TSTP Solution File: SET018+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET018+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 15:23:09 EDT 2023
% Result : Theorem 174.70s 23.82s
% Output : Proof 175.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SET018+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 10:57:39 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.61 ________ _____
% 0.22/0.61 ___ __ \_________(_)________________________________
% 0.22/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.61
% 0.22/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.61 (2023-06-19)
% 0.22/0.61
% 0.22/0.61 (c) Philipp Rümmer, 2009-2023
% 0.22/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.61 Amanda Stjerna.
% 0.22/0.61 Free software under BSD-3-Clause.
% 0.22/0.61
% 0.22/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.61
% 0.22/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.62 Running up to 7 provers in parallel.
% 0.22/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.18/1.20 Prover 1: Preprocessing ...
% 3.18/1.20 Prover 4: Preprocessing ...
% 3.68/1.24 Prover 3: Preprocessing ...
% 3.68/1.24 Prover 0: Preprocessing ...
% 3.68/1.24 Prover 2: Preprocessing ...
% 3.68/1.24 Prover 5: Preprocessing ...
% 3.68/1.26 Prover 6: Preprocessing ...
% 8.54/1.99 Prover 1: Warning: ignoring some quantifiers
% 9.67/2.05 Prover 3: Warning: ignoring some quantifiers
% 9.67/2.06 Prover 6: Proving ...
% 9.67/2.06 Prover 5: Proving ...
% 9.67/2.09 Prover 3: Constructing countermodel ...
% 10.05/2.09 Prover 1: Constructing countermodel ...
% 10.05/2.12 Prover 4: Warning: ignoring some quantifiers
% 10.46/2.19 Prover 4: Constructing countermodel ...
% 10.82/2.21 Prover 2: Proving ...
% 11.18/2.30 Prover 0: Proving ...
% 73.56/10.32 Prover 2: stopped
% 73.71/10.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.45/10.43 Prover 7: Preprocessing ...
% 75.59/10.59 Prover 7: Warning: ignoring some quantifiers
% 75.85/10.61 Prover 7: Constructing countermodel ...
% 101.33/13.97 Prover 5: stopped
% 101.94/13.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 101.94/14.04 Prover 8: Preprocessing ...
% 103.00/14.15 Prover 8: Warning: ignoring some quantifiers
% 103.00/14.15 Prover 8: Constructing countermodel ...
% 116.76/15.98 Prover 1: stopped
% 116.76/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 116.76/16.01 Prover 9: Preprocessing ...
% 118.39/16.24 Prover 9: Warning: ignoring some quantifiers
% 118.39/16.24 Prover 9: Constructing countermodel ...
% 130.75/17.88 Prover 6: stopped
% 130.75/17.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 131.33/17.97 Prover 10: Preprocessing ...
% 131.33/18.03 Prover 10: Warning: ignoring some quantifiers
% 131.33/18.04 Prover 10: Constructing countermodel ...
% 132.36/18.13 Prover 10: gave up
% 132.36/18.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 133.14/18.15 Prover 11: Preprocessing ...
% 134.07/18.29 Prover 11: Warning: ignoring some quantifiers
% 134.07/18.29 Prover 11: Constructing countermodel ...
% 174.70/23.80 Prover 7: Found proof (size 203)
% 174.70/23.80 Prover 7: proved (13342ms)
% 174.70/23.80 Prover 9: stopped
% 174.70/23.80 Prover 0: stopped
% 174.70/23.80 Prover 8: stopped
% 174.70/23.81 Prover 4: stopped
% 174.70/23.81 Prover 11: stopped
% 174.70/23.82 Prover 3: stopped
% 174.70/23.82
% 174.70/23.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 174.70/23.82
% 174.70/23.83 % SZS output start Proof for theBenchmark
% 174.70/23.83 Assumptions after simplification:
% 174.70/23.83 ---------------------------------
% 174.70/23.83
% 174.70/23.83 (first_second)
% 174.70/23.86 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 174.70/23.86 (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v1,
% 174.70/23.86 universal_class) | ~ member(v0, universal_class) | (first(v2) = v0 &
% 174.70/23.86 second(v2) = v1))
% 174.70/23.86
% 174.70/23.86 (ordered_pair_defn)
% 174.70/23.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (singleton(v1) =
% 174.70/23.87 v2) | ~ (unordered_pair(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 174.70/23.87 $i] : ? [v5: $i] : (ordered_pair(v0, v1) = v4 & singleton(v0) = v5 &
% 174.70/23.87 unordered_pair(v5, v3) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1:
% 174.70/23.87 $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 174.70/23.87 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (singleton(v1) = v4 &
% 174.70/23.87 singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4)
% 174.70/23.87 = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 174.70/23.87
% 174.70/23.87 (ordered_pair_determines_components2)
% 174.70/23.87 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 174.70/23.87 ? [v4: $i] : ( ~ (v3 = v1) & ordered_pair(v2, v3) = v4 & ordered_pair(v0, v1)
% 174.70/23.87 = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & member(v1,
% 174.70/23.87 universal_class))
% 174.70/23.87
% 174.70/23.87 (singleton_set_defn)
% 174.70/23.87 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 174.70/23.87 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 174.70/23.87 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1)))
% 174.70/23.87
% 174.70/23.87 (unordered_pair)
% 174.70/23.87 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 174.70/23.87 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | member(v2,
% 174.70/23.87 universal_class))
% 174.70/23.87
% 174.70/23.87 (unordered_pair_defn)
% 174.70/23.88 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 174.70/23.88 (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 174.70/23.88 | ~ $i(v0) | ~ member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 174.70/23.88 ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 174.70/23.88 $i(v0) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0: $i] : !
% 174.70/23.88 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~
% 174.70/23.88 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0: $i] : !
% 174.70/23.88 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~
% 174.70/23.88 $i(v0) | ~ member(v0, universal_class) | member(v0, v2))
% 174.70/23.88
% 174.70/23.88 (function-axioms)
% 175.11/23.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 175.11/23.89 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0:
% 175.11/23.89 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2)
% 175.11/23.89 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 175.11/23.89 : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) =
% 175.11/23.89 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 175.11/23.89 ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 175.11/23.89 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 175.11/23.89 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 175.11/23.89 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 175.11/23.89 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 175.11/23.89 ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) & ! [v0:
% 175.11/23.89 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 175.11/23.89 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 175.11/23.89 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3,
% 175.11/23.89 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 175.11/23.89 $i] : ! [v2: $i] : (v1 = v0 | ~ (power_class(v2) = v1) | ~
% 175.11/23.89 (power_class(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 175.11/23.89 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0: $i] : ! [v1:
% 175.11/23.89 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) =
% 175.11/23.89 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 175.11/23.89 (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 175.11/23.89 [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & !
% 175.11/23.89 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (flip(v2) = v1) | ~
% 175.11/23.89 (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 175.11/23.89 (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 175.11/23.89 [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & !
% 175.11/23.89 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2) = v1) |
% 175.11/23.89 ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 175.11/23.89 v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 175.11/23.89 : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & !
% 175.11/23.89 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 175.11/23.89 (singleton(v2) = v0))
% 175.11/23.89
% 175.11/23.89 Further assumptions not needed in the proof:
% 175.11/23.89 --------------------------------------------
% 175.11/23.89 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 175.11/23.89 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 175.11/23.89 element_relation, element_relation_defn, extensionality, flip, flip_defn,
% 175.11/23.89 function_defn, identity_relation, image_defn, inductive_defn, infinity,
% 175.11/23.89 intersection, inverse_defn, null_class_defn, power_class, power_class_defn,
% 175.11/23.89 range_of_defn, regularity, replacement, restrict_defn, rotate, rotate_defn,
% 175.11/23.89 subclass_defn, successor_defn, successor_relation_defn1,
% 175.11/23.89 successor_relation_defn2, sum_class, sum_class_defn, union_defn
% 175.11/23.89
% 175.11/23.89 Those formulas are unsatisfiable:
% 175.11/23.89 ---------------------------------
% 175.11/23.89
% 175.11/23.89 Begin of proof
% 175.11/23.89 |
% 175.11/23.89 | ALPHA: (unordered_pair_defn) implies:
% 175.11/23.90 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 175.11/23.90 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) |
% 175.11/23.90 | member(v0, v2))
% 175.11/23.90 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 175.11/23.90 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) |
% 175.11/23.90 | member(v0, v2))
% 175.11/23.90 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 =
% 175.11/23.90 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 175.11/23.90 | $i(v0) | ~ member(v0, v3))
% 175.11/23.90 |
% 175.11/23.90 | ALPHA: (unordered_pair) implies:
% 175.11/23.90 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 175.11/23.90 | v2) | ~ $i(v1) | ~ $i(v0) | member(v2, universal_class))
% 175.11/23.90 |
% 175.11/23.90 | ALPHA: (singleton_set_defn) implies:
% 175.11/23.90 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 175.11/23.90 | (unordered_pair(v0, v0) = v1 & $i(v1)))
% 175.11/23.90 |
% 175.11/23.90 | ALPHA: (ordered_pair_defn) implies:
% 175.11/23.90 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 175.11/23.90 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 175.11/23.90 | $i] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3,
% 175.11/23.90 | v5) = v2 & unordered_pair(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3)
% 175.11/23.90 | & $i(v2)))
% 175.11/23.90 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 175.11/23.90 | (singleton(v1) = v2) | ~ (unordered_pair(v0, v2) = v3) | ~ $i(v1) |
% 175.11/23.90 | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v0, v1) = v4 &
% 175.11/23.90 | singleton(v0) = v5 & unordered_pair(v5, v3) = v4 & $i(v5) &
% 175.11/23.90 | $i(v4)))
% 175.11/23.90 |
% 175.11/23.90 | ALPHA: (first_second) implies:
% 175.11/23.90 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 175.11/23.90 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v1, universal_class) | ~
% 175.11/23.90 | member(v0, universal_class) | (first(v2) = v0 & second(v2) = v1))
% 175.11/23.90 |
% 175.11/23.90 | ALPHA: (ordered_pair_determines_components2) implies:
% 175.11/23.90 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (
% 175.11/23.90 | ~ (v3 = v1) & ordered_pair(v2, v3) = v4 & ordered_pair(v0, v1) = v4 &
% 175.11/23.90 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & member(v1,
% 175.11/23.90 | universal_class))
% 175.11/23.90 |
% 175.11/23.90 | ALPHA: (function-axioms) implies:
% 175.11/23.90 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 175.11/23.90 | = v1) | ~ (singleton(v2) = v0))
% 175.11/23.91 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 175.11/23.91 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 175.11/23.91 |
% 175.11/23.91 | DELTA: instantiating (9) with fresh symbols all_59_0, all_59_1, all_59_2,
% 175.11/23.91 | all_59_3, all_59_4 gives:
% 175.11/23.91 | (12) ~ (all_59_1 = all_59_3) & ordered_pair(all_59_2, all_59_1) = all_59_0
% 175.11/23.91 | & ordered_pair(all_59_4, all_59_3) = all_59_0 & $i(all_59_0) &
% 175.11/23.91 | $i(all_59_1) & $i(all_59_2) & $i(all_59_3) & $i(all_59_4) &
% 175.11/23.91 | member(all_59_3, universal_class)
% 175.11/23.91 |
% 175.11/23.91 | ALPHA: (12) implies:
% 175.11/23.91 | (13) ~ (all_59_1 = all_59_3)
% 175.11/23.91 | (14) member(all_59_3, universal_class)
% 175.11/23.91 | (15) $i(all_59_4)
% 175.11/23.91 | (16) $i(all_59_3)
% 175.11/23.91 | (17) $i(all_59_2)
% 175.11/23.91 | (18) $i(all_59_1)
% 175.11/23.91 | (19) ordered_pair(all_59_4, all_59_3) = all_59_0
% 175.11/23.91 | (20) ordered_pair(all_59_2, all_59_1) = all_59_0
% 175.11/23.91 |
% 175.11/23.91 | GROUND_INST: instantiating (8) with all_59_4, all_59_4, all_59_0, simplifying
% 175.11/23.91 | with (15) gives:
% 175.11/23.91 | (21) ~ (ordered_pair(all_59_4, all_59_4) = all_59_0) | ~ member(all_59_4,
% 175.11/23.91 | universal_class) | (first(all_59_0) = all_59_4 & second(all_59_0) =
% 175.11/23.91 | all_59_4)
% 175.11/23.91 |
% 175.11/23.91 | GROUND_INST: instantiating (6) with all_59_4, all_59_3, all_59_0, simplifying
% 175.11/23.91 | with (15), (16), (19) gives:
% 175.11/23.91 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(all_59_3) = v1 &
% 175.11/23.91 | singleton(all_59_4) = v0 & unordered_pair(v0, v2) = all_59_0 &
% 175.11/23.91 | unordered_pair(all_59_4, v1) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 175.11/23.91 | $i(all_59_0))
% 175.11/23.91 |
% 175.11/23.91 | GROUND_INST: instantiating (6) with all_59_2, all_59_1, all_59_0, simplifying
% 175.11/23.91 | with (17), (18), (20) gives:
% 175.11/23.91 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(all_59_1) = v1 &
% 175.11/23.91 | singleton(all_59_2) = v0 & unordered_pair(v0, v2) = all_59_0 &
% 175.11/23.91 | unordered_pair(all_59_2, v1) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 175.11/23.91 | $i(all_59_0))
% 175.11/23.91 |
% 175.11/23.91 | DELTA: instantiating (22) with fresh symbols all_96_0, all_96_1, all_96_2
% 175.11/23.91 | gives:
% 175.11/23.91 | (24) singleton(all_59_3) = all_96_1 & singleton(all_59_4) = all_96_2 &
% 175.11/23.91 | unordered_pair(all_96_2, all_96_0) = all_59_0 &
% 175.11/23.91 | unordered_pair(all_59_4, all_96_1) = all_96_0 & $i(all_96_0) &
% 175.11/23.91 | $i(all_96_1) & $i(all_96_2) & $i(all_59_0)
% 175.11/23.91 |
% 175.11/23.91 | ALPHA: (24) implies:
% 175.11/23.91 | (25) $i(all_96_1)
% 175.11/23.91 | (26) $i(all_96_0)
% 175.11/23.91 | (27) unordered_pair(all_59_4, all_96_1) = all_96_0
% 175.11/23.91 | (28) unordered_pair(all_96_2, all_96_0) = all_59_0
% 175.11/23.91 | (29) singleton(all_59_4) = all_96_2
% 175.11/23.91 | (30) singleton(all_59_3) = all_96_1
% 175.11/23.91 |
% 175.11/23.91 | DELTA: instantiating (23) with fresh symbols all_98_0, all_98_1, all_98_2
% 175.11/23.91 | gives:
% 175.11/23.91 | (31) singleton(all_59_1) = all_98_1 & singleton(all_59_2) = all_98_2 &
% 175.11/23.91 | unordered_pair(all_98_2, all_98_0) = all_59_0 &
% 175.11/23.91 | unordered_pair(all_59_2, all_98_1) = all_98_0 & $i(all_98_0) &
% 175.11/23.91 | $i(all_98_1) & $i(all_98_2) & $i(all_59_0)
% 175.11/23.91 |
% 175.11/23.91 | ALPHA: (31) implies:
% 175.11/23.91 | (32) $i(all_98_2)
% 175.11/23.91 | (33) $i(all_98_1)
% 175.11/23.92 | (34) $i(all_98_0)
% 175.11/23.92 | (35) unordered_pair(all_59_2, all_98_1) = all_98_0
% 175.11/23.92 | (36) unordered_pair(all_98_2, all_98_0) = all_59_0
% 175.11/23.92 | (37) singleton(all_59_2) = all_98_2
% 175.11/23.92 | (38) singleton(all_59_1) = all_98_1
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (10) with all_96_2, all_98_2, all_59_4, simplifying
% 175.11/23.92 | with (29) gives:
% 175.11/23.92 | (39) all_98_2 = all_96_2 | ~ (singleton(all_59_4) = all_98_2)
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (1) with all_59_4, all_96_1, all_96_0, simplifying
% 175.11/23.92 | with (15), (25), (27) gives:
% 175.11/23.92 | (40) ~ member(all_59_4, universal_class) | member(all_59_4, all_96_0)
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (4) with all_59_4, all_96_1, all_96_0, simplifying
% 175.11/23.92 | with (15), (25), (27) gives:
% 175.11/23.92 | (41) member(all_96_0, universal_class)
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (4) with all_59_2, all_98_1, all_98_0, simplifying
% 175.11/23.92 | with (17), (33), (35) gives:
% 175.11/23.92 | (42) member(all_98_0, universal_class)
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (7) with all_98_2, all_59_4, all_96_2, all_59_0,
% 175.11/23.92 | simplifying with (15), (29), (32) gives:
% 175.11/23.92 | (43) ~ (unordered_pair(all_98_2, all_96_2) = all_59_0) | ? [v0: $i] : ?
% 175.11/23.92 | [v1: $i] : (ordered_pair(all_98_2, all_59_4) = v0 &
% 175.11/23.92 | singleton(all_98_2) = v1 & unordered_pair(v1, all_59_0) = v0 &
% 175.11/23.92 | $i(v1) & $i(v0))
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (5) with all_59_4, all_96_2, simplifying with (15),
% 175.11/23.92 | (29) gives:
% 175.11/23.92 | (44) unordered_pair(all_59_4, all_59_4) = all_96_2 & $i(all_96_2)
% 175.11/23.92 |
% 175.11/23.92 | ALPHA: (44) implies:
% 175.11/23.92 | (45) $i(all_96_2)
% 175.11/23.92 | (46) unordered_pair(all_59_4, all_59_4) = all_96_2
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (5) with all_59_3, all_96_1, simplifying with (16),
% 175.11/23.92 | (30) gives:
% 175.11/23.92 | (47) unordered_pair(all_59_3, all_59_3) = all_96_1 & $i(all_96_1)
% 175.11/23.92 |
% 175.11/23.92 | ALPHA: (47) implies:
% 175.11/23.92 | (48) unordered_pair(all_59_3, all_59_3) = all_96_1
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (5) with all_59_2, all_98_2, simplifying with (17),
% 175.11/23.92 | (37) gives:
% 175.11/23.92 | (49) unordered_pair(all_59_2, all_59_2) = all_98_2 & $i(all_98_2)
% 175.11/23.92 |
% 175.11/23.92 | ALPHA: (49) implies:
% 175.11/23.92 | (50) unordered_pair(all_59_2, all_59_2) = all_98_2
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (5) with all_59_1, all_98_1, simplifying with (18),
% 175.11/23.92 | (38) gives:
% 175.11/23.92 | (51) unordered_pair(all_59_1, all_59_1) = all_98_1 & $i(all_98_1)
% 175.11/23.92 |
% 175.11/23.92 | ALPHA: (51) implies:
% 175.11/23.92 | (52) unordered_pair(all_59_1, all_59_1) = all_98_1
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (2) with all_96_0, all_96_2, all_59_0, simplifying
% 175.11/23.92 | with (26), (28), (41), (45) gives:
% 175.11/23.92 | (53) member(all_96_0, all_59_0)
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (2) with all_98_0, all_98_2, all_59_0, simplifying
% 175.11/23.92 | with (32), (34), (36), (42) gives:
% 175.11/23.92 | (54) member(all_98_0, all_59_0)
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (1) with all_96_2, all_96_0, all_59_0, simplifying
% 175.11/23.92 | with (26), (28), (45) gives:
% 175.11/23.92 | (55) ~ member(all_96_2, universal_class) | member(all_96_2, all_59_0)
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (2) with all_96_1, all_59_4, all_96_0, simplifying
% 175.11/23.92 | with (15), (25), (27) gives:
% 175.11/23.92 | (56) ~ member(all_96_1, universal_class) | member(all_96_1, all_96_0)
% 175.11/23.92 |
% 175.11/23.92 | GROUND_INST: instantiating (2) with all_59_4, all_59_4, all_96_2, simplifying
% 175.11/23.92 | with (15), (46) gives:
% 175.11/23.92 | (57) ~ member(all_59_4, universal_class) | member(all_59_4, all_96_2)
% 175.11/23.92 |
% 175.11/23.93 | GROUND_INST: instantiating (4) with all_59_4, all_59_4, all_96_2, simplifying
% 175.11/23.93 | with (15), (46) gives:
% 175.11/23.93 | (58) member(all_96_2, universal_class)
% 175.11/23.93 |
% 175.11/23.93 | GROUND_INST: instantiating (2) with all_59_3, all_59_3, all_96_1, simplifying
% 175.11/23.93 | with (14), (16), (48) gives:
% 175.11/23.93 | (59) member(all_59_3, all_96_1)
% 175.11/23.93 |
% 175.11/23.93 | GROUND_INST: instantiating (4) with all_59_3, all_59_3, all_96_1, simplifying
% 175.11/23.93 | with (16), (48) gives:
% 175.11/23.93 | (60) member(all_96_1, universal_class)
% 175.11/23.93 |
% 175.11/23.93 | GROUND_INST: instantiating (7) with all_59_2, all_59_1, all_59_2, all_98_2,
% 175.11/23.93 | simplifying with (17), (18), (50) gives:
% 175.11/23.93 | (61) ~ (singleton(all_59_1) = all_59_2) | ? [v0: $i] : ? [v1: $i] :
% 175.11/23.93 | (ordered_pair(all_59_2, all_59_1) = v0 & singleton(all_59_2) = v1 &
% 175.11/23.93 | unordered_pair(v1, all_98_2) = v0 & $i(v1) & $i(v0))
% 175.11/23.93 |
% 175.11/23.93 | GROUND_INST: instantiating (4) with all_59_2, all_59_2, all_98_2, simplifying
% 175.11/23.93 | with (17), (50) gives:
% 175.11/23.93 | (62) member(all_98_2, universal_class)
% 175.11/23.93 |
% 175.11/23.93 | GROUND_INST: instantiating (4) with all_59_1, all_59_1, all_98_1, simplifying
% 175.11/23.93 | with (18), (52) gives:
% 175.11/23.93 | (63) member(all_98_1, universal_class)
% 175.11/23.93 |
% 175.11/23.93 | BETA: splitting (56) gives:
% 175.11/23.93 |
% 175.11/23.93 | Case 1:
% 175.11/23.93 | |
% 175.11/23.93 | | (64) ~ member(all_96_1, universal_class)
% 175.11/23.93 | |
% 175.11/23.93 | | PRED_UNIFY: (60), (64) imply:
% 175.11/23.93 | | (65) $false
% 175.11/23.93 | |
% 175.11/23.93 | | CLOSE: (65) is inconsistent.
% 175.11/23.93 | |
% 175.11/23.93 | Case 2:
% 175.11/23.93 | |
% 175.11/23.93 | | (66) member(all_96_1, all_96_0)
% 175.11/23.93 | |
% 175.11/23.93 | | BETA: splitting (55) gives:
% 175.11/23.93 | |
% 175.11/23.93 | | Case 1:
% 175.11/23.93 | | |
% 175.11/23.93 | | | (67) ~ member(all_96_2, universal_class)
% 175.11/23.93 | | |
% 175.11/23.93 | | | PRED_UNIFY: (58), (67) imply:
% 175.11/23.93 | | | (68) $false
% 175.11/23.93 | | |
% 175.11/23.93 | | | CLOSE: (68) is inconsistent.
% 175.11/23.93 | | |
% 175.11/23.93 | | Case 2:
% 175.11/23.93 | | |
% 175.11/23.93 | | | (69) member(all_96_2, all_59_0)
% 175.11/23.93 | | |
% 175.11/23.93 | | | GROUND_INST: instantiating (3) with all_59_3, all_59_1, all_59_1,
% 175.11/23.93 | | | all_96_1, simplifying with (16), (18), (59) gives:
% 175.11/23.93 | | | (70) all_59_1 = all_59_3 | ~ (unordered_pair(all_59_1, all_59_1) =
% 175.11/23.93 | | | all_96_1)
% 175.11/23.93 | | |
% 175.11/23.93 | | | GROUND_INST: instantiating (3) with all_96_2, all_98_2, all_98_0,
% 175.11/23.93 | | | all_59_0, simplifying with (32), (34), (36), (45), (69)
% 175.11/23.93 | | | gives:
% 175.11/23.93 | | | (71) all_98_0 = all_96_2 | all_98_2 = all_96_2
% 175.11/23.93 | | |
% 175.11/23.93 | | | GROUND_INST: instantiating (3) with all_96_1, all_59_2, all_98_1,
% 175.11/23.93 | | | all_96_0, simplifying with (17), (25), (33), (66) gives:
% 175.11/23.93 | | | (72) all_98_1 = all_96_1 | all_96_1 = all_59_2 | ~
% 175.11/23.93 | | | (unordered_pair(all_59_2, all_98_1) = all_96_0)
% 175.11/23.93 | | |
% 175.11/23.93 | | | GROUND_INST: instantiating (3) with all_96_0, all_98_2, all_98_0,
% 175.11/23.93 | | | all_59_0, simplifying with (26), (32), (34), (36), (53)
% 175.11/23.93 | | | gives:
% 175.11/23.93 | | | (73) all_98_0 = all_96_0 | all_98_2 = all_96_0
% 175.11/23.93 | | |
% 175.11/23.93 | | | GROUND_INST: instantiating (1) with all_98_2, all_98_0, all_59_0,
% 175.11/23.93 | | | simplifying with (32), (34), (36), (62) gives:
% 175.11/23.94 | | | (74) member(all_98_2, all_59_0)
% 175.11/23.94 | | |
% 175.11/23.94 | | | GROUND_INST: instantiating (3) with all_98_1, all_59_4, all_96_1,
% 175.11/23.94 | | | universal_class, simplifying with (15), (25), (33), (63)
% 175.11/23.94 | | | gives:
% 175.11/23.94 | | | (75) all_98_1 = all_96_1 | all_98_1 = all_59_4 | ~
% 175.11/23.94 | | | (unordered_pair(all_59_4, all_96_1) = universal_class)
% 175.11/23.94 | | |
% 175.11/23.94 | | | GROUND_INST: instantiating (2) with all_98_1, all_59_2, all_98_0,
% 175.11/23.94 | | | simplifying with (17), (33), (35), (63) gives:
% 175.11/23.94 | | | (76) member(all_98_1, all_98_0)
% 175.11/23.94 | | |
% 175.11/23.94 | | | GROUND_INST: instantiating (3) with all_98_0, all_96_2, all_96_0,
% 175.11/23.94 | | | all_59_0, simplifying with (26), (28), (34), (45), (54)
% 175.11/23.94 | | | gives:
% 175.11/23.94 | | | (77) all_98_0 = all_96_0 | all_98_0 = all_96_2
% 175.11/23.94 | | |
% 175.11/23.94 | | | BETA: splitting (70) gives:
% 175.11/23.94 | | |
% 175.11/23.94 | | | Case 1:
% 175.11/23.94 | | | |
% 175.11/23.94 | | | | (78) ~ (unordered_pair(all_59_1, all_59_1) = all_96_1)
% 175.11/23.94 | | | |
% 175.11/23.94 | | | | PRED_UNIFY: (52), (78) imply:
% 175.11/23.94 | | | | (79) ~ (all_98_1 = all_96_1)
% 175.11/23.94 | | | |
% 175.11/23.94 | | | | GROUND_INST: instantiating (3) with all_98_2, all_96_2, all_96_0,
% 175.11/23.94 | | | | all_59_0, simplifying with (26), (28), (32), (45), (74)
% 175.11/23.94 | | | | gives:
% 175.11/23.94 | | | | (80) all_98_2 = all_96_0 | all_98_2 = all_96_2
% 175.11/23.94 | | | |
% 175.11/23.94 | | | | GROUND_INST: instantiating (3) with all_98_1, all_59_2, all_59_2,
% 175.11/23.94 | | | | all_98_2, simplifying with (17), (33), (50) gives:
% 175.11/23.94 | | | | (81) all_98_1 = all_59_2 | ~ member(all_98_1, all_98_2)
% 175.11/23.94 | | | |
% 175.11/23.94 | | | | GROUND_INST: instantiating (3) with all_98_1, all_59_4, all_96_1,
% 175.11/23.94 | | | | all_96_0, simplifying with (15), (25), (27), (33) gives:
% 175.11/23.94 | | | | (82) all_98_1 = all_96_1 | all_98_1 = all_59_4 | ~ member(all_98_1,
% 175.11/23.94 | | | | all_96_0)
% 175.11/23.94 | | | |
% 175.11/23.94 | | | | GROUND_INST: instantiating (3) with all_98_1, all_59_4, all_59_4,
% 175.11/23.94 | | | | all_96_2, simplifying with (15), (33), (46) gives:
% 175.11/23.94 | | | | (83) all_98_1 = all_59_4 | ~ member(all_98_1, all_96_2)
% 175.11/23.94 | | | |
% 175.11/23.94 | | | | BETA: splitting (21) gives:
% 175.11/23.94 | | | |
% 175.11/23.94 | | | | Case 1:
% 175.11/23.94 | | | | |
% 175.11/23.94 | | | | | (84) ~ member(all_59_4, universal_class)
% 175.11/23.94 | | | | |
% 175.11/23.94 | | | | | PRED_UNIFY: (63), (84) imply:
% 175.11/23.94 | | | | | (85) ~ (all_98_1 = all_59_4)
% 175.11/23.94 | | | | |
% 175.11/23.94 | | | | | BETA: splitting (83) gives:
% 175.11/23.94 | | | | |
% 175.11/23.94 | | | | | Case 1:
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | | (86) ~ member(all_98_1, all_96_2)
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | | BETA: splitting (82) gives:
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | | Case 1:
% 175.11/23.94 | | | | | | |
% 175.11/23.94 | | | | | | | (87) ~ member(all_98_1, all_96_0)
% 175.11/23.94 | | | | | | |
% 175.11/23.94 | | | | | | | BETA: splitting (75) gives:
% 175.11/23.94 | | | | | | |
% 175.11/23.94 | | | | | | | Case 1:
% 175.11/23.94 | | | | | | | |
% 175.11/23.94 | | | | | | | |
% 175.11/23.94 | | | | | | | | PRED_UNIFY: (76), (86) imply:
% 175.11/23.94 | | | | | | | | (88) ~ (all_98_0 = all_96_2)
% 175.11/23.94 | | | | | | | |
% 175.11/23.94 | | | | | | | | PRED_UNIFY: (76), (87) imply:
% 175.11/23.94 | | | | | | | | (89) ~ (all_98_0 = all_96_0)
% 175.11/23.94 | | | | | | | |
% 175.11/23.94 | | | | | | | | REF_CLOSE: (77), (88), (89) are inconsistent by sub-proof #2.
% 175.11/23.94 | | | | | | | |
% 175.11/23.94 | | | | | | | Case 2:
% 175.11/23.94 | | | | | | | |
% 175.11/23.94 | | | | | | | | (90) all_98_1 = all_96_1 | all_98_1 = all_59_4
% 175.11/23.94 | | | | | | | |
% 175.11/23.94 | | | | | | | | REF_CLOSE: (79), (85), (90) are inconsistent by sub-proof #1.
% 175.11/23.94 | | | | | | | |
% 175.11/23.94 | | | | | | | End of split
% 175.11/23.94 | | | | | | |
% 175.11/23.94 | | | | | | Case 2:
% 175.11/23.94 | | | | | | |
% 175.11/23.94 | | | | | | | (91) all_98_1 = all_96_1 | all_98_1 = all_59_4
% 175.11/23.94 | | | | | | |
% 175.11/23.94 | | | | | | | REF_CLOSE: (79), (85), (91) are inconsistent by sub-proof #1.
% 175.11/23.94 | | | | | | |
% 175.11/23.94 | | | | | | End of split
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | Case 2:
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | | (92) all_98_1 = all_59_4
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | | REDUCE: (85), (92) imply:
% 175.11/23.94 | | | | | | (93) $false
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | | CLOSE: (93) is inconsistent.
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | End of split
% 175.11/23.94 | | | | |
% 175.11/23.94 | | | | Case 2:
% 175.11/23.94 | | | | |
% 175.11/23.94 | | | | | (94) member(all_59_4, universal_class)
% 175.11/23.94 | | | | |
% 175.11/23.94 | | | | | BETA: splitting (40) gives:
% 175.11/23.94 | | | | |
% 175.11/23.94 | | | | | Case 1:
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | | (95) ~ member(all_59_4, universal_class)
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | | PRED_UNIFY: (94), (95) imply:
% 175.11/23.94 | | | | | | (96) $false
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | | CLOSE: (96) is inconsistent.
% 175.11/23.94 | | | | | |
% 175.11/23.94 | | | | | Case 2:
% 175.11/23.94 | | | | | |
% 175.11/23.95 | | | | | | (97) member(all_59_4, all_96_0)
% 175.11/23.95 | | | | | |
% 175.11/23.95 | | | | | | BETA: splitting (57) gives:
% 175.11/23.95 | | | | | |
% 175.11/23.95 | | | | | | Case 1:
% 175.11/23.95 | | | | | | |
% 175.11/23.95 | | | | | | | (98) ~ member(all_59_4, universal_class)
% 175.11/23.95 | | | | | | |
% 175.11/23.95 | | | | | | | PRED_UNIFY: (94), (98) imply:
% 175.11/23.95 | | | | | | | (99) $false
% 175.11/23.95 | | | | | | |
% 175.11/23.95 | | | | | | | CLOSE: (99) is inconsistent.
% 175.11/23.95 | | | | | | |
% 175.11/23.95 | | | | | | Case 2:
% 175.11/23.95 | | | | | | |
% 175.11/23.95 | | | | | | | (100) member(all_59_4, all_96_2)
% 175.11/23.95 | | | | | | |
% 175.11/23.95 | | | | | | | BETA: splitting (39) gives:
% 175.11/23.95 | | | | | | |
% 175.11/23.95 | | | | | | | Case 1:
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | | (101) ~ (singleton(all_59_4) = all_98_2)
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | | PRED_UNIFY: (37), (101) imply:
% 175.11/23.95 | | | | | | | | (102) ~ (all_59_2 = all_59_4)
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | | PRED_UNIFY: (29), (101) imply:
% 175.11/23.95 | | | | | | | | (103) ~ (all_98_2 = all_96_2)
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | | BETA: splitting (71) gives:
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | | Case 1:
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | | (104) all_98_0 = all_96_2
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | | REDUCE: (76), (104) imply:
% 175.11/23.95 | | | | | | | | | (105) member(all_98_1, all_96_2)
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | | BETA: splitting (83) gives:
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | | Case 1:
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | (106) ~ member(all_98_1, all_96_2)
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | PRED_UNIFY: (105), (106) imply:
% 175.11/23.95 | | | | | | | | | | (107) $false
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | CLOSE: (107) is inconsistent.
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | Case 2:
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | (108) all_98_1 = all_59_4
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | BETA: splitting (80) gives:
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | Case 1:
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | (109) all_98_2 = all_96_0
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | BETA: splitting (81) gives:
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | Case 1:
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | (110) ~ member(all_98_1, all_98_2)
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | REDUCE: (108), (109), (110) imply:
% 175.11/23.95 | | | | | | | | | | | | (111) ~ member(all_59_4, all_96_0)
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | PRED_UNIFY: (97), (111) imply:
% 175.11/23.95 | | | | | | | | | | | | (112) $false
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | CLOSE: (112) is inconsistent.
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | Case 2:
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | (113) all_98_1 = all_59_2
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | COMBINE_EQS: (108), (113) imply:
% 175.11/23.95 | | | | | | | | | | | | (114) all_59_2 = all_59_4
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | SIMP: (114) implies:
% 175.11/23.95 | | | | | | | | | | | | (115) all_59_2 = all_59_4
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | REDUCE: (102), (115) imply:
% 175.11/23.95 | | | | | | | | | | | | (116) $false
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | CLOSE: (116) is inconsistent.
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | End of split
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | Case 2:
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | (117) all_98_2 = all_96_2
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | REDUCE: (103), (117) imply:
% 175.11/23.95 | | | | | | | | | | | (118) $false
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | CLOSE: (118) is inconsistent.
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | End of split
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | End of split
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | Case 2:
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | | (119) all_98_2 = all_96_2
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | | REDUCE: (103), (119) imply:
% 175.11/23.95 | | | | | | | | | (120) $false
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | | CLOSE: (120) is inconsistent.
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | End of split
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | Case 2:
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | | (121) all_98_2 = all_96_2
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | | REDUCE: (37), (121) imply:
% 175.11/23.95 | | | | | | | | (122) singleton(all_59_2) = all_96_2
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | | REDUCE: (36), (121) imply:
% 175.11/23.95 | | | | | | | | (123) unordered_pair(all_96_2, all_98_0) = all_59_0
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | | REDUCE: (50), (121) imply:
% 175.11/23.95 | | | | | | | | (124) unordered_pair(all_59_2, all_59_2) = all_96_2
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | | BETA: splitting (43) gives:
% 175.11/23.95 | | | | | | | |
% 175.11/23.95 | | | | | | | | Case 1:
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | | (125) ~ (unordered_pair(all_98_2, all_96_2) = all_59_0)
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | | REDUCE: (121), (125) imply:
% 175.11/23.95 | | | | | | | | | (126) ~ (unordered_pair(all_96_2, all_96_2) = all_59_0)
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | | BETA: splitting (61) gives:
% 175.11/23.95 | | | | | | | | |
% 175.11/23.95 | | | | | | | | | Case 1:
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | (127) ~ (singleton(all_59_1) = all_59_2)
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | PRED_UNIFY: (123), (126) imply:
% 175.11/23.95 | | | | | | | | | | (128) ~ (all_98_0 = all_96_2)
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | PRED_UNIFY: (38), (127) imply:
% 175.11/23.95 | | | | | | | | | | (129) ~ (all_98_1 = all_59_2)
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | BETA: splitting (73) gives:
% 175.11/23.95 | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | Case 1:
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | (130) all_98_0 = all_96_0
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | REDUCE: (35), (130) imply:
% 175.11/23.95 | | | | | | | | | | | (131) unordered_pair(all_59_2, all_98_1) = all_96_0
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | REDUCE: (76), (130) imply:
% 175.11/23.95 | | | | | | | | | | | (132) member(all_98_1, all_96_0)
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | BETA: splitting (82) gives:
% 175.11/23.95 | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | Case 1:
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | (133) ~ member(all_98_1, all_96_0)
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | PRED_UNIFY: (132), (133) imply:
% 175.11/23.95 | | | | | | | | | | | | (134) $false
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | Case 2:
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | (135) all_98_1 = all_96_1 | all_98_1 = all_59_4
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | BETA: splitting (72) gives:
% 175.11/23.95 | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | Case 1:
% 175.11/23.95 | | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | | (136) ~ (unordered_pair(all_59_2, all_98_1) = all_96_0)
% 175.11/23.95 | | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | | PRED_UNIFY: (131), (136) imply:
% 175.11/23.95 | | | | | | | | | | | | | (137) $false
% 175.11/23.95 | | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | | CLOSE: (137) is inconsistent.
% 175.11/23.95 | | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | Case 2:
% 175.11/23.95 | | | | | | | | | | | | |
% 175.11/23.95 | | | | | | | | | | | | | (138) all_98_1 = all_96_1 | all_96_1 = all_59_2
% 175.11/23.95 | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | BETA: splitting (81) gives:
% 175.11/23.96 | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | Case 1:
% 175.11/23.96 | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | (139) ~ member(all_98_1, all_98_2)
% 175.11/23.96 | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | REDUCE: (121), (139) imply:
% 175.11/23.96 | | | | | | | | | | | | | | (140) ~ member(all_98_1, all_96_2)
% 175.11/23.96 | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 175.11/23.96 | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | Case 1:
% 175.11/23.96 | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | (141) all_98_1 = all_96_1
% 175.11/23.96 | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | REDUCE: (79), (141) imply:
% 175.11/23.96 | | | | | | | | | | | | | | | (142) $false
% 175.11/23.96 | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | CLOSE: (142) is inconsistent.
% 175.11/23.96 | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | Case 2:
% 175.11/23.96 | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | (143) all_96_1 = all_59_2
% 175.11/23.96 | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 175.11/23.96 | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | Case 1:
% 175.11/23.96 | | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | | (144) all_98_1 = all_96_1
% 175.11/23.96 | | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (144) imply:
% 175.11/23.96 | | | | | | | | | | | | | | | | (145) all_98_1 = all_59_2
% 175.11/23.96 | | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | | REDUCE: (129), (145) imply:
% 175.11/23.96 | | | | | | | | | | | | | | | | (146) $false
% 175.11/23.96 | | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 175.11/23.96 | | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | Case 2:
% 175.11/23.96 | | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | | (147) all_98_1 = all_59_4
% 175.11/23.96 | | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | | REDUCE: (140), (147) imply:
% 175.11/23.96 | | | | | | | | | | | | | | | | (148) ~ member(all_59_4, all_96_2)
% 175.11/23.96 | | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | | PRED_UNIFY: (100), (148) imply:
% 175.11/23.96 | | | | | | | | | | | | | | | | (149) $false
% 175.11/23.96 | | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 175.11/23.96 | | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | | End of split
% 175.11/23.96 | | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | End of split
% 175.11/23.96 | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | Case 2:
% 175.11/23.96 | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | (150) all_98_1 = all_59_2
% 175.11/23.96 | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | REDUCE: (129), (150) imply:
% 175.11/23.96 | | | | | | | | | | | | | | (151) $false
% 175.11/23.96 | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | | CLOSE: (151) is inconsistent.
% 175.11/23.96 | | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | | End of split
% 175.11/23.96 | | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | | End of split
% 175.11/23.96 | | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | End of split
% 175.11/23.96 | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | Case 2:
% 175.11/23.96 | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | (152) ~ (all_98_0 = all_96_0)
% 175.11/23.96 | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | | REF_CLOSE: (77), (128), (152) are inconsistent by sub-proof
% 175.11/23.96 | | | | | | | | | | | #2.
% 175.11/23.96 | | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | End of split
% 175.11/23.96 | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | Case 2:
% 175.11/23.96 | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | (153) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_59_2,
% 175.11/23.96 | | | | | | | | | | all_59_1) = v0 & singleton(all_59_2) = v1 &
% 175.11/23.96 | | | | | | | | | | unordered_pair(v1, all_98_2) = v0 & $i(v1) &
% 175.11/23.96 | | | | | | | | | | $i(v0))
% 175.11/23.96 | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | DELTA: instantiating (153) with fresh symbols all_642_0,
% 175.11/23.96 | | | | | | | | | | all_642_1 gives:
% 175.11/23.96 | | | | | | | | | | (154) ordered_pair(all_59_2, all_59_1) = all_642_1 &
% 175.11/23.96 | | | | | | | | | | singleton(all_59_2) = all_642_0 &
% 175.11/23.96 | | | | | | | | | | unordered_pair(all_642_0, all_98_2) = all_642_1 &
% 175.11/23.96 | | | | | | | | | | $i(all_642_0) & $i(all_642_1)
% 175.11/23.96 | | | | | | | | | |
% 175.11/23.96 | | | | | | | | | | ALPHA: (154) implies:
% 175.11/23.96 | | | | | | | | | | (155) unordered_pair(all_642_0, all_98_2) = all_642_1
% 175.11/23.96 | | | | | | | | | | (156) singleton(all_59_2) = all_642_0
% 175.49/23.96 | | | | | | | | | | (157) ordered_pair(all_59_2, all_59_1) = all_642_1
% 175.49/23.96 | | | | | | | | | |
% 175.49/23.96 | | | | | | | | | | REDUCE: (121), (155) imply:
% 175.49/23.96 | | | | | | | | | | (158) unordered_pair(all_642_0, all_96_2) = all_642_1
% 175.49/23.96 | | | | | | | | | |
% 175.49/23.96 | | | | | | | | | | GROUND_INST: instantiating (10) with all_96_2, all_642_0,
% 175.49/23.96 | | | | | | | | | | all_59_2, simplifying with (122), (156) gives:
% 175.49/23.96 | | | | | | | | | | (159) all_642_0 = all_96_2
% 175.49/23.96 | | | | | | | | | |
% 175.49/23.96 | | | | | | | | | | GROUND_INST: instantiating (11) with all_59_0, all_642_1,
% 175.49/23.96 | | | | | | | | | | all_59_1, all_59_2, simplifying with (20), (157)
% 175.49/23.96 | | | | | | | | | | gives:
% 175.49/23.96 | | | | | | | | | | (160) all_642_1 = all_59_0
% 175.49/23.96 | | | | | | | | | |
% 175.49/23.96 | | | | | | | | | | REDUCE: (158), (159), (160) imply:
% 175.49/23.96 | | | | | | | | | | (161) unordered_pair(all_96_2, all_96_2) = all_59_0
% 175.49/23.96 | | | | | | | | | |
% 175.49/23.96 | | | | | | | | | | PRED_UNIFY: (126), (161) imply:
% 175.49/23.96 | | | | | | | | | | (162) $false
% 175.49/23.96 | | | | | | | | | |
% 175.49/23.96 | | | | | | | | | | CLOSE: (162) is inconsistent.
% 175.49/23.96 | | | | | | | | | |
% 175.49/23.96 | | | | | | | | | End of split
% 175.49/23.96 | | | | | | | | |
% 175.49/23.96 | | | | | | | | Case 2:
% 175.49/23.96 | | | | | | | | |
% 175.49/23.96 | | | | | | | | | (163) unordered_pair(all_98_2, all_96_2) = all_59_0
% 175.49/23.96 | | | | | | | | |
% 175.49/23.96 | | | | | | | | | REDUCE: (121), (163) imply:
% 175.49/23.96 | | | | | | | | | (164) unordered_pair(all_96_2, all_96_2) = all_59_0
% 175.49/23.96 | | | | | | | | |
% 175.49/23.96 | | | | | | | | | GROUND_INST: instantiating (3) with all_96_1, all_59_2,
% 175.49/23.96 | | | | | | | | | all_59_2, all_96_2, simplifying with (17), (25),
% 175.49/23.96 | | | | | | | | | (124) gives:
% 175.49/23.96 | | | | | | | | | (165) all_96_1 = all_59_2 | ~ member(all_96_1, all_96_2)
% 175.49/23.96 | | | | | | | | |
% 175.49/23.96 | | | | | | | | | GROUND_INST: instantiating (3) with all_59_4, all_59_2,
% 175.49/23.96 | | | | | | | | | all_59_2, all_96_2, simplifying with (15), (17),
% 175.49/23.96 | | | | | | | | | (100), (124) gives:
% 175.49/23.96 | | | | | | | | | (166) all_59_2 = all_59_4
% 175.49/23.96 | | | | | | | | |
% 175.49/23.97 | | | | | | | | | GROUND_INST: instantiating (3) with all_98_0, all_96_2,
% 175.49/23.97 | | | | | | | | | all_96_2, all_59_0, simplifying with (34), (45),
% 175.49/23.97 | | | | | | | | | (54), (164) gives:
% 175.49/23.97 | | | | | | | | | (167) all_98_0 = all_96_2
% 175.49/23.97 | | | | | | | | |
% 175.49/23.97 | | | | | | | | | GROUND_INST: instantiating (3) with all_96_0, all_96_2,
% 175.49/23.97 | | | | | | | | | all_96_2, all_59_0, simplifying with (26), (45),
% 175.49/23.97 | | | | | | | | | (53), (164) gives:
% 175.49/23.97 | | | | | | | | | (168) all_96_0 = all_96_2
% 175.49/23.97 | | | | | | | | |
% 175.49/23.97 | | | | | | | | | REDUCE: (76), (167) imply:
% 175.49/23.97 | | | | | | | | | (169) member(all_98_1, all_96_2)
% 175.49/23.97 | | | | | | | | |
% 175.49/23.97 | | | | | | | | | REDUCE: (66), (168) imply:
% 175.49/23.97 | | | | | | | | | (170) member(all_96_1, all_96_2)
% 175.49/23.97 | | | | | | | | |
% 175.49/23.97 | | | | | | | | | BETA: splitting (165) gives:
% 175.49/23.97 | | | | | | | | |
% 175.49/23.97 | | | | | | | | | Case 1:
% 175.49/23.97 | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | (171) ~ member(all_96_1, all_96_2)
% 175.49/23.97 | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | PRED_UNIFY: (170), (171) imply:
% 175.49/23.97 | | | | | | | | | | (172) $false
% 175.49/23.97 | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | CLOSE: (172) is inconsistent.
% 175.49/23.97 | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | Case 2:
% 175.49/23.97 | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | (173) all_96_1 = all_59_2
% 175.49/23.97 | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | COMBINE_EQS: (166), (173) imply:
% 175.49/23.97 | | | | | | | | | | (174) all_96_1 = all_59_4
% 175.49/23.97 | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | REDUCE: (79), (174) imply:
% 175.49/23.97 | | | | | | | | | | (175) ~ (all_98_1 = all_59_4)
% 175.49/23.97 | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | BETA: splitting (83) gives:
% 175.49/23.97 | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | Case 1:
% 175.49/23.97 | | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | | (176) ~ member(all_98_1, all_96_2)
% 175.49/23.97 | | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | | PRED_UNIFY: (169), (176) imply:
% 175.49/23.97 | | | | | | | | | | | (177) $false
% 175.49/23.97 | | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | | CLOSE: (177) is inconsistent.
% 175.49/23.97 | | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | Case 2:
% 175.49/23.97 | | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | | (178) all_98_1 = all_59_4
% 175.49/23.97 | | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | | REDUCE: (175), (178) imply:
% 175.49/23.97 | | | | | | | | | | | (179) $false
% 175.49/23.97 | | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | | CLOSE: (179) is inconsistent.
% 175.49/23.97 | | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | | End of split
% 175.49/23.97 | | | | | | | | | |
% 175.49/23.97 | | | | | | | | | End of split
% 175.49/23.97 | | | | | | | | |
% 175.49/23.97 | | | | | | | | End of split
% 175.49/23.97 | | | | | | | |
% 175.49/23.97 | | | | | | | End of split
% 175.49/23.97 | | | | | | |
% 175.49/23.97 | | | | | | End of split
% 175.49/23.97 | | | | | |
% 175.49/23.97 | | | | | End of split
% 175.49/23.97 | | | | |
% 175.49/23.97 | | | | End of split
% 175.49/23.97 | | | |
% 175.49/23.97 | | | Case 2:
% 175.49/23.97 | | | |
% 175.49/23.97 | | | | (180) all_59_1 = all_59_3
% 175.49/23.97 | | | |
% 175.49/23.97 | | | | REDUCE: (13), (180) imply:
% 175.49/23.97 | | | | (181) $false
% 175.49/23.97 | | | |
% 175.49/23.97 | | | | CLOSE: (181) is inconsistent.
% 175.49/23.97 | | | |
% 175.49/23.97 | | | End of split
% 175.49/23.97 | | |
% 175.49/23.97 | | End of split
% 175.49/23.97 | |
% 175.49/23.97 | End of split
% 175.49/23.97 |
% 175.49/23.97 End of proof
% 175.49/23.97
% 175.49/23.97 Sub-proof #1 shows that the following formulas are inconsistent:
% 175.49/23.97 ----------------------------------------------------------------
% 175.49/23.97 (1) all_98_1 = all_96_1 | all_98_1 = all_59_4
% 175.49/23.97 (2) ~ (all_98_1 = all_96_1)
% 175.49/23.97 (3) ~ (all_98_1 = all_59_4)
% 175.49/23.97
% 175.49/23.97 Begin of proof
% 175.49/23.97 |
% 175.49/23.97 | BETA: splitting (1) gives:
% 175.49/23.97 |
% 175.49/23.97 | Case 1:
% 175.49/23.97 | |
% 175.49/23.97 | | (4) all_98_1 = all_96_1
% 175.49/23.97 | |
% 175.49/23.97 | | REDUCE: (2), (4) imply:
% 175.49/23.97 | | (5) $false
% 175.49/23.97 | |
% 175.49/23.97 | | CLOSE: (5) is inconsistent.
% 175.49/23.97 | |
% 175.49/23.97 | Case 2:
% 175.49/23.97 | |
% 175.49/23.97 | | (6) all_98_1 = all_59_4
% 175.49/23.97 | |
% 175.49/23.97 | | REDUCE: (3), (6) imply:
% 175.49/23.97 | | (7) $false
% 175.49/23.97 | |
% 175.49/23.97 | | CLOSE: (7) is inconsistent.
% 175.49/23.97 | |
% 175.49/23.97 | End of split
% 175.49/23.97 |
% 175.49/23.97 End of proof
% 175.49/23.97
% 175.49/23.97 Sub-proof #2 shows that the following formulas are inconsistent:
% 175.49/23.97 ----------------------------------------------------------------
% 175.49/23.97 (1) all_98_0 = all_96_0 | all_98_0 = all_96_2
% 175.49/23.97 (2) ~ (all_98_0 = all_96_0)
% 175.49/23.97 (3) ~ (all_98_0 = all_96_2)
% 175.49/23.97
% 175.49/23.97 Begin of proof
% 175.49/23.97 |
% 175.49/23.97 | BETA: splitting (1) gives:
% 175.49/23.97 |
% 175.49/23.97 | Case 1:
% 175.49/23.97 | |
% 175.49/23.97 | | (4) all_98_0 = all_96_0
% 175.49/23.97 | |
% 175.49/23.97 | | REDUCE: (2), (4) imply:
% 175.49/23.97 | | (5) $false
% 175.49/23.97 | |
% 175.49/23.97 | | CLOSE: (5) is inconsistent.
% 175.49/23.97 | |
% 175.49/23.97 | Case 2:
% 175.49/23.97 | |
% 175.49/23.97 | | (6) all_98_0 = all_96_2
% 175.49/23.97 | |
% 175.49/23.97 | | REDUCE: (3), (6) imply:
% 175.49/23.97 | | (7) $false
% 175.49/23.97 | |
% 175.49/23.97 | | CLOSE: (7) is inconsistent.
% 175.49/23.97 | |
% 175.49/23.97 | End of split
% 175.49/23.97 |
% 175.49/23.97 End of proof
% 175.49/23.97 % SZS output end Proof for theBenchmark
% 175.49/23.97
% 175.49/23.97 23363ms
%------------------------------------------------------------------------------