TSTP Solution File: SET020+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET020+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 : n011.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 15:23:11 EDT 2023
% Result : Theorem 11.84s 2.38s
% Output : Proof 16.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET020+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 14:47:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.67 ________ _____
% 0.21/0.67 ___ __ \_________(_)________________________________
% 0.21/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.67
% 0.21/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.67 (2023-06-19)
% 0.21/0.67
% 0.21/0.67 (c) Philipp Rümmer, 2009-2023
% 0.21/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.67 Amanda Stjerna.
% 0.21/0.67 Free software under BSD-3-Clause.
% 0.21/0.67
% 0.21/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.67
% 0.21/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.69 Running up to 7 provers in parallel.
% 0.21/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.30/1.26 Prover 1: Preprocessing ...
% 3.30/1.26 Prover 4: Preprocessing ...
% 3.30/1.29 Prover 0: Preprocessing ...
% 3.30/1.29 Prover 5: Preprocessing ...
% 3.30/1.29 Prover 6: Preprocessing ...
% 3.30/1.29 Prover 3: Preprocessing ...
% 3.30/1.30 Prover 2: Preprocessing ...
% 8.01/1.99 Prover 1: Warning: ignoring some quantifiers
% 8.82/2.05 Prover 3: Warning: ignoring some quantifiers
% 9.55/2.06 Prover 5: Proving ...
% 9.55/2.07 Prover 1: Constructing countermodel ...
% 9.55/2.07 Prover 4: Warning: ignoring some quantifiers
% 9.55/2.08 Prover 6: Proving ...
% 9.55/2.08 Prover 3: Constructing countermodel ...
% 10.04/2.13 Prover 4: Constructing countermodel ...
% 10.37/2.18 Prover 2: Proving ...
% 10.37/2.21 Prover 0: Proving ...
% 11.84/2.38 Prover 3: proved (1685ms)
% 11.84/2.38
% 11.84/2.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.84/2.38
% 11.84/2.38 Prover 0: stopped
% 11.84/2.38 Prover 5: stopped
% 11.84/2.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.84/2.40 Prover 2: stopped
% 11.84/2.41 Prover 6: stopped
% 12.34/2.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.34/2.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.34/2.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.34/2.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.34/2.44 Prover 7: Preprocessing ...
% 12.34/2.44 Prover 8: Preprocessing ...
% 12.34/2.45 Prover 10: Preprocessing ...
% 12.67/2.48 Prover 13: Preprocessing ...
% 12.67/2.49 Prover 11: Preprocessing ...
% 13.29/2.65 Prover 10: Warning: ignoring some quantifiers
% 13.68/2.67 Prover 8: Warning: ignoring some quantifiers
% 13.68/2.68 Prover 7: Warning: ignoring some quantifiers
% 13.68/2.68 Prover 8: Constructing countermodel ...
% 13.68/2.69 Prover 10: Constructing countermodel ...
% 14.59/2.72 Prover 7: Constructing countermodel ...
% 14.59/2.73 Prover 13: Warning: ignoring some quantifiers
% 14.76/2.75 Prover 13: Constructing countermodel ...
% 14.76/2.80 Prover 11: Warning: ignoring some quantifiers
% 15.38/2.82 Prover 4: Found proof (size 72)
% 15.38/2.82 Prover 4: proved (2127ms)
% 15.38/2.82 Prover 7: stopped
% 15.38/2.82 Prover 1: stopped
% 15.38/2.82 Prover 13: stopped
% 15.38/2.82 Prover 8: stopped
% 15.38/2.83 Prover 11: Constructing countermodel ...
% 15.38/2.83 Prover 10: stopped
% 15.38/2.84 Prover 11: stopped
% 15.38/2.84
% 15.38/2.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.38/2.84
% 15.38/2.86 % SZS output start Proof for theBenchmark
% 15.38/2.86 Assumptions after simplification:
% 15.38/2.86 ---------------------------------
% 15.38/2.86
% 15.38/2.86 (complement)
% 15.70/2.89 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] :
% 15.70/2.89 (v3 = 0 | ~ (complement(v0) = v2) | ~ (member(v1, v2) = v3) | ~ $i(v1) | ~
% 15.70/2.89 $i(v0) | ? [v4: any] : ? [v5: any] : (member(v1, v0) = v5 & member(v1,
% 15.70/2.89 universal_class) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1:
% 15.70/2.89 $i] : ! [v2: int] : (v2 = 0 | ~ (member(v1, v0) = v2) | ~ $i(v1) | ~
% 15.70/2.89 $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : (complement(v0) = v4 &
% 15.70/2.89 member(v1, v4) = v5 & member(v1, universal_class) = v3 & $i(v4) & ( ~ (v3
% 15.70/2.89 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.70/2.89 (complement(v0) = v2) | ~ (member(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 15.70/2.89 [v3: int] : ( ~ (v3 = 0) & member(v1, v0) = v3 & member(v1, universal_class)
% 15.70/2.89 = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (member(v1, v0) =
% 15.70/2.89 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] :
% 15.70/2.89 (complement(v0) = v3 & member(v1, v3) = v4 & member(v1, universal_class) =
% 15.70/2.89 v5 & $i(v3) & ( ~ (v4 = 0) | (v5 = 0 & ~ (v2 = 0)))))
% 15.70/2.89
% 15.70/2.89 (element_relation_defn)
% 15.70/2.90 $i(element_relation) & $i(universal_class) & ! [v0: $i] : ! [v1: $i] : !
% 15.70/2.90 [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 15.70/2.90 any] : ? [v4: any] : ? [v5: any] : (member(v2, element_relation) = v5 &
% 15.70/2.90 member(v1, universal_class) = v3 & member(v0, v1) = v4 & ( ~ (v4 = 0) | ~
% 15.70/2.90 (v3 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.70/2.90 (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 15.70/2.90 any] : ? [v5: any] : (member(v2, element_relation) = v3 & member(v1,
% 15.70/2.90 universal_class) = v4 & member(v0, v1) = v5 & ( ~ (v3 = 0) | (v5 = 0 &
% 15.70/2.90 v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 15.70/2.90 (member(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 15.70/2.90 ? [v5: any] : (ordered_pair(v0, v1) = v3 & member(v3, element_relation) =
% 15.70/2.90 v4 & member(v1, universal_class) = v5 & $i(v3) & ( ~ (v4 = 0) | (v5 = 0 &
% 15.70/2.90 v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0, v1) = 0) | ~
% 15.70/2.90 $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 15.70/2.90 (ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4 & member(v1,
% 15.70/2.90 universal_class) = v2 & $i(v3) & ( ~ (v2 = 0) | v4 = 0)))
% 15.70/2.90
% 15.70/2.90 (first_second)
% 15.70/2.90 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.70/2.90 (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 15.70/2.90 any] : ? [v5: $i] : ? [v6: $i] : (first(v2) = v5 & second(v2) = v6 &
% 15.70/2.90 member(v1, universal_class) = v4 & member(v0, universal_class) = v3 &
% 15.70/2.90 $i(v6) & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = v1 & v5 = v0))))
% 15.70/2.90
% 15.70/2.90 (successor_relation_defn2)
% 15.70/2.90 $i(successor_relation) & $i(universal_class) & ! [v0: $i] : ! [v1: $i] : !
% 15.70/2.90 [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 15.70/2.90 any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : (successor(v0) = v6 &
% 15.70/2.90 member(v2, successor_relation) = v3 & member(v1, universal_class) = v5 &
% 15.70/2.90 member(v0, universal_class) = v4 & $i(v6) & ( ~ (v3 = 0) | (v6 = v1 & v5 =
% 15.70/2.90 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.70/2.90 (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 15.70/2.90 any] : ? [v5: $i] : ? [v6: any] : (successor(v0) = v5 & member(v2,
% 15.70/2.90 successor_relation) = v6 & member(v1, universal_class) = v4 & member(v0,
% 15.70/2.90 universal_class) = v3 & $i(v5) & ( ~ (v5 = v1) | ~ (v4 = 0) | ~ (v3 =
% 15.70/2.90 0) | v6 = 0)))
% 15.70/2.90
% 15.70/2.90 (unique_1st_and_2nd_in_pair_of_sets1)
% 15.70/2.91 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 15.70/2.91 ? [v4: $i] : (first(v2) = v3 & second(v2) = v4 & ordered_pair(v0, v1) = v2 &
% 15.70/2.91 member(v1, universal_class) = 0 & member(v0, universal_class) = 0 & $i(v4) &
% 15.70/2.91 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v4 = v1) | ~ (v3 = v0)))
% 15.70/2.91
% 15.70/2.91 (function-axioms)
% 15.70/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 15.70/2.91 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0:
% 15.70/2.91 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2)
% 15.70/2.91 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.70/2.91 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 15.70/2.91 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 15.70/2.91 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~
% 15.70/2.91 (compose(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 15.70/2.91 $i] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & !
% 15.70/2.91 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3,
% 15.70/2.91 v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 15.70/2.91 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~
% 15.70/2.91 (intersection(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 15.70/2.91 [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3,
% 15.70/2.91 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 15.70/2.91 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & !
% 15.70/2.91 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.70/2.91 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 15.70/2.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.70/2.91 : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0)) & !
% 15.70/2.91 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 15.70/2.91 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & !
% 15.70/2.91 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 15.70/2.91 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: $i] : ! [v1:
% 15.70/2.91 $i] : ! [v2: $i] : (v1 = v0 | ~ (power_class(v2) = v1) | ~
% 15.70/2.91 (power_class(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 15.70/2.91 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0:
% 15.70/2.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 15.70/2.91 ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0)) & ! [v0: $i] : ! [v1:
% 15.70/2.91 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) =
% 15.70/2.91 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.70/2.91 (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 15.70/2.91 [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & !
% 15.70/2.91 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (flip(v2) = v1) | ~
% 15.70/2.91 (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.70/2.91 (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 15.70/2.91 [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & !
% 15.70/2.91 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2) = v1) |
% 15.70/2.91 ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 15.70/2.91 v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 15.70/2.91 : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & !
% 15.70/2.91 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 15.70/2.91 (singleton(v2) = v0))
% 15.70/2.91
% 15.70/2.91 Further assumptions not needed in the proof:
% 15.70/2.91 --------------------------------------------
% 15.70/2.91 apply_defn, choice, class_elements_are_sets, compose_defn1, compose_defn2,
% 15.70/2.91 cross_product, cross_product_defn, disjoint_defn, domain_of, element_relation,
% 15.70/2.91 extensionality, flip, flip_defn, function_defn, identity_relation, image_defn,
% 15.70/2.91 inductive_defn, infinity, intersection, inverse_defn, null_class_defn,
% 15.70/2.91 ordered_pair_defn, power_class, power_class_defn, range_of_defn, regularity,
% 15.70/2.91 replacement, restrict_defn, rotate, rotate_defn, singleton_set_defn,
% 15.70/2.91 subclass_defn, successor_defn, successor_relation_defn1, sum_class,
% 15.70/2.91 sum_class_defn, union_defn, unordered_pair, unordered_pair_defn
% 15.70/2.91
% 15.70/2.91 Those formulas are unsatisfiable:
% 15.70/2.91 ---------------------------------
% 15.70/2.91
% 15.70/2.91 Begin of proof
% 15.70/2.92 |
% 15.70/2.92 | ALPHA: (first_second) implies:
% 15.70/2.92 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 15.70/2.92 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 15.70/2.92 | $i] : ? [v6: $i] : (first(v2) = v5 & second(v2) = v6 & member(v1,
% 15.70/2.92 | universal_class) = v4 & member(v0, universal_class) = v3 & $i(v6)
% 15.70/2.92 | & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = v1 & v5 = v0))))
% 15.70/2.92 |
% 15.70/2.92 | ALPHA: (element_relation_defn) implies:
% 15.70/2.92 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 15.70/2.92 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 15.70/2.92 | any] : (member(v2, element_relation) = v3 & member(v1,
% 15.70/2.92 | universal_class) = v4 & member(v0, v1) = v5 & ( ~ (v3 = 0) | (v5
% 15.70/2.92 | = 0 & v4 = 0))))
% 15.70/2.92 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 15.70/2.92 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 15.70/2.92 | any] : (member(v2, element_relation) = v5 & member(v1,
% 15.70/2.92 | universal_class) = v3 & member(v0, v1) = v4 & ( ~ (v4 = 0) | ~
% 15.70/2.92 | (v3 = 0) | v5 = 0)))
% 15.70/2.92 |
% 15.70/2.92 | ALPHA: (complement) implies:
% 15.70/2.92 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (member(v1, v0) = v2) |
% 15.70/2.92 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] :
% 15.70/2.92 | (complement(v0) = v3 & member(v1, v3) = v4 & member(v1,
% 15.70/2.92 | universal_class) = v5 & $i(v3) & ( ~ (v4 = 0) | (v5 = 0 & ~ (v2
% 15.70/2.92 | = 0)))))
% 15.70/2.92 |
% 15.70/2.92 | ALPHA: (successor_relation_defn2) implies:
% 15.70/2.92 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 15.70/2.92 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 15.70/2.92 | $i] : ? [v6: any] : (successor(v0) = v5 & member(v2,
% 15.70/2.92 | successor_relation) = v6 & member(v1, universal_class) = v4 &
% 15.70/2.92 | member(v0, universal_class) = v3 & $i(v5) & ( ~ (v5 = v1) | ~ (v4
% 15.70/2.92 | = 0) | ~ (v3 = 0) | v6 = 0)))
% 15.70/2.92 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 15.70/2.92 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 15.70/2.92 | any] : ? [v6: $i] : (successor(v0) = v6 & member(v2,
% 15.70/2.92 | successor_relation) = v3 & member(v1, universal_class) = v5 &
% 15.70/2.92 | member(v0, universal_class) = v4 & $i(v6) & ( ~ (v3 = 0) | (v6 = v1
% 15.70/2.92 | & v5 = 0 & v4 = 0))))
% 15.70/2.92 |
% 15.70/2.92 | ALPHA: (unique_1st_and_2nd_in_pair_of_sets1) implies:
% 15.70/2.92 | (7) $i(universal_class)
% 15.70/2.92 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 15.70/2.92 | (first(v2) = v3 & second(v2) = v4 & ordered_pair(v0, v1) = v2 &
% 15.70/2.92 | member(v1, universal_class) = 0 & member(v0, universal_class) = 0 &
% 15.70/2.92 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v4 = v1) | ~ (v3 =
% 15.70/2.93 | v0)))
% 15.70/2.93 |
% 15.70/2.93 | ALPHA: (function-axioms) implies:
% 15.70/2.93 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (second(v2) =
% 15.70/2.93 | v1) | ~ (second(v2) = v0))
% 15.70/2.93 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (first(v2) =
% 15.70/2.93 | v1) | ~ (first(v2) = v0))
% 15.70/2.93 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.70/2.93 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3,
% 15.70/2.93 | v2) = v0))
% 15.70/2.93 |
% 15.70/2.93 | DELTA: instantiating (8) with fresh symbols all_53_0, all_53_1, all_53_2,
% 15.70/2.93 | all_53_3, all_53_4 gives:
% 15.70/2.93 | (12) first(all_53_2) = all_53_1 & second(all_53_2) = all_53_0 &
% 15.70/2.93 | ordered_pair(all_53_4, all_53_3) = all_53_2 & member(all_53_3,
% 15.70/2.93 | universal_class) = 0 & member(all_53_4, universal_class) = 0 &
% 15.70/2.93 | $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3) &
% 15.70/2.93 | $i(all_53_4) & ( ~ (all_53_0 = all_53_3) | ~ (all_53_1 = all_53_4))
% 15.70/2.93 |
% 15.70/2.93 | ALPHA: (12) implies:
% 15.70/2.93 | (13) $i(all_53_4)
% 15.70/2.93 | (14) $i(all_53_3)
% 15.70/2.93 | (15) member(all_53_4, universal_class) = 0
% 15.70/2.93 | (16) member(all_53_3, universal_class) = 0
% 15.70/2.93 | (17) ordered_pair(all_53_4, all_53_3) = all_53_2
% 15.70/2.93 | (18) second(all_53_2) = all_53_0
% 15.70/2.93 | (19) first(all_53_2) = all_53_1
% 15.70/2.93 | (20) ~ (all_53_0 = all_53_3) | ~ (all_53_1 = all_53_4)
% 15.70/2.93 |
% 15.70/2.93 | GROUND_INST: instantiating (4) with universal_class, all_53_4, 0, simplifying
% 15.70/2.93 | with (7), (13), (15) gives:
% 15.70/2.93 | (21) ? [v0: $i] : ? [v1: int] : ? [v2: MultipleValueBool] : ( ~ (v1 = 0)
% 15.70/2.93 | & complement(universal_class) = v0 & member(all_53_4, v0) = v1 &
% 15.70/2.93 | member(all_53_4, universal_class) = v2 & $i(v0))
% 15.70/2.93 |
% 15.70/2.93 | GROUND_INST: instantiating (4) with universal_class, all_53_3, 0, simplifying
% 15.70/2.93 | with (7), (14), (16) gives:
% 15.70/2.93 | (22) ? [v0: $i] : ? [v1: int] : ? [v2: MultipleValueBool] : ( ~ (v1 = 0)
% 15.70/2.93 | & complement(universal_class) = v0 & member(all_53_3, v0) = v1 &
% 15.70/2.93 | member(all_53_3, universal_class) = v2 & $i(v0))
% 15.70/2.93 |
% 15.70/2.93 | GROUND_INST: instantiating (6) with all_53_4, all_53_3, all_53_2, simplifying
% 15.70/2.93 | with (13), (14), (17) gives:
% 15.70/2.93 | (23) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] :
% 15.70/2.93 | (successor(all_53_4) = v3 & member(all_53_2, successor_relation) = v0
% 15.70/2.93 | & member(all_53_3, universal_class) = v2 & member(all_53_4,
% 15.70/2.93 | universal_class) = v1 & $i(v3) & ( ~ (v0 = 0) | (v3 = all_53_3 &
% 15.70/2.93 | v2 = 0 & v1 = 0)))
% 15.70/2.93 |
% 15.70/2.93 | GROUND_INST: instantiating (5) with all_53_4, all_53_3, all_53_2, simplifying
% 15.70/2.93 | with (13), (14), (17) gives:
% 15.70/2.94 | (24) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 15.70/2.94 | (successor(all_53_4) = v2 & member(all_53_2, successor_relation) = v3
% 15.70/2.94 | & member(all_53_3, universal_class) = v1 & member(all_53_4,
% 15.70/2.94 | universal_class) = v0 & $i(v2) & ( ~ (v2 = all_53_3) | ~ (v1 = 0)
% 15.70/2.94 | | ~ (v0 = 0) | v3 = 0))
% 15.70/2.94 |
% 15.70/2.94 | GROUND_INST: instantiating (1) with all_53_4, all_53_3, all_53_2, simplifying
% 15.70/2.94 | with (13), (14), (17) gives:
% 15.70/2.94 | (25) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 15.70/2.94 | (first(all_53_2) = v2 & second(all_53_2) = v3 & member(all_53_3,
% 15.70/2.94 | universal_class) = v1 & member(all_53_4, universal_class) = v0 &
% 15.70/2.94 | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = all_53_3 & v2 =
% 15.70/2.94 | all_53_4)))
% 15.70/2.94 |
% 15.70/2.94 | GROUND_INST: instantiating (3) with all_53_4, all_53_3, all_53_2, simplifying
% 15.70/2.94 | with (13), (14), (17) gives:
% 15.70/2.94 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : (member(all_53_2,
% 15.70/2.94 | element_relation) = v2 & member(all_53_3, universal_class) = v0 &
% 15.70/2.94 | member(all_53_4, all_53_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 =
% 15.70/2.94 | 0))
% 15.70/2.94 |
% 15.70/2.94 | GROUND_INST: instantiating (2) with all_53_4, all_53_3, all_53_2, simplifying
% 15.70/2.94 | with (13), (14), (17) gives:
% 15.70/2.94 | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : (member(all_53_2,
% 15.70/2.94 | element_relation) = v0 & member(all_53_3, universal_class) = v1 &
% 15.70/2.94 | member(all_53_4, all_53_3) = v2 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 15.70/2.94 |
% 15.70/2.94 | DELTA: instantiating (21) with fresh symbols all_95_0, all_95_1, all_95_2
% 15.70/2.94 | gives:
% 15.70/2.94 | (28) ~ (all_95_1 = 0) & complement(universal_class) = all_95_2 &
% 15.70/2.94 | member(all_53_4, all_95_2) = all_95_1 & member(all_53_4,
% 15.70/2.94 | universal_class) = all_95_0 & $i(all_95_2)
% 15.70/2.94 |
% 15.70/2.94 | ALPHA: (28) implies:
% 15.70/2.94 | (29) member(all_53_4, universal_class) = all_95_0
% 15.70/2.94 |
% 15.70/2.94 | DELTA: instantiating (22) with fresh symbols all_101_0, all_101_1, all_101_2
% 15.70/2.94 | gives:
% 15.70/2.94 | (30) ~ (all_101_1 = 0) & complement(universal_class) = all_101_2 &
% 15.70/2.94 | member(all_53_3, all_101_2) = all_101_1 & member(all_53_3,
% 15.70/2.94 | universal_class) = all_101_0 & $i(all_101_2)
% 15.70/2.94 |
% 15.70/2.94 | ALPHA: (30) implies:
% 15.70/2.94 | (31) member(all_53_3, universal_class) = all_101_0
% 15.70/2.94 |
% 15.70/2.94 | DELTA: instantiating (27) with fresh symbols all_121_0, all_121_1, all_121_2
% 15.70/2.94 | gives:
% 15.70/2.94 | (32) member(all_53_2, element_relation) = all_121_2 & member(all_53_3,
% 15.70/2.94 | universal_class) = all_121_1 & member(all_53_4, all_53_3) =
% 15.70/2.94 | all_121_0 & ( ~ (all_121_2 = 0) | (all_121_0 = 0 & all_121_1 = 0))
% 15.70/2.94 |
% 15.70/2.94 | ALPHA: (32) implies:
% 15.70/2.94 | (33) member(all_53_3, universal_class) = all_121_1
% 15.70/2.94 |
% 15.70/2.94 | DELTA: instantiating (26) with fresh symbols all_123_0, all_123_1, all_123_2
% 15.70/2.94 | gives:
% 15.70/2.94 | (34) member(all_53_2, element_relation) = all_123_0 & member(all_53_3,
% 15.70/2.94 | universal_class) = all_123_2 & member(all_53_4, all_53_3) =
% 15.70/2.94 | all_123_1 & ( ~ (all_123_1 = 0) | ~ (all_123_2 = 0) | all_123_0 = 0)
% 15.70/2.94 |
% 15.70/2.94 | ALPHA: (34) implies:
% 15.70/2.94 | (35) member(all_53_3, universal_class) = all_123_2
% 15.70/2.94 |
% 15.70/2.94 | DELTA: instantiating (24) with fresh symbols all_133_0, all_133_1, all_133_2,
% 15.70/2.94 | all_133_3 gives:
% 15.70/2.94 | (36) successor(all_53_4) = all_133_1 & member(all_53_2, successor_relation)
% 15.70/2.94 | = all_133_0 & member(all_53_3, universal_class) = all_133_2 &
% 15.70/2.94 | member(all_53_4, universal_class) = all_133_3 & $i(all_133_1) & ( ~
% 15.70/2.94 | (all_133_1 = all_53_3) | ~ (all_133_2 = 0) | ~ (all_133_3 = 0) |
% 15.70/2.94 | all_133_0 = 0)
% 15.70/2.94 |
% 15.70/2.94 | ALPHA: (36) implies:
% 15.70/2.94 | (37) member(all_53_4, universal_class) = all_133_3
% 15.70/2.94 | (38) member(all_53_3, universal_class) = all_133_2
% 15.70/2.94 |
% 15.70/2.94 | DELTA: instantiating (23) with fresh symbols all_135_0, all_135_1, all_135_2,
% 15.70/2.94 | all_135_3 gives:
% 15.70/2.94 | (39) successor(all_53_4) = all_135_0 & member(all_53_2, successor_relation)
% 15.70/2.94 | = all_135_3 & member(all_53_3, universal_class) = all_135_1 &
% 15.70/2.94 | member(all_53_4, universal_class) = all_135_2 & $i(all_135_0) & ( ~
% 15.70/2.94 | (all_135_3 = 0) | (all_135_0 = all_53_3 & all_135_1 = 0 & all_135_2
% 15.70/2.94 | = 0))
% 15.70/2.94 |
% 15.70/2.94 | ALPHA: (39) implies:
% 15.70/2.94 | (40) member(all_53_4, universal_class) = all_135_2
% 15.70/2.94 | (41) member(all_53_3, universal_class) = all_135_1
% 15.70/2.94 |
% 15.70/2.94 | DELTA: instantiating (25) with fresh symbols all_137_0, all_137_1, all_137_2,
% 15.70/2.94 | all_137_3 gives:
% 15.70/2.95 | (42) first(all_53_2) = all_137_1 & second(all_53_2) = all_137_0 &
% 15.70/2.95 | member(all_53_3, universal_class) = all_137_2 & member(all_53_4,
% 15.70/2.95 | universal_class) = all_137_3 & $i(all_137_0) & $i(all_137_1) & ( ~
% 15.70/2.95 | (all_137_2 = 0) | ~ (all_137_3 = 0) | (all_137_0 = all_53_3 &
% 15.70/2.95 | all_137_1 = all_53_4))
% 15.70/2.95 |
% 15.70/2.95 | ALPHA: (42) implies:
% 15.70/2.95 | (43) member(all_53_4, universal_class) = all_137_3
% 15.70/2.95 | (44) member(all_53_3, universal_class) = all_137_2
% 15.70/2.95 | (45) second(all_53_2) = all_137_0
% 15.70/2.95 | (46) first(all_53_2) = all_137_1
% 15.70/2.95 | (47) ~ (all_137_2 = 0) | ~ (all_137_3 = 0) | (all_137_0 = all_53_3 &
% 15.70/2.95 | all_137_1 = all_53_4)
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (11) with 0, all_133_3, universal_class, all_53_4,
% 15.70/2.95 | simplifying with (15), (37) gives:
% 15.70/2.95 | (48) all_133_3 = 0
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (11) with all_133_3, all_135_2, universal_class,
% 15.70/2.95 | all_53_4, simplifying with (37), (40) gives:
% 15.70/2.95 | (49) all_135_2 = all_133_3
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (11) with all_135_2, all_137_3, universal_class,
% 15.70/2.95 | all_53_4, simplifying with (40), (43) gives:
% 15.70/2.95 | (50) all_137_3 = all_135_2
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (11) with all_95_0, all_137_3, universal_class,
% 15.70/2.95 | all_53_4, simplifying with (29), (43) gives:
% 15.70/2.95 | (51) all_137_3 = all_95_0
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (11) with 0, all_121_1, universal_class, all_53_3,
% 15.70/2.95 | simplifying with (16), (33) gives:
% 15.70/2.95 | (52) all_121_1 = 0
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (11) with all_133_2, all_135_1, universal_class,
% 15.70/2.95 | all_53_3, simplifying with (38), (41) gives:
% 15.70/2.95 | (53) all_135_1 = all_133_2
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (11) with all_123_2, all_135_1, universal_class,
% 15.70/2.95 | all_53_3, simplifying with (35), (41) gives:
% 15.70/2.95 | (54) all_135_1 = all_123_2
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (11) with all_121_1, all_135_1, universal_class,
% 15.70/2.95 | all_53_3, simplifying with (33), (41) gives:
% 15.70/2.95 | (55) all_135_1 = all_121_1
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (11) with all_133_2, all_137_2, universal_class,
% 15.70/2.95 | all_53_3, simplifying with (38), (44) gives:
% 15.70/2.95 | (56) all_137_2 = all_133_2
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (11) with all_101_0, all_137_2, universal_class,
% 15.70/2.95 | all_53_3, simplifying with (31), (44) gives:
% 15.70/2.95 | (57) all_137_2 = all_101_0
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (9) with all_53_0, all_137_0, all_53_2, simplifying
% 15.70/2.95 | with (18), (45) gives:
% 15.70/2.95 | (58) all_137_0 = all_53_0
% 15.70/2.95 |
% 15.70/2.95 | GROUND_INST: instantiating (10) with all_53_1, all_137_1, all_53_2,
% 15.70/2.95 | simplifying with (19), (46) gives:
% 15.70/2.95 | (59) all_137_1 = all_53_1
% 15.70/2.95 |
% 15.70/2.95 | COMBINE_EQS: (56), (57) imply:
% 15.70/2.95 | (60) all_133_2 = all_101_0
% 15.70/2.95 |
% 15.70/2.95 | SIMP: (60) implies:
% 15.70/2.95 | (61) all_133_2 = all_101_0
% 15.70/2.95 |
% 15.70/2.95 | COMBINE_EQS: (50), (51) imply:
% 15.70/2.95 | (62) all_135_2 = all_95_0
% 15.70/2.95 |
% 15.70/2.95 | SIMP: (62) implies:
% 15.70/2.95 | (63) all_135_2 = all_95_0
% 15.70/2.95 |
% 15.70/2.95 | COMBINE_EQS: (53), (54) imply:
% 15.70/2.95 | (64) all_133_2 = all_123_2
% 15.70/2.95 |
% 15.70/2.95 | SIMP: (64) implies:
% 15.70/2.95 | (65) all_133_2 = all_123_2
% 15.70/2.95 |
% 15.70/2.95 | COMBINE_EQS: (54), (55) imply:
% 15.70/2.95 | (66) all_123_2 = all_121_1
% 15.70/2.95 |
% 15.70/2.95 | COMBINE_EQS: (49), (63) imply:
% 15.70/2.95 | (67) all_133_3 = all_95_0
% 15.70/2.95 |
% 15.70/2.95 | SIMP: (67) implies:
% 15.70/2.95 | (68) all_133_3 = all_95_0
% 15.70/2.95 |
% 15.70/2.95 | COMBINE_EQS: (61), (65) imply:
% 15.70/2.95 | (69) all_123_2 = all_101_0
% 15.70/2.95 |
% 15.70/2.95 | SIMP: (69) implies:
% 15.70/2.95 | (70) all_123_2 = all_101_0
% 15.70/2.96 |
% 15.70/2.96 | COMBINE_EQS: (48), (68) imply:
% 15.70/2.96 | (71) all_95_0 = 0
% 15.70/2.96 |
% 15.70/2.96 | COMBINE_EQS: (66), (70) imply:
% 15.70/2.96 | (72) all_121_1 = all_101_0
% 15.70/2.96 |
% 15.70/2.96 | SIMP: (72) implies:
% 15.70/2.96 | (73) all_121_1 = all_101_0
% 15.70/2.96 |
% 15.70/2.96 | COMBINE_EQS: (52), (73) imply:
% 15.70/2.96 | (74) all_101_0 = 0
% 15.70/2.96 |
% 15.70/2.96 | COMBINE_EQS: (51), (71) imply:
% 15.70/2.96 | (75) all_137_3 = 0
% 15.70/2.96 |
% 15.70/2.96 | COMBINE_EQS: (57), (74) imply:
% 15.70/2.96 | (76) all_137_2 = 0
% 15.70/2.96 |
% 15.70/2.96 | BETA: splitting (47) gives:
% 15.70/2.96 |
% 15.70/2.96 | Case 1:
% 15.70/2.96 | |
% 15.70/2.96 | | (77) ~ (all_137_2 = 0)
% 15.70/2.96 | |
% 15.70/2.96 | | REDUCE: (76), (77) imply:
% 15.70/2.96 | | (78) $false
% 16.09/2.96 | |
% 16.09/2.96 | | CLOSE: (78) is inconsistent.
% 16.09/2.96 | |
% 16.09/2.96 | Case 2:
% 16.09/2.96 | |
% 16.09/2.96 | | (79) ~ (all_137_3 = 0) | (all_137_0 = all_53_3 & all_137_1 = all_53_4)
% 16.09/2.96 | |
% 16.09/2.96 | | BETA: splitting (79) gives:
% 16.09/2.96 | |
% 16.09/2.96 | | Case 1:
% 16.09/2.96 | | |
% 16.09/2.96 | | | (80) ~ (all_137_3 = 0)
% 16.09/2.96 | | |
% 16.09/2.96 | | | REDUCE: (75), (80) imply:
% 16.09/2.96 | | | (81) $false
% 16.09/2.96 | | |
% 16.09/2.96 | | | CLOSE: (81) is inconsistent.
% 16.09/2.96 | | |
% 16.09/2.96 | | Case 2:
% 16.09/2.96 | | |
% 16.09/2.96 | | | (82) all_137_0 = all_53_3 & all_137_1 = all_53_4
% 16.09/2.96 | | |
% 16.09/2.96 | | | ALPHA: (82) implies:
% 16.09/2.96 | | | (83) all_137_1 = all_53_4
% 16.09/2.96 | | | (84) all_137_0 = all_53_3
% 16.09/2.96 | | |
% 16.09/2.96 | | | COMBINE_EQS: (58), (84) imply:
% 16.09/2.96 | | | (85) all_53_0 = all_53_3
% 16.09/2.96 | | |
% 16.09/2.96 | | | COMBINE_EQS: (59), (83) imply:
% 16.09/2.96 | | | (86) all_53_1 = all_53_4
% 16.09/2.96 | | |
% 16.09/2.96 | | | BETA: splitting (20) gives:
% 16.09/2.96 | | |
% 16.09/2.96 | | | Case 1:
% 16.09/2.96 | | | |
% 16.09/2.96 | | | | (87) ~ (all_53_0 = all_53_3)
% 16.09/2.96 | | | |
% 16.09/2.96 | | | | REDUCE: (85), (87) imply:
% 16.09/2.96 | | | | (88) $false
% 16.09/2.96 | | | |
% 16.09/2.96 | | | | CLOSE: (88) is inconsistent.
% 16.09/2.96 | | | |
% 16.09/2.96 | | | Case 2:
% 16.09/2.96 | | | |
% 16.09/2.96 | | | | (89) ~ (all_53_1 = all_53_4)
% 16.09/2.96 | | | |
% 16.09/2.96 | | | | REDUCE: (86), (89) imply:
% 16.09/2.96 | | | | (90) $false
% 16.09/2.96 | | | |
% 16.09/2.96 | | | | CLOSE: (90) is inconsistent.
% 16.09/2.96 | | | |
% 16.09/2.96 | | | End of split
% 16.09/2.96 | | |
% 16.09/2.96 | | End of split
% 16.09/2.96 | |
% 16.09/2.96 | End of split
% 16.09/2.96 |
% 16.09/2.96 End of proof
% 16.09/2.96 % SZS output end Proof for theBenchmark
% 16.09/2.96
% 16.09/2.96 2286ms
%------------------------------------------------------------------------------