TSTP Solution File: SET712+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET712+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 : n002.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 17.59s 3.11s
% Output : Proof 18.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET712+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 13:43:33 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.43/1.17 Prover 4: Preprocessing ...
% 3.43/1.17 Prover 1: Preprocessing ...
% 3.43/1.21 Prover 2: Preprocessing ...
% 3.43/1.21 Prover 6: Preprocessing ...
% 3.43/1.21 Prover 0: Preprocessing ...
% 3.43/1.21 Prover 3: Preprocessing ...
% 3.43/1.23 Prover 5: Preprocessing ...
% 8.66/1.92 Prover 5: Proving ...
% 8.66/1.94 Prover 2: Proving ...
% 8.66/1.98 Prover 6: Proving ...
% 8.66/2.03 Prover 1: Constructing countermodel ...
% 8.66/2.04 Prover 3: Constructing countermodel ...
% 10.44/2.20 Prover 3: gave up
% 10.44/2.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.12/2.28 Prover 7: Preprocessing ...
% 12.51/2.42 Prover 1: gave up
% 12.51/2.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.69/2.46 Prover 7: Warning: ignoring some quantifiers
% 12.69/2.49 Prover 8: Preprocessing ...
% 12.69/2.51 Prover 7: Constructing countermodel ...
% 12.69/2.58 Prover 4: Constructing countermodel ...
% 15.25/2.79 Prover 0: Proving ...
% 15.79/2.86 Prover 8: Warning: ignoring some quantifiers
% 15.96/2.89 Prover 8: Constructing countermodel ...
% 17.59/3.10 Prover 4: Found proof (size 91)
% 17.59/3.10 Prover 4: proved (2481ms)
% 17.59/3.11 Prover 5: stopped
% 17.59/3.11 Prover 2: stopped
% 17.59/3.11 Prover 6: stopped
% 17.59/3.11 Prover 8: stopped
% 17.59/3.11 Prover 0: proved (2489ms)
% 17.59/3.11 Prover 7: stopped
% 17.59/3.11
% 17.59/3.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.59/3.11
% 17.59/3.12 % SZS output start Proof for theBenchmark
% 17.59/3.13 Assumptions after simplification:
% 17.59/3.13 ---------------------------------
% 17.59/3.13
% 17.59/3.13 (injective)
% 18.01/3.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.01/3.17 $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0)
% 18.01/3.17 | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 18.01/3.17 | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 18.01/3.17 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 =
% 18.01/3.17 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 18.01/3.17 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~
% 18.01/3.17 (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3,
% 18.01/3.17 v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 18.01/3.17 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v5) =
% 18.01/3.17 v8 & member(v5, v2) = v7 & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 =
% 18.01/3.17 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 18.01/3.17 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) =
% 18.01/3.17 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ~ $i(v5) | ~
% 18.01/3.17 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 18.01/3.17 [v7: any] : ? [v8: any] : (apply(v0, v4, v5) = v8 & member(v5, v2) = v7 &
% 18.01/3.17 member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & !
% 18.01/3.17 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 18.01/3.17 : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~
% 18.01/3.17 (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 18.01/3.17 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 18.01/3.17 (apply(v0, v4, v5) = v7 & apply(v0, v3, v5) = v6 & ( ~ (v7 = 0) | ~ (v6 =
% 18.01/3.17 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 18.01/3.17 0 | ~ (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 18.01/3.17 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0
% 18.01/3.17 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 &
% 18.01/3.17 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4)))
% 18.01/3.17
% 18.01/3.17 (inverse_function)
% 18.01/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.01/3.18 $i] : ! [v6: any] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5,
% 18.01/3.18 v4, v3) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 18.01/3.18 $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) =
% 18.01/3.18 v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 =
% 18.01/3.18 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0)))))
% 18.01/3.18
% 18.01/3.18 (maps)
% 18.01/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.01/3.19 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~
% 18.01/3.19 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 18.01/3.19 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 18.01/3.19 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 =
% 18.01/3.19 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 18.01/3.19 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0,
% 18.01/3.19 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~
% 18.01/3.19 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 18.01/3.19 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5,
% 18.01/3.19 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 =
% 18.01/3.19 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 18.01/3.19 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0,
% 18.01/3.19 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 18.01/3.19 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 18.01/3.19 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1)
% 18.01/3.19 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1:
% 18.01/3.19 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 18.01/3.19 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) |
% 18.01/3.19 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 18.01/3.19 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 &
% 18.01/3.19 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : !
% 18.01/3.19 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) |
% 18.01/3.19 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 18.01/3.19 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int]
% 18.01/3.19 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13
% 18.01/3.19 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) =
% 18.01/3.19 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2)
% 18.01/3.19 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) |
% 18.01/3.19 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 =
% 18.01/3.19 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4,
% 18.01/3.19 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5,
% 18.01/3.19 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 18.01/3.19 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0)
% 18.01/3.19 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0,
% 18.01/3.19 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4)))
% 18.01/3.19
% 18.01/3.19 (one_to_one)
% 18.01/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 18.01/3.19 (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 18.01/3.19 any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 & injective(v0, v1, v2)
% 18.01/3.19 = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 18.01/3.19 $i] : ! [v3: any] : ( ~ (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~
% 18.01/3.19 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) =
% 18.01/3.19 v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & !
% 18.01/3.19 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (injective(v0, v1,
% 18.01/3.19 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 18.01/3.19 any] : (one_to_one(v0, v1, v2) = v4 & surjective(v0, v1, v2) = v5 & ( ~
% 18.01/3.19 (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 18.01/3.19 $i] : ( ~ (one_to_one(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 18.01/3.19 (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0: $i] : !
% 18.01/3.19 [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ $i(v2) | ~
% 18.01/3.19 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) =
% 18.01/3.19 v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] :
% 18.01/3.19 ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~
% 18.01/3.19 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) =
% 18.01/3.19 v4 & surjective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 18.01/3.19
% 18.01/3.19 (surjective)
% 18.01/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 18.01/3.19 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 18.01/3.19 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4)
% 18.01/3.19 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))
% 18.01/3.19 & ! [v5: $i] : ( ~ (member(v5, v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~
% 18.01/3.19 (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0: $i] : ! [v1: $i] : !
% 18.01/3.19 [v2: $i] : ! [v3: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2)
% 18.01/3.19 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 18.01/3.19 (apply(v0, v4, v3) = 0 & member(v4, v1) = 0 & $i(v4)))
% 18.01/3.19
% 18.01/3.19 (thII03)
% 18.01/3.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 18.01/3.19 = 0) & inverse_function(v0, v1, v2) = v3 & one_to_one(v0, v1, v2) = 0 &
% 18.01/3.19 maps(v3, v2, v1) = v4 & maps(v0, v1, v2) = 0 & $i(v3) & $i(v2) & $i(v1) &
% 18.01/3.19 $i(v0))
% 18.01/3.19
% 18.01/3.19 (function-axioms)
% 18.01/3.20 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 18.01/3.20 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 18.01/3.20 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 18.01/3.20 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 18.01/3.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.01/3.20 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 18.01/3.20 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 18.01/3.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.01/3.20 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 18.01/3.20 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 18.01/3.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.01/3.20 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 18.01/3.20 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 18.01/3.20 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 18.01/3.20 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 18.01/3.20 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 18.01/3.20 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.01/3.20 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 18.01/3.20 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 18.01/3.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.01/3.20 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 18.01/3.20 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 18.01/3.20 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 18.01/3.20 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 18.01/3.20 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 18.01/3.20 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 18.01/3.20 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 18.01/3.20 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 18.01/3.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 18.01/3.20 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 18.01/3.20 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 18.01/3.20 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 18.01/3.20 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.01/3.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 18.01/3.20 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 18.01/3.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.01/3.20 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 18.01/3.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 18.01/3.20 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 18.01/3.20 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 18.01/3.20 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 18.01/3.20 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 18.01/3.20 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 18.01/3.20 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 18.01/3.20 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 18.01/3.20 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.01/3.20 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 18.01/3.20 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.01/3.20 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 18.01/3.20 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 18.01/3.20 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 18.01/3.20 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 18.01/3.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 18.01/3.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 18.01/3.20 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.01/3.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 18.01/3.20 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 18.01/3.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.01/3.20 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 18.01/3.20 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 18.01/3.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 18.01/3.20 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 18.01/3.20 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 18.01/3.20 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 18.01/3.20 (power_set(v2) = v0))
% 18.01/3.20
% 18.01/3.20 Further assumptions not needed in the proof:
% 18.01/3.20 --------------------------------------------
% 18.01/3.20 compose_function, compose_predicate, decreasing_function, difference, empty_set,
% 18.01/3.20 equal_maps, equal_set, identity, image2, image3, increasing_function,
% 18.01/3.20 intersection, inverse_image2, inverse_image3, inverse_predicate, isomorphism,
% 18.01/3.20 power_set, product, singleton, subset, sum, union, unordered_pair
% 18.01/3.20
% 18.01/3.20 Those formulas are unsatisfiable:
% 18.01/3.20 ---------------------------------
% 18.01/3.20
% 18.01/3.20 Begin of proof
% 18.01/3.20 |
% 18.01/3.21 | ALPHA: (maps) implies:
% 18.01/3.21 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 18.01/3.21 | (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 18.01/3.21 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: int] : ?
% 18.01/3.21 | [v9: int] : ? [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13:
% 18.01/3.21 | int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13 = 0 &
% 18.01/3.21 | member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) =
% 18.01/3.21 | 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) &
% 18.01/3.21 | member(v14, v2) = v15)) & ! [v14: $i] : ( ~ (member(v14,
% 18.01/3.21 | v2) = 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) &
% 18.01/3.21 | apply(v0, v12, v14) = v15))) | (v11 = 0 & v10 = 0 & v9 = 0
% 18.01/3.21 | & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, v6) = 0 &
% 18.01/3.21 | apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0
% 18.01/3.21 | & member(v4, v1) = 0))))
% 18.01/3.21 |
% 18.01/3.21 | ALPHA: (injective) implies:
% 18.01/3.21 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 18.01/3.21 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5,
% 18.01/3.21 | v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~
% 18.01/3.21 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 18.01/3.21 | ? [v6: any] : ? [v7: any] : (apply(v0, v4, v5) = v7 & apply(v0, v3,
% 18.01/3.21 | v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 18.01/3.21 |
% 18.01/3.21 | ALPHA: (surjective) implies:
% 18.01/3.21 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 18.01/3.21 | (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ~ $i(v3) |
% 18.01/3.21 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v4, v3) =
% 18.01/3.21 | 0 & member(v4, v1) = 0 & $i(v4)))
% 18.01/3.21 |
% 18.01/3.21 | ALPHA: (one_to_one) implies:
% 18.01/3.21 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (one_to_one(v0, v1, v2) =
% 18.01/3.21 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (surjective(v0, v1, v2) =
% 18.01/3.21 | 0 & injective(v0, v1, v2) = 0))
% 18.01/3.21 |
% 18.01/3.21 | ALPHA: (function-axioms) implies:
% 18.01/3.21 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 18.01/3.21 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 18.01/3.21 | = v0))
% 18.01/3.21 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 18.01/3.21 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 18.01/3.21 | (apply(v4, v3, v2) = v0))
% 18.01/3.21 |
% 18.01/3.21 | DELTA: instantiating (thII03) with fresh symbols all_32_0, all_32_1, all_32_2,
% 18.01/3.21 | all_32_3, all_32_4 gives:
% 18.01/3.21 | (7) ~ (all_32_0 = 0) & inverse_function(all_32_4, all_32_3, all_32_2) =
% 18.01/3.21 | all_32_1 & one_to_one(all_32_4, all_32_3, all_32_2) = 0 &
% 18.01/3.21 | maps(all_32_1, all_32_2, all_32_3) = all_32_0 & maps(all_32_4,
% 18.01/3.21 | all_32_3, all_32_2) = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3)
% 18.01/3.21 | & $i(all_32_4)
% 18.01/3.21 |
% 18.01/3.21 | ALPHA: (7) implies:
% 18.01/3.21 | (8) ~ (all_32_0 = 0)
% 18.01/3.21 | (9) $i(all_32_4)
% 18.01/3.21 | (10) $i(all_32_3)
% 18.01/3.21 | (11) $i(all_32_2)
% 18.01/3.21 | (12) $i(all_32_1)
% 18.01/3.22 | (13) maps(all_32_1, all_32_2, all_32_3) = all_32_0
% 18.01/3.22 | (14) one_to_one(all_32_4, all_32_3, all_32_2) = 0
% 18.01/3.22 | (15) inverse_function(all_32_4, all_32_3, all_32_2) = all_32_1
% 18.01/3.22 |
% 18.01/3.22 | GROUND_INST: instantiating (1) with all_32_1, all_32_2, all_32_3, all_32_0,
% 18.01/3.22 | simplifying with (10), (11), (12), (13) gives:
% 18.01/3.22 | (16) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int]
% 18.01/3.22 | : ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8:
% 18.01/3.22 | $i] : ? [v9: int] : ($i(v8) & $i(v2) & $i(v1) & $i(v0) & ((v9 = 0 &
% 18.01/3.22 | member(v8, all_32_2) = 0 & ! [v10: $i] : ( ~ (apply(all_32_1,
% 18.01/3.22 | v8, v10) = 0) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = 0)
% 18.01/3.22 | & member(v10, all_32_3) = v11)) & ! [v10: $i] : ( ~
% 18.01/3.22 | (member(v10, all_32_3) = 0) | ~ $i(v10) | ? [v11: int] : ( ~
% 18.01/3.22 | (v11 = 0) & apply(all_32_1, v8, v10) = v11))) | (v7 = 0 & v6
% 18.01/3.22 | = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v2 = v1) & apply(all_32_1,
% 18.01/3.22 | v0, v2) = 0 & apply(all_32_1, v0, v1) = 0 & member(v2,
% 18.01/3.22 | all_32_3) = 0 & member(v1, all_32_3) = 0 & member(v0,
% 18.01/3.22 | all_32_2) = 0)))
% 18.01/3.22 |
% 18.01/3.22 | GROUND_INST: instantiating (4) with all_32_4, all_32_3, all_32_2, simplifying
% 18.01/3.22 | with (9), (10), (11), (14) gives:
% 18.01/3.22 | (17) surjective(all_32_4, all_32_3, all_32_2) = 0 & injective(all_32_4,
% 18.01/3.22 | all_32_3, all_32_2) = 0
% 18.01/3.22 |
% 18.01/3.22 | ALPHA: (17) implies:
% 18.01/3.22 | (18) injective(all_32_4, all_32_3, all_32_2) = 0
% 18.01/3.22 | (19) surjective(all_32_4, all_32_3, all_32_2) = 0
% 18.01/3.22 |
% 18.01/3.22 | BETA: splitting (16) gives:
% 18.01/3.22 |
% 18.01/3.22 | Case 1:
% 18.01/3.22 | |
% 18.01/3.22 | | (20) all_32_0 = 0
% 18.01/3.22 | |
% 18.01/3.22 | | REDUCE: (8), (20) imply:
% 18.01/3.22 | | (21) $false
% 18.01/3.22 | |
% 18.01/3.22 | | CLOSE: (21) is inconsistent.
% 18.01/3.22 | |
% 18.01/3.22 | Case 2:
% 18.01/3.22 | |
% 18.01/3.22 | | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4:
% 18.01/3.22 | | int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: $i] :
% 18.01/3.22 | | ? [v9: int] : ($i(v8) & $i(v2) & $i(v1) & $i(v0) & ((v9 = 0 &
% 18.01/3.22 | | member(v8, all_32_2) = 0 & ! [v10: $i] : ( ~ (apply(all_32_1,
% 18.01/3.22 | | v8, v10) = 0) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 =
% 18.01/3.22 | | 0) & member(v10, all_32_3) = v11)) & ! [v10: $i] : ( ~
% 18.01/3.22 | | (member(v10, all_32_3) = 0) | ~ $i(v10) | ? [v11: int] : (
% 18.01/3.22 | | ~ (v11 = 0) & apply(all_32_1, v8, v10) = v11))) | (v7 = 0
% 18.01/3.22 | | & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v2 = v1) &
% 18.01/3.22 | | apply(all_32_1, v0, v2) = 0 & apply(all_32_1, v0, v1) = 0 &
% 18.01/3.22 | | member(v2, all_32_3) = 0 & member(v1, all_32_3) = 0 &
% 18.01/3.22 | | member(v0, all_32_2) = 0)))
% 18.01/3.22 | |
% 18.01/3.22 | | DELTA: instantiating (22) with fresh symbols all_44_0, all_44_1, all_44_2,
% 18.01/3.22 | | all_44_3, all_44_4, all_44_5, all_44_6, all_44_7, all_44_8, all_44_9
% 18.01/3.22 | | gives:
% 18.01/3.23 | | (23) $i(all_44_1) & $i(all_44_7) & $i(all_44_8) & $i(all_44_9) &
% 18.01/3.23 | | ((all_44_0 = 0 & member(all_44_1, all_32_2) = 0 & ! [v0: $i] : ( ~
% 18.01/3.23 | | (apply(all_32_1, all_44_1, v0) = 0) | ~ $i(v0) | ? [v1: int]
% 18.01/3.23 | | : ( ~ (v1 = 0) & member(v0, all_32_3) = v1)) & ! [v0: $i] : (
% 18.01/3.23 | | ~ (member(v0, all_32_3) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 18.01/3.23 | | (v1 = 0) & apply(all_32_1, all_44_1, v0) = v1))) | (all_44_2
% 18.01/3.23 | | = 0 & all_44_3 = 0 & all_44_4 = 0 & all_44_5 = 0 & all_44_6 = 0
% 18.01/3.23 | | & ~ (all_44_7 = all_44_8) & apply(all_32_1, all_44_9, all_44_7)
% 18.01/3.23 | | = 0 & apply(all_32_1, all_44_9, all_44_8) = 0 & member(all_44_7,
% 18.01/3.23 | | all_32_3) = 0 & member(all_44_8, all_32_3) = 0 &
% 18.01/3.23 | | member(all_44_9, all_32_2) = 0))
% 18.01/3.23 | |
% 18.01/3.23 | | ALPHA: (23) implies:
% 18.01/3.23 | | (24) $i(all_44_9)
% 18.01/3.23 | | (25) $i(all_44_8)
% 18.01/3.23 | | (26) $i(all_44_7)
% 18.01/3.23 | | (27) $i(all_44_1)
% 18.01/3.23 | | (28) (all_44_0 = 0 & member(all_44_1, all_32_2) = 0 & ! [v0: $i] : ( ~
% 18.01/3.23 | | (apply(all_32_1, all_44_1, v0) = 0) | ~ $i(v0) | ? [v1: int] :
% 18.01/3.23 | | ( ~ (v1 = 0) & member(v0, all_32_3) = v1)) & ! [v0: $i] : ( ~
% 18.01/3.23 | | (member(v0, all_32_3) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 18.01/3.23 | | = 0) & apply(all_32_1, all_44_1, v0) = v1))) | (all_44_2 = 0
% 18.01/3.23 | | & all_44_3 = 0 & all_44_4 = 0 & all_44_5 = 0 & all_44_6 = 0 & ~
% 18.01/3.23 | | (all_44_7 = all_44_8) & apply(all_32_1, all_44_9, all_44_7) = 0 &
% 18.01/3.23 | | apply(all_32_1, all_44_9, all_44_8) = 0 & member(all_44_7,
% 18.01/3.23 | | all_32_3) = 0 & member(all_44_8, all_32_3) = 0 &
% 18.01/3.23 | | member(all_44_9, all_32_2) = 0)
% 18.01/3.23 | |
% 18.01/3.23 | | BETA: splitting (28) gives:
% 18.01/3.23 | |
% 18.01/3.23 | | Case 1:
% 18.01/3.23 | | |
% 18.01/3.23 | | | (29) all_44_0 = 0 & member(all_44_1, all_32_2) = 0 & ! [v0: $i] : ( ~
% 18.01/3.23 | | | (apply(all_32_1, all_44_1, v0) = 0) | ~ $i(v0) | ? [v1: int] :
% 18.01/3.23 | | | ( ~ (v1 = 0) & member(v0, all_32_3) = v1)) & ! [v0: $i] : ( ~
% 18.01/3.23 | | | (member(v0, all_32_3) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 18.01/3.23 | | | = 0) & apply(all_32_1, all_44_1, v0) = v1))
% 18.01/3.23 | | |
% 18.01/3.23 | | | ALPHA: (29) implies:
% 18.01/3.23 | | | (30) member(all_44_1, all_32_2) = 0
% 18.01/3.23 | | | (31) ! [v0: $i] : ( ~ (member(v0, all_32_3) = 0) | ~ $i(v0) | ? [v1:
% 18.01/3.23 | | | int] : ( ~ (v1 = 0) & apply(all_32_1, all_44_1, v0) = v1))
% 18.01/3.23 | | |
% 18.01/3.23 | | | GROUND_INST: instantiating (3) with all_32_4, all_32_3, all_32_2,
% 18.01/3.23 | | | all_44_1, simplifying with (9), (10), (11), (19), (27), (30)
% 18.01/3.23 | | | gives:
% 18.01/3.23 | | | (32) ? [v0: $i] : (apply(all_32_4, v0, all_44_1) = 0 & member(v0,
% 18.01/3.23 | | | all_32_3) = 0 & $i(v0))
% 18.01/3.23 | | |
% 18.01/3.23 | | | DELTA: instantiating (32) with fresh symbol all_59_0 gives:
% 18.01/3.23 | | | (33) apply(all_32_4, all_59_0, all_44_1) = 0 & member(all_59_0,
% 18.01/3.23 | | | all_32_3) = 0 & $i(all_59_0)
% 18.01/3.23 | | |
% 18.01/3.23 | | | ALPHA: (33) implies:
% 18.23/3.23 | | | (34) $i(all_59_0)
% 18.23/3.23 | | | (35) member(all_59_0, all_32_3) = 0
% 18.23/3.23 | | | (36) apply(all_32_4, all_59_0, all_44_1) = 0
% 18.23/3.23 | | |
% 18.23/3.23 | | | GROUND_INST: instantiating (31) with all_59_0, simplifying with (34), (35)
% 18.23/3.23 | | | gives:
% 18.23/3.23 | | | (37) ? [v0: int] : ( ~ (v0 = 0) & apply(all_32_1, all_44_1, all_59_0)
% 18.23/3.23 | | | = v0)
% 18.23/3.23 | | |
% 18.23/3.23 | | | DELTA: instantiating (37) with fresh symbol all_66_0 gives:
% 18.23/3.23 | | | (38) ~ (all_66_0 = 0) & apply(all_32_1, all_44_1, all_59_0) = all_66_0
% 18.23/3.23 | | |
% 18.23/3.23 | | | ALPHA: (38) implies:
% 18.23/3.23 | | | (39) ~ (all_66_0 = 0)
% 18.23/3.23 | | | (40) apply(all_32_1, all_44_1, all_59_0) = all_66_0
% 18.23/3.23 | | |
% 18.23/3.24 | | | GROUND_INST: instantiating (inverse_function) with all_32_4, all_32_3,
% 18.23/3.24 | | | all_32_2, all_59_0, all_44_1, all_32_1, all_66_0, simplifying
% 18.23/3.24 | | | with (9), (10), (11), (15), (27), (34), (40) gives:
% 18.23/3.24 | | | (41) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_4,
% 18.23/3.24 | | | all_59_0, all_44_1) = v2 & member(all_59_0, all_32_3) = v0 &
% 18.23/3.24 | | | member(all_44_1, all_32_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 18.23/3.24 | | | (( ~ (v2 = 0) | all_66_0 = 0) & ( ~ (all_66_0 = 0) | v2 =
% 18.23/3.24 | | | 0))))
% 18.23/3.24 | | |
% 18.23/3.24 | | | DELTA: instantiating (41) with fresh symbols all_77_0, all_77_1, all_77_2
% 18.23/3.24 | | | gives:
% 18.23/3.24 | | | (42) apply(all_32_4, all_59_0, all_44_1) = all_77_0 & member(all_59_0,
% 18.23/3.24 | | | all_32_3) = all_77_2 & member(all_44_1, all_32_2) = all_77_1 & (
% 18.23/3.24 | | | ~ (all_77_1 = 0) | ~ (all_77_2 = 0) | (( ~ (all_77_0 = 0) |
% 18.23/3.24 | | | all_66_0 = 0) & ( ~ (all_66_0 = 0) | all_77_0 = 0)))
% 18.23/3.24 | | |
% 18.23/3.24 | | | ALPHA: (42) implies:
% 18.23/3.24 | | | (43) member(all_44_1, all_32_2) = all_77_1
% 18.23/3.24 | | | (44) member(all_59_0, all_32_3) = all_77_2
% 18.23/3.24 | | | (45) apply(all_32_4, all_59_0, all_44_1) = all_77_0
% 18.23/3.24 | | | (46) ~ (all_77_1 = 0) | ~ (all_77_2 = 0) | (( ~ (all_77_0 = 0) |
% 18.23/3.24 | | | all_66_0 = 0) & ( ~ (all_66_0 = 0) | all_77_0 = 0))
% 18.23/3.24 | | |
% 18.23/3.24 | | | GROUND_INST: instantiating (5) with 0, all_77_1, all_32_2, all_44_1,
% 18.23/3.24 | | | simplifying with (30), (43) gives:
% 18.23/3.24 | | | (47) all_77_1 = 0
% 18.23/3.24 | | |
% 18.23/3.24 | | | GROUND_INST: instantiating (5) with 0, all_77_2, all_32_3, all_59_0,
% 18.23/3.24 | | | simplifying with (35), (44) gives:
% 18.23/3.24 | | | (48) all_77_2 = 0
% 18.23/3.24 | | |
% 18.23/3.24 | | | GROUND_INST: instantiating (6) with 0, all_77_0, all_44_1, all_59_0,
% 18.23/3.24 | | | all_32_4, simplifying with (36), (45) gives:
% 18.23/3.24 | | | (49) all_77_0 = 0
% 18.23/3.24 | | |
% 18.23/3.24 | | | BETA: splitting (46) gives:
% 18.23/3.24 | | |
% 18.23/3.24 | | | Case 1:
% 18.23/3.24 | | | |
% 18.23/3.24 | | | | (50) ~ (all_77_1 = 0)
% 18.23/3.24 | | | |
% 18.23/3.24 | | | | REDUCE: (47), (50) imply:
% 18.23/3.24 | | | | (51) $false
% 18.23/3.24 | | | |
% 18.23/3.24 | | | | CLOSE: (51) is inconsistent.
% 18.23/3.24 | | | |
% 18.23/3.24 | | | Case 2:
% 18.23/3.24 | | | |
% 18.23/3.24 | | | | (52) ~ (all_77_2 = 0) | (( ~ (all_77_0 = 0) | all_66_0 = 0) & ( ~
% 18.23/3.24 | | | | (all_66_0 = 0) | all_77_0 = 0))
% 18.23/3.24 | | | |
% 18.23/3.24 | | | | BETA: splitting (52) gives:
% 18.23/3.24 | | | |
% 18.23/3.24 | | | | Case 1:
% 18.23/3.24 | | | | |
% 18.23/3.24 | | | | | (53) ~ (all_77_2 = 0)
% 18.23/3.24 | | | | |
% 18.23/3.24 | | | | | REDUCE: (48), (53) imply:
% 18.23/3.24 | | | | | (54) $false
% 18.23/3.24 | | | | |
% 18.23/3.24 | | | | | CLOSE: (54) is inconsistent.
% 18.23/3.24 | | | | |
% 18.23/3.24 | | | | Case 2:
% 18.23/3.24 | | | | |
% 18.23/3.24 | | | | | (55) ( ~ (all_77_0 = 0) | all_66_0 = 0) & ( ~ (all_66_0 = 0) |
% 18.23/3.24 | | | | | all_77_0 = 0)
% 18.23/3.24 | | | | |
% 18.23/3.24 | | | | | ALPHA: (55) implies:
% 18.23/3.24 | | | | | (56) ~ (all_77_0 = 0) | all_66_0 = 0
% 18.23/3.24 | | | | |
% 18.23/3.24 | | | | | BETA: splitting (56) gives:
% 18.23/3.24 | | | | |
% 18.23/3.24 | | | | | Case 1:
% 18.23/3.24 | | | | | |
% 18.23/3.24 | | | | | | (57) ~ (all_77_0 = 0)
% 18.23/3.24 | | | | | |
% 18.23/3.24 | | | | | | REDUCE: (49), (57) imply:
% 18.23/3.24 | | | | | | (58) $false
% 18.23/3.24 | | | | | |
% 18.23/3.24 | | | | | | CLOSE: (58) is inconsistent.
% 18.23/3.24 | | | | | |
% 18.23/3.24 | | | | | Case 2:
% 18.23/3.24 | | | | | |
% 18.23/3.24 | | | | | | (59) all_66_0 = 0
% 18.23/3.24 | | | | | |
% 18.23/3.24 | | | | | | REDUCE: (39), (59) imply:
% 18.23/3.24 | | | | | | (60) $false
% 18.23/3.24 | | | | | |
% 18.23/3.24 | | | | | | CLOSE: (60) is inconsistent.
% 18.23/3.24 | | | | | |
% 18.23/3.24 | | | | | End of split
% 18.23/3.24 | | | | |
% 18.23/3.24 | | | | End of split
% 18.23/3.24 | | | |
% 18.23/3.24 | | | End of split
% 18.23/3.24 | | |
% 18.23/3.24 | | Case 2:
% 18.23/3.24 | | |
% 18.23/3.24 | | | (61) all_44_2 = 0 & all_44_3 = 0 & all_44_4 = 0 & all_44_5 = 0 &
% 18.23/3.24 | | | all_44_6 = 0 & ~ (all_44_7 = all_44_8) & apply(all_32_1,
% 18.23/3.24 | | | all_44_9, all_44_7) = 0 & apply(all_32_1, all_44_9, all_44_8) =
% 18.23/3.24 | | | 0 & member(all_44_7, all_32_3) = 0 & member(all_44_8, all_32_3) =
% 18.23/3.24 | | | 0 & member(all_44_9, all_32_2) = 0
% 18.23/3.24 | | |
% 18.23/3.24 | | | ALPHA: (61) implies:
% 18.23/3.24 | | | (62) ~ (all_44_7 = all_44_8)
% 18.23/3.24 | | | (63) member(all_44_9, all_32_2) = 0
% 18.23/3.24 | | | (64) member(all_44_8, all_32_3) = 0
% 18.23/3.24 | | | (65) member(all_44_7, all_32_3) = 0
% 18.23/3.24 | | | (66) apply(all_32_1, all_44_9, all_44_8) = 0
% 18.23/3.24 | | | (67) apply(all_32_1, all_44_9, all_44_7) = 0
% 18.23/3.24 | | |
% 18.23/3.25 | | | GROUND_INST: instantiating (2) with all_32_4, all_32_3, all_32_2,
% 18.23/3.25 | | | all_44_8, all_44_7, all_44_9, simplifying with (9), (10),
% 18.23/3.25 | | | (11), (18), (24), (25), (26), (63), (64), (65) gives:
% 18.23/3.25 | | | (68) all_44_7 = all_44_8 | ? [v0: any] : ? [v1: any] :
% 18.23/3.25 | | | (apply(all_32_4, all_44_7, all_44_9) = v1 & apply(all_32_4,
% 18.23/3.25 | | | all_44_8, all_44_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 18.23/3.25 | | |
% 18.23/3.25 | | | GROUND_INST: instantiating (2) with all_32_4, all_32_3, all_32_2,
% 18.23/3.25 | | | all_44_7, all_44_8, all_44_9, simplifying with (9), (10),
% 18.23/3.25 | | | (11), (18), (24), (25), (26), (63), (64), (65) gives:
% 18.23/3.25 | | | (69) all_44_7 = all_44_8 | ? [v0: any] : ? [v1: any] :
% 18.23/3.25 | | | (apply(all_32_4, all_44_7, all_44_9) = v0 & apply(all_32_4,
% 18.23/3.25 | | | all_44_8, all_44_9) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 18.23/3.25 | | |
% 18.23/3.25 | | | GROUND_INST: instantiating (inverse_function) with all_32_4, all_32_3,
% 18.23/3.25 | | | all_32_2, all_44_8, all_44_9, all_32_1, 0, simplifying with
% 18.23/3.25 | | | (9), (10), (11), (15), (24), (25), (66) gives:
% 18.23/3.25 | | | (70) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_4,
% 18.23/3.25 | | | all_44_8, all_44_9) = v2 & member(all_44_8, all_32_3) = v0 &
% 18.23/3.25 | | | member(all_44_9, all_32_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 18.23/3.25 | | | v2 = 0))
% 18.23/3.25 | | |
% 18.23/3.25 | | | GROUND_INST: instantiating (inverse_function) with all_32_4, all_32_3,
% 18.23/3.25 | | | all_32_2, all_44_7, all_44_9, all_32_1, 0, simplifying with
% 18.23/3.25 | | | (9), (10), (11), (15), (24), (26), (67) gives:
% 18.23/3.25 | | | (71) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_4,
% 18.23/3.25 | | | all_44_7, all_44_9) = v2 & member(all_44_7, all_32_3) = v0 &
% 18.23/3.25 | | | member(all_44_9, all_32_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 18.23/3.25 | | | v2 = 0))
% 18.23/3.25 | | |
% 18.23/3.25 | | | DELTA: instantiating (71) with fresh symbols all_64_0, all_64_1, all_64_2
% 18.23/3.25 | | | gives:
% 18.23/3.25 | | | (72) apply(all_32_4, all_44_7, all_44_9) = all_64_0 & member(all_44_7,
% 18.23/3.25 | | | all_32_3) = all_64_2 & member(all_44_9, all_32_2) = all_64_1 & (
% 18.23/3.25 | | | ~ (all_64_1 = 0) | ~ (all_64_2 = 0) | all_64_0 = 0)
% 18.23/3.25 | | |
% 18.23/3.25 | | | ALPHA: (72) implies:
% 18.23/3.25 | | | (73) member(all_44_9, all_32_2) = all_64_1
% 18.23/3.25 | | | (74) member(all_44_7, all_32_3) = all_64_2
% 18.23/3.25 | | | (75) apply(all_32_4, all_44_7, all_44_9) = all_64_0
% 18.23/3.25 | | | (76) ~ (all_64_1 = 0) | ~ (all_64_2 = 0) | all_64_0 = 0
% 18.23/3.25 | | |
% 18.23/3.25 | | | DELTA: instantiating (70) with fresh symbols all_66_0, all_66_1, all_66_2
% 18.23/3.25 | | | gives:
% 18.23/3.25 | | | (77) apply(all_32_4, all_44_8, all_44_9) = all_66_0 & member(all_44_8,
% 18.23/3.25 | | | all_32_3) = all_66_2 & member(all_44_9, all_32_2) = all_66_1 & (
% 18.23/3.25 | | | ~ (all_66_1 = 0) | ~ (all_66_2 = 0) | all_66_0 = 0)
% 18.23/3.25 | | |
% 18.23/3.25 | | | ALPHA: (77) implies:
% 18.23/3.25 | | | (78) member(all_44_9, all_32_2) = all_66_1
% 18.23/3.25 | | | (79) member(all_44_8, all_32_3) = all_66_2
% 18.23/3.25 | | | (80) apply(all_32_4, all_44_8, all_44_9) = all_66_0
% 18.23/3.25 | | | (81) ~ (all_66_1 = 0) | ~ (all_66_2 = 0) | all_66_0 = 0
% 18.23/3.25 | | |
% 18.23/3.25 | | | GROUND_INST: instantiating (5) with 0, all_66_1, all_32_2, all_44_9,
% 18.23/3.25 | | | simplifying with (63), (78) gives:
% 18.23/3.25 | | | (82) all_66_1 = 0
% 18.23/3.25 | | |
% 18.23/3.25 | | | GROUND_INST: instantiating (5) with all_64_1, all_66_1, all_32_2,
% 18.23/3.25 | | | all_44_9, simplifying with (73), (78) gives:
% 18.23/3.25 | | | (83) all_66_1 = all_64_1
% 18.23/3.25 | | |
% 18.23/3.25 | | | GROUND_INST: instantiating (5) with 0, all_66_2, all_32_3, all_44_8,
% 18.23/3.25 | | | simplifying with (64), (79) gives:
% 18.23/3.25 | | | (84) all_66_2 = 0
% 18.23/3.25 | | |
% 18.23/3.25 | | | GROUND_INST: instantiating (5) with 0, all_64_2, all_32_3, all_44_7,
% 18.23/3.25 | | | simplifying with (65), (74) gives:
% 18.23/3.25 | | | (85) all_64_2 = 0
% 18.23/3.25 | | |
% 18.23/3.25 | | | COMBINE_EQS: (82), (83) imply:
% 18.23/3.25 | | | (86) all_64_1 = 0
% 18.23/3.25 | | |
% 18.23/3.25 | | | BETA: splitting (76) gives:
% 18.23/3.25 | | |
% 18.23/3.25 | | | Case 1:
% 18.23/3.25 | | | |
% 18.23/3.25 | | | | (87) ~ (all_64_1 = 0)
% 18.23/3.25 | | | |
% 18.23/3.25 | | | | REDUCE: (86), (87) imply:
% 18.23/3.25 | | | | (88) $false
% 18.23/3.25 | | | |
% 18.23/3.25 | | | | CLOSE: (88) is inconsistent.
% 18.23/3.25 | | | |
% 18.23/3.25 | | | Case 2:
% 18.23/3.25 | | | |
% 18.23/3.25 | | | | (89) ~ (all_64_2 = 0) | all_64_0 = 0
% 18.23/3.25 | | | |
% 18.23/3.25 | | | | BETA: splitting (89) gives:
% 18.23/3.25 | | | |
% 18.23/3.25 | | | | Case 1:
% 18.23/3.25 | | | | |
% 18.23/3.26 | | | | | (90) ~ (all_64_2 = 0)
% 18.23/3.26 | | | | |
% 18.23/3.26 | | | | | REDUCE: (85), (90) imply:
% 18.23/3.26 | | | | | (91) $false
% 18.23/3.26 | | | | |
% 18.23/3.26 | | | | | CLOSE: (91) is inconsistent.
% 18.23/3.26 | | | | |
% 18.23/3.26 | | | | Case 2:
% 18.23/3.26 | | | | |
% 18.23/3.26 | | | | | (92) all_64_0 = 0
% 18.23/3.26 | | | | |
% 18.23/3.26 | | | | | REDUCE: (75), (92) imply:
% 18.23/3.26 | | | | | (93) apply(all_32_4, all_44_7, all_44_9) = 0
% 18.23/3.26 | | | | |
% 18.23/3.26 | | | | | BETA: splitting (69) gives:
% 18.23/3.26 | | | | |
% 18.23/3.26 | | | | | Case 1:
% 18.23/3.26 | | | | | |
% 18.23/3.26 | | | | | | (94) all_44_7 = all_44_8
% 18.23/3.26 | | | | | |
% 18.23/3.26 | | | | | | REDUCE: (62), (94) imply:
% 18.23/3.26 | | | | | | (95) $false
% 18.23/3.26 | | | | | |
% 18.23/3.26 | | | | | | CLOSE: (95) is inconsistent.
% 18.23/3.26 | | | | | |
% 18.23/3.26 | | | | | Case 2:
% 18.23/3.26 | | | | | |
% 18.23/3.26 | | | | | | (96) ? [v0: any] : ? [v1: any] : (apply(all_32_4, all_44_7,
% 18.23/3.26 | | | | | | all_44_9) = v0 & apply(all_32_4, all_44_8, all_44_9) =
% 18.23/3.26 | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 18.23/3.26 | | | | | |
% 18.23/3.26 | | | | | | DELTA: instantiating (96) with fresh symbols all_84_0, all_84_1
% 18.23/3.26 | | | | | | gives:
% 18.23/3.26 | | | | | | (97) apply(all_32_4, all_44_7, all_44_9) = all_84_1 &
% 18.23/3.26 | | | | | | apply(all_32_4, all_44_8, all_44_9) = all_84_0 & ( ~
% 18.23/3.26 | | | | | | (all_84_0 = 0) | ~ (all_84_1 = 0))
% 18.23/3.26 | | | | | |
% 18.23/3.26 | | | | | | ALPHA: (97) implies:
% 18.23/3.26 | | | | | | (98) apply(all_32_4, all_44_8, all_44_9) = all_84_0
% 18.23/3.26 | | | | | |
% 18.23/3.26 | | | | | | BETA: splitting (81) gives:
% 18.23/3.26 | | | | | |
% 18.23/3.26 | | | | | | Case 1:
% 18.23/3.26 | | | | | | |
% 18.23/3.26 | | | | | | | (99) ~ (all_66_1 = 0)
% 18.23/3.26 | | | | | | |
% 18.23/3.26 | | | | | | | REDUCE: (82), (99) imply:
% 18.23/3.26 | | | | | | | (100) $false
% 18.23/3.26 | | | | | | |
% 18.23/3.26 | | | | | | | CLOSE: (100) is inconsistent.
% 18.23/3.26 | | | | | | |
% 18.23/3.26 | | | | | | Case 2:
% 18.23/3.26 | | | | | | |
% 18.23/3.26 | | | | | | | (101) ~ (all_66_2 = 0) | all_66_0 = 0
% 18.23/3.26 | | | | | | |
% 18.23/3.26 | | | | | | | BETA: splitting (101) gives:
% 18.23/3.26 | | | | | | |
% 18.23/3.26 | | | | | | | Case 1:
% 18.23/3.26 | | | | | | | |
% 18.23/3.26 | | | | | | | | (102) ~ (all_66_2 = 0)
% 18.23/3.26 | | | | | | | |
% 18.23/3.26 | | | | | | | | REDUCE: (84), (102) imply:
% 18.23/3.26 | | | | | | | | (103) $false
% 18.23/3.26 | | | | | | | |
% 18.23/3.26 | | | | | | | | CLOSE: (103) is inconsistent.
% 18.23/3.26 | | | | | | | |
% 18.23/3.26 | | | | | | | Case 2:
% 18.23/3.26 | | | | | | | |
% 18.23/3.26 | | | | | | | | (104) all_66_0 = 0
% 18.23/3.26 | | | | | | | |
% 18.23/3.26 | | | | | | | | REDUCE: (80), (104) imply:
% 18.23/3.26 | | | | | | | | (105) apply(all_32_4, all_44_8, all_44_9) = 0
% 18.23/3.26 | | | | | | | |
% 18.23/3.26 | | | | | | | | BETA: splitting (68) gives:
% 18.23/3.26 | | | | | | | |
% 18.23/3.26 | | | | | | | | Case 1:
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | (106) all_44_7 = all_44_8
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | REDUCE: (62), (106) imply:
% 18.23/3.26 | | | | | | | | | (107) $false
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | CLOSE: (107) is inconsistent.
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | Case 2:
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | (108) ? [v0: any] : ? [v1: any] : (apply(all_32_4,
% 18.23/3.26 | | | | | | | | | all_44_7, all_44_9) = v1 & apply(all_32_4,
% 18.23/3.26 | | | | | | | | | all_44_8, all_44_9) = v0 & ( ~ (v1 = 0) | ~ (v0
% 18.23/3.26 | | | | | | | | | = 0)))
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | DELTA: instantiating (108) with fresh symbols all_98_0,
% 18.23/3.26 | | | | | | | | | all_98_1 gives:
% 18.23/3.26 | | | | | | | | | (109) apply(all_32_4, all_44_7, all_44_9) = all_98_0 &
% 18.23/3.26 | | | | | | | | | apply(all_32_4, all_44_8, all_44_9) = all_98_1 & ( ~
% 18.23/3.26 | | | | | | | | | (all_98_0 = 0) | ~ (all_98_1 = 0))
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | ALPHA: (109) implies:
% 18.23/3.26 | | | | | | | | | (110) apply(all_32_4, all_44_8, all_44_9) = all_98_1
% 18.23/3.26 | | | | | | | | | (111) apply(all_32_4, all_44_7, all_44_9) = all_98_0
% 18.23/3.26 | | | | | | | | | (112) ~ (all_98_0 = 0) | ~ (all_98_1 = 0)
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | GROUND_INST: instantiating (6) with all_84_0, all_98_1,
% 18.23/3.26 | | | | | | | | | all_44_9, all_44_8, all_32_4, simplifying with
% 18.23/3.26 | | | | | | | | | (98), (110) gives:
% 18.23/3.26 | | | | | | | | | (113) all_98_1 = all_84_0
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_98_1, all_44_9,
% 18.23/3.26 | | | | | | | | | all_44_8, all_32_4, simplifying with (105), (110)
% 18.23/3.26 | | | | | | | | | gives:
% 18.23/3.26 | | | | | | | | | (114) all_98_1 = 0
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_98_0, all_44_9,
% 18.23/3.26 | | | | | | | | | all_44_7, all_32_4, simplifying with (93), (111)
% 18.23/3.26 | | | | | | | | | gives:
% 18.23/3.26 | | | | | | | | | (115) all_98_0 = 0
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | COMBINE_EQS: (113), (114) imply:
% 18.23/3.26 | | | | | | | | | (116) all_84_0 = 0
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | BETA: splitting (112) gives:
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | | Case 1:
% 18.23/3.26 | | | | | | | | | |
% 18.23/3.26 | | | | | | | | | | (117) ~ (all_98_0 = 0)
% 18.23/3.26 | | | | | | | | | |
% 18.23/3.26 | | | | | | | | | | REDUCE: (115), (117) imply:
% 18.23/3.26 | | | | | | | | | | (118) $false
% 18.23/3.26 | | | | | | | | | |
% 18.23/3.26 | | | | | | | | | | CLOSE: (118) is inconsistent.
% 18.23/3.26 | | | | | | | | | |
% 18.23/3.26 | | | | | | | | | Case 2:
% 18.23/3.26 | | | | | | | | | |
% 18.23/3.26 | | | | | | | | | | (119) ~ (all_98_1 = 0)
% 18.23/3.26 | | | | | | | | | |
% 18.23/3.26 | | | | | | | | | | REDUCE: (114), (119) imply:
% 18.23/3.26 | | | | | | | | | | (120) $false
% 18.23/3.26 | | | | | | | | | |
% 18.23/3.26 | | | | | | | | | | CLOSE: (120) is inconsistent.
% 18.23/3.26 | | | | | | | | | |
% 18.23/3.26 | | | | | | | | | End of split
% 18.23/3.26 | | | | | | | | |
% 18.23/3.26 | | | | | | | | End of split
% 18.23/3.26 | | | | | | | |
% 18.23/3.26 | | | | | | | End of split
% 18.23/3.26 | | | | | | |
% 18.23/3.26 | | | | | | End of split
% 18.23/3.26 | | | | | |
% 18.23/3.26 | | | | | End of split
% 18.23/3.26 | | | | |
% 18.23/3.26 | | | | End of split
% 18.23/3.26 | | | |
% 18.23/3.26 | | | End of split
% 18.23/3.26 | | |
% 18.23/3.26 | | End of split
% 18.23/3.26 | |
% 18.23/3.26 | End of split
% 18.23/3.26 |
% 18.23/3.26 End of proof
% 18.23/3.26 % SZS output end Proof for theBenchmark
% 18.23/3.26
% 18.23/3.26 2660ms
%------------------------------------------------------------------------------