TSTP Solution File: SET108+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET108+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 : n012.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 15:23:50 EDT 2023
% Result : Theorem 10.24s 2.14s
% Output : Proof 14.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET108+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 16:19:10 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.58 ________ _____
% 0.19/0.58 ___ __ \_________(_)________________________________
% 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58 (2023-06-19)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2023
% 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58 Amanda Stjerna.
% 0.19/0.58 Free software under BSD-3-Clause.
% 0.19/0.58
% 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.59 Running up to 7 provers in parallel.
% 0.19/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.94/1.16 Prover 4: Preprocessing ...
% 2.94/1.16 Prover 1: Preprocessing ...
% 3.71/1.19 Prover 0: Preprocessing ...
% 3.71/1.19 Prover 6: Preprocessing ...
% 3.71/1.20 Prover 2: Preprocessing ...
% 3.71/1.20 Prover 3: Preprocessing ...
% 3.71/1.20 Prover 5: Preprocessing ...
% 8.01/1.82 Prover 1: Warning: ignoring some quantifiers
% 8.58/1.87 Prover 1: Constructing countermodel ...
% 8.71/1.88 Prover 6: Proving ...
% 8.71/1.90 Prover 5: Proving ...
% 8.71/1.90 Prover 4: Warning: ignoring some quantifiers
% 8.71/1.90 Prover 3: Warning: ignoring some quantifiers
% 9.02/1.92 Prover 3: Constructing countermodel ...
% 9.02/1.94 Prover 4: Constructing countermodel ...
% 9.17/1.98 Prover 2: Proving ...
% 9.79/2.08 Prover 0: Proving ...
% 10.24/2.13 Prover 3: proved (1535ms)
% 10.24/2.13
% 10.24/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.24/2.14
% 10.24/2.14 Prover 5: stopped
% 10.24/2.14 Prover 2: stopped
% 10.24/2.14 Prover 6: stopped
% 10.24/2.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.24/2.15 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.24/2.15 Prover 0: stopped
% 10.24/2.15 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.24/2.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.24/2.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.24/2.25 Prover 8: Preprocessing ...
% 10.24/2.26 Prover 10: Preprocessing ...
% 10.24/2.27 Prover 7: Preprocessing ...
% 10.24/2.28 Prover 11: Preprocessing ...
% 11.82/2.30 Prover 13: Preprocessing ...
% 12.86/2.45 Prover 10: Warning: ignoring some quantifiers
% 12.86/2.45 Prover 7: Warning: ignoring some quantifiers
% 12.86/2.48 Prover 10: Constructing countermodel ...
% 12.86/2.48 Prover 7: Constructing countermodel ...
% 13.30/2.51 Prover 8: Warning: ignoring some quantifiers
% 13.30/2.51 Prover 13: Warning: ignoring some quantifiers
% 13.30/2.53 Prover 8: Constructing countermodel ...
% 13.30/2.54 Prover 13: Constructing countermodel ...
% 13.78/2.57 Prover 11: Warning: ignoring some quantifiers
% 13.78/2.59 Prover 4: Found proof (size 71)
% 13.78/2.59 Prover 4: proved (1992ms)
% 13.78/2.59 Prover 7: stopped
% 13.78/2.59 Prover 10: stopped
% 13.78/2.59 Prover 8: stopped
% 13.78/2.59 Prover 13: stopped
% 13.78/2.59 Prover 1: stopped
% 13.78/2.59 Prover 11: Constructing countermodel ...
% 14.10/2.61 Prover 11: stopped
% 14.10/2.61
% 14.10/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.10/2.61
% 14.10/2.63 % SZS output start Proof for theBenchmark
% 14.10/2.63 Assumptions after simplification:
% 14.10/2.63 ---------------------------------
% 14.10/2.63
% 14.10/2.63 (complement)
% 14.30/2.66 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] :
% 14.30/2.66 (v3 = 0 | ~ (complement(v0) = v2) | ~ (member(v1, v2) = v3) | ~ $i(v1) | ~
% 14.30/2.66 $i(v0) | ? [v4: any] : ? [v5: any] : (member(v1, v0) = v5 & member(v1,
% 14.30/2.66 universal_class) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1:
% 14.30/2.66 $i] : ! [v2: int] : (v2 = 0 | ~ (member(v1, v0) = v2) | ~ $i(v1) | ~
% 14.30/2.66 $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : (complement(v0) = v4 &
% 14.30/2.66 member(v1, v4) = v5 & member(v1, universal_class) = v3 & $i(v4) & ( ~ (v3
% 14.30/2.66 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.30/2.66 (complement(v0) = v2) | ~ (member(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 14.30/2.66 [v3: int] : ( ~ (v3 = 0) & member(v1, v0) = v3 & member(v1, universal_class)
% 14.30/2.66 = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (member(v1, v0) =
% 14.30/2.66 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] :
% 14.30/2.66 (complement(v0) = v3 & member(v1, v3) = v4 & member(v1, universal_class) =
% 14.30/2.66 v5 & $i(v3) & ( ~ (v4 = 0) | (v5 = 0 & ~ (v2 = 0)))))
% 14.30/2.66
% 14.30/2.66 (element_relation_defn)
% 14.30/2.67 $i(element_relation) & $i(universal_class) & ! [v0: $i] : ! [v1: $i] : !
% 14.30/2.67 [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 14.30/2.67 any] : ? [v4: any] : ? [v5: any] : (member(v2, element_relation) = v5 &
% 14.30/2.67 member(v1, universal_class) = v3 & member(v0, v1) = v4 & ( ~ (v4 = 0) | ~
% 14.30/2.67 (v3 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.30/2.67 (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 14.30/2.67 any] : ? [v5: any] : (member(v2, element_relation) = v3 & member(v1,
% 14.30/2.67 universal_class) = v4 & member(v0, v1) = v5 & ( ~ (v3 = 0) | (v5 = 0 &
% 14.30/2.67 v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 14.30/2.67 (member(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 14.30/2.67 ? [v5: any] : (ordered_pair(v0, v1) = v3 & member(v3, element_relation) =
% 14.30/2.67 v4 & member(v1, universal_class) = v5 & $i(v3) & ( ~ (v4 = 0) | (v5 = 0 &
% 14.30/2.67 v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0, v1) = 0) | ~
% 14.30/2.67 $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 14.30/2.67 (ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4 & member(v1,
% 14.30/2.67 universal_class) = v2 & $i(v3) & ( ~ (v2 = 0) | v4 = 0)))
% 14.30/2.67
% 14.30/2.67 (existence_of_first_and_second)
% 14.30/2.67 $i(universal_class) & ? [v0: $i] : ($i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 14.30/2.67 (ordered_pair(v1, v2) = v0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ?
% 14.30/2.67 [v4: any] : (member(v2, universal_class) = v4 & member(v1,
% 14.30/2.67 universal_class) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ? [v1: $i] :
% 14.30/2.67 ? [v2: $i] : (ordered_pair(v1, v2) = v0 & member(v2, universal_class) = 0 &
% 14.30/2.67 member(v1, universal_class) = 0 & $i(v2) & $i(v1)))
% 14.30/2.67
% 14.30/2.67 (first_second)
% 14.30/2.67 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.30/2.67 (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 14.30/2.67 any] : ? [v5: $i] : ? [v6: $i] : (first(v2) = v5 & second(v2) = v6 &
% 14.30/2.67 member(v1, universal_class) = v4 & member(v0, universal_class) = v3 &
% 14.30/2.67 $i(v6) & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = v1 & v5 = v0))))
% 14.30/2.67
% 14.30/2.67 (successor_relation_defn2)
% 14.30/2.68 $i(successor_relation) & $i(universal_class) & ! [v0: $i] : ! [v1: $i] : !
% 14.30/2.68 [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 14.30/2.68 any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : (successor(v0) = v6 &
% 14.30/2.68 member(v2, successor_relation) = v3 & member(v1, universal_class) = v5 &
% 14.30/2.68 member(v0, universal_class) = v4 & $i(v6) & ( ~ (v3 = 0) | (v6 = v1 & v5 =
% 14.30/2.68 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.30/2.68 (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 14.30/2.68 any] : ? [v5: $i] : ? [v6: any] : (successor(v0) = v5 & member(v2,
% 14.30/2.68 successor_relation) = v6 & member(v1, universal_class) = v4 & member(v0,
% 14.30/2.68 universal_class) = v3 & $i(v5) & ( ~ (v5 = v1) | ~ (v4 = 0) | ~ (v3 =
% 14.30/2.68 0) | v6 = 0)))
% 14.30/2.68
% 14.30/2.68 (function-axioms)
% 14.30/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 14.30/2.69 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0:
% 14.30/2.69 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2)
% 14.30/2.69 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.30/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 14.30/2.69 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 14.30/2.69 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~
% 14.30/2.69 (compose(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 14.30/2.69 $i] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & !
% 14.30/2.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3,
% 14.30/2.69 v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 14.30/2.69 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~
% 14.30/2.69 (intersection(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.30/2.69 [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3,
% 14.30/2.69 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 14.30/2.69 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & !
% 14.30/2.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.30/2.69 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 14.30/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.30/2.69 : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0)) & !
% 14.30/2.69 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.30/2.69 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & !
% 14.30/2.69 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 14.30/2.69 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: $i] : ! [v1:
% 14.30/2.69 $i] : ! [v2: $i] : (v1 = v0 | ~ (power_class(v2) = v1) | ~
% 14.30/2.69 (power_class(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 14.30/2.69 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0:
% 14.30/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 14.30/2.69 ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0)) & ! [v0: $i] : ! [v1:
% 14.30/2.69 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) =
% 14.30/2.69 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.30/2.69 (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 14.30/2.69 [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & !
% 14.30/2.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (flip(v2) = v1) | ~
% 14.30/2.69 (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.30/2.69 (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 14.30/2.69 [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & !
% 14.30/2.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2) = v1) |
% 14.30/2.69 ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 14.30/2.69 v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 14.30/2.69 : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & !
% 14.30/2.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 14.30/2.69 (singleton(v2) = v0))
% 14.30/2.69
% 14.30/2.69 Further assumptions not needed in the proof:
% 14.30/2.69 --------------------------------------------
% 14.30/2.69 apply_defn, choice, class_elements_are_sets, compose_defn1, compose_defn2,
% 14.30/2.69 cross_product, cross_product_defn, disjoint_defn, domain_of, element_relation,
% 14.30/2.69 extensionality, flip, flip_defn, function_defn, identity_relation, image_defn,
% 14.30/2.69 inductive_defn, infinity, intersection, inverse_defn, null_class_defn,
% 14.30/2.69 ordered_pair_defn, power_class, power_class_defn, range_of_defn, regularity,
% 14.30/2.69 replacement, restrict_defn, rotate, rotate_defn, singleton_set_defn,
% 14.30/2.69 subclass_defn, successor_defn, successor_relation_defn1, sum_class,
% 14.30/2.69 sum_class_defn, union_defn, unordered_pair, unordered_pair_defn
% 14.30/2.69
% 14.30/2.69 Those formulas are unsatisfiable:
% 14.30/2.69 ---------------------------------
% 14.30/2.69
% 14.30/2.69 Begin of proof
% 14.30/2.69 |
% 14.30/2.69 | ALPHA: (first_second) implies:
% 14.30/2.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 14.30/2.69 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 14.30/2.69 | $i] : ? [v6: $i] : (first(v2) = v5 & second(v2) = v6 & member(v1,
% 14.30/2.69 | universal_class) = v4 & member(v0, universal_class) = v3 & $i(v6)
% 14.30/2.69 | & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = v1 & v5 = v0))))
% 14.30/2.69 |
% 14.30/2.69 | ALPHA: (element_relation_defn) implies:
% 14.30/2.69 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 14.30/2.69 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 14.30/2.69 | any] : (member(v2, element_relation) = v3 & member(v1,
% 14.30/2.69 | universal_class) = v4 & member(v0, v1) = v5 & ( ~ (v3 = 0) | (v5
% 14.30/2.69 | = 0 & v4 = 0))))
% 14.30/2.69 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 14.30/2.69 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 14.30/2.69 | any] : (member(v2, element_relation) = v5 & member(v1,
% 14.30/2.69 | universal_class) = v3 & member(v0, v1) = v4 & ( ~ (v4 = 0) | ~
% 14.30/2.69 | (v3 = 0) | v5 = 0)))
% 14.30/2.69 |
% 14.30/2.69 | ALPHA: (complement) implies:
% 14.30/2.69 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (member(v1, v0) = v2) |
% 14.30/2.69 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] :
% 14.30/2.69 | (complement(v0) = v3 & member(v1, v3) = v4 & member(v1,
% 14.30/2.69 | universal_class) = v5 & $i(v3) & ( ~ (v4 = 0) | (v5 = 0 & ~ (v2
% 14.30/2.69 | = 0)))))
% 14.30/2.69 |
% 14.30/2.69 | ALPHA: (successor_relation_defn2) implies:
% 14.30/2.70 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 14.30/2.70 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 14.30/2.70 | $i] : ? [v6: any] : (successor(v0) = v5 & member(v2,
% 14.30/2.70 | successor_relation) = v6 & member(v1, universal_class) = v4 &
% 14.30/2.70 | member(v0, universal_class) = v3 & $i(v5) & ( ~ (v5 = v1) | ~ (v4
% 14.30/2.70 | = 0) | ~ (v3 = 0) | v6 = 0)))
% 14.30/2.70 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 14.30/2.70 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 14.30/2.70 | any] : ? [v6: $i] : (successor(v0) = v6 & member(v2,
% 14.30/2.70 | successor_relation) = v3 & member(v1, universal_class) = v5 &
% 14.30/2.70 | member(v0, universal_class) = v4 & $i(v6) & ( ~ (v3 = 0) | (v6 = v1
% 14.30/2.70 | & v5 = 0 & v4 = 0))))
% 14.30/2.70 |
% 14.30/2.70 | ALPHA: (existence_of_first_and_second) implies:
% 14.30/2.70 | (7) $i(universal_class)
% 14.30/2.70 | (8) ? [v0: $i] : ($i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 14.30/2.70 | (ordered_pair(v1, v2) = v0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any]
% 14.30/2.70 | : ? [v4: any] : (member(v2, universal_class) = v4 & member(v1,
% 14.30/2.70 | universal_class) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ? [v1:
% 14.30/2.70 | $i] : ? [v2: $i] : (ordered_pair(v1, v2) = v0 & member(v2,
% 14.30/2.70 | universal_class) = 0 & member(v1, universal_class) = 0 & $i(v2) &
% 14.30/2.70 | $i(v1)))
% 14.30/2.70 |
% 14.30/2.70 | ALPHA: (function-axioms) implies:
% 14.30/2.70 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.30/2.70 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 14.30/2.70 | = v0))
% 14.30/2.70 |
% 14.30/2.70 | DELTA: instantiating (8) with fresh symbol all_53_0 gives:
% 14.30/2.70 | (10) $i(all_53_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) =
% 14.30/2.70 | all_53_0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 14.30/2.70 | (member(v1, universal_class) = v3 & member(v0, universal_class) = v2
% 14.30/2.70 | & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ? [v0: $i] : ? [v1: $i] :
% 14.30/2.70 | (ordered_pair(v0, v1) = all_53_0 & member(v1, universal_class) = 0 &
% 14.30/2.70 | member(v0, universal_class) = 0 & $i(v1) & $i(v0))
% 14.30/2.70 |
% 14.30/2.70 | ALPHA: (10) implies:
% 14.30/2.70 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = all_53_0) | ~
% 14.30/2.70 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (member(v1,
% 14.30/2.70 | universal_class) = v3 & member(v0, universal_class) = v2 & ( ~
% 14.30/2.70 | (v3 = 0) | ~ (v2 = 0))))
% 14.30/2.70 | (12) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_53_0 &
% 14.30/2.70 | member(v1, universal_class) = 0 & member(v0, universal_class) = 0 &
% 14.30/2.70 | $i(v1) & $i(v0))
% 14.30/2.70 |
% 14.30/2.70 | DELTA: instantiating (12) with fresh symbols all_59_0, all_59_1 gives:
% 14.30/2.71 | (13) ordered_pair(all_59_1, all_59_0) = all_53_0 & member(all_59_0,
% 14.30/2.71 | universal_class) = 0 & member(all_59_1, universal_class) = 0 &
% 14.30/2.71 | $i(all_59_0) & $i(all_59_1)
% 14.30/2.71 |
% 14.30/2.71 | ALPHA: (13) implies:
% 14.30/2.71 | (14) $i(all_59_1)
% 14.30/2.71 | (15) $i(all_59_0)
% 14.30/2.71 | (16) member(all_59_1, universal_class) = 0
% 14.30/2.71 | (17) member(all_59_0, universal_class) = 0
% 14.30/2.71 | (18) ordered_pair(all_59_1, all_59_0) = all_53_0
% 14.30/2.71 |
% 14.30/2.71 | GROUND_INST: instantiating (4) with universal_class, all_59_1, 0, simplifying
% 14.30/2.71 | with (7), (14), (16) gives:
% 14.30/2.71 | (19) ? [v0: $i] : ? [v1: int] : ? [v2: MultipleValueBool] : ( ~ (v1 = 0)
% 14.30/2.71 | & complement(universal_class) = v0 & member(all_59_1, v0) = v1 &
% 14.30/2.71 | member(all_59_1, universal_class) = v2 & $i(v0))
% 14.30/2.71 |
% 14.30/2.71 | GROUND_INST: instantiating (4) with universal_class, all_59_0, 0, simplifying
% 14.30/2.71 | with (7), (15), (17) gives:
% 14.30/2.71 | (20) ? [v0: $i] : ? [v1: int] : ? [v2: MultipleValueBool] : ( ~ (v1 = 0)
% 14.30/2.71 | & complement(universal_class) = v0 & member(all_59_0, v0) = v1 &
% 14.30/2.71 | member(all_59_0, universal_class) = v2 & $i(v0))
% 14.30/2.71 |
% 14.30/2.71 | GROUND_INST: instantiating (11) with all_59_1, all_59_0, simplifying with
% 14.30/2.71 | (14), (15), (18) gives:
% 14.30/2.71 | (21) ? [v0: any] : ? [v1: any] : (member(all_59_0, universal_class) = v1
% 14.30/2.71 | & member(all_59_1, universal_class) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 14.30/2.71 | 0)))
% 14.30/2.71 |
% 14.30/2.71 | GROUND_INST: instantiating (6) with all_59_1, all_59_0, all_53_0, simplifying
% 14.30/2.71 | with (14), (15), (18) gives:
% 14.30/2.71 | (22) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] :
% 14.30/2.71 | (successor(all_59_1) = v3 & member(all_59_0, universal_class) = v2 &
% 14.30/2.71 | member(all_59_1, universal_class) = v1 & member(all_53_0,
% 14.30/2.71 | successor_relation) = v0 & $i(v3) & ( ~ (v0 = 0) | (v3 = all_59_0
% 14.30/2.71 | & v2 = 0 & v1 = 0)))
% 14.30/2.71 |
% 14.30/2.71 | GROUND_INST: instantiating (5) with all_59_1, all_59_0, all_53_0, simplifying
% 14.30/2.71 | with (14), (15), (18) gives:
% 14.30/2.71 | (23) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 14.30/2.71 | (successor(all_59_1) = v2 & member(all_59_0, universal_class) = v1 &
% 14.30/2.71 | member(all_59_1, universal_class) = v0 & member(all_53_0,
% 14.30/2.71 | successor_relation) = v3 & $i(v2) & ( ~ (v2 = all_59_0) | ~ (v1 =
% 14.30/2.71 | 0) | ~ (v0 = 0) | v3 = 0))
% 14.30/2.71 |
% 14.30/2.71 | GROUND_INST: instantiating (1) with all_59_1, all_59_0, all_53_0, simplifying
% 14.30/2.71 | with (14), (15), (18) gives:
% 14.30/2.71 | (24) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 14.30/2.71 | (first(all_53_0) = v2 & second(all_53_0) = v3 & member(all_59_0,
% 14.30/2.71 | universal_class) = v1 & member(all_59_1, universal_class) = v0 &
% 14.30/2.71 | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = all_59_0 & v2 =
% 14.30/2.71 | all_59_1)))
% 14.30/2.71 |
% 14.30/2.72 | GROUND_INST: instantiating (3) with all_59_1, all_59_0, all_53_0, simplifying
% 14.30/2.72 | with (14), (15), (18) gives:
% 14.30/2.72 | (25) ? [v0: any] : ? [v1: any] : ? [v2: any] : (member(all_59_0,
% 14.30/2.72 | universal_class) = v0 & member(all_59_1, all_59_0) = v1 &
% 14.30/2.72 | member(all_53_0, element_relation) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0)
% 14.30/2.72 | | v2 = 0))
% 14.30/2.72 |
% 14.30/2.72 | GROUND_INST: instantiating (2) with all_59_1, all_59_0, all_53_0, simplifying
% 14.30/2.72 | with (14), (15), (18) gives:
% 14.30/2.72 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : (member(all_59_0,
% 14.30/2.72 | universal_class) = v1 & member(all_59_1, all_59_0) = v2 &
% 14.30/2.72 | member(all_53_0, element_relation) = v0 & ( ~ (v0 = 0) | (v2 = 0 &
% 14.30/2.72 | v1 = 0)))
% 14.30/2.72 |
% 14.30/2.72 | DELTA: instantiating (21) with fresh symbols all_96_0, all_96_1 gives:
% 14.30/2.72 | (27) member(all_59_0, universal_class) = all_96_0 & member(all_59_1,
% 14.30/2.72 | universal_class) = all_96_1 & ( ~ (all_96_0 = 0) | ~ (all_96_1 =
% 14.30/2.72 | 0))
% 14.30/2.72 |
% 14.30/2.72 | ALPHA: (27) implies:
% 14.30/2.72 | (28) member(all_59_1, universal_class) = all_96_1
% 14.30/2.72 | (29) member(all_59_0, universal_class) = all_96_0
% 14.30/2.72 | (30) ~ (all_96_0 = 0) | ~ (all_96_1 = 0)
% 14.30/2.72 |
% 14.30/2.72 | DELTA: instantiating (19) with fresh symbols all_104_0, all_104_1, all_104_2
% 14.30/2.72 | gives:
% 14.30/2.72 | (31) ~ (all_104_1 = 0) & complement(universal_class) = all_104_2 &
% 14.30/2.72 | member(all_59_1, all_104_2) = all_104_1 & member(all_59_1,
% 14.30/2.72 | universal_class) = all_104_0 & $i(all_104_2)
% 14.30/2.72 |
% 14.30/2.72 | ALPHA: (31) implies:
% 14.30/2.72 | (32) member(all_59_1, universal_class) = all_104_0
% 14.30/2.72 |
% 14.30/2.72 | DELTA: instantiating (20) with fresh symbols all_108_0, all_108_1, all_108_2
% 14.30/2.72 | gives:
% 14.30/2.72 | (33) ~ (all_108_1 = 0) & complement(universal_class) = all_108_2 &
% 14.30/2.72 | member(all_59_0, all_108_2) = all_108_1 & member(all_59_0,
% 14.30/2.72 | universal_class) = all_108_0 & $i(all_108_2)
% 14.30/2.72 |
% 14.30/2.72 | ALPHA: (33) implies:
% 14.30/2.72 | (34) member(all_59_0, universal_class) = all_108_0
% 14.30/2.72 |
% 14.30/2.72 | DELTA: instantiating (26) with fresh symbols all_112_0, all_112_1, all_112_2
% 14.30/2.72 | gives:
% 14.30/2.72 | (35) member(all_59_0, universal_class) = all_112_1 & member(all_59_1,
% 14.30/2.72 | all_59_0) = all_112_0 & member(all_53_0, element_relation) =
% 14.30/2.72 | all_112_2 & ( ~ (all_112_2 = 0) | (all_112_0 = 0 & all_112_1 = 0))
% 14.30/2.72 |
% 14.30/2.72 | ALPHA: (35) implies:
% 14.30/2.72 | (36) member(all_59_0, universal_class) = all_112_1
% 14.30/2.72 |
% 14.30/2.72 | DELTA: instantiating (25) with fresh symbols all_132_0, all_132_1, all_132_2
% 14.30/2.72 | gives:
% 14.30/2.72 | (37) member(all_59_0, universal_class) = all_132_2 & member(all_59_1,
% 14.30/2.72 | all_59_0) = all_132_1 & member(all_53_0, element_relation) =
% 14.30/2.72 | all_132_0 & ( ~ (all_132_1 = 0) | ~ (all_132_2 = 0) | all_132_0 = 0)
% 14.30/2.72 |
% 14.30/2.72 | ALPHA: (37) implies:
% 14.30/2.72 | (38) member(all_59_0, universal_class) = all_132_2
% 14.30/2.72 |
% 14.30/2.72 | DELTA: instantiating (23) with fresh symbols all_138_0, all_138_1, all_138_2,
% 14.30/2.72 | all_138_3 gives:
% 14.30/2.72 | (39) successor(all_59_1) = all_138_1 & member(all_59_0, universal_class) =
% 14.30/2.72 | all_138_2 & member(all_59_1, universal_class) = all_138_3 &
% 14.30/2.72 | member(all_53_0, successor_relation) = all_138_0 & $i(all_138_1) & ( ~
% 14.30/2.72 | (all_138_1 = all_59_0) | ~ (all_138_2 = 0) | ~ (all_138_3 = 0) |
% 14.30/2.72 | all_138_0 = 0)
% 14.30/2.72 |
% 14.30/2.72 | ALPHA: (39) implies:
% 14.30/2.72 | (40) member(all_59_1, universal_class) = all_138_3
% 14.30/2.72 | (41) member(all_59_0, universal_class) = all_138_2
% 14.30/2.72 |
% 14.30/2.72 | DELTA: instantiating (22) with fresh symbols all_140_0, all_140_1, all_140_2,
% 14.30/2.72 | all_140_3 gives:
% 14.30/2.72 | (42) successor(all_59_1) = all_140_0 & member(all_59_0, universal_class) =
% 14.30/2.72 | all_140_1 & member(all_59_1, universal_class) = all_140_2 &
% 14.30/2.72 | member(all_53_0, successor_relation) = all_140_3 & $i(all_140_0) & ( ~
% 14.30/2.72 | (all_140_3 = 0) | (all_140_0 = all_59_0 & all_140_1 = 0 & all_140_2
% 14.30/2.72 | = 0))
% 14.30/2.72 |
% 14.30/2.72 | ALPHA: (42) implies:
% 14.30/2.73 | (43) member(all_59_1, universal_class) = all_140_2
% 14.30/2.73 | (44) member(all_59_0, universal_class) = all_140_1
% 14.30/2.73 |
% 14.30/2.73 | DELTA: instantiating (24) with fresh symbols all_142_0, all_142_1, all_142_2,
% 14.30/2.73 | all_142_3 gives:
% 14.30/2.73 | (45) first(all_53_0) = all_142_1 & second(all_53_0) = all_142_0 &
% 14.30/2.73 | member(all_59_0, universal_class) = all_142_2 & member(all_59_1,
% 14.30/2.73 | universal_class) = all_142_3 & $i(all_142_0) & $i(all_142_1) & ( ~
% 14.30/2.73 | (all_142_2 = 0) | ~ (all_142_3 = 0) | (all_142_0 = all_59_0 &
% 14.30/2.73 | all_142_1 = all_59_1))
% 14.30/2.73 |
% 14.30/2.73 | ALPHA: (45) implies:
% 14.30/2.73 | (46) member(all_59_1, universal_class) = all_142_3
% 14.30/2.73 | (47) member(all_59_0, universal_class) = all_142_2
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with all_104_0, all_138_3, universal_class,
% 14.30/2.73 | all_59_1, simplifying with (32), (40) gives:
% 14.30/2.73 | (48) all_138_3 = all_104_0
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with all_96_1, all_138_3, universal_class,
% 14.30/2.73 | all_59_1, simplifying with (28), (40) gives:
% 14.30/2.73 | (49) all_138_3 = all_96_1
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with 0, all_142_3, universal_class, all_59_1,
% 14.30/2.73 | simplifying with (16), (46) gives:
% 14.30/2.73 | (50) all_142_3 = 0
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with all_140_2, all_142_3, universal_class,
% 14.30/2.73 | all_59_1, simplifying with (43), (46) gives:
% 14.30/2.73 | (51) all_142_3 = all_140_2
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with all_138_3, all_142_3, universal_class,
% 14.30/2.73 | all_59_1, simplifying with (40), (46) gives:
% 14.30/2.73 | (52) all_142_3 = all_138_3
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with 0, all_108_0, universal_class, all_59_0,
% 14.30/2.73 | simplifying with (17), (34) gives:
% 14.30/2.73 | (53) all_108_0 = 0
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with all_138_2, all_140_1, universal_class,
% 14.30/2.73 | all_59_0, simplifying with (41), (44) gives:
% 14.30/2.73 | (54) all_140_1 = all_138_2
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with all_132_2, all_140_1, universal_class,
% 14.30/2.73 | all_59_0, simplifying with (38), (44) gives:
% 14.30/2.73 | (55) all_140_1 = all_132_2
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with all_112_1, all_140_1, universal_class,
% 14.30/2.73 | all_59_0, simplifying with (36), (44) gives:
% 14.30/2.73 | (56) all_140_1 = all_112_1
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with all_108_0, all_140_1, universal_class,
% 14.30/2.73 | all_59_0, simplifying with (34), (44) gives:
% 14.30/2.73 | (57) all_140_1 = all_108_0
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with all_138_2, all_142_2, universal_class,
% 14.30/2.73 | all_59_0, simplifying with (41), (47) gives:
% 14.30/2.73 | (58) all_142_2 = all_138_2
% 14.30/2.73 |
% 14.30/2.73 | GROUND_INST: instantiating (9) with all_96_0, all_142_2, universal_class,
% 14.30/2.73 | all_59_0, simplifying with (29), (47) gives:
% 14.30/2.73 | (59) all_142_2 = all_96_0
% 14.30/2.73 |
% 14.30/2.73 | COMBINE_EQS: (58), (59) imply:
% 14.30/2.73 | (60) all_138_2 = all_96_0
% 14.30/2.73 |
% 14.30/2.73 | SIMP: (60) implies:
% 14.30/2.73 | (61) all_138_2 = all_96_0
% 14.30/2.73 |
% 14.30/2.73 | COMBINE_EQS: (51), (52) imply:
% 14.30/2.73 | (62) all_140_2 = all_138_3
% 14.30/2.73 |
% 14.30/2.73 | COMBINE_EQS: (50), (51) imply:
% 14.30/2.73 | (63) all_140_2 = 0
% 14.30/2.73 |
% 14.30/2.73 | COMBINE_EQS: (54), (55) imply:
% 14.30/2.73 | (64) all_138_2 = all_132_2
% 14.30/2.73 |
% 14.30/2.73 | SIMP: (64) implies:
% 14.30/2.73 | (65) all_138_2 = all_132_2
% 14.30/2.73 |
% 14.30/2.73 | COMBINE_EQS: (55), (57) imply:
% 14.30/2.73 | (66) all_132_2 = all_108_0
% 14.30/2.73 |
% 14.30/2.73 | COMBINE_EQS: (55), (56) imply:
% 14.30/2.73 | (67) all_132_2 = all_112_1
% 14.30/2.73 |
% 14.30/2.73 | COMBINE_EQS: (62), (63) imply:
% 14.30/2.73 | (68) all_138_3 = 0
% 14.30/2.73 |
% 14.30/2.73 | SIMP: (68) implies:
% 14.30/2.73 | (69) all_138_3 = 0
% 14.30/2.73 |
% 14.30/2.73 | COMBINE_EQS: (61), (65) imply:
% 14.30/2.73 | (70) all_132_2 = all_96_0
% 14.30/2.73 |
% 14.30/2.73 | SIMP: (70) implies:
% 14.30/2.73 | (71) all_132_2 = all_96_0
% 14.30/2.73 |
% 14.30/2.73 | COMBINE_EQS: (48), (69) imply:
% 14.30/2.73 | (72) all_104_0 = 0
% 14.30/2.73 |
% 14.30/2.73 | COMBINE_EQS: (48), (49) imply:
% 14.30/2.73 | (73) all_104_0 = all_96_1
% 14.30/2.73 |
% 14.30/2.73 | COMBINE_EQS: (66), (67) imply:
% 14.30/2.73 | (74) all_112_1 = all_108_0
% 14.30/2.73 |
% 14.30/2.74 | COMBINE_EQS: (67), (71) imply:
% 14.30/2.74 | (75) all_112_1 = all_96_0
% 14.30/2.74 |
% 14.30/2.74 | COMBINE_EQS: (74), (75) imply:
% 14.30/2.74 | (76) all_108_0 = all_96_0
% 14.30/2.74 |
% 14.30/2.74 | SIMP: (76) implies:
% 14.30/2.74 | (77) all_108_0 = all_96_0
% 14.30/2.74 |
% 14.30/2.74 | COMBINE_EQS: (53), (77) imply:
% 14.30/2.74 | (78) all_96_0 = 0
% 14.30/2.74 |
% 14.30/2.74 | COMBINE_EQS: (72), (73) imply:
% 14.30/2.74 | (79) all_96_1 = 0
% 14.30/2.74 |
% 14.30/2.74 | BETA: splitting (30) gives:
% 14.30/2.74 |
% 14.30/2.74 | Case 1:
% 14.30/2.74 | |
% 14.30/2.74 | | (80) ~ (all_96_0 = 0)
% 14.30/2.74 | |
% 14.30/2.74 | | REDUCE: (78), (80) imply:
% 14.30/2.74 | | (81) $false
% 14.30/2.74 | |
% 14.30/2.74 | | CLOSE: (81) is inconsistent.
% 14.30/2.74 | |
% 14.79/2.74 | Case 2:
% 14.79/2.74 | |
% 14.79/2.74 | | (82) ~ (all_96_1 = 0)
% 14.79/2.74 | |
% 14.79/2.74 | | REDUCE: (79), (82) imply:
% 14.79/2.74 | | (83) $false
% 14.79/2.74 | |
% 14.79/2.74 | | CLOSE: (83) is inconsistent.
% 14.79/2.74 | |
% 14.79/2.74 | End of split
% 14.79/2.74 |
% 14.79/2.74 End of proof
% 14.79/2.74 % SZS output end Proof for theBenchmark
% 14.79/2.74
% 14.79/2.74 2159ms
%------------------------------------------------------------------------------