TSTP Solution File: SET638+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET638+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 15:25:48 EDT 2023
% Result : Theorem 8.51s 2.10s
% Output : Proof 13.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET638+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 15:02:16 EDT 2023
% 0.14/0.34 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.69 Running up to 7 provers in parallel.
% 0.21/0.72 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.72 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.72 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.72 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.72 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.72 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.72 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.83/1.09 Prover 4: Preprocessing ...
% 1.83/1.10 Prover 1: Preprocessing ...
% 2.54/1.14 Prover 3: Preprocessing ...
% 2.54/1.14 Prover 5: Preprocessing ...
% 2.54/1.14 Prover 6: Preprocessing ...
% 2.54/1.14 Prover 0: Preprocessing ...
% 2.54/1.15 Prover 2: Preprocessing ...
% 5.15/1.53 Prover 3: Warning: ignoring some quantifiers
% 5.15/1.54 Prover 1: Warning: ignoring some quantifiers
% 5.15/1.54 Prover 4: Warning: ignoring some quantifiers
% 5.15/1.55 Prover 6: Proving ...
% 5.15/1.55 Prover 3: Constructing countermodel ...
% 5.15/1.55 Prover 5: Proving ...
% 5.15/1.55 Prover 4: Constructing countermodel ...
% 5.15/1.55 Prover 1: Constructing countermodel ...
% 5.15/1.56 Prover 0: Proving ...
% 5.15/1.56 Prover 2: Proving ...
% 8.51/1.99 Prover 1: gave up
% 8.51/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.51/2.01 Prover 3: gave up
% 8.51/2.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.51/2.05 Prover 8: Preprocessing ...
% 8.51/2.05 Prover 7: Preprocessing ...
% 8.51/2.10 Prover 0: proved (1399ms)
% 8.51/2.10
% 8.51/2.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.51/2.10
% 8.51/2.10 Prover 2: stopped
% 8.51/2.10 Prover 5: stopped
% 8.51/2.10 Prover 6: stopped
% 8.51/2.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.51/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.51/2.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.51/2.12 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.51/2.12 Prover 7: Warning: ignoring some quantifiers
% 8.51/2.13 Prover 13: Preprocessing ...
% 8.51/2.13 Prover 7: Constructing countermodel ...
% 8.51/2.14 Prover 11: Preprocessing ...
% 8.51/2.15 Prover 10: Preprocessing ...
% 8.51/2.16 Prover 8: Warning: ignoring some quantifiers
% 8.51/2.16 Prover 16: Preprocessing ...
% 8.51/2.16 Prover 8: Constructing countermodel ...
% 9.34/2.22 Prover 13: Warning: ignoring some quantifiers
% 9.34/2.22 Prover 16: Warning: ignoring some quantifiers
% 10.35/2.26 Prover 13: Constructing countermodel ...
% 10.35/2.26 Prover 10: Warning: ignoring some quantifiers
% 10.35/2.26 Prover 16: Constructing countermodel ...
% 10.35/2.26 Prover 10: Constructing countermodel ...
% 10.35/2.27 Prover 11: Warning: ignoring some quantifiers
% 10.35/2.27 Prover 11: Constructing countermodel ...
% 10.35/2.32 Prover 10: gave up
% 10.87/2.32 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 10.87/2.33 Prover 13: gave up
% 10.87/2.33 Prover 19: Preprocessing ...
% 11.78/2.46 Prover 19: Warning: ignoring some quantifiers
% 11.78/2.46 Prover 7: gave up
% 11.78/2.46 Prover 8: gave up
% 11.78/2.48 Prover 19: Constructing countermodel ...
% 12.00/2.52 Prover 16: gave up
% 12.57/2.62 Prover 4: Found proof (size 49)
% 12.57/2.62 Prover 4: proved (1905ms)
% 12.57/2.62 Prover 19: gave up
% 12.57/2.62 Prover 11: stopped
% 12.57/2.62
% 12.57/2.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.57/2.62
% 13.02/2.63 % SZS output start Proof for theBenchmark
% 13.02/2.63 Assumptions after simplification:
% 13.02/2.63 ---------------------------------
% 13.02/2.63
% 13.02/2.63 (commutativity_of_intersection)
% 13.02/2.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) | ~
% 13.02/2.65 $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) & ! [v0: $i] :
% 13.02/2.65 ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ $i(v1) | ~
% 13.02/2.65 $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 13.02/2.65
% 13.02/2.65 (commutativity_of_union)
% 13.02/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~ $i(v1)
% 13.02/2.66 | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] :
% 13.02/2.66 ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (union(v1, v0)
% 13.02/2.66 = v2 & $i(v2)))
% 13.02/2.66
% 13.02/2.66 (intersection_distributes_over_union)
% 13.02/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.02/2.66 $i] : ( ~ (union(v3, v4) = v5) | ~ (intersection(v0, v2) = v4) | ~
% 13.02/2.66 (intersection(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 13.02/2.66 $i] : (union(v1, v2) = v6 & intersection(v0, v6) = v5 & $i(v6) & $i(v5)))
% 13.02/2.66 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 13.02/2.66 (union(v1, v2) = v3) | ~ (intersection(v0, v3) = v4) | ~ $i(v2) | ~
% 13.02/2.66 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (union(v5, v6) = v4 &
% 13.02/2.66 intersection(v0, v2) = v6 & intersection(v0, v1) = v5 & $i(v6) & $i(v5) &
% 13.02/2.66 $i(v4)))
% 13.02/2.66
% 13.02/2.66 (intersection_is_subset)
% 13.02/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~
% 13.02/2.66 $i(v1) | ~ $i(v0) | subset(v2, v0) = 0)
% 13.02/2.66
% 13.02/2.66 (prove_th120)
% 13.24/2.66 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 13.24/2.66 [v4: int] : ( ~ (v4 = 0) & union(v1, v2) = v3 & intersection(v0, v2) =
% 13.24/2.66 empty_set & subset(v0, v3) = 0 & subset(v0, v1) = v4 & $i(v3) & $i(v2) &
% 13.24/2.66 $i(v1) & $i(v0))
% 13.24/2.66
% 13.24/2.66 (subset_intersection)
% 13.24/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (intersection(v0, v1)
% 13.24/2.66 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & subset(v0,
% 13.24/2.66 v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 13.24/2.66 $i(v1) | ~ $i(v0) | intersection(v0, v1) = v0)
% 13.24/2.66
% 13.24/2.67 (union_empty_set)
% 13.24/2.67 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (union(v0,
% 13.24/2.67 empty_set) = v1) | ~ $i(v0))
% 13.24/2.67
% 13.24/2.67 (function-axioms)
% 13.24/2.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.24/2.67 [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) &
% 13.24/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.24/2.67 (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 13.24/2.67 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~
% 13.24/2.67 (intersection(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.24/2.67 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 13.24/2.67 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.24/2.67 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 13.24/2.67 (empty(v2) = v0))
% 13.24/2.67
% 13.24/2.67 Further assumptions not needed in the proof:
% 13.24/2.67 --------------------------------------------
% 13.24/2.67 empty_defn, empty_set_defn, equal_defn, equal_member_defn, intersection_defn,
% 13.24/2.67 reflexivity_of_subset, subset_defn, union_defn
% 13.24/2.67
% 13.24/2.67 Those formulas are unsatisfiable:
% 13.24/2.67 ---------------------------------
% 13.24/2.67
% 13.24/2.67 Begin of proof
% 13.24/2.67 |
% 13.24/2.67 | ALPHA: (subset_intersection) implies:
% 13.24/2.67 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 13.24/2.67 | $i(v0) | intersection(v0, v1) = v0)
% 13.24/2.67 |
% 13.24/2.67 | ALPHA: (union_empty_set) implies:
% 13.24/2.67 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (union(v0, empty_set) = v1) |
% 13.24/2.67 | ~ $i(v0))
% 13.24/2.67 |
% 13.24/2.67 | ALPHA: (intersection_distributes_over_union) implies:
% 13.24/2.67 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 13.24/2.67 | ~ (union(v1, v2) = v3) | ~ (intersection(v0, v3) = v4) | ~ $i(v2) |
% 13.24/2.67 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (union(v5, v6) =
% 13.24/2.67 | v4 & intersection(v0, v2) = v6 & intersection(v0, v1) = v5 & $i(v6)
% 13.24/2.67 | & $i(v5) & $i(v4)))
% 13.24/2.67 |
% 13.24/2.67 | ALPHA: (commutativity_of_union) implies:
% 13.24/2.68 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~
% 13.24/2.68 | $i(v1) | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2)))
% 13.24/2.68 |
% 13.24/2.68 | ALPHA: (commutativity_of_intersection) implies:
% 13.24/2.68 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) =
% 13.24/2.68 | v2) | ~ $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2)))
% 13.24/2.68 |
% 13.24/2.68 | ALPHA: (prove_th120) implies:
% 13.24/2.68 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] :
% 13.24/2.68 | ( ~ (v4 = 0) & union(v1, v2) = v3 & intersection(v0, v2) = empty_set &
% 13.24/2.68 | subset(v0, v3) = 0 & subset(v0, v1) = v4 & $i(v3) & $i(v2) & $i(v1) &
% 13.24/2.68 | $i(v0))
% 13.24/2.68 |
% 13.24/2.68 | ALPHA: (function-axioms) implies:
% 13.24/2.68 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.24/2.68 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2)
% 13.24/2.68 | = v0))
% 13.24/2.68 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.24/2.68 | (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 13.24/2.68 |
% 13.24/2.68 | DELTA: instantiating (6) with fresh symbols all_17_0, all_17_1, all_17_2,
% 13.24/2.68 | all_17_3, all_17_4 gives:
% 13.24/2.68 | (9) ~ (all_17_0 = 0) & union(all_17_3, all_17_2) = all_17_1 &
% 13.24/2.68 | intersection(all_17_4, all_17_2) = empty_set & subset(all_17_4,
% 13.24/2.68 | all_17_1) = 0 & subset(all_17_4, all_17_3) = all_17_0 & $i(all_17_1)
% 13.24/2.68 | & $i(all_17_2) & $i(all_17_3) & $i(all_17_4)
% 13.24/2.68 |
% 13.24/2.68 | ALPHA: (9) implies:
% 13.24/2.68 | (10) ~ (all_17_0 = 0)
% 13.24/2.68 | (11) $i(all_17_4)
% 13.24/2.68 | (12) $i(all_17_3)
% 13.24/2.68 | (13) $i(all_17_2)
% 13.24/2.68 | (14) $i(all_17_1)
% 13.24/2.68 | (15) subset(all_17_4, all_17_3) = all_17_0
% 13.24/2.68 | (16) subset(all_17_4, all_17_1) = 0
% 13.24/2.68 | (17) intersection(all_17_4, all_17_2) = empty_set
% 13.24/2.68 | (18) union(all_17_3, all_17_2) = all_17_1
% 13.24/2.68 |
% 13.24/2.68 | GROUND_INST: instantiating (1) with all_17_4, all_17_1, simplifying with (11),
% 13.24/2.68 | (14), (16) gives:
% 13.24/2.68 | (19) intersection(all_17_4, all_17_1) = all_17_4
% 13.24/2.68 |
% 13.24/2.68 | GROUND_INST: instantiating (4) with all_17_2, all_17_3, all_17_1, simplifying
% 13.24/2.68 | with (12), (13), (18) gives:
% 13.24/2.68 | (20) union(all_17_2, all_17_3) = all_17_1 & $i(all_17_1)
% 13.24/2.68 |
% 13.24/2.68 | ALPHA: (20) implies:
% 13.24/2.68 | (21) union(all_17_2, all_17_3) = all_17_1
% 13.24/2.68 |
% 13.24/2.68 | GROUND_INST: instantiating (3) with all_17_4, all_17_3, all_17_2, all_17_1,
% 13.24/2.68 | all_17_4, simplifying with (11), (12), (13), (18), (19) gives:
% 13.24/2.69 | (22) ? [v0: $i] : ? [v1: $i] : (union(v0, v1) = all_17_4 &
% 13.24/2.69 | intersection(all_17_4, all_17_2) = v1 & intersection(all_17_4,
% 13.24/2.69 | all_17_3) = v0 & $i(v1) & $i(v0))
% 13.24/2.69 |
% 13.24/2.69 | GROUND_INST: instantiating (5) with all_17_1, all_17_4, all_17_4, simplifying
% 13.24/2.69 | with (11), (14), (19) gives:
% 13.24/2.69 | (23) intersection(all_17_1, all_17_4) = all_17_4
% 13.24/2.69 |
% 13.24/2.69 | GROUND_INST: instantiating (3) with all_17_4, all_17_2, all_17_3, all_17_1,
% 13.24/2.69 | all_17_4, simplifying with (11), (12), (13), (19), (21) gives:
% 13.24/2.69 | (24) ? [v0: $i] : ? [v1: $i] : (union(v0, v1) = all_17_4 &
% 13.24/2.69 | intersection(all_17_4, all_17_2) = v0 & intersection(all_17_4,
% 13.24/2.69 | all_17_3) = v1 & $i(v1) & $i(v0))
% 13.24/2.69 |
% 13.24/2.69 | DELTA: instantiating (22) with fresh symbols all_38_0, all_38_1 gives:
% 13.24/2.69 | (25) union(all_38_1, all_38_0) = all_17_4 & intersection(all_17_4,
% 13.24/2.69 | all_17_2) = all_38_0 & intersection(all_17_4, all_17_3) = all_38_1 &
% 13.24/2.69 | $i(all_38_0) & $i(all_38_1)
% 13.24/2.69 |
% 13.24/2.69 | ALPHA: (25) implies:
% 13.24/2.69 | (26) $i(all_38_0)
% 13.24/2.69 | (27) intersection(all_17_4, all_17_3) = all_38_1
% 13.24/2.69 | (28) intersection(all_17_4, all_17_2) = all_38_0
% 13.24/2.69 | (29) union(all_38_1, all_38_0) = all_17_4
% 13.24/2.69 |
% 13.24/2.69 | DELTA: instantiating (24) with fresh symbols all_40_0, all_40_1 gives:
% 13.24/2.69 | (30) union(all_40_1, all_40_0) = all_17_4 & intersection(all_17_4,
% 13.24/2.69 | all_17_2) = all_40_1 & intersection(all_17_4, all_17_3) = all_40_0 &
% 13.24/2.69 | $i(all_40_0) & $i(all_40_1)
% 13.24/2.69 |
% 13.24/2.69 | ALPHA: (30) implies:
% 13.24/2.69 | (31) intersection(all_17_4, all_17_3) = all_40_0
% 13.24/2.69 | (32) intersection(all_17_4, all_17_2) = all_40_1
% 13.24/2.69 | (33) union(all_40_1, all_40_0) = all_17_4
% 13.24/2.69 |
% 13.24/2.69 | GROUND_INST: instantiating (8) with all_38_1, all_40_0, all_17_3, all_17_4,
% 13.24/2.69 | simplifying with (27), (31) gives:
% 13.24/2.69 | (34) all_40_0 = all_38_1
% 13.24/2.69 |
% 13.24/2.69 | GROUND_INST: instantiating (8) with empty_set, all_40_1, all_17_2, all_17_4,
% 13.24/2.69 | simplifying with (17), (32) gives:
% 13.24/2.69 | (35) all_40_1 = empty_set
% 13.24/2.69 |
% 13.24/2.69 | GROUND_INST: instantiating (8) with all_38_0, all_40_1, all_17_2, all_17_4,
% 13.24/2.69 | simplifying with (28), (32) gives:
% 13.24/2.69 | (36) all_40_1 = all_38_0
% 13.24/2.69 |
% 13.24/2.69 | COMBINE_EQS: (35), (36) imply:
% 13.24/2.69 | (37) all_38_0 = empty_set
% 13.24/2.69 |
% 13.24/2.69 | SIMP: (37) implies:
% 13.24/2.69 | (38) all_38_0 = empty_set
% 13.24/2.69 |
% 13.24/2.69 | REDUCE: (33), (34), (35) imply:
% 13.24/2.69 | (39) union(empty_set, all_38_1) = all_17_4
% 13.24/2.69 |
% 13.24/2.69 | REDUCE: (29), (38) imply:
% 13.24/2.69 | (40) union(all_38_1, empty_set) = all_17_4
% 13.24/2.69 |
% 13.24/2.69 | REDUCE: (26), (38) imply:
% 13.24/2.69 | (41) $i(empty_set)
% 13.24/2.69 |
% 13.24/2.69 | GROUND_INST: instantiating (5) with all_17_3, all_17_4, all_38_1, simplifying
% 13.24/2.69 | with (11), (12), (27) gives:
% 13.24/2.69 | (42) intersection(all_17_3, all_17_4) = all_38_1 & $i(all_38_1)
% 13.24/2.69 |
% 13.24/2.69 | ALPHA: (42) implies:
% 13.24/2.69 | (43) $i(all_38_1)
% 13.24/2.69 | (44) intersection(all_17_3, all_17_4) = all_38_1
% 13.24/2.69 |
% 13.24/2.69 | GROUND_INST: instantiating (3) with all_17_1, empty_set, all_38_1, all_17_4,
% 13.24/2.69 | all_17_4, simplifying with (14), (23), (39), (41), (43) gives:
% 13.24/2.69 | (45) ? [v0: $i] : ? [v1: $i] : (union(v0, v1) = all_17_4 &
% 13.24/2.69 | intersection(all_17_1, all_38_1) = v1 & intersection(all_17_1,
% 13.24/2.69 | empty_set) = v0 & $i(v1) & $i(v0) & $i(all_17_4))
% 13.24/2.69 |
% 13.24/2.69 | GROUND_INST: instantiating (3) with all_17_1, all_38_1, empty_set, all_17_4,
% 13.24/2.69 | all_17_4, simplifying with (14), (23), (40), (41), (43) gives:
% 13.24/2.70 | (46) ? [v0: $i] : ? [v1: $i] : (union(v0, v1) = all_17_4 &
% 13.24/2.70 | intersection(all_17_1, all_38_1) = v0 & intersection(all_17_1,
% 13.24/2.70 | empty_set) = v1 & $i(v1) & $i(v0) & $i(all_17_4))
% 13.24/2.70 |
% 13.24/2.70 | GROUND_INST: instantiating (2) with all_38_1, all_17_4, simplifying with (40),
% 13.24/2.70 | (43) gives:
% 13.24/2.70 | (47) all_38_1 = all_17_4
% 13.24/2.70 |
% 13.24/2.70 | DELTA: instantiating (46) with fresh symbols all_68_0, all_68_1 gives:
% 13.24/2.70 | (48) union(all_68_1, all_68_0) = all_17_4 & intersection(all_17_1,
% 13.24/2.70 | all_38_1) = all_68_1 & intersection(all_17_1, empty_set) = all_68_0
% 13.24/2.70 | & $i(all_68_0) & $i(all_68_1) & $i(all_17_4)
% 13.24/2.70 |
% 13.24/2.70 | ALPHA: (48) implies:
% 13.24/2.70 | (49) $i(all_68_1)
% 13.24/2.70 | (50) intersection(all_17_1, all_38_1) = all_68_1
% 13.24/2.70 |
% 13.24/2.70 | DELTA: instantiating (45) with fresh symbols all_70_0, all_70_1 gives:
% 13.24/2.70 | (51) union(all_70_1, all_70_0) = all_17_4 & intersection(all_17_1,
% 13.24/2.70 | all_38_1) = all_70_0 & intersection(all_17_1, empty_set) = all_70_1
% 13.24/2.70 | & $i(all_70_0) & $i(all_70_1) & $i(all_17_4)
% 13.24/2.70 |
% 13.24/2.70 | ALPHA: (51) implies:
% 13.24/2.70 | (52) intersection(all_17_1, all_38_1) = all_70_0
% 13.24/2.70 |
% 13.24/2.70 | REDUCE: (47), (52) imply:
% 13.24/2.70 | (53) intersection(all_17_1, all_17_4) = all_70_0
% 13.24/2.70 |
% 13.24/2.70 | REDUCE: (47), (50) imply:
% 13.24/2.70 | (54) intersection(all_17_1, all_17_4) = all_68_1
% 13.24/2.70 |
% 13.24/2.70 | REDUCE: (44), (47) imply:
% 13.24/2.70 | (55) intersection(all_17_3, all_17_4) = all_17_4
% 13.24/2.70 |
% 13.24/2.70 | GROUND_INST: instantiating (8) with all_17_4, all_70_0, all_17_4, all_17_1,
% 13.24/2.70 | simplifying with (23), (53) gives:
% 13.24/2.70 | (56) all_70_0 = all_17_4
% 13.24/2.70 |
% 13.24/2.70 | GROUND_INST: instantiating (8) with all_68_1, all_70_0, all_17_4, all_17_1,
% 13.24/2.70 | simplifying with (53), (54) gives:
% 13.24/2.70 | (57) all_70_0 = all_68_1
% 13.24/2.70 |
% 13.24/2.70 | COMBINE_EQS: (56), (57) imply:
% 13.24/2.70 | (58) all_68_1 = all_17_4
% 13.24/2.70 |
% 13.24/2.70 | GROUND_INST: instantiating (intersection_is_subset) with all_17_3, all_17_4,
% 13.24/2.70 | all_17_4, simplifying with (11), (12), (55) gives:
% 13.24/2.70 | (59) subset(all_17_4, all_17_3) = 0
% 13.24/2.70 |
% 13.24/2.70 | GROUND_INST: instantiating (7) with all_17_0, 0, all_17_3, all_17_4,
% 13.24/2.70 | simplifying with (15), (59) gives:
% 13.24/2.70 | (60) all_17_0 = 0
% 13.24/2.70 |
% 13.24/2.70 | REDUCE: (10), (60) imply:
% 13.24/2.70 | (61) $false
% 13.24/2.70 |
% 13.24/2.70 | CLOSE: (61) is inconsistent.
% 13.24/2.70 |
% 13.24/2.70 End of proof
% 13.24/2.70 % SZS output end Proof for theBenchmark
% 13.24/2.70
% 13.24/2.70 2029ms
%------------------------------------------------------------------------------