TSTP Solution File: SET717+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET717+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 : n004.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 15:26:07 EDT 2023
% Result : Theorem 21.10s 3.71s
% Output : Proof 25.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET717+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.34 % Computer : n004.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Sat Aug 26 15:24:22 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.17/0.64 ________ _____
% 0.17/0.64 ___ __ \_________(_)________________________________
% 0.17/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.64
% 0.17/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.64 (2023-06-19)
% 0.17/0.64
% 0.17/0.64 (c) Philipp Rümmer, 2009-2023
% 0.17/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.64 Amanda Stjerna.
% 0.17/0.64 Free software under BSD-3-Clause.
% 0.17/0.64
% 0.17/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.64
% 0.17/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.66 Running up to 7 provers in parallel.
% 0.17/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.57/1.29 Prover 1: Preprocessing ...
% 3.57/1.31 Prover 4: Preprocessing ...
% 3.57/1.35 Prover 5: Preprocessing ...
% 3.57/1.35 Prover 0: Preprocessing ...
% 3.57/1.35 Prover 3: Preprocessing ...
% 3.57/1.35 Prover 6: Preprocessing ...
% 3.57/1.35 Prover 2: Preprocessing ...
% 10.89/2.30 Prover 5: Proving ...
% 11.11/2.37 Prover 2: Proving ...
% 11.11/2.40 Prover 6: Proving ...
% 11.84/2.49 Prover 1: Constructing countermodel ...
% 12.41/2.49 Prover 3: Constructing countermodel ...
% 15.01/2.95 Prover 4: Constructing countermodel ...
% 17.78/3.23 Prover 0: Proving ...
% 21.10/3.71 Prover 0: proved (3038ms)
% 21.10/3.71
% 21.10/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.10/3.71
% 21.10/3.71 Prover 6: stopped
% 21.10/3.71 Prover 2: stopped
% 21.10/3.73 Prover 5: stopped
% 21.10/3.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.10/3.73 Prover 3: stopped
% 21.10/3.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.10/3.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.10/3.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.10/3.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 22.24/3.85 Prover 13: Preprocessing ...
% 22.41/3.85 Prover 4: Found proof (size 83)
% 22.41/3.85 Prover 4: proved (3183ms)
% 22.41/3.86 Prover 1: stopped
% 22.41/3.87 Prover 10: Preprocessing ...
% 22.41/3.87 Prover 7: Preprocessing ...
% 22.41/3.87 Prover 8: Preprocessing ...
% 22.41/3.88 Prover 11: Preprocessing ...
% 22.41/3.91 Prover 10: stopped
% 22.41/3.92 Prover 7: stopped
% 22.95/3.93 Prover 13: stopped
% 23.15/4.01 Prover 11: stopped
% 23.70/4.12 Prover 8: Warning: ignoring some quantifiers
% 23.70/4.13 Prover 8: Constructing countermodel ...
% 23.70/4.15 Prover 8: stopped
% 23.70/4.15
% 23.70/4.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.70/4.15
% 23.70/4.17 % SZS output start Proof for theBenchmark
% 23.70/4.18 Assumptions after simplification:
% 23.70/4.18 ---------------------------------
% 23.70/4.18
% 23.70/4.18 (compose_function)
% 23.70/4.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 23.70/4.23 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~
% 23.70/4.23 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) |
% 23.70/4.23 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 23.70/4.23 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any]
% 23.70/4.23 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10
% 23.70/4.23 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 =
% 23.70/4.23 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 23.70/4.23 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 23.70/4.23 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) =
% 23.70/4.23 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9)
% 23.70/4.23 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 23.70/4.23 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 &
% 23.70/4.23 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4)
% 23.70/4.23 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & !
% 23.70/4.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 23.70/4.23 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~
% 23.70/4.23 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) |
% 23.70/4.23 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 23.70/4.23 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] :
% 23.70/4.24 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~
% 23.70/4.24 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11
% 23.70/4.24 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.70/4.24 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 23.70/4.24 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) |
% 23.70/4.24 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 23.70/4.24 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ?
% 23.70/4.24 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 &
% 23.70/4.24 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0)
% 23.70/4.24 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 =
% 23.70/4.24 0))))))
% 23.70/4.24
% 23.70/4.24 (maps)
% 24.41/4.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 24.41/4.25 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~
% 24.41/4.25 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 24.41/4.25 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 24.41/4.25 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 =
% 24.41/4.25 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 24.41/4.25 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0,
% 24.41/4.25 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~
% 24.41/4.25 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 24.41/4.25 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5,
% 24.41/4.25 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 =
% 24.41/4.25 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 24.41/4.25 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0,
% 24.41/4.25 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 24.41/4.25 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 24.41/4.25 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1)
% 24.41/4.25 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1:
% 24.41/4.25 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 24.41/4.25 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) |
% 24.41/4.25 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 24.41/4.25 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 &
% 24.41/4.25 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : !
% 24.41/4.25 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) |
% 24.41/4.25 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 24.41/4.25 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int]
% 24.41/4.25 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13
% 24.41/4.25 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) =
% 24.41/4.25 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2)
% 24.41/4.25 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) |
% 24.41/4.25 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 =
% 24.41/4.25 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4,
% 24.41/4.25 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5,
% 24.41/4.25 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 24.41/4.25 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0)
% 24.41/4.25 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0,
% 24.41/4.25 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4)))
% 24.41/4.25
% 24.41/4.25 (one_to_one)
% 24.41/4.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 24.41/4.26 (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 24.41/4.26 any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 & injective(v0, v1, v2)
% 24.41/4.26 = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 24.41/4.26 $i] : ! [v3: any] : ( ~ (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~
% 24.41/4.26 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) =
% 24.41/4.26 v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & !
% 24.41/4.26 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (injective(v0, v1,
% 24.41/4.26 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 24.41/4.26 any] : (one_to_one(v0, v1, v2) = v4 & surjective(v0, v1, v2) = v5 & ( ~
% 24.41/4.26 (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 24.41/4.26 $i] : ( ~ (one_to_one(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.41/4.26 (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0: $i] : !
% 24.41/4.26 [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ $i(v2) | ~
% 24.41/4.26 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) =
% 24.41/4.26 v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] :
% 24.41/4.26 ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~
% 24.41/4.26 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) =
% 24.41/4.26 v4 & surjective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 24.41/4.26
% 24.41/4.26 (surjective)
% 24.58/4.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 24.58/4.27 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 24.58/4.27 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4)
% 24.58/4.27 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))
% 24.58/4.27 & ! [v5: $i] : ( ~ (member(v5, v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~
% 24.58/4.27 (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0: $i] : ! [v1: $i] : !
% 24.58/4.27 [v2: $i] : ! [v3: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2)
% 24.58/4.27 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 24.58/4.27 (apply(v0, v4, v3) = 0 & member(v4, v1) = 0 & $i(v4)))
% 24.58/4.27
% 24.58/4.27 (thII08)
% 24.58/4.27 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 24.58/4.27 $i] : ? [v6: int] : ( ~ (v6 = 0) & surjective(v5, v2, v4) = v6 &
% 24.58/4.27 surjective(v1, v3, v4) = 0 & surjective(v0, v2, v3) = 0 &
% 24.58/4.27 compose_function(v1, v0, v2, v3, v4) = v5 & maps(v1, v3, v4) = 0 & maps(v0,
% 24.58/4.27 v2, v3) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 24.58/4.27
% 24.58/4.27 (function-axioms)
% 24.58/4.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 24.58/4.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 24.58/4.29 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 24.58/4.29 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 24.58/4.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.58/4.29 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 24.58/4.29 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 24.58/4.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.58/4.29 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 24.58/4.29 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 24.58/4.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.58/4.29 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 24.58/4.29 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 24.58/4.29 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 24.58/4.29 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 24.58/4.29 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 24.58/4.29 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 24.58/4.29 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 24.58/4.29 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 24.58/4.29 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 24.58/4.29 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 24.58/4.29 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 24.58/4.29 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 24.58/4.29 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 24.58/4.29 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 24.58/4.29 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.58/4.29 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 24.58/4.29 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 24.58/4.29 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 24.58/4.29 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 24.58/4.29 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 24.58/4.29 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 24.58/4.29 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.58/4.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 24.58/4.29 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 24.58/4.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.58/4.29 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 24.58/4.29 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 24.58/4.29 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 24.58/4.29 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.58/4.29 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 24.58/4.29 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 24.58/4.29 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 24.58/4.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 24.58/4.29 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 24.58/4.29 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.58/4.29 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 24.58/4.29 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.58/4.29 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 24.58/4.29 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 24.58/4.29 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 24.58/4.29 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 24.58/4.29 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 24.58/4.29 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 24.58/4.29 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.58/4.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 24.58/4.29 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 24.58/4.29 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.58/4.29 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 24.58/4.29 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 24.58/4.29 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 24.58/4.29 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 24.58/4.29 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 24.58/4.29 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 24.58/4.29 (power_set(v2) = v0))
% 24.58/4.29
% 24.58/4.29 Further assumptions not needed in the proof:
% 24.58/4.29 --------------------------------------------
% 24.58/4.29 compose_predicate, decreasing_function, difference, empty_set, equal_maps,
% 24.58/4.29 equal_set, identity, image2, image3, increasing_function, injective,
% 24.58/4.29 intersection, inverse_function, inverse_image2, inverse_image3,
% 24.58/4.29 inverse_predicate, isomorphism, power_set, product, singleton, subset, sum,
% 24.58/4.29 union, unordered_pair
% 24.58/4.29
% 24.58/4.29 Those formulas are unsatisfiable:
% 24.58/4.29 ---------------------------------
% 24.58/4.29
% 24.58/4.29 Begin of proof
% 24.58/4.29 |
% 24.58/4.29 | ALPHA: (maps) implies:
% 24.58/4.30 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0,
% 24.58/4.30 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) |
% 24.58/4.30 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 &
% 24.58/4.30 | member(v4, v2) = 0 & $i(v4)))
% 24.58/4.30 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 24.58/4.30 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2)
% 24.58/4.30 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~
% 24.58/4.30 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.58/4.30 | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3,
% 24.58/4.30 | v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 24.58/4.30 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 24.58/4.30 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3,
% 24.58/4.30 | v5) = 0) | ~ (member(v4, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 24.58/4.30 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 24.58/4.30 | any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, v2) = v7
% 24.58/4.30 | & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 24.58/4.30 |
% 24.58/4.30 | ALPHA: (compose_function) implies:
% 24.58/4.31 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 24.58/4.31 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] :
% 24.58/4.31 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~
% 24.58/4.31 | (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) |
% 24.58/4.31 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 24.58/4.31 | | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) =
% 24.58/4.31 | v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) |
% 24.58/4.31 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~
% 24.58/4.31 | (v10 = 0)))))
% 24.58/4.31 |
% 24.58/4.31 | ALPHA: (surjective) implies:
% 24.58/4.31 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 24.58/4.31 | (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ~ $i(v3) |
% 24.58/4.31 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v4, v3) =
% 24.58/4.31 | 0 & member(v4, v1) = 0 & $i(v4)))
% 24.58/4.31 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 24.58/4.31 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.58/4.31 | ? [v4: $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~
% 24.58/4.31 | (apply(v0, v5, v4) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0)
% 24.58/4.31 | & member(v5, v1) = v6)) & ! [v5: $i] : ( ~ (member(v5, v1) =
% 24.58/4.31 | 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & apply(v0, v5,
% 24.58/4.31 | v4) = v6))))
% 24.58/4.31 |
% 24.58/4.31 | ALPHA: (one_to_one) implies:
% 24.58/4.31 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) =
% 24.58/4.31 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 24.58/4.31 | any] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v3 &
% 24.58/4.31 | ( ~ (v3 = 0) | v4 = 0)))
% 24.58/4.31 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.58/4.31 | (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.58/4.31 | [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) = v4 &
% 24.58/4.31 | surjective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0))))
% 24.58/4.32 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.58/4.32 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.58/4.32 | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) = v4 &
% 24.58/4.32 | injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0))))
% 24.58/4.32 |
% 24.58/4.32 | ALPHA: (function-axioms) implies:
% 24.58/4.32 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.58/4.32 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3,
% 24.58/4.32 | v2) = v0))
% 24.58/4.32 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.58/4.32 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 24.58/4.32 | ~ (apply(v4, v3, v2) = v0))
% 24.58/4.32 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.58/4.32 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (injective(v4, v3, v2) =
% 24.58/4.32 | v1) | ~ (injective(v4, v3, v2) = v0))
% 24.58/4.32 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.58/4.32 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) =
% 24.58/4.32 | v1) | ~ (surjective(v4, v3, v2) = v0))
% 24.58/4.32 |
% 24.58/4.32 | DELTA: instantiating (thII08) with fresh symbols all_32_0, all_32_1, all_32_2,
% 24.58/4.32 | all_32_3, all_32_4, all_32_5, all_32_6 gives:
% 24.58/4.32 | (14) ~ (all_32_0 = 0) & surjective(all_32_1, all_32_4, all_32_2) =
% 24.58/4.32 | all_32_0 & surjective(all_32_5, all_32_3, all_32_2) = 0 &
% 24.58/4.32 | surjective(all_32_6, all_32_4, all_32_3) = 0 &
% 24.58/4.32 | compose_function(all_32_5, all_32_6, all_32_4, all_32_3, all_32_2) =
% 24.58/4.32 | all_32_1 & maps(all_32_5, all_32_3, all_32_2) = 0 & maps(all_32_6,
% 24.58/4.32 | all_32_4, all_32_3) = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3)
% 24.58/4.32 | & $i(all_32_4) & $i(all_32_5) & $i(all_32_6)
% 24.58/4.32 |
% 24.58/4.32 | ALPHA: (14) implies:
% 24.58/4.32 | (15) ~ (all_32_0 = 0)
% 24.58/4.32 | (16) $i(all_32_6)
% 24.58/4.32 | (17) $i(all_32_5)
% 24.58/4.32 | (18) $i(all_32_4)
% 24.58/4.32 | (19) $i(all_32_3)
% 24.58/4.32 | (20) $i(all_32_2)
% 24.58/4.32 | (21) $i(all_32_1)
% 24.58/4.32 | (22) maps(all_32_5, all_32_3, all_32_2) = 0
% 24.58/4.32 | (23) compose_function(all_32_5, all_32_6, all_32_4, all_32_3, all_32_2) =
% 24.58/4.32 | all_32_1
% 24.58/4.33 | (24) surjective(all_32_6, all_32_4, all_32_3) = 0
% 24.58/4.33 | (25) surjective(all_32_5, all_32_3, all_32_2) = 0
% 24.58/4.33 | (26) surjective(all_32_1, all_32_4, all_32_2) = all_32_0
% 24.58/4.33 |
% 24.58/4.33 | GROUND_INST: instantiating (7) with all_32_6, all_32_4, all_32_3, simplifying
% 24.58/4.33 | with (16), (18), (19), (24) gives:
% 24.58/4.33 | (27) ? [v0: any] : ? [v1: any] : (one_to_one(all_32_6, all_32_4,
% 24.58/4.33 | all_32_3) = v1 & injective(all_32_6, all_32_4, all_32_3) = v0 & (
% 24.58/4.33 | ~ (v0 = 0) | v1 = 0))
% 24.58/4.33 |
% 24.58/4.33 | GROUND_INST: instantiating (9) with all_32_6, all_32_4, all_32_3, 0,
% 24.58/4.33 | simplifying with (16), (18), (19), (24) gives:
% 24.58/4.33 | (28) ? [v0: any] : ? [v1: any] : (one_to_one(all_32_6, all_32_4,
% 24.58/4.33 | all_32_3) = v0 & injective(all_32_6, all_32_4, all_32_3) = v1 & (
% 24.58/4.33 | ~ (v0 = 0) | v1 = 0))
% 24.58/4.33 |
% 24.58/4.33 | GROUND_INST: instantiating (6) with all_32_1, all_32_4, all_32_2, all_32_0,
% 24.58/4.33 | simplifying with (18), (20), (21), (26) gives:
% 24.92/4.33 | (29) all_32_0 = 0 | ? [v0: $i] : (member(v0, all_32_2) = 0 & $i(v0) & !
% 24.92/4.33 | [v1: $i] : ( ~ (apply(all_32_1, v1, v0) = 0) | ~ $i(v1) | ? [v2:
% 24.92/4.33 | int] : ( ~ (v2 = 0) & member(v1, all_32_4) = v2)) & ! [v1: $i]
% 24.92/4.33 | : ( ~ (member(v1, all_32_4) = 0) | ~ $i(v1) | ? [v2: int] : ( ~
% 24.92/4.33 | (v2 = 0) & apply(all_32_1, v1, v0) = v2)))
% 24.92/4.33 |
% 24.92/4.33 | DELTA: instantiating (28) with fresh symbols all_43_0, all_43_1 gives:
% 24.92/4.33 | (30) one_to_one(all_32_6, all_32_4, all_32_3) = all_43_1 &
% 24.92/4.33 | injective(all_32_6, all_32_4, all_32_3) = all_43_0 & ( ~ (all_43_1 =
% 24.92/4.33 | 0) | all_43_0 = 0)
% 24.92/4.33 |
% 24.92/4.33 | ALPHA: (30) implies:
% 24.92/4.33 | (31) injective(all_32_6, all_32_4, all_32_3) = all_43_0
% 24.92/4.33 |
% 24.92/4.33 | DELTA: instantiating (27) with fresh symbols all_45_0, all_45_1 gives:
% 24.92/4.33 | (32) one_to_one(all_32_6, all_32_4, all_32_3) = all_45_0 &
% 24.92/4.33 | injective(all_32_6, all_32_4, all_32_3) = all_45_1 & ( ~ (all_45_1 =
% 24.92/4.33 | 0) | all_45_0 = 0)
% 24.92/4.33 |
% 24.92/4.33 | ALPHA: (32) implies:
% 24.92/4.33 | (33) injective(all_32_6, all_32_4, all_32_3) = all_45_1
% 24.92/4.33 |
% 24.92/4.33 | BETA: splitting (29) gives:
% 24.92/4.33 |
% 24.92/4.33 | Case 1:
% 24.92/4.33 | |
% 24.92/4.34 | | (34) all_32_0 = 0
% 24.92/4.34 | |
% 24.92/4.34 | | REDUCE: (15), (34) imply:
% 24.92/4.34 | | (35) $false
% 24.92/4.34 | |
% 24.92/4.34 | | CLOSE: (35) is inconsistent.
% 24.92/4.34 | |
% 24.92/4.34 | Case 2:
% 24.92/4.34 | |
% 24.92/4.34 | | (36) ? [v0: $i] : (member(v0, all_32_2) = 0 & $i(v0) & ! [v1: $i] : ( ~
% 24.92/4.34 | | (apply(all_32_1, v1, v0) = 0) | ~ $i(v1) | ? [v2: int] : ( ~
% 24.92/4.34 | | (v2 = 0) & member(v1, all_32_4) = v2)) & ! [v1: $i] : ( ~
% 24.92/4.34 | | (member(v1, all_32_4) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2
% 24.92/4.34 | | = 0) & apply(all_32_1, v1, v0) = v2)))
% 24.92/4.34 | |
% 24.92/4.34 | | DELTA: instantiating (36) with fresh symbol all_56_0 gives:
% 24.92/4.34 | | (37) member(all_56_0, all_32_2) = 0 & $i(all_56_0) & ! [v0: $i] : ( ~
% 24.92/4.34 | | (apply(all_32_1, v0, all_56_0) = 0) | ~ $i(v0) | ? [v1: int] : (
% 24.92/4.34 | | ~ (v1 = 0) & member(v0, all_32_4) = v1)) & ! [v0: $i] : ( ~
% 24.92/4.34 | | (member(v0, all_32_4) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 24.92/4.34 | | 0) & apply(all_32_1, v0, all_56_0) = v1))
% 24.92/4.34 | |
% 24.92/4.34 | | ALPHA: (37) implies:
% 24.92/4.34 | | (38) $i(all_56_0)
% 24.92/4.34 | | (39) member(all_56_0, all_32_2) = 0
% 24.92/4.34 | | (40) ! [v0: $i] : ( ~ (member(v0, all_32_4) = 0) | ~ $i(v0) | ? [v1:
% 24.92/4.34 | | int] : ( ~ (v1 = 0) & apply(all_32_1, v0, all_56_0) = v1))
% 24.92/4.34 | |
% 24.92/4.34 | | GROUND_INST: instantiating (12) with all_43_0, all_45_1, all_32_3, all_32_4,
% 24.92/4.34 | | all_32_6, simplifying with (31), (33) gives:
% 24.92/4.34 | | (41) all_45_1 = all_43_0
% 24.92/4.34 | |
% 24.92/4.34 | | GROUND_INST: instantiating (5) with all_32_5, all_32_3, all_32_2, all_56_0,
% 24.92/4.34 | | simplifying with (17), (19), (20), (25), (38), (39) gives:
% 24.92/4.34 | | (42) ? [v0: $i] : (apply(all_32_5, v0, all_56_0) = 0 & member(v0,
% 24.92/4.34 | | all_32_3) = 0 & $i(v0))
% 24.92/4.34 | |
% 24.92/4.35 | | GROUND_INST: instantiating (8) with all_32_6, all_32_4, all_32_3, all_43_0,
% 24.92/4.35 | | simplifying with (16), (18), (19), (31) gives:
% 24.92/4.35 | | (43) ? [v0: any] : ? [v1: any] : (one_to_one(all_32_6, all_32_4,
% 24.92/4.35 | | all_32_3) = v0 & surjective(all_32_6, all_32_4, all_32_3) = v1 &
% 24.92/4.35 | | ( ~ (v0 = 0) | (v1 = 0 & all_43_0 = 0)))
% 24.92/4.35 | |
% 24.92/4.35 | | DELTA: instantiating (42) with fresh symbol all_68_0 gives:
% 24.92/4.35 | | (44) apply(all_32_5, all_68_0, all_56_0) = 0 & member(all_68_0, all_32_3)
% 24.92/4.35 | | = 0 & $i(all_68_0)
% 24.92/4.35 | |
% 24.92/4.35 | | ALPHA: (44) implies:
% 24.92/4.35 | | (45) $i(all_68_0)
% 24.92/4.35 | | (46) member(all_68_0, all_32_3) = 0
% 24.92/4.35 | | (47) apply(all_32_5, all_68_0, all_56_0) = 0
% 24.92/4.35 | |
% 24.92/4.35 | | DELTA: instantiating (43) with fresh symbols all_72_0, all_72_1 gives:
% 24.92/4.35 | | (48) one_to_one(all_32_6, all_32_4, all_32_3) = all_72_1 &
% 24.92/4.35 | | surjective(all_32_6, all_32_4, all_32_3) = all_72_0 & ( ~ (all_72_1
% 24.92/4.35 | | = 0) | (all_72_0 = 0 & all_43_0 = 0))
% 24.92/4.35 | |
% 24.92/4.35 | | ALPHA: (48) implies:
% 24.92/4.35 | | (49) surjective(all_32_6, all_32_4, all_32_3) = all_72_0
% 24.92/4.35 | |
% 24.92/4.35 | | GROUND_INST: instantiating (13) with 0, all_72_0, all_32_3, all_32_4,
% 24.92/4.35 | | all_32_6, simplifying with (24), (49) gives:
% 24.92/4.35 | | (50) all_72_0 = 0
% 24.92/4.35 | |
% 24.92/4.35 | | GROUND_INST: instantiating (1) with all_32_5, all_32_3, all_32_2, all_68_0,
% 24.92/4.35 | | simplifying with (17), (19), (20), (22), (45), (46) gives:
% 24.92/4.35 | | (51) ? [v0: $i] : (apply(all_32_5, all_68_0, v0) = 0 & member(v0,
% 24.92/4.35 | | all_32_2) = 0 & $i(v0))
% 24.92/4.35 | |
% 24.92/4.35 | | GROUND_INST: instantiating (5) with all_32_6, all_32_4, all_32_3, all_68_0,
% 24.92/4.35 | | simplifying with (16), (18), (19), (24), (45), (46) gives:
% 24.92/4.35 | | (52) ? [v0: $i] : (apply(all_32_6, v0, all_68_0) = 0 & member(v0,
% 24.92/4.35 | | all_32_4) = 0 & $i(v0))
% 24.92/4.35 | |
% 24.92/4.35 | | DELTA: instantiating (52) with fresh symbol all_89_0 gives:
% 24.92/4.35 | | (53) apply(all_32_6, all_89_0, all_68_0) = 0 & member(all_89_0, all_32_4)
% 24.92/4.35 | | = 0 & $i(all_89_0)
% 24.92/4.35 | |
% 24.92/4.35 | | ALPHA: (53) implies:
% 24.92/4.35 | | (54) $i(all_89_0)
% 24.92/4.35 | | (55) member(all_89_0, all_32_4) = 0
% 24.92/4.35 | | (56) apply(all_32_6, all_89_0, all_68_0) = 0
% 24.92/4.35 | |
% 24.92/4.35 | | DELTA: instantiating (51) with fresh symbol all_91_0 gives:
% 24.92/4.35 | | (57) apply(all_32_5, all_68_0, all_91_0) = 0 & member(all_91_0, all_32_2)
% 24.92/4.35 | | = 0 & $i(all_91_0)
% 24.92/4.35 | |
% 24.92/4.35 | | ALPHA: (57) implies:
% 24.92/4.35 | | (58) $i(all_91_0)
% 24.92/4.35 | | (59) member(all_91_0, all_32_2) = 0
% 24.92/4.35 | | (60) apply(all_32_5, all_68_0, all_91_0) = 0
% 24.92/4.35 | |
% 24.92/4.35 | | GROUND_INST: instantiating (40) with all_89_0, simplifying with (54), (55)
% 24.92/4.35 | | gives:
% 24.92/4.35 | | (61) ? [v0: int] : ( ~ (v0 = 0) & apply(all_32_1, all_89_0, all_56_0) =
% 24.92/4.35 | | v0)
% 24.92/4.35 | |
% 24.92/4.36 | | GROUND_INST: instantiating (2) with all_32_5, all_32_3, all_32_2, all_68_0,
% 24.92/4.36 | | all_56_0, all_91_0, simplifying with (17), (19), (20), (22),
% 24.92/4.36 | | (38), (39), (45), (46), (58), (59) gives:
% 24.92/4.36 | | (62) all_91_0 = all_56_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_5,
% 24.92/4.36 | | all_68_0, all_91_0) = v1 & apply(all_32_5, all_68_0, all_56_0) =
% 24.92/4.36 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 24.92/4.36 | |
% 24.92/4.36 | | GROUND_INST: instantiating (3) with all_32_5, all_32_3, all_32_2, all_68_0,
% 24.92/4.36 | | all_56_0, all_91_0, simplifying with (17), (19), (20), (22),
% 24.92/4.36 | | (38), (39), (45), (58), (60) gives:
% 24.92/4.36 | | (63) all_91_0 = all_56_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 24.92/4.36 | | (apply(all_32_5, all_68_0, all_56_0) = v2 & member(all_91_0,
% 24.92/4.36 | | all_32_2) = v1 & member(all_68_0, all_32_3) = v0 & ( ~ (v2 = 0)
% 24.92/4.36 | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 24.92/4.36 | |
% 24.92/4.36 | | DELTA: instantiating (61) with fresh symbol all_98_0 gives:
% 24.92/4.36 | | (64) ~ (all_98_0 = 0) & apply(all_32_1, all_89_0, all_56_0) = all_98_0
% 24.92/4.36 | |
% 24.92/4.36 | | ALPHA: (64) implies:
% 24.92/4.36 | | (65) ~ (all_98_0 = 0)
% 24.92/4.36 | | (66) apply(all_32_1, all_89_0, all_56_0) = all_98_0
% 24.92/4.36 | |
% 24.92/4.36 | | BETA: splitting (63) gives:
% 24.92/4.36 | |
% 24.92/4.36 | | Case 1:
% 24.92/4.36 | | |
% 24.92/4.36 | | | (67) all_91_0 = all_56_0
% 24.92/4.36 | | |
% 24.92/4.36 | | | GROUND_INST: instantiating (4) with all_32_5, all_32_6, all_32_4,
% 24.92/4.36 | | | all_32_3, all_32_2, all_89_0, all_56_0, all_32_1, all_98_0,
% 24.92/4.36 | | | all_68_0, simplifying with (16), (17), (18), (19), (20),
% 24.92/4.36 | | | (23), (38), (45), (47), (54), (66) gives:
% 24.92/4.36 | | | (68) all_98_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_6,
% 24.92/4.36 | | | all_89_0, all_68_0) = v1 & member(all_68_0, all_32_3) = v0 &
% 24.92/4.36 | | | ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_89_0, all_32_4) =
% 24.92/4.36 | | | v0 & member(all_56_0, all_32_2) = v1 & ( ~ (v1 = 0) | ~ (v0 =
% 24.92/4.36 | | | 0))))
% 24.92/4.36 | | |
% 24.92/4.36 | | | BETA: splitting (68) gives:
% 24.92/4.36 | | |
% 24.92/4.36 | | | Case 1:
% 24.92/4.36 | | | |
% 24.92/4.36 | | | | (69) all_98_0 = 0
% 24.92/4.36 | | | |
% 24.92/4.36 | | | | REDUCE: (65), (69) imply:
% 24.92/4.36 | | | | (70) $false
% 24.92/4.36 | | | |
% 24.92/4.36 | | | | CLOSE: (70) is inconsistent.
% 24.92/4.36 | | | |
% 24.92/4.36 | | | Case 2:
% 24.92/4.36 | | | |
% 25.08/4.36 | | | | (71) ? [v0: any] : ? [v1: any] : ((apply(all_32_6, all_89_0,
% 25.08/4.36 | | | | all_68_0) = v1 & member(all_68_0, all_32_3) = v0 & ( ~ (v1
% 25.08/4.36 | | | | = 0) | ~ (v0 = 0))) | (member(all_89_0, all_32_4) = v0
% 25.08/4.36 | | | | & member(all_56_0, all_32_2) = v1 & ( ~ (v1 = 0) | ~ (v0 =
% 25.08/4.36 | | | | 0))))
% 25.08/4.36 | | | |
% 25.08/4.36 | | | | DELTA: instantiating (71) with fresh symbols all_161_0, all_161_1 gives:
% 25.08/4.37 | | | | (72) (apply(all_32_6, all_89_0, all_68_0) = all_161_0 &
% 25.08/4.37 | | | | member(all_68_0, all_32_3) = all_161_1 & ( ~ (all_161_0 = 0) |
% 25.08/4.37 | | | | ~ (all_161_1 = 0))) | (member(all_89_0, all_32_4) =
% 25.08/4.37 | | | | all_161_1 & member(all_56_0, all_32_2) = all_161_0 & ( ~
% 25.08/4.37 | | | | (all_161_0 = 0) | ~ (all_161_1 = 0)))
% 25.08/4.37 | | | |
% 25.08/4.37 | | | | BETA: splitting (72) gives:
% 25.08/4.37 | | | |
% 25.08/4.37 | | | | Case 1:
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | | (73) apply(all_32_6, all_89_0, all_68_0) = all_161_0 &
% 25.08/4.37 | | | | | member(all_68_0, all_32_3) = all_161_1 & ( ~ (all_161_0 = 0) |
% 25.08/4.37 | | | | | ~ (all_161_1 = 0))
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | | ALPHA: (73) implies:
% 25.08/4.37 | | | | | (74) member(all_68_0, all_32_3) = all_161_1
% 25.08/4.37 | | | | | (75) apply(all_32_6, all_89_0, all_68_0) = all_161_0
% 25.08/4.37 | | | | | (76) ~ (all_161_0 = 0) | ~ (all_161_1 = 0)
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | | GROUND_INST: instantiating (10) with 0, all_161_1, all_32_3, all_68_0,
% 25.08/4.37 | | | | | simplifying with (46), (74) gives:
% 25.08/4.37 | | | | | (77) all_161_1 = 0
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | | GROUND_INST: instantiating (11) with 0, all_161_0, all_68_0, all_89_0,
% 25.08/4.37 | | | | | all_32_6, simplifying with (56), (75) gives:
% 25.08/4.37 | | | | | (78) all_161_0 = 0
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | | REF_CLOSE: (76), (77), (78) are inconsistent by sub-proof #1.
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | Case 2:
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | | (79) member(all_89_0, all_32_4) = all_161_1 & member(all_56_0,
% 25.08/4.37 | | | | | all_32_2) = all_161_0 & ( ~ (all_161_0 = 0) | ~ (all_161_1
% 25.08/4.37 | | | | | = 0))
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | | ALPHA: (79) implies:
% 25.08/4.37 | | | | | (80) member(all_56_0, all_32_2) = all_161_0
% 25.08/4.37 | | | | | (81) member(all_89_0, all_32_4) = all_161_1
% 25.08/4.37 | | | | | (82) ~ (all_161_0 = 0) | ~ (all_161_1 = 0)
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | | GROUND_INST: instantiating (10) with 0, all_161_0, all_32_2, all_56_0,
% 25.08/4.37 | | | | | simplifying with (39), (80) gives:
% 25.08/4.37 | | | | | (83) all_161_0 = 0
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | | GROUND_INST: instantiating (10) with 0, all_161_1, all_32_4, all_89_0,
% 25.08/4.37 | | | | | simplifying with (55), (81) gives:
% 25.08/4.37 | | | | | (84) all_161_1 = 0
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | | REF_CLOSE: (82), (83), (84) are inconsistent by sub-proof #1.
% 25.08/4.37 | | | | |
% 25.08/4.37 | | | | End of split
% 25.08/4.37 | | | |
% 25.08/4.37 | | | End of split
% 25.08/4.37 | | |
% 25.08/4.37 | | Case 2:
% 25.08/4.37 | | |
% 25.08/4.37 | | | (85) ~ (all_91_0 = all_56_0)
% 25.08/4.37 | | |
% 25.08/4.37 | | | BETA: splitting (62) gives:
% 25.08/4.37 | | |
% 25.08/4.37 | | | Case 1:
% 25.08/4.37 | | | |
% 25.08/4.37 | | | | (86) all_91_0 = all_56_0
% 25.08/4.37 | | | |
% 25.08/4.37 | | | | REDUCE: (85), (86) imply:
% 25.08/4.37 | | | | (87) $false
% 25.08/4.37 | | | |
% 25.08/4.37 | | | | CLOSE: (87) is inconsistent.
% 25.08/4.37 | | | |
% 25.08/4.37 | | | Case 2:
% 25.08/4.37 | | | |
% 25.08/4.38 | | | | (88) ? [v0: any] : ? [v1: any] : (apply(all_32_5, all_68_0,
% 25.08/4.38 | | | | all_91_0) = v1 & apply(all_32_5, all_68_0, all_56_0) = v0 &
% 25.08/4.38 | | | | ( ~ (v1 = 0) | ~ (v0 = 0)))
% 25.08/4.38 | | | |
% 25.08/4.38 | | | | DELTA: instantiating (88) with fresh symbols all_114_0, all_114_1 gives:
% 25.08/4.38 | | | | (89) apply(all_32_5, all_68_0, all_91_0) = all_114_0 &
% 25.08/4.38 | | | | apply(all_32_5, all_68_0, all_56_0) = all_114_1 & ( ~ (all_114_0
% 25.08/4.38 | | | | = 0) | ~ (all_114_1 = 0))
% 25.08/4.38 | | | |
% 25.08/4.38 | | | | ALPHA: (89) implies:
% 25.08/4.38 | | | | (90) apply(all_32_5, all_68_0, all_56_0) = all_114_1
% 25.08/4.38 | | | | (91) apply(all_32_5, all_68_0, all_91_0) = all_114_0
% 25.08/4.38 | | | | (92) ~ (all_114_0 = 0) | ~ (all_114_1 = 0)
% 25.08/4.38 | | | |
% 25.08/4.38 | | | | GROUND_INST: instantiating (11) with 0, all_114_1, all_56_0, all_68_0,
% 25.08/4.38 | | | | all_32_5, simplifying with (47), (90) gives:
% 25.08/4.38 | | | | (93) all_114_1 = 0
% 25.08/4.38 | | | |
% 25.08/4.38 | | | | GROUND_INST: instantiating (11) with 0, all_114_0, all_91_0, all_68_0,
% 25.08/4.38 | | | | all_32_5, simplifying with (60), (91) gives:
% 25.08/4.38 | | | | (94) all_114_0 = 0
% 25.08/4.38 | | | |
% 25.08/4.38 | | | | BETA: splitting (92) gives:
% 25.08/4.38 | | | |
% 25.08/4.38 | | | | Case 1:
% 25.08/4.38 | | | | |
% 25.08/4.38 | | | | | (95) ~ (all_114_0 = 0)
% 25.08/4.38 | | | | |
% 25.08/4.38 | | | | | REDUCE: (94), (95) imply:
% 25.08/4.38 | | | | | (96) $false
% 25.08/4.38 | | | | |
% 25.08/4.38 | | | | | CLOSE: (96) is inconsistent.
% 25.08/4.38 | | | | |
% 25.08/4.38 | | | | Case 2:
% 25.08/4.38 | | | | |
% 25.08/4.38 | | | | | (97) ~ (all_114_1 = 0)
% 25.08/4.38 | | | | |
% 25.08/4.38 | | | | | REDUCE: (93), (97) imply:
% 25.08/4.38 | | | | | (98) $false
% 25.08/4.38 | | | | |
% 25.08/4.38 | | | | | CLOSE: (98) is inconsistent.
% 25.08/4.38 | | | | |
% 25.08/4.38 | | | | End of split
% 25.08/4.38 | | | |
% 25.08/4.38 | | | End of split
% 25.08/4.38 | | |
% 25.08/4.38 | | End of split
% 25.08/4.38 | |
% 25.08/4.38 | End of split
% 25.08/4.38 |
% 25.08/4.38 End of proof
% 25.08/4.38
% 25.08/4.38 Sub-proof #1 shows that the following formulas are inconsistent:
% 25.08/4.38 ----------------------------------------------------------------
% 25.08/4.38 (1) ~ (all_161_0 = 0) | ~ (all_161_1 = 0)
% 25.08/4.38 (2) all_161_0 = 0
% 25.08/4.38 (3) all_161_1 = 0
% 25.08/4.38
% 25.08/4.38 Begin of proof
% 25.08/4.38 |
% 25.08/4.38 | BETA: splitting (1) gives:
% 25.08/4.38 |
% 25.08/4.38 | Case 1:
% 25.08/4.38 | |
% 25.08/4.38 | | (4) ~ (all_161_0 = 0)
% 25.08/4.38 | |
% 25.08/4.38 | | REDUCE: (2), (4) imply:
% 25.08/4.38 | | (5) $false
% 25.08/4.38 | |
% 25.08/4.38 | | CLOSE: (5) is inconsistent.
% 25.08/4.38 | |
% 25.08/4.38 | Case 2:
% 25.08/4.38 | |
% 25.08/4.38 | | (6) ~ (all_161_1 = 0)
% 25.08/4.38 | |
% 25.08/4.38 | | REDUCE: (3), (6) imply:
% 25.08/4.38 | | (7) $false
% 25.08/4.38 | |
% 25.08/4.38 | | CLOSE: (7) is inconsistent.
% 25.08/4.38 | |
% 25.08/4.38 | End of split
% 25.08/4.38 |
% 25.08/4.38 End of proof
% 25.08/4.38 % SZS output end Proof for theBenchmark
% 25.08/4.38
% 25.08/4.39 3739ms
%------------------------------------------------------------------------------