TSTP Solution File: SET722+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET722+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 : n032.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 15:26:09 EDT 2023
% Result : Theorem 11.00s 2.21s
% Output : Proof 14.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET722+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Sat Aug 26 10:51:29 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.57 ________ _____
% 0.14/0.57 ___ __ \_________(_)________________________________
% 0.14/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.57
% 0.14/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.58 (2023-06-19)
% 0.14/0.58
% 0.14/0.58 (c) Philipp Rümmer, 2009-2023
% 0.14/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.58 Amanda Stjerna.
% 0.14/0.58 Free software under BSD-3-Clause.
% 0.14/0.58
% 0.14/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.58
% 0.14/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.59 Running up to 7 provers in parallel.
% 0.14/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.14/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.84/1.10 Prover 4: Preprocessing ...
% 2.84/1.10 Prover 1: Preprocessing ...
% 3.23/1.14 Prover 6: Preprocessing ...
% 3.23/1.14 Prover 5: Preprocessing ...
% 3.23/1.14 Prover 0: Preprocessing ...
% 3.23/1.15 Prover 2: Preprocessing ...
% 3.23/1.15 Prover 3: Preprocessing ...
% 8.55/1.88 Prover 5: Proving ...
% 8.91/1.92 Prover 2: Proving ...
% 8.91/1.94 Prover 6: Proving ...
% 8.91/1.97 Prover 3: Constructing countermodel ...
% 8.91/2.00 Prover 1: Constructing countermodel ...
% 11.00/2.21 Prover 3: proved (1610ms)
% 11.00/2.21
% 11.00/2.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.00/2.21
% 11.00/2.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.00/2.21 Prover 2: stopped
% 11.00/2.21 Prover 5: stopped
% 11.00/2.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.00/2.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.00/2.23 Prover 6: stopped
% 11.00/2.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.37/2.29 Prover 8: Preprocessing ...
% 11.37/2.31 Prover 7: Preprocessing ...
% 11.37/2.31 Prover 10: Preprocessing ...
% 12.09/2.36 Prover 11: Preprocessing ...
% 12.45/2.41 Prover 10: Warning: ignoring some quantifiers
% 12.45/2.41 Prover 1: Found proof (size 33)
% 12.45/2.41 Prover 1: proved (1823ms)
% 12.90/2.46 Prover 10: Constructing countermodel ...
% 12.90/2.46 Prover 7: Warning: ignoring some quantifiers
% 12.90/2.47 Prover 4: Constructing countermodel ...
% 12.90/2.47 Prover 10: stopped
% 12.90/2.49 Prover 7: Constructing countermodel ...
% 12.90/2.50 Prover 11: stopped
% 13.31/2.51 Prover 7: stopped
% 13.31/2.51 Prover 4: stopped
% 13.60/2.56 Prover 8: Warning: ignoring some quantifiers
% 13.60/2.57 Prover 0: Proving ...
% 13.60/2.57 Prover 0: stopped
% 13.60/2.57 Prover 8: Constructing countermodel ...
% 13.60/2.58 Prover 8: stopped
% 13.60/2.58
% 13.60/2.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.60/2.58
% 13.60/2.59 % SZS output start Proof for theBenchmark
% 13.60/2.59 Assumptions after simplification:
% 13.60/2.59 ---------------------------------
% 13.60/2.59
% 13.60/2.59 (compose_function)
% 13.60/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.60/2.62 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: any] : ( ~ (compose_function(v0,
% 13.60/2.62 v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ $i(v6) | ~
% 13.60/2.62 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9:
% 13.60/2.62 any] : ? [v10: any] : (member(v6, v4) = v10 & member(v5, v2) = v9 & ( ~
% 13.60/2.62 (v10 = 0) | ~ (v9 = 0))) | (( ~ (v8 = 0) | ? [v9: $i] : (apply(v1, v5,
% 13.60/2.62 v9) = 0 & apply(v0, v9, v6) = 0 & member(v9, v3) = 0 & $i(v9))) &
% 13.60/2.62 (v8 = 0 | ! [v9: $i] : ( ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) | ? [v10:
% 13.60/2.62 any] : ? [v11: any] : (apply(v1, v5, v9) = v11 & member(v9, v3) =
% 13.60/2.62 v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))))))
% 13.60/2.62
% 13.60/2.62 (surjective)
% 13.60/2.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.60/2.63 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 13.60/2.63 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4)
% 13.60/2.63 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) =
% 13.60/2.63 v6)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0,
% 13.60/2.63 v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~
% 13.60/2.63 (member(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v4, v3) = 0 &
% 13.60/2.63 member(v4, v1) = 0 & $i(v4))))
% 13.60/2.63
% 13.60/2.63 (thII13)
% 13.60/2.63 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 13.60/2.63 $i] : ? [v6: int] : ( ~ (v6 = 0) & surjective(v5, v2, v4) = 0 &
% 13.60/2.63 surjective(v1, v3, v4) = v6 & compose_function(v1, v0, v2, v3, v4) = v5 &
% 13.60/2.63 maps(v1, v3, v4) = 0 & maps(v0, v2, v3) = 0 & $i(v5) & $i(v4) & $i(v3) &
% 13.60/2.63 $i(v2) & $i(v1) & $i(v0))
% 13.60/2.63
% 13.60/2.63 (function-axioms)
% 14.09/2.65 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.09/2.65 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 14.09/2.65 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 14.09/2.65 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 14.09/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.09/2.65 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 14.09/2.65 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 14.09/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.09/2.65 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 14.09/2.65 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 14.09/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.09/2.65 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 14.09/2.65 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 14.09/2.65 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 14.09/2.65 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 14.09/2.65 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 14.09/2.65 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.09/2.65 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 14.09/2.65 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.09/2.65 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.09/2.65 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 14.09/2.65 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 14.09/2.65 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 14.09/2.65 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 14.09/2.65 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 14.09/2.65 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.09/2.65 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 14.09/2.65 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.09/2.65 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 14.09/2.65 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 14.09/2.65 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.09/2.65 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 14.09/2.65 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.09/2.65 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 14.09/2.65 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 14.09/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.09/2.65 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 14.09/2.65 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.09/2.65 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 14.09/2.65 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.09/2.65 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 14.09/2.65 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.09/2.65 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 14.09/2.65 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.09/2.65 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 14.09/2.65 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.09/2.65 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 14.09/2.65 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.09/2.65 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 14.09/2.65 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 14.09/2.65 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 14.09/2.65 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 14.09/2.65 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.09/2.65 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 14.09/2.65 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.09/2.65 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 14.09/2.65 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.09/2.65 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.09/2.65 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 14.09/2.65 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 14.09/2.65 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 14.09/2.65 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 14.09/2.65 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 14.09/2.65 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 14.09/2.65 (power_set(v2) = v0))
% 14.09/2.65
% 14.09/2.65 Further assumptions not needed in the proof:
% 14.09/2.65 --------------------------------------------
% 14.09/2.65 compose_predicate, decreasing_function, difference, empty_set, equal_maps,
% 14.09/2.65 equal_set, identity, image2, image3, increasing_function, injective,
% 14.09/2.65 intersection, inverse_function, inverse_image2, inverse_image3,
% 14.09/2.65 inverse_predicate, isomorphism, maps, one_to_one, power_set, product, singleton,
% 14.09/2.65 subset, sum, union, unordered_pair
% 14.09/2.65
% 14.09/2.65 Those formulas are unsatisfiable:
% 14.09/2.65 ---------------------------------
% 14.09/2.65
% 14.09/2.65 Begin of proof
% 14.09/2.65 |
% 14.09/2.65 | ALPHA: (surjective) implies:
% 14.09/2.65 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) =
% 14.09/2.65 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~
% 14.09/2.65 | (member(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v4, v3)
% 14.09/2.65 | = 0 & member(v4, v1) = 0 & $i(v4))))
% 14.09/2.65 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.09/2.65 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 14.09/2.65 | ? [v4: $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~
% 14.09/2.65 | (apply(v0, v5, v4) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0)
% 14.09/2.65 | & member(v5, v1) = v6))))
% 14.09/2.65 |
% 14.09/2.65 | ALPHA: (function-axioms) implies:
% 14.09/2.66 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.09/2.66 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 14.09/2.66 | = v0))
% 14.09/2.66 |
% 14.09/2.66 | DELTA: instantiating (thII13) with fresh symbols all_32_0, all_32_1, all_32_2,
% 14.09/2.66 | all_32_3, all_32_4, all_32_5, all_32_6 gives:
% 14.09/2.66 | (4) ~ (all_32_0 = 0) & surjective(all_32_1, all_32_4, all_32_2) = 0 &
% 14.09/2.66 | surjective(all_32_5, all_32_3, all_32_2) = all_32_0 &
% 14.09/2.66 | compose_function(all_32_5, all_32_6, all_32_4, all_32_3, all_32_2) =
% 14.09/2.66 | all_32_1 & maps(all_32_5, all_32_3, all_32_2) = 0 & maps(all_32_6,
% 14.09/2.66 | all_32_4, all_32_3) = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3)
% 14.09/2.66 | & $i(all_32_4) & $i(all_32_5) & $i(all_32_6)
% 14.09/2.66 |
% 14.09/2.66 | ALPHA: (4) implies:
% 14.09/2.66 | (5) ~ (all_32_0 = 0)
% 14.09/2.66 | (6) $i(all_32_6)
% 14.09/2.66 | (7) $i(all_32_5)
% 14.09/2.66 | (8) $i(all_32_4)
% 14.09/2.66 | (9) $i(all_32_3)
% 14.09/2.66 | (10) $i(all_32_2)
% 14.09/2.66 | (11) $i(all_32_1)
% 14.09/2.66 | (12) compose_function(all_32_5, all_32_6, all_32_4, all_32_3, all_32_2) =
% 14.09/2.66 | all_32_1
% 14.09/2.66 | (13) surjective(all_32_5, all_32_3, all_32_2) = all_32_0
% 14.09/2.66 | (14) surjective(all_32_1, all_32_4, all_32_2) = 0
% 14.09/2.66 |
% 14.09/2.66 | GROUND_INST: instantiating (2) with all_32_5, all_32_3, all_32_2, all_32_0,
% 14.09/2.66 | simplifying with (7), (9), (10), (13) gives:
% 14.09/2.66 | (15) all_32_0 = 0 | ? [v0: $i] : (member(v0, all_32_2) = 0 & $i(v0) & !
% 14.09/2.66 | [v1: $i] : ( ~ (apply(all_32_5, v1, v0) = 0) | ~ $i(v1) | ? [v2:
% 14.09/2.66 | int] : ( ~ (v2 = 0) & member(v1, all_32_3) = v2)))
% 14.09/2.66 |
% 14.09/2.66 | GROUND_INST: instantiating (1) with all_32_1, all_32_4, all_32_2, simplifying
% 14.09/2.66 | with (8), (10), (11), (14) gives:
% 14.09/2.66 | (16) ! [v0: $i] : ( ~ (member(v0, all_32_2) = 0) | ~ $i(v0) | ? [v1: $i]
% 14.09/2.66 | : (apply(all_32_1, v1, v0) = 0 & member(v1, all_32_4) = 0 & $i(v1)))
% 14.09/2.66 |
% 14.09/2.66 | BETA: splitting (15) gives:
% 14.09/2.66 |
% 14.09/2.66 | Case 1:
% 14.09/2.66 | |
% 14.09/2.66 | | (17) all_32_0 = 0
% 14.09/2.66 | |
% 14.09/2.66 | | REDUCE: (5), (17) imply:
% 14.09/2.66 | | (18) $false
% 14.09/2.66 | |
% 14.09/2.66 | | CLOSE: (18) is inconsistent.
% 14.09/2.66 | |
% 14.09/2.66 | Case 2:
% 14.09/2.66 | |
% 14.09/2.66 | | (19) ? [v0: $i] : (member(v0, all_32_2) = 0 & $i(v0) & ! [v1: $i] : ( ~
% 14.09/2.66 | | (apply(all_32_5, v1, v0) = 0) | ~ $i(v1) | ? [v2: int] : ( ~
% 14.09/2.66 | | (v2 = 0) & member(v1, all_32_3) = v2)))
% 14.09/2.67 | |
% 14.09/2.67 | | DELTA: instantiating (19) with fresh symbol all_45_0 gives:
% 14.09/2.67 | | (20) member(all_45_0, all_32_2) = 0 & $i(all_45_0) & ! [v0: $i] : ( ~
% 14.09/2.67 | | (apply(all_32_5, v0, all_45_0) = 0) | ~ $i(v0) | ? [v1: int] : (
% 14.09/2.67 | | ~ (v1 = 0) & member(v0, all_32_3) = v1))
% 14.09/2.67 | |
% 14.09/2.67 | | ALPHA: (20) implies:
% 14.09/2.67 | | (21) $i(all_45_0)
% 14.09/2.67 | | (22) member(all_45_0, all_32_2) = 0
% 14.09/2.67 | | (23) ! [v0: $i] : ( ~ (apply(all_32_5, v0, all_45_0) = 0) | ~ $i(v0) |
% 14.09/2.67 | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_3) = v1))
% 14.09/2.67 | |
% 14.09/2.67 | | GROUND_INST: instantiating (16) with all_45_0, simplifying with (21), (22)
% 14.09/2.67 | | gives:
% 14.09/2.67 | | (24) ? [v0: $i] : (apply(all_32_1, v0, all_45_0) = 0 & member(v0,
% 14.09/2.67 | | all_32_4) = 0 & $i(v0))
% 14.09/2.67 | |
% 14.09/2.67 | | DELTA: instantiating (24) with fresh symbol all_53_0 gives:
% 14.09/2.67 | | (25) apply(all_32_1, all_53_0, all_45_0) = 0 & member(all_53_0, all_32_4)
% 14.09/2.67 | | = 0 & $i(all_53_0)
% 14.09/2.67 | |
% 14.09/2.67 | | ALPHA: (25) implies:
% 14.09/2.67 | | (26) $i(all_53_0)
% 14.09/2.67 | | (27) member(all_53_0, all_32_4) = 0
% 14.09/2.67 | | (28) apply(all_32_1, all_53_0, all_45_0) = 0
% 14.09/2.67 | |
% 14.09/2.67 | | GROUND_INST: instantiating (compose_function) with all_32_5, all_32_6,
% 14.09/2.67 | | all_32_4, all_32_3, all_32_2, all_53_0, all_45_0, all_32_1, 0,
% 14.09/2.67 | | simplifying with (6), (7), (8), (9), (10), (12), (21), (26),
% 14.09/2.67 | | (28) gives:
% 14.09/2.67 | | (29) ? [v0: any] : ? [v1: any] : (member(all_53_0, all_32_4) = v0 &
% 14.09/2.67 | | member(all_45_0, all_32_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) |
% 14.09/2.67 | | ? [v0: $i] : (apply(all_32_5, v0, all_45_0) = 0 & apply(all_32_6,
% 14.09/2.67 | | all_53_0, v0) = 0 & member(v0, all_32_3) = 0 & $i(v0))
% 14.09/2.67 | |
% 14.09/2.67 | | BETA: splitting (29) gives:
% 14.09/2.67 | |
% 14.09/2.67 | | Case 1:
% 14.09/2.67 | | |
% 14.09/2.67 | | | (30) ? [v0: any] : ? [v1: any] : (member(all_53_0, all_32_4) = v0 &
% 14.09/2.67 | | | member(all_45_0, all_32_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.09/2.67 | | |
% 14.09/2.67 | | | DELTA: instantiating (30) with fresh symbols all_65_0, all_65_1 gives:
% 14.09/2.67 | | | (31) member(all_53_0, all_32_4) = all_65_1 & member(all_45_0, all_32_2)
% 14.09/2.67 | | | = all_65_0 & ( ~ (all_65_0 = 0) | ~ (all_65_1 = 0))
% 14.09/2.67 | | |
% 14.09/2.67 | | | ALPHA: (31) implies:
% 14.09/2.67 | | | (32) member(all_45_0, all_32_2) = all_65_0
% 14.09/2.67 | | | (33) member(all_53_0, all_32_4) = all_65_1
% 14.09/2.67 | | | (34) ~ (all_65_0 = 0) | ~ (all_65_1 = 0)
% 14.09/2.67 | | |
% 14.09/2.67 | | | GROUND_INST: instantiating (3) with 0, all_65_0, all_32_2, all_45_0,
% 14.09/2.67 | | | simplifying with (22), (32) gives:
% 14.09/2.67 | | | (35) all_65_0 = 0
% 14.09/2.67 | | |
% 14.09/2.67 | | | GROUND_INST: instantiating (3) with 0, all_65_1, all_32_4, all_53_0,
% 14.09/2.67 | | | simplifying with (27), (33) gives:
% 14.09/2.67 | | | (36) all_65_1 = 0
% 14.09/2.67 | | |
% 14.09/2.67 | | | BETA: splitting (34) gives:
% 14.09/2.67 | | |
% 14.09/2.67 | | | Case 1:
% 14.09/2.67 | | | |
% 14.09/2.68 | | | | (37) ~ (all_65_0 = 0)
% 14.09/2.68 | | | |
% 14.09/2.68 | | | | REDUCE: (35), (37) imply:
% 14.09/2.68 | | | | (38) $false
% 14.09/2.68 | | | |
% 14.09/2.68 | | | | CLOSE: (38) is inconsistent.
% 14.09/2.68 | | | |
% 14.09/2.68 | | | Case 2:
% 14.09/2.68 | | | |
% 14.09/2.68 | | | | (39) ~ (all_65_1 = 0)
% 14.09/2.68 | | | |
% 14.09/2.68 | | | | REDUCE: (36), (39) imply:
% 14.09/2.68 | | | | (40) $false
% 14.09/2.68 | | | |
% 14.09/2.68 | | | | CLOSE: (40) is inconsistent.
% 14.09/2.68 | | | |
% 14.09/2.68 | | | End of split
% 14.09/2.68 | | |
% 14.09/2.68 | | Case 2:
% 14.09/2.68 | | |
% 14.09/2.68 | | | (41) ? [v0: $i] : (apply(all_32_5, v0, all_45_0) = 0 & apply(all_32_6,
% 14.09/2.68 | | | all_53_0, v0) = 0 & member(v0, all_32_3) = 0 & $i(v0))
% 14.09/2.68 | | |
% 14.09/2.68 | | | DELTA: instantiating (41) with fresh symbol all_65_0 gives:
% 14.09/2.68 | | | (42) apply(all_32_5, all_65_0, all_45_0) = 0 & apply(all_32_6,
% 14.09/2.68 | | | all_53_0, all_65_0) = 0 & member(all_65_0, all_32_3) = 0 &
% 14.09/2.68 | | | $i(all_65_0)
% 14.09/2.68 | | |
% 14.09/2.68 | | | ALPHA: (42) implies:
% 14.09/2.68 | | | (43) $i(all_65_0)
% 14.09/2.68 | | | (44) member(all_65_0, all_32_3) = 0
% 14.09/2.68 | | | (45) apply(all_32_5, all_65_0, all_45_0) = 0
% 14.09/2.68 | | |
% 14.09/2.68 | | | GROUND_INST: instantiating (23) with all_65_0, simplifying with (43), (45)
% 14.09/2.68 | | | gives:
% 14.09/2.68 | | | (46) ? [v0: int] : ( ~ (v0 = 0) & member(all_65_0, all_32_3) = v0)
% 14.09/2.68 | | |
% 14.09/2.68 | | | DELTA: instantiating (46) with fresh symbol all_72_0 gives:
% 14.09/2.68 | | | (47) ~ (all_72_0 = 0) & member(all_65_0, all_32_3) = all_72_0
% 14.09/2.68 | | |
% 14.09/2.68 | | | ALPHA: (47) implies:
% 14.09/2.68 | | | (48) ~ (all_72_0 = 0)
% 14.09/2.68 | | | (49) member(all_65_0, all_32_3) = all_72_0
% 14.09/2.68 | | |
% 14.09/2.68 | | | GROUND_INST: instantiating (3) with 0, all_72_0, all_32_3, all_65_0,
% 14.09/2.68 | | | simplifying with (44), (49) gives:
% 14.09/2.68 | | | (50) all_72_0 = 0
% 14.09/2.68 | | |
% 14.09/2.68 | | | REDUCE: (48), (50) imply:
% 14.09/2.68 | | | (51) $false
% 14.09/2.68 | | |
% 14.09/2.68 | | | CLOSE: (51) is inconsistent.
% 14.09/2.68 | | |
% 14.09/2.68 | | End of split
% 14.09/2.68 | |
% 14.09/2.68 | End of split
% 14.09/2.68 |
% 14.09/2.68 End of proof
% 14.09/2.68 % SZS output end Proof for theBenchmark
% 14.09/2.68
% 14.09/2.68 2104ms
%------------------------------------------------------------------------------