TSTP Solution File: SET016+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET016+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 : n019.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 15:23:07 EDT 2023
% Result : Theorem 97.67s 13.87s
% Output : Proof 98.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET016+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 10:28:28 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.62 ________ _____
% 0.22/0.62 ___ __ \_________(_)________________________________
% 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.62
% 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.62 (2023-06-19)
% 0.22/0.62
% 0.22/0.62 (c) Philipp Rümmer, 2009-2023
% 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.62 Amanda Stjerna.
% 0.22/0.62 Free software under BSD-3-Clause.
% 0.22/0.62
% 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.62
% 0.22/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.63 Running up to 7 provers in parallel.
% 0.22/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.22/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.20/1.16 Prover 4: Preprocessing ...
% 3.20/1.17 Prover 1: Preprocessing ...
% 3.55/1.20 Prover 3: Preprocessing ...
% 3.55/1.20 Prover 5: Preprocessing ...
% 3.55/1.20 Prover 2: Preprocessing ...
% 3.55/1.20 Prover 0: Preprocessing ...
% 3.55/1.20 Prover 6: Preprocessing ...
% 8.69/1.93 Prover 1: Warning: ignoring some quantifiers
% 9.06/2.01 Prover 1: Constructing countermodel ...
% 9.06/2.04 Prover 5: Proving ...
% 9.06/2.04 Prover 3: Warning: ignoring some quantifiers
% 9.78/2.07 Prover 6: Proving ...
% 10.12/2.10 Prover 3: Constructing countermodel ...
% 10.12/2.13 Prover 4: Warning: ignoring some quantifiers
% 10.12/2.16 Prover 4: Constructing countermodel ...
% 10.12/2.24 Prover 2: Proving ...
% 10.12/2.26 Prover 0: Proving ...
% 71.26/10.34 Prover 2: stopped
% 71.26/10.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 71.26/10.47 Prover 7: Preprocessing ...
% 74.17/10.71 Prover 7: Warning: ignoring some quantifiers
% 74.17/10.72 Prover 7: Constructing countermodel ...
% 96.88/13.70 Prover 7: Found proof (size 66)
% 96.88/13.70 Prover 7: proved (3348ms)
% 96.88/13.70 Prover 5: stopped
% 96.88/13.70 Prover 6: stopped
% 96.88/13.70 Prover 3: stopped
% 96.88/13.71 Prover 1: stopped
% 97.30/13.77 Prover 0: stopped
% 97.67/13.87 Prover 4: stopped
% 97.67/13.87
% 97.67/13.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 97.67/13.87
% 97.91/13.88 % SZS output start Proof for theBenchmark
% 97.91/13.89 Assumptions after simplification:
% 97.91/13.89 ---------------------------------
% 97.91/13.89
% 97.91/13.89 (ordered_pair_defn)
% 97.91/13.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (singleton(v1) =
% 97.91/13.93 v2) | ~ (unordered_pair(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 97.91/13.93 $i] : ? [v5: $i] : (ordered_pair(v0, v1) = v4 & singleton(v0) = v5 &
% 97.91/13.93 unordered_pair(v5, v3) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1:
% 97.91/13.93 $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 97.91/13.93 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (singleton(v1) = v4 &
% 97.91/13.93 singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4)
% 97.91/13.93 = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 97.91/13.94
% 97.91/13.94 (ordered_pair_determines_components1)
% 97.91/13.94 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 97.91/13.94 ? [v4: $i] : ( ~ (v2 = v0) & ordered_pair(v2, v3) = v4 & ordered_pair(v0, v1)
% 97.91/13.94 = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & member(v0,
% 97.91/13.94 universal_class))
% 97.91/13.94
% 97.91/13.94 (singleton_set_defn)
% 97.91/13.94 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 97.91/13.94 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 97.91/13.94 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1)))
% 97.91/13.94
% 97.91/13.94 (unordered_pair)
% 97.91/13.94 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 97.91/13.94 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | member(v2,
% 97.91/13.94 universal_class))
% 97.91/13.94
% 97.91/13.94 (unordered_pair_defn)
% 97.91/13.95 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 97.91/13.95 (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 97.91/13.95 | ~ $i(v0) | ~ member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 97.91/13.95 ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 97.91/13.95 $i(v0) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0: $i] : !
% 97.91/13.95 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~
% 97.91/13.95 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0: $i] : !
% 97.91/13.95 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~
% 97.91/13.95 $i(v0) | ~ member(v0, universal_class) | member(v0, v2))
% 97.91/13.95
% 97.91/13.95 Further assumptions not needed in the proof:
% 97.91/13.95 --------------------------------------------
% 97.91/13.95 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 97.91/13.95 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 97.91/13.95 element_relation, element_relation_defn, extensionality, first_second, flip,
% 97.91/13.95 flip_defn, function_defn, identity_relation, image_defn, inductive_defn,
% 97.91/13.95 infinity, intersection, inverse_defn, null_class_defn, power_class,
% 97.91/13.95 power_class_defn, range_of_defn, regularity, replacement, restrict_defn, rotate,
% 97.91/13.95 rotate_defn, subclass_defn, successor_defn, successor_relation_defn1,
% 97.91/13.95 successor_relation_defn2, sum_class, sum_class_defn, union_defn
% 97.91/13.95
% 97.91/13.95 Those formulas are unsatisfiable:
% 97.91/13.95 ---------------------------------
% 97.91/13.95
% 97.91/13.95 Begin of proof
% 97.91/13.95 |
% 97.91/13.95 | ALPHA: (unordered_pair_defn) implies:
% 97.91/13.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 97.91/13.95 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) |
% 97.91/13.95 | member(v0, v2))
% 97.91/13.95 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 97.91/13.95 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) |
% 97.91/13.95 | member(v0, v2))
% 97.91/13.96 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 =
% 97.91/13.96 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 98.26/13.96 | $i(v0) | ~ member(v0, v3))
% 98.26/13.96 |
% 98.26/13.96 | ALPHA: (unordered_pair) implies:
% 98.26/13.96 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 98.26/13.96 | v2) | ~ $i(v1) | ~ $i(v0) | member(v2, universal_class))
% 98.26/13.96 |
% 98.26/13.96 | ALPHA: (singleton_set_defn) implies:
% 98.26/13.96 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 98.26/13.96 | (unordered_pair(v0, v0) = v1 & $i(v1)))
% 98.26/13.96 |
% 98.26/13.96 | ALPHA: (ordered_pair_defn) implies:
% 98.26/13.96 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 98.26/13.96 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 98.26/13.96 | $i] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3,
% 98.26/13.96 | v5) = v2 & unordered_pair(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3)
% 98.26/13.96 | & $i(v2)))
% 98.26/13.96 |
% 98.26/13.96 | ALPHA: (ordered_pair_determines_components1) implies:
% 98.26/13.96 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (
% 98.26/13.96 | ~ (v2 = v0) & ordered_pair(v2, v3) = v4 & ordered_pair(v0, v1) = v4 &
% 98.26/13.96 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & member(v0,
% 98.26/13.96 | universal_class))
% 98.26/13.96 |
% 98.26/13.96 | DELTA: instantiating (7) with fresh symbols all_59_0, all_59_1, all_59_2,
% 98.26/13.96 | all_59_3, all_59_4 gives:
% 98.26/13.96 | (8) ~ (all_59_2 = all_59_4) & ordered_pair(all_59_2, all_59_1) = all_59_0
% 98.26/13.96 | & ordered_pair(all_59_4, all_59_3) = all_59_0 & $i(all_59_0) &
% 98.26/13.96 | $i(all_59_1) & $i(all_59_2) & $i(all_59_3) & $i(all_59_4) &
% 98.26/13.96 | member(all_59_4, universal_class)
% 98.26/13.96 |
% 98.26/13.96 | ALPHA: (8) implies:
% 98.26/13.96 | (9) ~ (all_59_2 = all_59_4)
% 98.26/13.96 | (10) member(all_59_4, universal_class)
% 98.26/13.96 | (11) $i(all_59_4)
% 98.26/13.96 | (12) $i(all_59_3)
% 98.26/13.96 | (13) $i(all_59_2)
% 98.26/13.96 | (14) $i(all_59_1)
% 98.26/13.96 | (15) ordered_pair(all_59_4, all_59_3) = all_59_0
% 98.26/13.96 | (16) ordered_pair(all_59_2, all_59_1) = all_59_0
% 98.26/13.96 |
% 98.26/13.96 | GROUND_INST: instantiating (6) with all_59_4, all_59_3, all_59_0, simplifying
% 98.26/13.96 | with (11), (12), (15) gives:
% 98.26/13.97 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(all_59_3) = v1 &
% 98.26/13.97 | singleton(all_59_4) = v0 & unordered_pair(v0, v2) = all_59_0 &
% 98.26/13.97 | unordered_pair(all_59_4, v1) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 98.26/13.97 | $i(all_59_0))
% 98.26/13.97 |
% 98.26/13.97 | GROUND_INST: instantiating (6) with all_59_2, all_59_1, all_59_0, simplifying
% 98.26/13.97 | with (13), (14), (16) gives:
% 98.26/13.97 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(all_59_1) = v1 &
% 98.26/13.97 | singleton(all_59_2) = v0 & unordered_pair(v0, v2) = all_59_0 &
% 98.26/13.97 | unordered_pair(all_59_2, v1) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 98.26/13.97 | $i(all_59_0))
% 98.26/13.97 |
% 98.26/13.97 | DELTA: instantiating (17) with fresh symbols all_96_0, all_96_1, all_96_2
% 98.26/13.97 | gives:
% 98.26/13.97 | (19) singleton(all_59_3) = all_96_1 & singleton(all_59_4) = all_96_2 &
% 98.26/13.97 | unordered_pair(all_96_2, all_96_0) = all_59_0 &
% 98.26/13.97 | unordered_pair(all_59_4, all_96_1) = all_96_0 & $i(all_96_0) &
% 98.26/13.97 | $i(all_96_1) & $i(all_96_2) & $i(all_59_0)
% 98.26/13.97 |
% 98.26/13.97 | ALPHA: (19) implies:
% 98.26/13.97 | (20) $i(all_96_1)
% 98.26/13.97 | (21) $i(all_96_0)
% 98.26/13.97 | (22) unordered_pair(all_59_4, all_96_1) = all_96_0
% 98.26/13.97 | (23) unordered_pair(all_96_2, all_96_0) = all_59_0
% 98.26/13.97 | (24) singleton(all_59_4) = all_96_2
% 98.26/13.97 | (25) singleton(all_59_3) = all_96_1
% 98.26/13.97 |
% 98.26/13.97 | DELTA: instantiating (18) with fresh symbols all_98_0, all_98_1, all_98_2
% 98.26/13.97 | gives:
% 98.26/13.97 | (26) singleton(all_59_1) = all_98_1 & singleton(all_59_2) = all_98_2 &
% 98.26/13.97 | unordered_pair(all_98_2, all_98_0) = all_59_0 &
% 98.26/13.97 | unordered_pair(all_59_2, all_98_1) = all_98_0 & $i(all_98_0) &
% 98.26/13.97 | $i(all_98_1) & $i(all_98_2) & $i(all_59_0)
% 98.26/13.97 |
% 98.26/13.97 | ALPHA: (26) implies:
% 98.26/13.97 | (27) $i(all_98_0)
% 98.26/13.97 | (28) unordered_pair(all_98_2, all_98_0) = all_59_0
% 98.26/13.97 | (29) singleton(all_59_2) = all_98_2
% 98.26/13.97 |
% 98.26/13.97 | GROUND_INST: instantiating (1) with all_59_4, all_96_1, all_96_0, simplifying
% 98.26/13.97 | with (10), (11), (20), (22) gives:
% 98.26/13.97 | (30) member(all_59_4, all_96_0)
% 98.26/13.97 |
% 98.26/13.97 | GROUND_INST: instantiating (4) with all_59_4, all_96_1, all_96_0, simplifying
% 98.26/13.97 | with (11), (20), (22) gives:
% 98.26/13.97 | (31) member(all_96_0, universal_class)
% 98.26/13.97 |
% 98.26/13.97 | GROUND_INST: instantiating (5) with all_59_4, all_96_2, simplifying with (11),
% 98.26/13.97 | (24) gives:
% 98.35/13.97 | (32) unordered_pair(all_59_4, all_59_4) = all_96_2 & $i(all_96_2)
% 98.35/13.97 |
% 98.35/13.97 | ALPHA: (32) implies:
% 98.35/13.97 | (33) $i(all_96_2)
% 98.35/13.97 | (34) unordered_pair(all_59_4, all_59_4) = all_96_2
% 98.35/13.97 |
% 98.35/13.97 | GROUND_INST: instantiating (5) with all_59_3, all_96_1, simplifying with (12),
% 98.35/13.97 | (25) gives:
% 98.35/13.97 | (35) unordered_pair(all_59_3, all_59_3) = all_96_1 & $i(all_96_1)
% 98.35/13.97 |
% 98.35/13.97 | ALPHA: (35) implies:
% 98.35/13.97 | (36) unordered_pair(all_59_3, all_59_3) = all_96_1
% 98.35/13.97 |
% 98.35/13.98 | GROUND_INST: instantiating (5) with all_59_2, all_98_2, simplifying with (13),
% 98.35/13.98 | (29) gives:
% 98.35/13.98 | (37) unordered_pair(all_59_2, all_59_2) = all_98_2 & $i(all_98_2)
% 98.35/13.98 |
% 98.35/13.98 | ALPHA: (37) implies:
% 98.35/13.98 | (38) $i(all_98_2)
% 98.35/13.98 | (39) unordered_pair(all_59_2, all_59_2) = all_98_2
% 98.35/13.98 |
% 98.35/13.98 | GROUND_INST: instantiating (2) with all_96_0, all_96_2, all_59_0, simplifying
% 98.35/13.98 | with (21), (23), (31), (33) gives:
% 98.35/13.98 | (40) member(all_96_0, all_59_0)
% 98.35/13.98 |
% 98.35/13.98 | GROUND_INST: instantiating (1) with all_96_2, all_96_0, all_59_0, simplifying
% 98.35/13.98 | with (21), (23), (33) gives:
% 98.35/13.98 | (41) ~ member(all_96_2, universal_class) | member(all_96_2, all_59_0)
% 98.35/13.98 |
% 98.35/13.98 | GROUND_INST: instantiating (2) with all_96_1, all_59_4, all_96_0, simplifying
% 98.35/13.98 | with (11), (20), (22) gives:
% 98.35/13.98 | (42) ~ member(all_96_1, universal_class) | member(all_96_1, all_96_0)
% 98.35/13.98 |
% 98.35/13.98 | GROUND_INST: instantiating (2) with all_59_4, all_59_4, all_96_2, simplifying
% 98.35/13.98 | with (10), (11), (34) gives:
% 98.35/13.98 | (43) member(all_59_4, all_96_2)
% 98.35/13.98 |
% 98.35/13.98 | GROUND_INST: instantiating (4) with all_59_4, all_59_4, all_96_2, simplifying
% 98.35/13.98 | with (11), (34) gives:
% 98.35/13.98 | (44) member(all_96_2, universal_class)
% 98.35/13.98 |
% 98.35/13.98 | GROUND_INST: instantiating (4) with all_59_3, all_59_3, all_96_1, simplifying
% 98.35/13.98 | with (12), (36) gives:
% 98.35/13.98 | (45) member(all_96_1, universal_class)
% 98.35/13.98 |
% 98.35/13.98 | GROUND_INST: instantiating (3) with all_59_4, all_59_2, all_59_2, all_96_0,
% 98.35/13.98 | simplifying with (11), (13), (30) gives:
% 98.35/13.98 | (46) all_59_2 = all_59_4 | ~ (unordered_pair(all_59_2, all_59_2) =
% 98.35/13.98 | all_96_0)
% 98.35/13.98 |
% 98.35/13.98 | GROUND_INST: instantiating (4) with all_59_2, all_59_2, all_98_2, simplifying
% 98.35/13.98 | with (13), (39) gives:
% 98.35/13.98 | (47) member(all_98_2, universal_class)
% 98.35/13.98 |
% 98.35/13.98 | BETA: splitting (46) gives:
% 98.35/13.98 |
% 98.35/13.98 | Case 1:
% 98.35/13.98 | |
% 98.35/13.98 | | (48) ~ (unordered_pair(all_59_2, all_59_2) = all_96_0)
% 98.35/13.98 | |
% 98.35/13.98 | | BETA: splitting (41) gives:
% 98.35/13.98 | |
% 98.35/13.98 | | Case 1:
% 98.35/13.99 | | |
% 98.35/13.99 | | | (49) ~ member(all_96_2, universal_class)
% 98.35/13.99 | | |
% 98.35/13.99 | | | PRED_UNIFY: (44), (49) imply:
% 98.35/13.99 | | | (50) $false
% 98.35/13.99 | | |
% 98.35/13.99 | | | CLOSE: (50) is inconsistent.
% 98.35/13.99 | | |
% 98.35/13.99 | | Case 2:
% 98.35/13.99 | | |
% 98.35/13.99 | | | (51) member(all_96_2, all_59_0)
% 98.35/13.99 | | |
% 98.35/13.99 | | | BETA: splitting (42) gives:
% 98.35/13.99 | | |
% 98.35/13.99 | | | Case 1:
% 98.35/13.99 | | | |
% 98.35/13.99 | | | | (52) ~ member(all_96_1, universal_class)
% 98.35/13.99 | | | |
% 98.35/13.99 | | | | PRED_UNIFY: (45), (52) imply:
% 98.35/13.99 | | | | (53) $false
% 98.35/13.99 | | | |
% 98.35/13.99 | | | | CLOSE: (53) is inconsistent.
% 98.35/13.99 | | | |
% 98.35/13.99 | | | Case 2:
% 98.35/13.99 | | | |
% 98.35/13.99 | | | |
% 98.35/13.99 | | | | PRED_UNIFY: (39), (48) imply:
% 98.35/13.99 | | | | (54) ~ (all_98_2 = all_96_0)
% 98.35/13.99 | | | |
% 98.35/13.99 | | | | GROUND_INST: instantiating (3) with all_59_4, all_59_2, all_59_2,
% 98.35/13.99 | | | | all_98_2, simplifying with (11), (13), (39) gives:
% 98.35/13.99 | | | | (55) all_59_2 = all_59_4 | ~ member(all_59_4, all_98_2)
% 98.35/13.99 | | | |
% 98.35/13.99 | | | | GROUND_INST: instantiating (3) with all_96_2, all_98_2, all_98_0,
% 98.35/13.99 | | | | all_59_0, simplifying with (27), (28), (33), (38), (51)
% 98.35/13.99 | | | | gives:
% 98.35/13.99 | | | | (56) all_98_0 = all_96_2 | all_98_2 = all_96_2
% 98.35/13.99 | | | |
% 98.35/13.99 | | | | GROUND_INST: instantiating (3) with all_96_0, all_98_2, all_98_0,
% 98.35/13.99 | | | | all_59_0, simplifying with (21), (27), (28), (38), (40)
% 98.35/13.99 | | | | gives:
% 98.35/13.99 | | | | (57) all_98_0 = all_96_0 | all_98_2 = all_96_0
% 98.35/13.99 | | | |
% 98.35/13.99 | | | | GROUND_INST: instantiating (1) with all_98_2, all_98_0, all_59_0,
% 98.35/13.99 | | | | simplifying with (27), (28), (38), (47) gives:
% 98.35/13.99 | | | | (58) member(all_98_2, all_59_0)
% 98.35/13.99 | | | |
% 98.35/13.99 | | | | BETA: splitting (55) gives:
% 98.35/13.99 | | | |
% 98.35/13.99 | | | | Case 1:
% 98.35/13.99 | | | | |
% 98.35/13.99 | | | | | (59) ~ member(all_59_4, all_98_2)
% 98.35/13.99 | | | | |
% 98.35/13.99 | | | | | BETA: splitting (57) gives:
% 98.35/13.99 | | | | |
% 98.35/13.99 | | | | | Case 1:
% 98.35/13.99 | | | | | |
% 98.35/13.99 | | | | | | (60) all_98_0 = all_96_0
% 98.35/13.99 | | | | | |
% 98.35/13.99 | | | | | | PRED_UNIFY: (43), (59) imply:
% 98.35/13.99 | | | | | | (61) ~ (all_98_2 = all_96_2)
% 98.35/13.99 | | | | | |
% 98.35/13.99 | | | | | | BETA: splitting (56) gives:
% 98.35/13.99 | | | | | |
% 98.35/13.99 | | | | | | Case 1:
% 98.35/13.99 | | | | | | |
% 98.35/13.99 | | | | | | | (62) all_98_0 = all_96_2
% 98.35/13.99 | | | | | | |
% 98.35/13.99 | | | | | | | COMBINE_EQS: (60), (62) imply:
% 98.35/13.99 | | | | | | | (63) all_96_0 = all_96_2
% 98.35/13.99 | | | | | | |
% 98.35/13.99 | | | | | | | REDUCE: (23), (63) imply:
% 98.35/13.99 | | | | | | | (64) unordered_pair(all_96_2, all_96_2) = all_59_0
% 98.35/14.00 | | | | | | |
% 98.35/14.00 | | | | | | | GROUND_INST: instantiating (3) with all_98_2, all_96_2, all_96_2,
% 98.35/14.00 | | | | | | | all_59_0, simplifying with (33), (38), (58), (64)
% 98.35/14.00 | | | | | | | gives:
% 98.35/14.00 | | | | | | | (65) all_98_2 = all_96_2
% 98.35/14.00 | | | | | | |
% 98.35/14.00 | | | | | | | REDUCE: (61), (65) imply:
% 98.35/14.00 | | | | | | | (66) $false
% 98.35/14.00 | | | | | | |
% 98.35/14.00 | | | | | | | CLOSE: (66) is inconsistent.
% 98.35/14.00 | | | | | | |
% 98.35/14.00 | | | | | | Case 2:
% 98.35/14.00 | | | | | | |
% 98.35/14.00 | | | | | | | (67) all_98_2 = all_96_2
% 98.35/14.00 | | | | | | |
% 98.35/14.00 | | | | | | | REDUCE: (61), (67) imply:
% 98.35/14.00 | | | | | | | (68) $false
% 98.35/14.00 | | | | | | |
% 98.35/14.00 | | | | | | | CLOSE: (68) is inconsistent.
% 98.35/14.00 | | | | | | |
% 98.35/14.00 | | | | | | End of split
% 98.35/14.00 | | | | | |
% 98.35/14.00 | | | | | Case 2:
% 98.35/14.00 | | | | | |
% 98.35/14.00 | | | | | | (69) all_98_2 = all_96_0
% 98.35/14.00 | | | | | |
% 98.35/14.00 | | | | | | REDUCE: (54), (69) imply:
% 98.35/14.00 | | | | | | (70) $false
% 98.35/14.00 | | | | | |
% 98.35/14.00 | | | | | | CLOSE: (70) is inconsistent.
% 98.35/14.00 | | | | | |
% 98.35/14.00 | | | | | End of split
% 98.35/14.00 | | | | |
% 98.35/14.00 | | | | Case 2:
% 98.35/14.00 | | | | |
% 98.35/14.00 | | | | | (71) all_59_2 = all_59_4
% 98.35/14.00 | | | | |
% 98.35/14.00 | | | | | REDUCE: (9), (71) imply:
% 98.35/14.00 | | | | | (72) $false
% 98.35/14.00 | | | | |
% 98.35/14.00 | | | | | CLOSE: (72) is inconsistent.
% 98.35/14.00 | | | | |
% 98.35/14.00 | | | | End of split
% 98.35/14.00 | | | |
% 98.35/14.00 | | | End of split
% 98.35/14.00 | | |
% 98.35/14.00 | | End of split
% 98.35/14.00 | |
% 98.35/14.00 | Case 2:
% 98.35/14.00 | |
% 98.35/14.00 | | (73) all_59_2 = all_59_4
% 98.35/14.00 | |
% 98.35/14.00 | | REDUCE: (9), (73) imply:
% 98.35/14.00 | | (74) $false
% 98.35/14.00 | |
% 98.35/14.00 | | CLOSE: (74) is inconsistent.
% 98.35/14.00 | |
% 98.35/14.00 | End of split
% 98.35/14.00 |
% 98.35/14.00 End of proof
% 98.35/14.00 % SZS output end Proof for theBenchmark
% 98.35/14.00
% 98.35/14.00 13378ms
%------------------------------------------------------------------------------