TSTP Solution File: SET067+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET067+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n024.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 15:23:33 EDT 2023
% Result : Theorem 13.32s 2.62s
% Output : Proof 22.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET067+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:57:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.25/1.21 Prover 4: Preprocessing ...
% 3.25/1.21 Prover 1: Preprocessing ...
% 3.84/1.25 Prover 0: Preprocessing ...
% 3.84/1.25 Prover 5: Preprocessing ...
% 3.84/1.25 Prover 6: Preprocessing ...
% 3.84/1.25 Prover 2: Preprocessing ...
% 3.84/1.25 Prover 3: Preprocessing ...
% 9.66/2.07 Prover 1: Warning: ignoring some quantifiers
% 9.72/2.08 Prover 5: Proving ...
% 9.72/2.08 Prover 4: Warning: ignoring some quantifiers
% 9.72/2.10 Prover 3: Warning: ignoring some quantifiers
% 9.72/2.10 Prover 6: Proving ...
% 10.12/2.13 Prover 3: Constructing countermodel ...
% 10.12/2.14 Prover 1: Constructing countermodel ...
% 10.12/2.15 Prover 4: Constructing countermodel ...
% 10.12/2.18 Prover 2: Proving ...
% 10.81/2.23 Prover 0: Proving ...
% 13.32/2.62 Prover 3: proved (1977ms)
% 13.32/2.62
% 13.32/2.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.32/2.62
% 13.32/2.62 Prover 5: stopped
% 13.32/2.62 Prover 0: stopped
% 13.32/2.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.32/2.63 Prover 6: stopped
% 13.32/2.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.32/2.63 Prover 2: stopped
% 13.32/2.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.32/2.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.32/2.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.03/2.71 Prover 7: Preprocessing ...
% 14.62/2.75 Prover 8: Preprocessing ...
% 14.62/2.75 Prover 10: Preprocessing ...
% 14.62/2.77 Prover 11: Preprocessing ...
% 14.99/2.80 Prover 13: Preprocessing ...
% 15.71/2.89 Prover 10: Warning: ignoring some quantifiers
% 15.71/2.90 Prover 7: Warning: ignoring some quantifiers
% 15.71/2.91 Prover 10: Constructing countermodel ...
% 16.10/2.92 Prover 7: Constructing countermodel ...
% 16.10/2.94 Prover 8: Warning: ignoring some quantifiers
% 16.33/2.95 Prover 8: Constructing countermodel ...
% 16.33/3.02 Prover 13: Warning: ignoring some quantifiers
% 16.93/3.04 Prover 13: Constructing countermodel ...
% 16.93/3.07 Prover 11: Warning: ignoring some quantifiers
% 17.32/3.08 Prover 11: Constructing countermodel ...
% 17.88/3.16 Prover 10: gave up
% 17.88/3.16 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 17.88/3.25 Prover 16: Preprocessing ...
% 19.89/3.43 Prover 16: Warning: ignoring some quantifiers
% 19.89/3.44 Prover 16: Constructing countermodel ...
% 22.63/3.80 Prover 1: Found proof (size 27)
% 22.63/3.80 Prover 1: proved (3159ms)
% 22.63/3.80 Prover 4: stopped
% 22.63/3.80 Prover 7: stopped
% 22.63/3.80 Prover 16: stopped
% 22.63/3.80 Prover 8: stopped
% 22.63/3.80 Prover 11: stopped
% 22.63/3.80 Prover 13: stopped
% 22.63/3.80
% 22.63/3.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.63/3.80
% 22.63/3.81 % SZS output start Proof for theBenchmark
% 22.63/3.81 Assumptions after simplification:
% 22.63/3.81 ---------------------------------
% 22.63/3.81
% 22.63/3.81 (pair_contains_other)
% 22.63/3.83 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 22.63/3.83 = 0) & unordered_pair(v0, v1) = v3 & unordered_pair(v0, v0) = v2 &
% 22.63/3.83 subclass(v2, v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 22.63/3.83
% 22.63/3.83 (subclass_defn)
% 22.63/3.84 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0, v1) =
% 22.63/3.84 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 22.63/3.84 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 22.63/3.84 [v1: $i] : ( ~ (subclass(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] :
% 22.63/3.84 ( ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 22.63/3.84
% 22.63/3.84 (unordered_pair_defn)
% 22.63/3.84 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 22.63/3.84 ! [v4: int] : (v4 = 0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3)
% 22.63/3.84 = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 22.63/3.84 member(v0, universal_class) = v5) | ( ~ (v2 = v0) & ~ (v1 = v0))) & !
% 22.63/3.84 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (unordered_pair(v1,
% 22.63/3.84 v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 22.63/3.84 | (member(v0, universal_class) = 0 & (v2 = v0 | v1 = v0)))
% 22.63/3.84
% 22.63/3.84 (function-axioms)
% 22.63/3.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 22.63/3.85 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0:
% 22.63/3.85 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2)
% 22.63/3.85 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 22.63/3.85 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 22.63/3.85 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 22.63/3.85 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~
% 22.63/3.85 (compose(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 22.63/3.85 $i] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & !
% 22.63/3.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3,
% 22.63/3.85 v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 22.63/3.85 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~
% 22.63/3.85 (intersection(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 22.63/3.85 [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3,
% 22.63/3.85 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 22.63/3.85 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & !
% 22.63/3.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.63/3.85 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 22.63/3.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 22.63/3.85 : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0)) & !
% 22.63/3.85 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 22.63/3.85 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & !
% 22.63/3.85 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 22.63/3.85 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: $i] : ! [v1:
% 22.63/3.85 $i] : ! [v2: $i] : (v1 = v0 | ~ (power_class(v2) = v1) | ~
% 22.63/3.85 (power_class(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 22.63/3.85 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0:
% 22.63/3.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 22.63/3.85 ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0)) & ! [v0: $i] : ! [v1:
% 22.63/3.85 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) =
% 22.63/3.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.63/3.85 (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 22.63/3.85 [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & !
% 22.63/3.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (flip(v2) = v1) | ~
% 22.63/3.85 (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.63/3.85 (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 22.63/3.85 [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & !
% 22.63/3.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2) = v1) |
% 22.63/3.85 ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 22.63/3.85 v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 22.63/3.85 : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & !
% 22.63/3.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 22.63/3.85 (singleton(v2) = v0))
% 22.63/3.85
% 22.63/3.85 Further assumptions not needed in the proof:
% 22.63/3.85 --------------------------------------------
% 22.63/3.85 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 22.63/3.85 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 22.63/3.85 element_relation, element_relation_defn, extensionality, first_second, flip,
% 22.63/3.85 flip_defn, function_defn, identity_relation, image_defn, inductive_defn,
% 22.63/3.85 infinity, intersection, inverse_defn, null_class_defn, ordered_pair_defn,
% 22.63/3.85 power_class, power_class_defn, range_of_defn, regularity, replacement,
% 22.63/3.85 restrict_defn, rotate, rotate_defn, singleton_set_defn, successor_defn,
% 22.63/3.85 successor_relation_defn1, successor_relation_defn2, sum_class, sum_class_defn,
% 22.63/3.85 union_defn, unordered_pair
% 22.63/3.85
% 22.63/3.85 Those formulas are unsatisfiable:
% 22.63/3.85 ---------------------------------
% 22.63/3.85
% 22.63/3.85 Begin of proof
% 22.63/3.85 |
% 22.63/3.86 | ALPHA: (subclass_defn) implies:
% 22.63/3.86 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0,
% 22.63/3.86 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 22.63/3.86 | ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 22.63/3.86 |
% 22.63/3.86 | ALPHA: (unordered_pair_defn) implies:
% 22.63/3.86 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 22.63/3.86 | (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) |
% 22.63/3.86 | ~ $i(v1) | ~ $i(v0) | (member(v0, universal_class) = 0 & (v2 = v0 |
% 22.63/3.86 | v1 = v0)))
% 22.63/3.86 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 22.63/3.86 | (v4 = 0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) |
% 22.63/3.86 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 22.63/3.86 | member(v0, universal_class) = v5) | ( ~ (v2 = v0) & ~ (v1 = v0)))
% 22.63/3.86 |
% 22.63/3.86 | ALPHA: (function-axioms) implies:
% 22.63/3.86 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 22.63/3.86 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 22.63/3.86 | = v0))
% 22.63/3.86 |
% 22.63/3.86 | DELTA: instantiating (pair_contains_other) with fresh symbols all_53_0,
% 22.63/3.86 | all_53_1, all_53_2, all_53_3, all_53_4 gives:
% 22.63/3.86 | (5) ~ (all_53_0 = 0) & unordered_pair(all_53_4, all_53_3) = all_53_1 &
% 22.63/3.86 | unordered_pair(all_53_4, all_53_4) = all_53_2 & subclass(all_53_2,
% 22.63/3.86 | all_53_1) = all_53_0 & $i(all_53_1) & $i(all_53_2) & $i(all_53_3) &
% 22.63/3.86 | $i(all_53_4)
% 22.63/3.86 |
% 22.63/3.86 | ALPHA: (5) implies:
% 22.63/3.86 | (6) ~ (all_53_0 = 0)
% 22.63/3.86 | (7) $i(all_53_4)
% 22.63/3.86 | (8) $i(all_53_3)
% 22.63/3.86 | (9) $i(all_53_2)
% 22.63/3.86 | (10) $i(all_53_1)
% 22.63/3.86 | (11) subclass(all_53_2, all_53_1) = all_53_0
% 22.63/3.86 | (12) unordered_pair(all_53_4, all_53_4) = all_53_2
% 22.63/3.86 | (13) unordered_pair(all_53_4, all_53_3) = all_53_1
% 22.63/3.86 |
% 22.63/3.86 | GROUND_INST: instantiating (1) with all_53_2, all_53_1, all_53_0, simplifying
% 22.63/3.86 | with (9), (10), (11) gives:
% 22.63/3.86 | (14) all_53_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 22.63/3.86 | all_53_1) = v1 & member(v0, all_53_2) = 0 & $i(v0))
% 22.63/3.86 |
% 22.63/3.86 | BETA: splitting (14) gives:
% 22.63/3.86 |
% 22.63/3.87 | Case 1:
% 22.63/3.87 | |
% 22.63/3.87 | | (15) all_53_0 = 0
% 22.63/3.87 | |
% 22.63/3.87 | | REDUCE: (6), (15) imply:
% 22.63/3.87 | | (16) $false
% 22.63/3.87 | |
% 22.63/3.87 | | CLOSE: (16) is inconsistent.
% 22.63/3.87 | |
% 22.63/3.87 | Case 2:
% 22.63/3.87 | |
% 22.63/3.87 | | (17) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_53_1) =
% 22.63/3.87 | | v1 & member(v0, all_53_2) = 0 & $i(v0))
% 22.63/3.87 | |
% 22.63/3.87 | | DELTA: instantiating (17) with fresh symbols all_103_0, all_103_1 gives:
% 22.63/3.87 | | (18) ~ (all_103_0 = 0) & member(all_103_1, all_53_1) = all_103_0 &
% 22.63/3.87 | | member(all_103_1, all_53_2) = 0 & $i(all_103_1)
% 22.63/3.87 | |
% 22.63/3.87 | | ALPHA: (18) implies:
% 22.63/3.87 | | (19) ~ (all_103_0 = 0)
% 22.63/3.87 | | (20) $i(all_103_1)
% 22.63/3.87 | | (21) member(all_103_1, all_53_2) = 0
% 22.63/3.87 | | (22) member(all_103_1, all_53_1) = all_103_0
% 22.63/3.87 | |
% 22.63/3.87 | | GROUND_INST: instantiating (2) with all_103_1, all_53_4, all_53_4, all_53_2,
% 22.63/3.87 | | simplifying with (7), (12), (20), (21) gives:
% 22.63/3.87 | | (23) all_103_1 = all_53_4 & member(all_53_4, universal_class) = 0
% 22.63/3.87 | |
% 22.63/3.87 | | ALPHA: (23) implies:
% 22.63/3.87 | | (24) all_103_1 = all_53_4
% 22.63/3.87 | | (25) member(all_53_4, universal_class) = 0
% 22.63/3.87 | |
% 22.63/3.87 | | GROUND_INST: instantiating (3) with all_103_1, all_53_4, all_53_3, all_53_1,
% 22.63/3.87 | | all_103_0, simplifying with (7), (8), (13), (20), (22) gives:
% 22.63/3.87 | | (26) all_103_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_103_1,
% 22.63/3.87 | | universal_class) = v0) | ( ~ (all_103_1 = all_53_3) & ~
% 22.63/3.87 | | (all_103_1 = all_53_4))
% 22.63/3.87 | |
% 22.63/3.87 | | BETA: splitting (26) gives:
% 22.63/3.87 | |
% 22.63/3.87 | | Case 1:
% 22.63/3.87 | | |
% 22.63/3.87 | | | (27) all_103_0 = 0
% 22.63/3.87 | | |
% 22.63/3.87 | | | REDUCE: (19), (27) imply:
% 22.63/3.87 | | | (28) $false
% 22.63/3.87 | | |
% 22.63/3.87 | | | CLOSE: (28) is inconsistent.
% 22.63/3.87 | | |
% 22.63/3.87 | | Case 2:
% 22.63/3.87 | | |
% 22.63/3.87 | | | (29) ? [v0: int] : ( ~ (v0 = 0) & member(all_103_1, universal_class) =
% 22.63/3.87 | | | v0) | ( ~ (all_103_1 = all_53_3) & ~ (all_103_1 = all_53_4))
% 22.63/3.87 | | |
% 22.63/3.87 | | | BETA: splitting (29) gives:
% 22.63/3.87 | | |
% 22.63/3.87 | | | Case 1:
% 22.63/3.87 | | | |
% 22.63/3.87 | | | | (30) ? [v0: int] : ( ~ (v0 = 0) & member(all_103_1, universal_class)
% 22.63/3.87 | | | | = v0)
% 22.63/3.87 | | | |
% 22.63/3.87 | | | | DELTA: instantiating (30) with fresh symbol all_370_0 gives:
% 22.63/3.87 | | | | (31) ~ (all_370_0 = 0) & member(all_103_1, universal_class) =
% 22.63/3.87 | | | | all_370_0
% 22.63/3.87 | | | |
% 22.63/3.87 | | | | ALPHA: (31) implies:
% 22.63/3.87 | | | | (32) ~ (all_370_0 = 0)
% 22.63/3.87 | | | | (33) member(all_103_1, universal_class) = all_370_0
% 22.63/3.87 | | | |
% 22.63/3.87 | | | | REDUCE: (24), (33) imply:
% 22.63/3.87 | | | | (34) member(all_53_4, universal_class) = all_370_0
% 22.63/3.87 | | | |
% 22.63/3.87 | | | | GROUND_INST: instantiating (4) with 0, all_370_0, universal_class,
% 22.63/3.87 | | | | all_53_4, simplifying with (25), (34) gives:
% 22.63/3.87 | | | | (35) all_370_0 = 0
% 22.63/3.87 | | | |
% 22.63/3.87 | | | | REDUCE: (32), (35) imply:
% 22.63/3.87 | | | | (36) $false
% 22.63/3.87 | | | |
% 22.63/3.87 | | | | CLOSE: (36) is inconsistent.
% 22.63/3.87 | | | |
% 22.63/3.87 | | | Case 2:
% 22.63/3.87 | | | |
% 22.63/3.87 | | | | (37) ~ (all_103_1 = all_53_3) & ~ (all_103_1 = all_53_4)
% 22.63/3.87 | | | |
% 22.63/3.87 | | | | ALPHA: (37) implies:
% 22.63/3.87 | | | | (38) ~ (all_103_1 = all_53_4)
% 22.63/3.87 | | | |
% 22.63/3.87 | | | | REDUCE: (24), (38) imply:
% 22.63/3.87 | | | | (39) $false
% 22.63/3.87 | | | |
% 22.63/3.87 | | | | CLOSE: (39) is inconsistent.
% 22.63/3.87 | | | |
% 22.63/3.87 | | | End of split
% 22.63/3.87 | | |
% 22.63/3.87 | | End of split
% 22.63/3.87 | |
% 22.63/3.88 | End of split
% 22.63/3.88 |
% 22.63/3.88 End of proof
% 22.63/3.88 % SZS output end Proof for theBenchmark
% 22.63/3.88
% 22.63/3.88 3259ms
%------------------------------------------------------------------------------