TSTP Solution File: SET635+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET635+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 : n005.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 15:25:47 EDT 2023
% Result : Theorem 9.68s 2.27s
% Output : Proof 13.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET635+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.35 % Computer : n005.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat Aug 26 12:24:23 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.21/0.66 ________ _____
% 0.21/0.66 ___ __ \_________(_)________________________________
% 0.21/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.66
% 0.21/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.66 (2023-06-19)
% 0.21/0.66
% 0.21/0.66 (c) Philipp Rümmer, 2009-2023
% 0.21/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.66 Amanda Stjerna.
% 0.21/0.66 Free software under BSD-3-Clause.
% 0.21/0.66
% 0.21/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.66
% 0.21/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.68 Running up to 7 provers in parallel.
% 0.21/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.35/1.16 Prover 1: Preprocessing ...
% 2.35/1.16 Prover 4: Preprocessing ...
% 2.35/1.21 Prover 5: Preprocessing ...
% 2.89/1.21 Prover 0: Preprocessing ...
% 2.89/1.22 Prover 6: Preprocessing ...
% 2.89/1.22 Prover 2: Preprocessing ...
% 2.89/1.22 Prover 3: Preprocessing ...
% 5.99/1.71 Prover 3: Warning: ignoring some quantifiers
% 5.99/1.73 Prover 3: Constructing countermodel ...
% 5.99/1.74 Prover 1: Warning: ignoring some quantifiers
% 5.99/1.75 Prover 4: Warning: ignoring some quantifiers
% 5.99/1.75 Prover 5: Proving ...
% 5.99/1.76 Prover 0: Proving ...
% 5.99/1.76 Prover 6: Proving ...
% 6.60/1.77 Prover 2: Proving ...
% 6.74/1.78 Prover 1: Constructing countermodel ...
% 6.74/1.78 Prover 4: Constructing countermodel ...
% 7.16/1.98 Prover 3: gave up
% 7.16/1.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.16/2.02 Prover 7: Preprocessing ...
% 7.16/2.04 Prover 1: gave up
% 8.07/2.05 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.07/2.10 Prover 8: Preprocessing ...
% 9.68/2.23 Prover 7: Warning: ignoring some quantifiers
% 9.68/2.24 Prover 7: Constructing countermodel ...
% 9.68/2.26 Prover 0: proved (1568ms)
% 9.68/2.26
% 9.68/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.68/2.27
% 9.68/2.27 Prover 2: stopped
% 9.68/2.27 Prover 6: stopped
% 9.68/2.28 Prover 5: stopped
% 9.68/2.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.68/2.28 Prover 8: Warning: ignoring some quantifiers
% 9.68/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.35/2.28 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.35/2.28 Prover 8: Constructing countermodel ...
% 10.35/2.29 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.56/2.31 Prover 13: Preprocessing ...
% 10.65/2.33 Prover 11: Preprocessing ...
% 10.65/2.33 Prover 10: Preprocessing ...
% 10.65/2.34 Prover 16: Preprocessing ...
% 10.65/2.41 Prover 16: Warning: ignoring some quantifiers
% 11.36/2.42 Prover 16: Constructing countermodel ...
% 11.36/2.42 Prover 13: Warning: ignoring some quantifiers
% 11.36/2.43 Prover 13: Constructing countermodel ...
% 11.36/2.46 Prover 10: Warning: ignoring some quantifiers
% 11.36/2.47 Prover 10: Constructing countermodel ...
% 11.96/2.49 Prover 8: gave up
% 11.96/2.51 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.96/2.53 Prover 11: Warning: ignoring some quantifiers
% 11.96/2.53 Prover 19: Preprocessing ...
% 11.96/2.54 Prover 11: Constructing countermodel ...
% 11.96/2.55 Prover 4: Found proof (size 40)
% 11.96/2.55 Prover 4: proved (1848ms)
% 11.96/2.55 Prover 7: stopped
% 11.96/2.55 Prover 10: stopped
% 11.96/2.55 Prover 16: stopped
% 11.96/2.55 Prover 11: stopped
% 11.96/2.56 Prover 13: stopped
% 12.67/2.66 Prover 19: Warning: ignoring some quantifiers
% 12.67/2.67 Prover 19: Constructing countermodel ...
% 12.67/2.67 Prover 19: stopped
% 12.67/2.67
% 12.67/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.67/2.67
% 12.67/2.69 % SZS output start Proof for theBenchmark
% 12.67/2.70 Assumptions after simplification:
% 12.67/2.70 ---------------------------------
% 12.67/2.70
% 12.67/2.70 (commutativity_of_intersection)
% 13.30/2.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) | ~
% 13.30/2.74 $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) & ! [v0: $i] :
% 13.30/2.74 ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ $i(v1) | ~
% 13.30/2.74 $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 13.30/2.74
% 13.30/2.74 (difference_and_intersection)
% 13.30/2.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 13.30/2.75 (difference(v3, v2) = v4) | ~ (intersection(v0, v1) = v3) | ~ $i(v2) | ~
% 13.30/2.75 $i(v1) | ~ $i(v0) | ? [v5: $i] : (difference(v1, v2) = v5 &
% 13.30/2.75 intersection(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i]
% 13.30/2.75 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (difference(v1, v2) = v3) | ~
% 13.30/2.75 (intersection(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 13.30/2.75 $i] : (difference(v5, v2) = v4 & intersection(v0, v1) = v5 & $i(v5) &
% 13.30/2.75 $i(v4)))
% 13.30/2.75
% 13.30/2.75 (difference_and_intersection_and_union)
% 13.30/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.30/2.75 $i] : ( ~ (union(v3, v4) = v5) | ~ (difference(v0, v2) = v4) | ~
% 13.30/2.75 (difference(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 13.30/2.75 : (difference(v0, v6) = v5 & intersection(v1, v2) = v6 & $i(v6) & $i(v5))) &
% 13.30/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 13.30/2.75 (difference(v0, v3) = v4) | ~ (intersection(v1, v2) = v3) | ~ $i(v2) | ~
% 13.30/2.75 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (union(v5, v6) = v4 &
% 13.30/2.75 difference(v0, v2) = v6 & difference(v0, v1) = v5 & $i(v6) & $i(v5) &
% 13.30/2.75 $i(v4)))
% 13.30/2.75
% 13.30/2.75 (difference_empty_set)
% 13.30/2.76 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 13.30/2.76 (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 =
% 13.30/2.76 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 13.30/2.76 (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~
% 13.30/2.76 (v3 = empty_set) & difference(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : !
% 13.30/2.76 [v1: $i] : ( ~ (difference(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) |
% 13.30/2.76 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |
% 13.30/2.76 ~ $i(v1) | ~ $i(v0) | difference(v0, v1) = empty_set)
% 13.30/2.76
% 13.30/2.76 (intersection_is_subset)
% 13.30/2.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~
% 13.30/2.76 $i(v1) | ~ $i(v0) | subset(v2, v0) = 0)
% 13.30/2.76
% 13.30/2.76 (prove_th117)
% 13.30/2.77 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 13.30/2.77 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v4) & difference(v5, v6) = v7 &
% 13.30/2.77 difference(v1, v2) = v3 & intersection(v0, v3) = v4 & intersection(v0, v2) =
% 13.30/2.77 v6 & intersection(v0, v1) = v5 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)
% 13.30/2.77 & $i(v2) & $i(v1) & $i(v0))
% 13.30/2.77
% 13.30/2.77 (union_empty_set)
% 13.30/2.77 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (union(v0,
% 13.30/2.77 empty_set) = v1) | ~ $i(v0))
% 13.30/2.77
% 13.30/2.77 (function-axioms)
% 13.30/2.78 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.30/2.78 [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) &
% 13.30/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.30/2.78 (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 13.30/2.78 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~
% 13.30/2.78 (difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.30/2.78 [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3,
% 13.30/2.78 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 13.30/2.78 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~
% 13.30/2.78 (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.30/2.78 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 13.30/2.78 (empty(v2) = v0))
% 13.30/2.78
% 13.30/2.78 Further assumptions not needed in the proof:
% 13.30/2.78 --------------------------------------------
% 13.30/2.78 commutativity_of_union, difference_defn, empty_defn, empty_set_defn, equal_defn,
% 13.30/2.78 equal_member_defn, intersection_defn, reflexivity_of_subset, subset_defn
% 13.30/2.78
% 13.30/2.78 Those formulas are unsatisfiable:
% 13.30/2.78 ---------------------------------
% 13.30/2.78
% 13.30/2.78 Begin of proof
% 13.30/2.78 |
% 13.30/2.78 | ALPHA: (difference_empty_set) implies:
% 13.30/2.78 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 13.30/2.78 | $i(v0) | difference(v0, v1) = empty_set)
% 13.30/2.78 |
% 13.30/2.78 | ALPHA: (union_empty_set) implies:
% 13.30/2.78 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (union(v0, empty_set) = v1) |
% 13.30/2.78 | ~ $i(v0))
% 13.30/2.78 |
% 13.30/2.78 | ALPHA: (difference_and_intersection_and_union) implies:
% 13.30/2.79 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 13.30/2.79 | ~ (difference(v0, v3) = v4) | ~ (intersection(v1, v2) = v3) | ~
% 13.30/2.79 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 13.30/2.79 | (union(v5, v6) = v4 & difference(v0, v2) = v6 & difference(v0, v1) =
% 13.30/2.79 | v5 & $i(v6) & $i(v5) & $i(v4)))
% 13.30/2.79 |
% 13.30/2.79 | ALPHA: (difference_and_intersection) implies:
% 13.30/2.79 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 13.30/2.79 | ~ (difference(v1, v2) = v3) | ~ (intersection(v0, v3) = v4) | ~
% 13.30/2.79 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (difference(v5, v2) =
% 13.30/2.79 | v4 & intersection(v0, v1) = v5 & $i(v5) & $i(v4)))
% 13.30/2.79 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 13.30/2.79 | ~ (difference(v3, v2) = v4) | ~ (intersection(v0, v1) = v3) | ~
% 13.30/2.79 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (difference(v1, v2) =
% 13.30/2.79 | v5 & intersection(v0, v5) = v4 & $i(v5) & $i(v4)))
% 13.30/2.79 |
% 13.30/2.79 | ALPHA: (commutativity_of_intersection) implies:
% 13.30/2.79 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) =
% 13.30/2.79 | v2) | ~ $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2)))
% 13.30/2.79 |
% 13.30/2.79 | ALPHA: (function-axioms) implies:
% 13.30/2.80 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.30/2.80 | (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 13.30/2.80 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.30/2.80 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 13.30/2.80 |
% 13.30/2.80 | DELTA: instantiating (prove_th117) with fresh symbols all_19_0, all_19_1,
% 13.30/2.80 | all_19_2, all_19_3, all_19_4, all_19_5, all_19_6, all_19_7 gives:
% 13.30/2.80 | (9) ~ (all_19_0 = all_19_3) & difference(all_19_2, all_19_1) = all_19_0 &
% 13.30/2.80 | difference(all_19_6, all_19_5) = all_19_4 & intersection(all_19_7,
% 13.30/2.80 | all_19_4) = all_19_3 & intersection(all_19_7, all_19_5) = all_19_1 &
% 13.30/2.80 | intersection(all_19_7, all_19_6) = all_19_2 & $i(all_19_0) &
% 13.30/2.80 | $i(all_19_1) & $i(all_19_2) & $i(all_19_3) & $i(all_19_4) &
% 13.30/2.80 | $i(all_19_5) & $i(all_19_6) & $i(all_19_7)
% 13.30/2.80 |
% 13.30/2.80 | ALPHA: (9) implies:
% 13.30/2.80 | (10) ~ (all_19_0 = all_19_3)
% 13.30/2.80 | (11) $i(all_19_7)
% 13.30/2.80 | (12) $i(all_19_6)
% 13.30/2.80 | (13) $i(all_19_5)
% 13.30/2.80 | (14) intersection(all_19_7, all_19_6) = all_19_2
% 13.30/2.80 | (15) intersection(all_19_7, all_19_5) = all_19_1
% 13.30/2.80 | (16) intersection(all_19_7, all_19_4) = all_19_3
% 13.30/2.80 | (17) difference(all_19_6, all_19_5) = all_19_4
% 13.30/2.80 | (18) difference(all_19_2, all_19_1) = all_19_0
% 13.30/2.80 |
% 13.30/2.81 | GROUND_INST: instantiating (6) with all_19_6, all_19_7, all_19_2, simplifying
% 13.30/2.81 | with (11), (12), (14) gives:
% 13.30/2.81 | (19) intersection(all_19_6, all_19_7) = all_19_2 & $i(all_19_2)
% 13.30/2.81 |
% 13.30/2.81 | ALPHA: (19) implies:
% 13.30/2.81 | (20) $i(all_19_2)
% 13.30/2.81 | (21) intersection(all_19_6, all_19_7) = all_19_2
% 13.30/2.81 |
% 13.30/2.81 | GROUND_INST: instantiating (intersection_is_subset) with all_19_7, all_19_6,
% 13.30/2.81 | all_19_2, simplifying with (11), (12), (14) gives:
% 13.30/2.81 | (22) subset(all_19_2, all_19_7) = 0
% 13.30/2.81 |
% 13.30/2.81 | GROUND_INST: instantiating (6) with all_19_5, all_19_7, all_19_1, simplifying
% 13.30/2.81 | with (11), (13), (15) gives:
% 13.30/2.81 | (23) intersection(all_19_5, all_19_7) = all_19_1 & $i(all_19_1)
% 13.30/2.81 |
% 13.30/2.81 | ALPHA: (23) implies:
% 13.72/2.81 | (24) intersection(all_19_5, all_19_7) = all_19_1
% 13.72/2.81 |
% 13.72/2.81 | GROUND_INST: instantiating (4) with all_19_7, all_19_6, all_19_5, all_19_4,
% 13.72/2.81 | all_19_3, simplifying with (11), (12), (13), (16), (17) gives:
% 13.72/2.81 | (25) ? [v0: $i] : (difference(v0, all_19_5) = all_19_3 &
% 13.72/2.81 | intersection(all_19_7, all_19_6) = v0 & $i(v0) & $i(all_19_3))
% 13.72/2.81 |
% 13.72/2.81 | GROUND_INST: instantiating (3) with all_19_2, all_19_7, all_19_5, all_19_1,
% 13.72/2.81 | all_19_0, simplifying with (11), (13), (15), (18), (20) gives:
% 13.72/2.81 | (26) ? [v0: $i] : ? [v1: $i] : (union(v0, v1) = all_19_0 &
% 13.72/2.81 | difference(all_19_2, all_19_5) = v1 & difference(all_19_2, all_19_7)
% 13.72/2.81 | = v0 & $i(v1) & $i(v0) & $i(all_19_0))
% 13.72/2.81 |
% 13.72/2.81 | DELTA: instantiating (25) with fresh symbol all_27_0 gives:
% 13.72/2.81 | (27) difference(all_27_0, all_19_5) = all_19_3 & intersection(all_19_7,
% 13.72/2.81 | all_19_6) = all_27_0 & $i(all_27_0) & $i(all_19_3)
% 13.72/2.81 |
% 13.72/2.82 | ALPHA: (27) implies:
% 13.72/2.82 | (28) $i(all_27_0)
% 13.72/2.82 | (29) intersection(all_19_7, all_19_6) = all_27_0
% 13.72/2.82 | (30) difference(all_27_0, all_19_5) = all_19_3
% 13.72/2.82 |
% 13.72/2.82 | DELTA: instantiating (26) with fresh symbols all_31_0, all_31_1 gives:
% 13.72/2.82 | (31) union(all_31_1, all_31_0) = all_19_0 & difference(all_19_2, all_19_5)
% 13.72/2.82 | = all_31_0 & difference(all_19_2, all_19_7) = all_31_1 & $i(all_31_0)
% 13.72/2.82 | & $i(all_31_1) & $i(all_19_0)
% 13.72/2.82 |
% 13.72/2.82 | ALPHA: (31) implies:
% 13.72/2.82 | (32) difference(all_19_2, all_19_5) = all_31_0
% 13.72/2.82 |
% 13.72/2.82 | GROUND_INST: instantiating (7) with all_19_2, all_27_0, all_19_6, all_19_7,
% 13.72/2.82 | simplifying with (14), (29) gives:
% 13.72/2.82 | (33) all_27_0 = all_19_2
% 13.72/2.82 |
% 13.72/2.82 | REDUCE: (30), (33) imply:
% 13.72/2.82 | (34) difference(all_19_2, all_19_5) = all_19_3
% 13.72/2.82 |
% 13.72/2.82 | GROUND_INST: instantiating (8) with all_31_0, all_19_3, all_19_5, all_19_2,
% 13.72/2.82 | simplifying with (32), (34) gives:
% 13.72/2.82 | (35) all_31_0 = all_19_3
% 13.72/2.82 |
% 13.72/2.82 | GROUND_INST: instantiating (1) with all_19_2, all_19_7, simplifying with (11),
% 13.72/2.82 | (20), (22) gives:
% 13.72/2.82 | (36) difference(all_19_2, all_19_7) = empty_set
% 13.72/2.82 |
% 13.72/2.82 | GROUND_INST: instantiating (3) with all_19_2, all_19_5, all_19_7, all_19_1,
% 13.72/2.82 | all_19_0, simplifying with (11), (13), (18), (20), (24) gives:
% 13.72/2.82 | (37) ? [v0: $i] : ? [v1: $i] : (union(v0, v1) = all_19_0 &
% 13.72/2.82 | difference(all_19_2, all_19_5) = v0 & difference(all_19_2, all_19_7)
% 13.72/2.82 | = v1 & $i(v1) & $i(v0) & $i(all_19_0))
% 13.72/2.82 |
% 13.72/2.82 | GROUND_INST: instantiating (5) with all_19_6, all_19_7, all_19_5, all_19_2,
% 13.72/2.83 | all_19_3, simplifying with (11), (12), (13), (21), (34) gives:
% 13.72/2.83 | (38) ? [v0: $i] : (difference(all_19_7, all_19_5) = v0 &
% 13.72/2.83 | intersection(all_19_6, v0) = all_19_3 & $i(v0) & $i(all_19_3))
% 13.72/2.83 |
% 13.72/2.83 | DELTA: instantiating (38) with fresh symbol all_47_0 gives:
% 13.72/2.83 | (39) difference(all_19_7, all_19_5) = all_47_0 & intersection(all_19_6,
% 13.72/2.83 | all_47_0) = all_19_3 & $i(all_47_0) & $i(all_19_3)
% 13.72/2.83 |
% 13.72/2.83 | ALPHA: (39) implies:
% 13.72/2.83 | (40) $i(all_47_0)
% 13.72/2.83 | (41) intersection(all_19_6, all_47_0) = all_19_3
% 13.72/2.83 |
% 13.72/2.83 | DELTA: instantiating (37) with fresh symbols all_59_0, all_59_1 gives:
% 13.72/2.83 | (42) union(all_59_1, all_59_0) = all_19_0 & difference(all_19_2, all_19_5)
% 13.72/2.83 | = all_59_1 & difference(all_19_2, all_19_7) = all_59_0 & $i(all_59_0)
% 13.72/2.83 | & $i(all_59_1) & $i(all_19_0)
% 13.72/2.83 |
% 13.72/2.83 | ALPHA: (42) implies:
% 13.72/2.83 | (43) difference(all_19_2, all_19_7) = all_59_0
% 13.72/2.83 | (44) difference(all_19_2, all_19_5) = all_59_1
% 13.72/2.83 | (45) union(all_59_1, all_59_0) = all_19_0
% 13.72/2.83 |
% 13.72/2.83 | GROUND_INST: instantiating (8) with empty_set, all_59_0, all_19_7, all_19_2,
% 13.72/2.83 | simplifying with (36), (43) gives:
% 13.72/2.83 | (46) all_59_0 = empty_set
% 13.72/2.83 |
% 13.72/2.83 | GROUND_INST: instantiating (8) with all_19_3, all_59_1, all_19_5, all_19_2,
% 13.72/2.83 | simplifying with (34), (44) gives:
% 13.72/2.83 | (47) all_59_1 = all_19_3
% 13.72/2.83 |
% 13.72/2.83 | REDUCE: (45), (46), (47) imply:
% 13.72/2.83 | (48) union(all_19_3, empty_set) = all_19_0
% 13.72/2.83 |
% 13.72/2.83 | GROUND_INST: instantiating (6) with all_47_0, all_19_6, all_19_3, simplifying
% 13.72/2.83 | with (12), (40), (41) gives:
% 13.72/2.83 | (49) intersection(all_47_0, all_19_6) = all_19_3 & $i(all_19_3)
% 13.72/2.83 |
% 13.72/2.83 | ALPHA: (49) implies:
% 13.72/2.83 | (50) $i(all_19_3)
% 13.72/2.83 |
% 13.72/2.84 | GROUND_INST: instantiating (2) with all_19_3, all_19_0, simplifying with (48),
% 13.72/2.84 | (50) gives:
% 13.72/2.84 | (51) all_19_0 = all_19_3
% 13.72/2.84 |
% 13.72/2.84 | REDUCE: (10), (51) imply:
% 13.72/2.84 | (52) $false
% 13.72/2.84 |
% 13.72/2.84 | CLOSE: (52) is inconsistent.
% 13.72/2.84 |
% 13.72/2.84 End of proof
% 13.72/2.84 % SZS output end Proof for theBenchmark
% 13.72/2.84
% 13.72/2.84 2173ms
%------------------------------------------------------------------------------