TSTP Solution File: SET617+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET617+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 : n004.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 15:25:39 EDT 2023
% Result : Theorem 5.59s 1.52s
% Output : Proof 7.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 11:18:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.13/1.01 Prover 1: Preprocessing ...
% 2.13/1.01 Prover 4: Preprocessing ...
% 2.40/1.06 Prover 6: Preprocessing ...
% 2.40/1.06 Prover 0: Preprocessing ...
% 2.40/1.06 Prover 3: Preprocessing ...
% 2.40/1.06 Prover 2: Preprocessing ...
% 2.40/1.06 Prover 5: Preprocessing ...
% 4.22/1.30 Prover 1: Warning: ignoring some quantifiers
% 4.22/1.31 Prover 1: Constructing countermodel ...
% 4.22/1.32 Prover 4: Warning: ignoring some quantifiers
% 4.22/1.33 Prover 5: Proving ...
% 4.22/1.33 Prover 6: Proving ...
% 4.22/1.33 Prover 3: Warning: ignoring some quantifiers
% 4.22/1.34 Prover 4: Constructing countermodel ...
% 4.22/1.34 Prover 2: Proving ...
% 4.22/1.34 Prover 3: Constructing countermodel ...
% 4.22/1.38 Prover 0: Proving ...
% 5.08/1.48 Prover 3: gave up
% 5.59/1.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.59/1.52 Prover 7: Preprocessing ...
% 5.59/1.52 Prover 2: proved (907ms)
% 5.59/1.52
% 5.59/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.59/1.52
% 5.59/1.53 Prover 5: stopped
% 5.59/1.53 Prover 6: stopped
% 5.59/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.59/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.59/1.53 Prover 1: gave up
% 5.59/1.53 Prover 0: stopped
% 5.59/1.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.59/1.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.59/1.54 Prover 8: Preprocessing ...
% 5.59/1.55 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.59/1.55 Prover 11: Preprocessing ...
% 5.59/1.56 Prover 13: Preprocessing ...
% 6.13/1.57 Prover 10: Preprocessing ...
% 6.13/1.57 Prover 16: Preprocessing ...
% 6.20/1.59 Prover 7: Warning: ignoring some quantifiers
% 6.20/1.59 Prover 7: Constructing countermodel ...
% 6.20/1.60 Prover 4: Found proof (size 36)
% 6.20/1.60 Prover 4: proved (979ms)
% 6.20/1.60 Prover 11: stopped
% 6.20/1.60 Prover 16: stopped
% 6.20/1.60 Prover 7: stopped
% 6.43/1.62 Prover 10: Warning: ignoring some quantifiers
% 6.43/1.62 Prover 8: Warning: ignoring some quantifiers
% 6.43/1.62 Prover 10: Constructing countermodel ...
% 6.43/1.63 Prover 10: stopped
% 6.58/1.63 Prover 8: Constructing countermodel ...
% 6.58/1.63 Prover 13: Warning: ignoring some quantifiers
% 6.58/1.64 Prover 13: Constructing countermodel ...
% 6.58/1.64 Prover 8: stopped
% 6.58/1.64 Prover 13: stopped
% 6.58/1.64
% 6.58/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.58/1.64
% 6.58/1.66 % SZS output start Proof for theBenchmark
% 6.58/1.66 Assumptions after simplification:
% 6.58/1.66 ---------------------------------
% 6.58/1.66
% 6.58/1.66 (commutativity_of_symmetric_difference)
% 6.58/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1, v0) =
% 6.58/1.69 v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) = v2 &
% 6.58/1.69 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 6.58/1.69 (symmetric_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 6.58/1.69 (symmetric_difference(v1, v0) = v2 & $i(v2)))
% 6.58/1.69
% 6.58/1.69 (no_difference_with_empty_set1)
% 6.58/1.69 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (difference(v0,
% 6.58/1.69 empty_set) = v1) | ~ $i(v0))
% 6.58/1.69
% 6.58/1.69 (no_difference_with_empty_set2)
% 6.58/1.69 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~
% 6.58/1.69 (difference(empty_set, v0) = v1) | ~ $i(v0))
% 6.58/1.69
% 6.58/1.69 (prove_th92)
% 6.58/1.69 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 6.58/1.69 (symmetric_difference(v0, empty_set) = v1 & symmetric_difference(empty_set,
% 6.58/1.69 v0) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = v0) | ~ (v1 = v0)))
% 6.58/1.69
% 6.58/1.69 (symmetric_difference_defn)
% 6.58/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) =
% 6.58/1.70 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (difference(v1,
% 6.58/1.70 v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2 & $i(v4) &
% 6.58/1.70 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 6.58/1.70 (difference(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 6.58/1.70 $i] : (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 &
% 6.58/1.70 union(v4, v2) = v3 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : !
% 6.58/1.70 [v2: $i] : ( ~ (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 6.58/1.70 : ? [v4: $i] : (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4
% 6.58/1.70 & union(v2, v4) = v3 & $i(v4) & $i(v3)))
% 6.58/1.70
% 6.58/1.70 (union_empty_set)
% 6.58/1.70 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (union(v0,
% 6.58/1.70 empty_set) = v1) | ~ $i(v0))
% 6.58/1.70
% 6.58/1.70 (function-axioms)
% 6.58/1.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.58/1.71 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 6.58/1.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 6.58/1.71 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & !
% 6.58/1.71 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.58/1.71 (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) =
% 6.58/1.71 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 6.58/1.71 ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] :
% 6.58/1.71 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) |
% 6.58/1.71 ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.58/1.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 6.58/1.71 (empty(v2) = v0))
% 6.58/1.71
% 6.58/1.71 Further assumptions not needed in the proof:
% 6.58/1.71 --------------------------------------------
% 6.58/1.71 commutativity_of_union, empty_defn, empty_set_defn, equal_defn,
% 6.58/1.71 equal_member_defn, reflexivity_of_subset, subset_defn
% 6.58/1.71
% 6.58/1.71 Those formulas are unsatisfiable:
% 6.58/1.71 ---------------------------------
% 6.58/1.71
% 6.58/1.71 Begin of proof
% 6.58/1.71 |
% 6.58/1.71 | ALPHA: (symmetric_difference_defn) implies:
% 6.58/1.71 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0,
% 6.58/1.71 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 6.58/1.71 | (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) =
% 6.58/1.71 | v2 & $i(v4) & $i(v3) & $i(v2)))
% 6.58/1.71 |
% 6.58/1.71 | ALPHA: (union_empty_set) implies:
% 6.58/1.71 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (union(v0, empty_set) = v1) |
% 6.58/1.71 | ~ $i(v0))
% 6.58/1.71 |
% 6.58/1.71 | ALPHA: (no_difference_with_empty_set1) implies:
% 6.58/1.71 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (difference(v0, empty_set) =
% 6.58/1.71 | v1) | ~ $i(v0))
% 6.58/1.72 |
% 6.58/1.72 | ALPHA: (no_difference_with_empty_set2) implies:
% 6.58/1.72 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ (difference(empty_set,
% 6.58/1.72 | v0) = v1) | ~ $i(v0))
% 6.58/1.72 |
% 6.58/1.72 | ALPHA: (commutativity_of_symmetric_difference) implies:
% 6.58/1.72 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1,
% 6.58/1.72 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1)
% 6.58/1.72 | = v2 & $i(v2)))
% 6.58/1.72 |
% 6.58/1.72 | ALPHA: (prove_th92) implies:
% 6.58/1.72 | (6) $i(empty_set)
% 6.58/1.72 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (symmetric_difference(v0,
% 6.58/1.72 | empty_set) = v1 & symmetric_difference(empty_set, v0) = v2 & $i(v2)
% 6.58/1.72 | & $i(v1) & $i(v0) & ( ~ (v2 = v0) | ~ (v1 = v0)))
% 6.58/1.72 |
% 6.58/1.72 | ALPHA: (function-axioms) implies:
% 7.05/1.72 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.05/1.72 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 7.05/1.72 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.05/1.72 | (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3,
% 7.05/1.72 | v2) = v0))
% 7.05/1.72 |
% 7.05/1.72 | DELTA: instantiating (7) with fresh symbols all_15_0, all_15_1, all_15_2
% 7.05/1.72 | gives:
% 7.05/1.72 | (10) symmetric_difference(all_15_2, empty_set) = all_15_1 &
% 7.05/1.72 | symmetric_difference(empty_set, all_15_2) = all_15_0 & $i(all_15_0) &
% 7.05/1.72 | $i(all_15_1) & $i(all_15_2) & ( ~ (all_15_0 = all_15_2) | ~ (all_15_1
% 7.05/1.72 | = all_15_2))
% 7.05/1.72 |
% 7.05/1.72 | ALPHA: (10) implies:
% 7.05/1.73 | (11) $i(all_15_2)
% 7.05/1.73 | (12) symmetric_difference(empty_set, all_15_2) = all_15_0
% 7.05/1.73 | (13) symmetric_difference(all_15_2, empty_set) = all_15_1
% 7.05/1.73 | (14) ~ (all_15_0 = all_15_2) | ~ (all_15_1 = all_15_2)
% 7.05/1.73 |
% 7.05/1.73 | GROUND_INST: instantiating (5) with all_15_2, empty_set, all_15_0, simplifying
% 7.05/1.73 | with (6), (11), (12) gives:
% 7.05/1.73 | (15) symmetric_difference(all_15_2, empty_set) = all_15_0 & $i(all_15_0)
% 7.05/1.73 |
% 7.05/1.73 | ALPHA: (15) implies:
% 7.05/1.73 | (16) symmetric_difference(all_15_2, empty_set) = all_15_0
% 7.05/1.73 |
% 7.05/1.73 | GROUND_INST: instantiating (1) with empty_set, all_15_2, all_15_0, simplifying
% 7.05/1.73 | with (6), (11), (12) gives:
% 7.05/1.73 | (17) ? [v0: $i] : ? [v1: $i] : (difference(all_15_2, empty_set) = v1 &
% 7.05/1.73 | difference(empty_set, all_15_2) = v0 & union(v0, v1) = all_15_0 &
% 7.05/1.73 | $i(v1) & $i(v0) & $i(all_15_0))
% 7.05/1.73 |
% 7.05/1.73 | GROUND_INST: instantiating (1) with all_15_2, empty_set, all_15_1, simplifying
% 7.05/1.73 | with (6), (11), (13) gives:
% 7.05/1.73 | (18) ? [v0: $i] : ? [v1: $i] : (difference(all_15_2, empty_set) = v0 &
% 7.05/1.73 | difference(empty_set, all_15_2) = v1 & union(v0, v1) = all_15_1 &
% 7.05/1.73 | $i(v1) & $i(v0) & $i(all_15_1))
% 7.05/1.73 |
% 7.05/1.73 | DELTA: instantiating (17) with fresh symbols all_24_0, all_24_1 gives:
% 7.05/1.73 | (19) difference(all_15_2, empty_set) = all_24_0 & difference(empty_set,
% 7.05/1.73 | all_15_2) = all_24_1 & union(all_24_1, all_24_0) = all_15_0 &
% 7.05/1.73 | $i(all_24_0) & $i(all_24_1) & $i(all_15_0)
% 7.05/1.73 |
% 7.05/1.73 | ALPHA: (19) implies:
% 7.05/1.73 | (20) difference(empty_set, all_15_2) = all_24_1
% 7.05/1.73 | (21) difference(all_15_2, empty_set) = all_24_0
% 7.05/1.73 |
% 7.05/1.73 | DELTA: instantiating (18) with fresh symbols all_26_0, all_26_1 gives:
% 7.05/1.73 | (22) difference(all_15_2, empty_set) = all_26_1 & difference(empty_set,
% 7.05/1.73 | all_15_2) = all_26_0 & union(all_26_1, all_26_0) = all_15_1 &
% 7.05/1.73 | $i(all_26_0) & $i(all_26_1) & $i(all_15_1)
% 7.05/1.73 |
% 7.05/1.73 | ALPHA: (22) implies:
% 7.05/1.73 | (23) $i(all_26_1)
% 7.05/1.73 | (24) union(all_26_1, all_26_0) = all_15_1
% 7.05/1.73 | (25) difference(empty_set, all_15_2) = all_26_0
% 7.05/1.73 | (26) difference(all_15_2, empty_set) = all_26_1
% 7.05/1.73 |
% 7.05/1.73 | GROUND_INST: instantiating (8) with all_24_1, all_26_0, all_15_2, empty_set,
% 7.05/1.73 | simplifying with (20), (25) gives:
% 7.05/1.73 | (27) all_26_0 = all_24_1
% 7.05/1.73 |
% 7.05/1.73 | GROUND_INST: instantiating (8) with all_24_0, all_26_1, empty_set, all_15_2,
% 7.05/1.73 | simplifying with (21), (26) gives:
% 7.05/1.73 | (28) all_26_1 = all_24_0
% 7.05/1.73 |
% 7.05/1.73 | GROUND_INST: instantiating (9) with all_15_1, all_15_0, empty_set, all_15_2,
% 7.05/1.73 | simplifying with (13), (16) gives:
% 7.05/1.73 | (29) all_15_0 = all_15_1
% 7.05/1.73 |
% 7.05/1.73 | REDUCE: (24), (27), (28) imply:
% 7.05/1.73 | (30) union(all_24_0, all_24_1) = all_15_1
% 7.05/1.73 |
% 7.05/1.73 | REDUCE: (23), (28) imply:
% 7.05/1.74 | (31) $i(all_24_0)
% 7.05/1.74 |
% 7.05/1.74 | BETA: splitting (14) gives:
% 7.05/1.74 |
% 7.05/1.74 | Case 1:
% 7.05/1.74 | |
% 7.05/1.74 | | (32) ~ (all_15_0 = all_15_2)
% 7.05/1.74 | |
% 7.05/1.74 | | REDUCE: (29), (32) imply:
% 7.05/1.74 | | (33) ~ (all_15_1 = all_15_2)
% 7.05/1.74 | |
% 7.05/1.74 | | GROUND_INST: instantiating (4) with all_15_2, all_24_1, simplifying with
% 7.05/1.74 | | (11), (20) gives:
% 7.05/1.74 | | (34) all_24_1 = empty_set
% 7.05/1.74 | |
% 7.05/1.74 | | GROUND_INST: instantiating (3) with all_15_2, all_24_0, simplifying with
% 7.05/1.74 | | (11), (21) gives:
% 7.05/1.74 | | (35) all_24_0 = all_15_2
% 7.05/1.74 | |
% 7.05/1.74 | | REDUCE: (30), (34), (35) imply:
% 7.05/1.74 | | (36) union(all_15_2, empty_set) = all_15_1
% 7.05/1.74 | |
% 7.05/1.74 | | GROUND_INST: instantiating (2) with all_15_2, all_15_1, simplifying with
% 7.05/1.74 | | (11), (36) gives:
% 7.05/1.74 | | (37) all_15_1 = all_15_2
% 7.05/1.74 | |
% 7.05/1.74 | | REDUCE: (33), (37) imply:
% 7.05/1.74 | | (38) $false
% 7.05/1.74 | |
% 7.05/1.74 | | CLOSE: (38) is inconsistent.
% 7.05/1.74 | |
% 7.05/1.74 | Case 2:
% 7.05/1.74 | |
% 7.05/1.74 | | (39) all_15_0 = all_15_2
% 7.05/1.74 | | (40) ~ (all_15_1 = all_15_2)
% 7.05/1.74 | |
% 7.05/1.74 | | COMBINE_EQS: (29), (39) imply:
% 7.05/1.74 | | (41) all_15_1 = all_15_2
% 7.05/1.74 | |
% 7.05/1.74 | | REDUCE: (40), (41) imply:
% 7.05/1.74 | | (42) $false
% 7.05/1.74 | |
% 7.05/1.74 | | CLOSE: (42) is inconsistent.
% 7.05/1.74 | |
% 7.05/1.74 | End of split
% 7.05/1.74 |
% 7.05/1.74 End of proof
% 7.05/1.74 % SZS output end Proof for theBenchmark
% 7.05/1.74
% 7.05/1.74 1145ms
%------------------------------------------------------------------------------