TSTP Solution File: SET633+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET633+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 : n027.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 15:25:46 EDT 2023
% Result : Theorem 5.40s 1.40s
% Output : Proof 7.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET633+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 09:47:34 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.59 ________ _____
% 0.21/0.59 ___ __ \_________(_)________________________________
% 0.21/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.59
% 0.21/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.59 (2023-06-19)
% 0.21/0.59
% 0.21/0.59 (c) Philipp Rümmer, 2009-2023
% 0.21/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.59 Amanda Stjerna.
% 0.21/0.59 Free software under BSD-3-Clause.
% 0.21/0.59
% 0.21/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.59
% 0.21/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.61 Running up to 7 provers in parallel.
% 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.03/0.96 Prover 1: Preprocessing ...
% 2.03/0.96 Prover 4: Preprocessing ...
% 2.03/1.01 Prover 0: Preprocessing ...
% 2.03/1.01 Prover 6: Preprocessing ...
% 2.03/1.01 Prover 3: Preprocessing ...
% 2.03/1.01 Prover 5: Preprocessing ...
% 2.03/1.01 Prover 2: Preprocessing ...
% 4.16/1.24 Prover 1: Warning: ignoring some quantifiers
% 4.16/1.26 Prover 5: Proving ...
% 4.16/1.26 Prover 3: Warning: ignoring some quantifiers
% 4.16/1.26 Prover 4: Warning: ignoring some quantifiers
% 4.16/1.27 Prover 1: Constructing countermodel ...
% 4.16/1.27 Prover 3: Constructing countermodel ...
% 4.16/1.27 Prover 6: Proving ...
% 4.16/1.27 Prover 4: Constructing countermodel ...
% 4.16/1.29 Prover 0: Proving ...
% 4.16/1.30 Prover 2: Proving ...
% 5.40/1.40 Prover 2: proved (784ms)
% 5.40/1.40
% 5.40/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.40/1.40
% 5.40/1.40 Prover 3: stopped
% 5.40/1.40 Prover 6: stopped
% 5.40/1.40 Prover 5: stopped
% 5.40/1.40 Prover 0: stopped
% 5.40/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.40/1.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.40/1.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.40/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.40/1.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.40/1.41 Prover 1: gave up
% 5.40/1.44 Prover 7: Preprocessing ...
% 5.40/1.44 Prover 13: Preprocessing ...
% 5.40/1.44 Prover 10: Preprocessing ...
% 5.40/1.44 Prover 11: Preprocessing ...
% 5.40/1.44 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.40/1.44 Prover 8: Preprocessing ...
% 5.40/1.46 Prover 16: Preprocessing ...
% 5.40/1.49 Prover 7: Warning: ignoring some quantifiers
% 5.40/1.49 Prover 10: Warning: ignoring some quantifiers
% 5.40/1.50 Prover 13: Warning: ignoring some quantifiers
% 5.40/1.50 Prover 7: Constructing countermodel ...
% 5.40/1.50 Prover 16: Warning: ignoring some quantifiers
% 5.40/1.51 Prover 10: Constructing countermodel ...
% 5.40/1.51 Prover 13: Constructing countermodel ...
% 5.40/1.51 Prover 8: Warning: ignoring some quantifiers
% 5.40/1.51 Prover 16: Constructing countermodel ...
% 5.40/1.52 Prover 8: Constructing countermodel ...
% 5.40/1.53 Prover 11: Warning: ignoring some quantifiers
% 5.40/1.54 Prover 11: Constructing countermodel ...
% 5.40/1.58 Prover 10: gave up
% 6.84/1.60 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 6.84/1.62 Prover 4: Found proof (size 56)
% 6.84/1.62 Prover 4: proved (1000ms)
% 6.84/1.62 Prover 8: stopped
% 6.84/1.62 Prover 16: stopped
% 6.84/1.62 Prover 7: stopped
% 6.84/1.62 Prover 11: stopped
% 6.84/1.62 Prover 19: Preprocessing ...
% 6.84/1.62 Prover 13: stopped
% 7.02/1.67 Prover 19: Warning: ignoring some quantifiers
% 7.02/1.67 Prover 19: Constructing countermodel ...
% 7.02/1.68 Prover 19: stopped
% 7.02/1.68
% 7.02/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.02/1.68
% 7.02/1.70 % SZS output start Proof for theBenchmark
% 7.02/1.70 Assumptions after simplification:
% 7.02/1.70 ---------------------------------
% 7.02/1.70
% 7.02/1.70 (commutativity_of_symmetric_difference)
% 7.50/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1, v0) =
% 7.50/1.73 v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) = v2 &
% 7.50/1.73 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 7.50/1.73 (symmetric_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 7.50/1.73 (symmetric_difference(v1, v0) = v2 & $i(v2)))
% 7.50/1.73
% 7.50/1.73 (prove_th115)
% 7.50/1.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.50/1.73 $i] : ? [v6: int] : ( ~ (v6 = 0) & subset(v5, v2) = v6 & subset(v4, v2) = 0
% 7.50/1.73 & subset(v3, v2) = 0 & symmetric_difference(v0, v1) = v5 & difference(v1,
% 7.50/1.73 v0) = v4 & difference(v0, v1) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 7.50/1.73 $i(v1) & $i(v0))
% 7.50/1.73
% 7.50/1.73 (symmetric_difference_defn)
% 7.50/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) =
% 7.50/1.74 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (difference(v1,
% 7.50/1.74 v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2 & $i(v4) &
% 7.50/1.74 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 7.50/1.74 (difference(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 7.50/1.74 $i] : (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 &
% 7.50/1.74 union(v4, v2) = v3 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : !
% 7.50/1.74 [v2: $i] : ( ~ (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 7.50/1.74 : ? [v4: $i] : (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4
% 7.50/1.74 & union(v2, v4) = v3 & $i(v4) & $i(v3)))
% 7.50/1.74
% 7.50/1.74 (union_subset)
% 7.50/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.50/1.74 | ~ (subset(v3, v1) = v4) | ~ (union(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 7.50/1.74 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (subset(v2, v1) = v6 &
% 7.50/1.74 subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 7.50/1.74
% 7.50/1.74 (function-axioms)
% 7.50/1.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.50/1.74 [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) &
% 7.50/1.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.50/1.74 $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & !
% 7.50/1.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.50/1.74 (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) =
% 7.50/1.74 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 7.50/1.74 ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] :
% 7.50/1.74 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) |
% 7.50/1.74 ~ (union(v3, v2) = v0))
% 7.50/1.74
% 7.50/1.74 Further assumptions not needed in the proof:
% 7.50/1.74 --------------------------------------------
% 7.50/1.75 commutativity_of_union, difference_defn, equal_member_defn,
% 7.50/1.75 reflexivity_of_subset, subset_defn
% 7.50/1.75
% 7.50/1.75 Those formulas are unsatisfiable:
% 7.50/1.75 ---------------------------------
% 7.50/1.75
% 7.50/1.75 Begin of proof
% 7.50/1.75 |
% 7.50/1.75 | ALPHA: (symmetric_difference_defn) implies:
% 7.50/1.75 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (difference(v0, v1) = v2)
% 7.50/1.75 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 7.50/1.75 | (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4 &
% 7.50/1.75 | union(v2, v4) = v3 & $i(v4) & $i(v3)))
% 7.50/1.75 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (difference(v1, v0) = v2)
% 7.50/1.75 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 7.50/1.75 | (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 &
% 7.50/1.75 | union(v4, v2) = v3 & $i(v4) & $i(v3)))
% 7.50/1.75 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0,
% 7.50/1.75 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 7.50/1.75 | (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) =
% 7.50/1.75 | v2 & $i(v4) & $i(v3) & $i(v2)))
% 7.50/1.75 |
% 7.50/1.75 | ALPHA: (commutativity_of_symmetric_difference) implies:
% 7.50/1.76 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1,
% 7.50/1.76 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1)
% 7.50/1.76 | = v2 & $i(v2)))
% 7.50/1.76 |
% 7.50/1.76 | ALPHA: (function-axioms) implies:
% 7.50/1.76 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.50/1.76 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 7.50/1.76 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.50/1.76 | (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3,
% 7.50/1.76 | v2) = v0))
% 7.50/1.76 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.50/1.76 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2)
% 7.50/1.76 | = v0))
% 7.50/1.76 |
% 7.50/1.76 | DELTA: instantiating (prove_th115) with fresh symbols all_11_0, all_11_1,
% 7.50/1.76 | all_11_2, all_11_3, all_11_4, all_11_5, all_11_6 gives:
% 7.50/1.76 | (8) ~ (all_11_0 = 0) & subset(all_11_1, all_11_4) = all_11_0 &
% 7.50/1.76 | subset(all_11_2, all_11_4) = 0 & subset(all_11_3, all_11_4) = 0 &
% 7.50/1.76 | symmetric_difference(all_11_6, all_11_5) = all_11_1 &
% 7.50/1.76 | difference(all_11_5, all_11_6) = all_11_2 & difference(all_11_6,
% 7.50/1.76 | all_11_5) = all_11_3 & $i(all_11_1) & $i(all_11_2) & $i(all_11_3) &
% 7.50/1.76 | $i(all_11_4) & $i(all_11_5) & $i(all_11_6)
% 7.50/1.76 |
% 7.50/1.76 | ALPHA: (8) implies:
% 7.50/1.76 | (9) ~ (all_11_0 = 0)
% 7.50/1.76 | (10) $i(all_11_6)
% 7.50/1.76 | (11) $i(all_11_5)
% 7.50/1.76 | (12) $i(all_11_4)
% 7.50/1.76 | (13) difference(all_11_6, all_11_5) = all_11_3
% 7.50/1.76 | (14) difference(all_11_5, all_11_6) = all_11_2
% 7.50/1.76 | (15) symmetric_difference(all_11_6, all_11_5) = all_11_1
% 7.50/1.76 | (16) subset(all_11_3, all_11_4) = 0
% 7.50/1.77 | (17) subset(all_11_2, all_11_4) = 0
% 7.50/1.77 | (18) subset(all_11_1, all_11_4) = all_11_0
% 7.50/1.77 |
% 7.50/1.77 | GROUND_INST: instantiating (2) with all_11_5, all_11_6, all_11_3, simplifying
% 7.50/1.77 | with (10), (11), (13) gives:
% 7.50/1.77 | (19) ? [v0: $i] : ? [v1: $i] : (symmetric_difference(all_11_5, all_11_6)
% 7.50/1.77 | = v0 & difference(all_11_5, all_11_6) = v1 & union(v1, all_11_3) =
% 7.50/1.77 | v0 & $i(v1) & $i(v0))
% 7.50/1.77 |
% 7.50/1.77 | GROUND_INST: instantiating (1) with all_11_6, all_11_5, all_11_3, simplifying
% 7.50/1.77 | with (10), (11), (13) gives:
% 7.50/1.77 | (20) ? [v0: $i] : ? [v1: $i] : (symmetric_difference(all_11_6, all_11_5)
% 7.50/1.77 | = v0 & difference(all_11_5, all_11_6) = v1 & union(all_11_3, v1) =
% 7.50/1.77 | v0 & $i(v1) & $i(v0))
% 7.50/1.77 |
% 7.50/1.77 | GROUND_INST: instantiating (2) with all_11_6, all_11_5, all_11_2, simplifying
% 7.50/1.77 | with (10), (11), (14) gives:
% 7.50/1.77 | (21) ? [v0: $i] : ? [v1: $i] : (symmetric_difference(all_11_6, all_11_5)
% 7.50/1.77 | = v0 & difference(all_11_6, all_11_5) = v1 & union(v1, all_11_2) =
% 7.50/1.77 | v0 & $i(v1) & $i(v0))
% 7.50/1.77 |
% 7.50/1.77 | GROUND_INST: instantiating (1) with all_11_5, all_11_6, all_11_2, simplifying
% 7.50/1.77 | with (10), (11), (14) gives:
% 7.50/1.77 | (22) ? [v0: $i] : ? [v1: $i] : (symmetric_difference(all_11_5, all_11_6)
% 7.50/1.77 | = v0 & difference(all_11_6, all_11_5) = v1 & union(all_11_2, v1) =
% 7.50/1.77 | v0 & $i(v1) & $i(v0))
% 7.50/1.77 |
% 7.50/1.77 | GROUND_INST: instantiating (4) with all_11_5, all_11_6, all_11_1, simplifying
% 7.50/1.77 | with (10), (11), (15) gives:
% 7.50/1.77 | (23) symmetric_difference(all_11_5, all_11_6) = all_11_1 & $i(all_11_1)
% 7.50/1.77 |
% 7.50/1.77 | ALPHA: (23) implies:
% 7.50/1.77 | (24) symmetric_difference(all_11_5, all_11_6) = all_11_1
% 7.50/1.77 |
% 7.50/1.77 | GROUND_INST: instantiating (3) with all_11_6, all_11_5, all_11_1, simplifying
% 7.50/1.77 | with (10), (11), (15) gives:
% 7.50/1.77 | (25) ? [v0: $i] : ? [v1: $i] : (difference(all_11_5, all_11_6) = v1 &
% 7.50/1.77 | difference(all_11_6, all_11_5) = v0 & union(v0, v1) = all_11_1 &
% 7.50/1.77 | $i(v1) & $i(v0) & $i(all_11_1))
% 7.50/1.77 |
% 7.50/1.77 | DELTA: instantiating (22) with fresh symbols all_19_0, all_19_1 gives:
% 7.50/1.77 | (26) symmetric_difference(all_11_5, all_11_6) = all_19_1 &
% 7.50/1.77 | difference(all_11_6, all_11_5) = all_19_0 & union(all_11_2, all_19_0)
% 7.50/1.77 | = all_19_1 & $i(all_19_0) & $i(all_19_1)
% 7.50/1.77 |
% 7.50/1.77 | ALPHA: (26) implies:
% 7.50/1.77 | (27) $i(all_19_0)
% 7.50/1.77 | (28) union(all_11_2, all_19_0) = all_19_1
% 7.50/1.78 | (29) difference(all_11_6, all_11_5) = all_19_0
% 7.50/1.78 | (30) symmetric_difference(all_11_5, all_11_6) = all_19_1
% 7.50/1.78 |
% 7.50/1.78 | DELTA: instantiating (21) with fresh symbols all_21_0, all_21_1 gives:
% 7.50/1.78 | (31) symmetric_difference(all_11_6, all_11_5) = all_21_1 &
% 7.50/1.78 | difference(all_11_6, all_11_5) = all_21_0 & union(all_21_0, all_11_2)
% 7.50/1.78 | = all_21_1 & $i(all_21_0) & $i(all_21_1)
% 7.50/1.78 |
% 7.50/1.78 | ALPHA: (31) implies:
% 7.50/1.78 | (32) difference(all_11_6, all_11_5) = all_21_0
% 7.50/1.78 |
% 7.50/1.78 | DELTA: instantiating (20) with fresh symbols all_23_0, all_23_1 gives:
% 7.50/1.78 | (33) symmetric_difference(all_11_6, all_11_5) = all_23_1 &
% 7.50/1.78 | difference(all_11_5, all_11_6) = all_23_0 & union(all_11_3, all_23_0)
% 7.50/1.78 | = all_23_1 & $i(all_23_0) & $i(all_23_1)
% 7.50/1.78 |
% 7.50/1.78 | ALPHA: (33) implies:
% 7.50/1.78 | (34) $i(all_23_0)
% 7.50/1.78 | (35) difference(all_11_5, all_11_6) = all_23_0
% 7.50/1.78 |
% 7.50/1.78 | DELTA: instantiating (19) with fresh symbols all_25_0, all_25_1 gives:
% 7.50/1.78 | (36) symmetric_difference(all_11_5, all_11_6) = all_25_1 &
% 7.50/1.78 | difference(all_11_5, all_11_6) = all_25_0 & union(all_25_0, all_11_3)
% 7.50/1.78 | = all_25_1 & $i(all_25_0) & $i(all_25_1)
% 7.50/1.78 |
% 7.50/1.78 | ALPHA: (36) implies:
% 7.50/1.78 | (37) difference(all_11_5, all_11_6) = all_25_0
% 7.50/1.78 | (38) symmetric_difference(all_11_5, all_11_6) = all_25_1
% 7.50/1.78 |
% 7.50/1.78 | DELTA: instantiating (25) with fresh symbols all_27_0, all_27_1 gives:
% 7.50/1.78 | (39) difference(all_11_5, all_11_6) = all_27_0 & difference(all_11_6,
% 7.50/1.78 | all_11_5) = all_27_1 & union(all_27_1, all_27_0) = all_11_1 &
% 7.50/1.78 | $i(all_27_0) & $i(all_27_1) & $i(all_11_1)
% 7.50/1.78 |
% 7.50/1.78 | ALPHA: (39) implies:
% 7.50/1.78 | (40) difference(all_11_6, all_11_5) = all_27_1
% 7.50/1.78 | (41) difference(all_11_5, all_11_6) = all_27_0
% 7.50/1.78 |
% 7.50/1.78 | GROUND_INST: instantiating (5) with all_19_0, all_21_0, all_11_5, all_11_6,
% 7.50/1.78 | simplifying with (29), (32) gives:
% 7.50/1.78 | (42) all_21_0 = all_19_0
% 7.50/1.78 |
% 7.50/1.78 | GROUND_INST: instantiating (5) with all_11_3, all_27_1, all_11_5, all_11_6,
% 7.50/1.78 | simplifying with (13), (40) gives:
% 7.50/1.78 | (43) all_27_1 = all_11_3
% 7.50/1.78 |
% 7.50/1.78 | GROUND_INST: instantiating (5) with all_21_0, all_27_1, all_11_5, all_11_6,
% 7.50/1.78 | simplifying with (32), (40) gives:
% 7.50/1.78 | (44) all_27_1 = all_21_0
% 7.50/1.78 |
% 7.50/1.78 | GROUND_INST: instantiating (5) with all_11_2, all_25_0, all_11_6, all_11_5,
% 7.50/1.78 | simplifying with (14), (37) gives:
% 7.50/1.78 | (45) all_25_0 = all_11_2
% 7.50/1.78 |
% 7.50/1.78 | GROUND_INST: instantiating (5) with all_25_0, all_27_0, all_11_6, all_11_5,
% 7.50/1.78 | simplifying with (37), (41) gives:
% 7.50/1.78 | (46) all_27_0 = all_25_0
% 7.50/1.78 |
% 7.50/1.78 | GROUND_INST: instantiating (5) with all_23_0, all_27_0, all_11_6, all_11_5,
% 7.50/1.78 | simplifying with (35), (41) gives:
% 7.50/1.78 | (47) all_27_0 = all_23_0
% 7.50/1.78 |
% 7.50/1.78 | GROUND_INST: instantiating (6) with all_19_1, all_25_1, all_11_6, all_11_5,
% 7.50/1.78 | simplifying with (30), (38) gives:
% 7.50/1.78 | (48) all_25_1 = all_19_1
% 7.50/1.78 |
% 7.50/1.78 | GROUND_INST: instantiating (6) with all_11_1, all_25_1, all_11_6, all_11_5,
% 7.50/1.78 | simplifying with (24), (38) gives:
% 7.50/1.78 | (49) all_25_1 = all_11_1
% 7.50/1.78 |
% 7.50/1.78 | COMBINE_EQS: (46), (47) imply:
% 7.50/1.78 | (50) all_25_0 = all_23_0
% 7.50/1.79 |
% 7.50/1.79 | SIMP: (50) implies:
% 7.50/1.79 | (51) all_25_0 = all_23_0
% 7.50/1.79 |
% 7.50/1.79 | COMBINE_EQS: (43), (44) imply:
% 7.50/1.79 | (52) all_21_0 = all_11_3
% 7.50/1.79 |
% 7.50/1.79 | SIMP: (52) implies:
% 7.50/1.79 | (53) all_21_0 = all_11_3
% 7.50/1.79 |
% 7.50/1.79 | COMBINE_EQS: (45), (51) imply:
% 7.50/1.79 | (54) all_23_0 = all_11_2
% 7.50/1.79 |
% 7.50/1.79 | COMBINE_EQS: (48), (49) imply:
% 7.50/1.79 | (55) all_19_1 = all_11_1
% 7.50/1.79 |
% 7.50/1.79 | COMBINE_EQS: (42), (53) imply:
% 7.50/1.79 | (56) all_19_0 = all_11_3
% 7.50/1.79 |
% 7.50/1.79 | SIMP: (56) implies:
% 7.50/1.79 | (57) all_19_0 = all_11_3
% 7.50/1.79 |
% 7.50/1.79 | REDUCE: (28), (55), (57) imply:
% 7.50/1.79 | (58) union(all_11_2, all_11_3) = all_11_1
% 7.50/1.79 |
% 7.50/1.79 | REDUCE: (34), (54) imply:
% 7.50/1.79 | (59) $i(all_11_2)
% 7.50/1.79 |
% 7.50/1.79 | REDUCE: (27), (57) imply:
% 7.50/1.79 | (60) $i(all_11_3)
% 7.50/1.79 |
% 7.50/1.79 | GROUND_INST: instantiating (union_subset) with all_11_2, all_11_4, all_11_3,
% 7.50/1.79 | all_11_1, all_11_0, simplifying with (12), (18), (58), (59), (60)
% 7.50/1.79 | gives:
% 7.50/1.79 | (61) all_11_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_11_2,
% 7.50/1.79 | all_11_4) = v0 & subset(all_11_3, all_11_4) = v1 & ( ~ (v1 = 0) |
% 7.50/1.79 | ~ (v0 = 0)))
% 7.50/1.79 |
% 7.50/1.79 | BETA: splitting (61) gives:
% 7.50/1.79 |
% 7.50/1.79 | Case 1:
% 7.50/1.79 | |
% 7.50/1.79 | | (62) all_11_0 = 0
% 7.50/1.79 | |
% 7.50/1.79 | | REDUCE: (9), (62) imply:
% 7.50/1.79 | | (63) $false
% 7.50/1.79 | |
% 7.50/1.79 | | CLOSE: (63) is inconsistent.
% 7.50/1.79 | |
% 7.50/1.79 | Case 2:
% 7.50/1.79 | |
% 7.50/1.79 | | (64) ? [v0: any] : ? [v1: any] : (subset(all_11_2, all_11_4) = v0 &
% 7.50/1.79 | | subset(all_11_3, all_11_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.50/1.79 | |
% 7.50/1.79 | | DELTA: instantiating (64) with fresh symbols all_50_0, all_50_1 gives:
% 7.50/1.79 | | (65) subset(all_11_2, all_11_4) = all_50_1 & subset(all_11_3, all_11_4) =
% 7.50/1.79 | | all_50_0 & ( ~ (all_50_0 = 0) | ~ (all_50_1 = 0))
% 7.50/1.79 | |
% 7.50/1.79 | | ALPHA: (65) implies:
% 7.50/1.79 | | (66) subset(all_11_3, all_11_4) = all_50_0
% 7.50/1.79 | | (67) subset(all_11_2, all_11_4) = all_50_1
% 7.50/1.79 | | (68) ~ (all_50_0 = 0) | ~ (all_50_1 = 0)
% 7.50/1.79 | |
% 7.50/1.80 | | GROUND_INST: instantiating (7) with 0, all_50_0, all_11_4, all_11_3,
% 7.50/1.80 | | simplifying with (16), (66) gives:
% 7.50/1.80 | | (69) all_50_0 = 0
% 7.50/1.80 | |
% 7.50/1.80 | | GROUND_INST: instantiating (7) with 0, all_50_1, all_11_4, all_11_2,
% 7.50/1.80 | | simplifying with (17), (67) gives:
% 7.50/1.80 | | (70) all_50_1 = 0
% 7.50/1.80 | |
% 7.50/1.80 | | BETA: splitting (68) gives:
% 7.50/1.80 | |
% 7.50/1.80 | | Case 1:
% 7.50/1.80 | | |
% 7.50/1.80 | | | (71) ~ (all_50_0 = 0)
% 7.50/1.80 | | |
% 7.50/1.80 | | | REDUCE: (69), (71) imply:
% 7.50/1.80 | | | (72) $false
% 7.50/1.80 | | |
% 7.50/1.80 | | | CLOSE: (72) is inconsistent.
% 7.50/1.80 | | |
% 7.50/1.80 | | Case 2:
% 7.50/1.80 | | |
% 7.50/1.80 | | | (73) ~ (all_50_1 = 0)
% 7.50/1.80 | | |
% 7.50/1.80 | | | REDUCE: (70), (73) imply:
% 7.50/1.80 | | | (74) $false
% 7.50/1.80 | | |
% 7.50/1.80 | | | CLOSE: (74) is inconsistent.
% 7.50/1.80 | | |
% 7.50/1.80 | | End of split
% 7.87/1.80 | |
% 7.87/1.80 | End of split
% 7.87/1.80 |
% 7.87/1.80 End of proof
% 7.87/1.80 % SZS output end Proof for theBenchmark
% 7.87/1.80
% 7.87/1.80 1203ms
%------------------------------------------------------------------------------