_44_1 = 0
% 25.45/4.37 | | | |
% 25.45/4.37 | | | | REDUCE: (64), (65) imply:
% 25.45/4.37 | | | | (66) $false
% 25.45/4.37 | | | |
% 25.45/4.37 | | | | CLOSE: (66) is inconsistent.
% 25.45/4.37 | | | |
% 25.45/4.37 | | | Case 2:
% 25.45/4.37 | | | |
% 25.45/4.37 | | | | (67) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 25.45/4.37 | | | | apply(all_32_1, v1, v2) = 0 & apply(all_32_1, v0, v2) = 0 &
% 25.45/4.37 | | | | member(v2, all_32_3) = 0 & member(v1, all_32_2) = 0 &
% 25.45/4.37 | | | | member(v0, all_32_2) = 0 & $i(v2) & $i(v1) & $i(v0))
% 25.45/4.37 | | | |
% 25.45/4.37 | | | | DELTA: instantiating (67) with fresh symbols all_57_0, all_57_1,
% 25.45/4.37 | | | | all_57_2 gives:
% 25.45/4.37 | | | | (68) ~ (all_57_1 = all_57_2) & apply(all_32_1, all_57_1, all_57_0) =
% 25.45/4.37 | | | | 0 & apply(all_32_1, all_57_2, all_57_0) = 0 & member(all_57_0,
% 25.45/4.37 | | | | all_32_3) = 0 & member(all_57_1, all_32_2) = 0 &
% 25.45/4.37 | | | | member(all_57_2, all_32_2) = 0 & $i(all_57_0) & $i(all_57_1) &
% 25.45/4.37 | | | | $i(all_57_2)
% 25.45/4.37 | | | |
% 25.45/4.37 | | | | ALPHA: (68) implies:
% 25.45/4.37 | | | | (69) ~ (all_57_1 = all_57_2)
% 25.45/4.37 | | | | (70) $i(all_57_2)
% 25.45/4.37 | | | | (71) $i(all_57_1)
% 25.45/4.37 | | | | (72) $i(all_57_0)
% 25.45/4.37 | | | | (73) member(all_57_2, all_32_2) = 0
% 25.45/4.37 | | | | (74) member(all_57_1, all_32_2) = 0
% 25.45/4.37 | | | | (75) member(all_57_0, all_32_3) = 0
% 25.45/4.37 | | | | (76) apply(all_32_1, all_57_2, all_57_0) = 0
% 25.45/4.37 | | | | (77) apply(all_32_1, all_57_1, all_57_0) = 0
% 25.45/4.37 | | | |
% 25.45/4.38 | | | | GROUND_INST: instantiating (2) with all_32_4, all_32_3, all_32_2,
% 25.45/4.38 | | | | all_57_0, all_57_2, all_57_1, simplifying with (10), (11),
% 25.45/4.38 | | | | (12), (14), (70), (71), (72), (73), (74), (75) gives:
% 25.45/4.38 | | | | (78) all_57_1 = all_57_2 | ? [v0: any] : ? [v1: any] :
% 25.45/4.38 | | | | (apply(all_32_4, all_57_0, all_57_1) = v1 & apply(all_32_4,
% 25.45/4.38 | | | | all_57_0, all_57_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 25.45/4.38 | | | |
% 25.45/4.38 | | | | GROUND_INST: instantiating (2) with all_32_4, all_32_3, all_32_2,
% 25.45/4.38 | | | | all_57_0, all_57_1, all_57_2, simplifying with (10), (11),
% 25.45/4.38 | | | | (12), (14), (70), (71), (72), (73), (74), (75) gives:
% 25.45/4.38 | | | | (79) all_57_1 = all_57_2 | ? [v0: any] : ? [v1: any] :
% 25.45/4.38 | | | | (apply(all_32_4, all_57_0, all_57_1) = v0 & apply(all_32_4,
% 25.45/4.38 | | | | all_57_0, all_57_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 25.45/4.38 | | | |
% 25.45/4.38 | | | | GROUND_INST: instantiating (inverse_function) with all_32_4, all_32_3,
% 25.45/4.38 | | | | all_32_2, all_57_0, all_57_2, all_32_1, 0, simplifying with
% 25.45/4.38 | | | | (10), (11), (12), (16), (70), (72), (76) gives:
% 25.45/4.38 | | | | (80) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_4,
% 25.45/4.38 | | | | all_57_0, all_57_2) = v2 & member(all_57_0, all_32_3) = v0 &
% 25.45/4.38 | | | | member(all_57_2, all_32_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 25.45/4.38 | | | | v2 = 0))
% 25.45/4.38 | | | |
% 25.45/4.39 | | | | GROUND_INST: instantiating (inverse_function) with all_32_4, all_32_3,
% 25.45/4.39 | | | | all_32_2, all_57_0, all_57_1, all_32_1, 0, simplifying with
% 25.45/4.39 | | | | (10), (11), (12), (16), (71), (72), (77) gives:
% 25.45/4.39 | | | | (81) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_4,
% 25.45/4.39 | | | | all_57_0, all_57_1) = v2 & member(all_57_0, all_32_3) = v0 &
% 25.45/4.39 | | | | member(all_57_1, all_32_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 25.45/4.39 | | | | v2 = 0))
% 25.45/4.39 | | | |
% 25.45/4.39 | | | | DELTA: instantiating (81) with fresh symbols all_72_0, all_72_1,
% 25.45/4.39 | | | | all_72_2 gives:
% 25.45/4.39 | | | | (82) apply(all_32_4, all_57_0, all_57_1) = all_72_0 &
% 25.45/4.39 | | | | member(all_57_0, all_32_3) = all_72_2 & member(all_57_1,
% 25.45/4.39 | | | | all_32_2) = all_72_1 & ( ~ (all_72_1 = 0) | ~ (all_72_2 = 0)
% 25.45/4.39 | | | | | all_72_0 = 0)
% 25.45/4.39 | | | |
% 25.45/4.39 | | | | ALPHA: (82) implies:
% 25.45/4.39 | | | | (83) member(all_57_1, all_32_2) = all_72_1
% 25.45/4.39 | | | | (84) member(all_57_0, all_32_3) = all_72_2
% 25.45/4.39 | | | | (85) apply(all_32_4, all_57_0, all_57_1) = all_72_0
% 25.45/4.39 | | | | (86) ~ (all_72_1 = 0) | ~ (all_72_2 = 0) | all_72_0 = 0
% 25.45/4.39 | | | |
% 25.45/4.39 | | | | DELTA: instantiating (80) with fresh symbols all_74_0, all_74_1,
% 25.45/4.39 | | | | all_74_2 gives:
% 25.45/4.39 | | | | (87) apply(all_32_4, all_57_0, all_57_2) = all_74_0 &
% 25.45/4.39 | | | | member(all_57_0, all_32_3) = all_74_2 & member(all_57_2,
% 25.45/4.39 | | | | all_32_2) = all_74_1 & ( ~ (all_74_1 = 0) | ~ (all_74_2 = 0)
% 25.45/4.39 | | | | | all_74_0 = 0)
% 25.45/4.39 | | | |
% 25.45/4.39 | | | | ALPHA: (87) implies:
% 25.45/4.39 | | | | (88) member(all_57_2, all_32_2) = all_74_1
% 25.45/4.39 | | | | (89) member(all_57_0, all_32_3) = all_74_2
% 25.45/4.39 | | | | (90) apply(all_32_4, all_57_0, all_57_2) = all_74_0
% 25.45/4.39 | | | | (91) ~ (all_74_1 = 0) | ~ (all_74_2 = 0) | all_74_0 = 0
% 25.45/4.39 | | | |
% 25.45/4.39 | | | | GROUND_INST: instantiating (6) with 0, all_74_1, all_32_2, all_57_2,
% 25.45/4.39 | | | | simplifying with (73), (88) gives:
% 25.45/4.39 | | | | (92) all_74_1 = 0
% 25.45/4.39 | | | |
% 25.45/4.39 | | | | GROUND_INST: instantiating (6) with 0, all_72_1, all_32_2, all_57_1,
% 25.45/4.39 | | | | simplifying with (74), (83) gives:
% 25.45/4.39 | | | | (93) all_72_1 = 0
% 25.45/4.39 | | | |
% 25.45/4.39 | | | | GROUND_INST: instantiating (6) with 0, all_74_2, all_32_3, all_57_0,
% 25.45/4.39 | | | | simplifying with (75), (89) gives:
% 25.45/4.40 | | | | (94) all_74_2 = 0
% 25.45/4.40 | | | |
% 25.45/4.40 | | | | GROUND_INST: instantiating (6) with all_72_2, all_74_2, all_32_3,
% 25.45/4.40 | | | | all_57_0, simplifying with (84), (89) gives:
% 25.45/4.40 | | | | (95) all_74_2 = all_72_2
% 25.45/4.40 | | | |
% 25.45/4.40 | | | | COMBINE_EQS: (94), (95) imply:
% 25.45/4.40 | | | | (96) all_72_2 = 0
% 25.45/4.40 | | | |
% 25.45/4.40 | | | | SIMP: (96) implies:
% 25.45/4.40 | | | | (97) all_72_2 = 0
% 25.45/4.40 | | | |
% 25.45/4.40 | | | | BETA: splitting (86) gives:
% 25.45/4.40 | | | |
% 25.45/4.40 | | | | Case 1:
% 25.45/4.40 | | | | |
% 25.45/4.40 | | | | | (98) ~ (all_72_1 = 0)
% 25.45/4.40 | | | | |
% 25.45/4.40 | | | | | REDUCE: (93), (98) imply:
% 25.45/4.40 | | | | | (99) $false
% 25.45/4.40 | | | | |
% 25.45/4.40 | | | | | CLOSE: (99) is inconsistent.
% 25.45/4.40 | | | | |
% 25.45/4.40 | | | | Case 2:
% 25.45/4.40 | | | | |
% 25.45/4.40 | | | | | (100) ~ (all_72_2 = 0) | all_72_0 = 0
% 25.45/4.40 | | | | |
% 25.45/4.40 | | | | | BETA: splitting (100) gives:
% 25.45/4.40 | | | | |
% 25.45/4.40 | | | | | Case 1:
% 25.45/4.40 | | | | | |
% 25.45/4.40 | | | | | | (101) ~ (all_72_2 = 0)
% 25.45/4.40 | | | | | |
% 25.45/4.40 | | | | | | REDUCE: (97), (101) imply:
% 25.45/4.40 | | | | | | (102) $false
% 25.45/4.40 | | | | | |
% 25.45/4.40 | | | | | | CLOSE: (102) is inconsistent.
% 25.45/4.40 | | | | | |
% 25.45/4.40 | | | | | Case 2:
% 25.45/4.40 | | | | | |
% 25.45/4.40 | | | | | | (103) all_72_0 = 0
% 25.45/4.40 | | | | | |
% 25.45/4.40 | | | | | | REDUCE: (85), (103) imply:
% 25.45/4.40 | | | | | | (104) apply(all_32_4, all_57_0, all_57_1) = 0
% 25.45/4.40 | | | | | |
% 25.45/4.40 | | | | | | BETA: splitting (79) gives:
% 25.45/4.40 | | | | | |
% 25.45/4.40 | | | | | | Case 1:
% 25.45/4.40 | | | | | | |
% 25.45/4.40 | | | | | | | (105) all_57_1 = all_57_2
% 25.45/4.40 | | | | | | |
% 25.45/4.40 | | | | | | | REDUCE: (69), (105) imply:
% 25.45/4.40 | | | | | | | (106) $false
% 25.45/4.40 | | | | | | |
% 25.45/4.40 | | | | | | | CLOSE: (106) is inconsistent.
% 25.45/4.40 | | | | | | |
% 25.45/4.40 | | | | | | Case 2:
% 25.45/4.40 | | | | | | |
% 25.45/4.40 | | | | | | | (107) ? [v0: any] : ? [v1: any] : (apply(all_32_4, all_57_0,
% 25.45/4.40 | | | | | | | all_57_1) = v0 & apply(all_32_4, all_57_0, all_57_2)
% 25.45/4.40 | | | | | | | = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 25.45/4.40 | | | | | | |
% 25.45/4.40 | | | | | | | DELTA: instantiating (107) with fresh symbols all_92_0, all_92_1
% 25.45/4.40 | | | | | | | gives:
% 25.45/4.40 | | | | | | | (108) apply(all_32_4, all_57_0, all_57_1) = all_92_1 &
% 25.45/4.40 | | | | | | | apply(all_32_4, all_57_0, all_57_2) = all_92_0 & ( ~
% 25.45/4.40 | | | | | | | (all_92_0 = 0) | ~ (all_92_1 = 0))
% 25.45/4.40 | | | | | | |
% 25.45/4.40 | | | | | | | ALPHA: (108) implies:
% 25.45/4.40 | | | | | | | (109) apply(all_32_4, all_57_0, all_57_2) = all_92_0
% 25.45/4.40 | | | | | | |
% 25.45/4.40 | | | | | | | BETA: splitting (91) gives:
% 25.45/4.40 | | | | | | |
% 25.45/4.40 | | | | | | | Case 1:
% 25.45/4.40 | | | | | | | |
% 25.45/4.40 | | | | | | | | (110) ~ (all_74_1 = 0)
% 25.45/4.40 | | | | | | | |
% 25.45/4.40 | | | | | | | | REDUCE: (92), (110) imply:
% 25.45/4.40 | | | | | | | | (111) $false
% 25.45/4.40 | | | | | | | |
% 25.45/4.40 | | | | | | | | CLOSE: (111) is inconsistent.
% 25.45/4.41 | | | | | | | |
% 25.45/4.41 | | | | | | | Case 2:
% 25.45/4.41 | | | | | | | |
% 25.45/4.41 | | | | | | | | (112) ~ (all_74_2 = 0) | all_74_0 = 0
% 25.45/4.41 | | | | | | | |
% 25.45/4.41 | | | | | | | | BETA: splitting (112) gives:
% 25.45/4.41 | | | | | | | |
% 25.45/4.41 | | | | | | | | Case 1:
% 25.45/4.41 | | | | | | | | |
% 25.45/4.41 | | | | | | | | | (113) ~ (all_74_2 = 0)
% 25.45/4.41 | | | | | | | | |
% 25.45/4.41 | | | | | | | | | REDUCE: (94), (113) imply:
% 25.45/4.41 | | | | | | | | | (114) $false
% 25.45/4.41 | | | | | | | | |
% 25.45/4.41 | | | | | | | | | CLOSE: (114) is inconsistent.
% 25.45/4.41 | | | | | | | | |
% 25.45/4.41 | | | | | | | | Case 2:
% 25.45/4.41 | | | | | | | | |
% 25.45/4.41 | | | | | | | | | (115) all_74_0 = 0
% 25.45/4.41 | | | | | | | | |
% 25.45/4.41 | | | | | | | | | REDUCE: (90), (115) imply:
% 25.45/4.41 | | | | | | | | | (116) apply(all_32_4, all_57_0, all_57_2) = 0
% 25.45/4.41 | | | | | | | | |
% 25.45/4.41 | | | | | | | | | BETA: splitting (78) gives:
% 25.45/4.41 | | | | | | | | |
% 25.45/4.41 | | | | | | | | | Case 1:
% 25.45/4.41 | | | | | | | | | |
% 25.45/4.41 | | | | | | | | | | (117) all_57_1 = all_57_2
% 25.45/4.41 | | | | | | | | | |
% 25.45/4.41 | | | | | | | | | | REDUCE: (69), (117) imply:
% 25.45/4.41 | | | | | | | | | | (118) $false
% 25.45/4.41 | | | | | | | | | |
% 25.45/4.41 | | | | | | | | | | CLOSE: (118) is inconsistent.
% 25.45/4.41 | | | | | | | | | |
% 25.45/4.41 | | | | | | | | | Case 2:
% 25.45/4.41 | | | | | | | | | |
% 25.45/4.41 | | | | | | | | | | (119) ? [v0: any] : ? [v1: any] : (apply(all_32_4,
% 25.45/4.41 | | | | | | | | | | all_57_0, all_57_1) = v1 & apply(all_32_4,
% 25.45/4.41 | | | | | | | | | | all_57_0, all_57_2) = v0 & ( ~ (v1 = 0) | ~
% 25.45/4.41 | | | | | | | | | | (v0 = 0)))
% 25.45/4.41 | | | | | | | | | |
% 25.45/4.41 | | | | | | | | | | DELTA: instantiating (119) with fresh symbols all_106_0,
% 25.45/4.41 | | | | | | | | | | all_106_1 gives:
% 25.45/4.41 | | | | | | | | | | (120) apply(all_32_4, all_57_0, all_57_1) = all_106_0 &
% 25.45/4.41 | | | | | | | | | | apply(all_32_4, all_57_0, all_57_2) = all_106_1 & (
% 25.45/4.41 | | | | | | | | | | ~ (all_106_0 = 0) | ~ (all_106_1 = 0))
% 25.45/4.41 | | | | | | | | | |
% 25.45/4.41 | | | | | | | | | | ALPHA: (120) implies:
% 25.45/4.41 | | | | | | | | | | (121) apply(all_32_4, all_57_0, all_57_2) = all_106_1
% 25.45/4.41 | | | | | | | | | | (122) apply(all_32_4, all_57_0, all_57_1) = all_106_0
% 25.45/4.41 | | | | | | | | | | (123) ~ (all_106_0 = 0) | ~ (all_106_1 = 0)
% 25.45/4.41 | | | | | | | | | |
% 25.45/4.41 | | | | | | | | | | GROUND_INST: instantiating (7) with all_92_0, all_106_1,
% 25.45/4.41 | | | | | | | | | | all_57_2, all_57_0, all_32_4, simplifying with
% 25.45/4.41 | | | | | | | | | | (109), (121) gives:
% 25.45/4.41 | | | | | | | | | | (124) all_106_1 = all_92_0
% 25.45/4.41 | | | | | | | | | |
% 25.45/4.41 | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_106_1, all_57_2,
% 25.45/4.41 | | | | | | | | | | all_57_0, all_32_4, simplifying with (116), (121)
% 25.45/4.41 | | | | | | | | | | gives:
% 25.45/4.42 | | | | | | | | | | (125) all_106_1 = 0
% 25.45/4.42 | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_106_0, all_57_1,
% 25.45/4.42 | | | | | | | | | | all_57_0, all_32_4, simplifying with (104), (122)
% 25.45/4.42 | | | | | | | | | | gives:
% 25.45/4.42 | | | | | | | | | | (126) all_106_0 = 0
% 25.45/4.42 | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | COMBINE_EQS: (124), (125) imply:
% 25.45/4.42 | | | | | | | | | | (127) all_92_0 = 0
% 25.45/4.42 | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | BETA: splitting (123) gives:
% 25.45/4.42 | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | Case 1:
% 25.45/4.42 | | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | | (128) ~ (all_106_0 = 0)
% 25.45/4.42 | | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | | REDUCE: (126), (128) imply:
% 25.45/4.42 | | | | | | | | | | | (129) $false
% 25.45/4.42 | | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | | CLOSE: (129) is inconsistent.
% 25.45/4.42 | | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | Case 2:
% 25.45/4.42 | | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | | (130) ~ (all_106_1 = 0)
% 25.45/4.42 | | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | | REDUCE: (125), (130) imply:
% 25.45/4.42 | | | | | | | | | | | (131) $false
% 25.45/4.42 | | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | | CLOSE: (131) is inconsistent.
% 25.45/4.42 | | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | | End of split
% 25.45/4.42 | | | | | | | | | |
% 25.45/4.42 | | | | | | | | | End of split
% 25.45/4.42 | | | | | | | | |
% 25.45/4.42 | | | | | | | | End of split
% 25.45/4.42 | | | | | | | |
% 25.45/4.42 | | | | | | | End of split
% 25.45/4.42 | | | | | | |
% 25.45/4.42 | | | | | | End of split
% 25.45/4.42 | | | | | |
% 25.45/4.42 | | | | | End of split
% 25.45/4.42 | | | | |
% 25.45/4.42 | | | | End of split
% 25.45/4.42 | | | |
% 25.45/4.42 | | | End of split
% 25.45/4.42 | | |
% 25.45/4.42 | | End of split
% 25.45/4.42 | |
% 25.45/4.42 | End of split
% 25.45/4.42 |
% 25.45/4.42 End of proof
% 25.45/4.42 % SZS output end Proof for theBenchmark
% 25.45/4.42
% 25.45/4.42 3805ms
%------------------------------------------------------------------------------