TSTP Solution File: SET201+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET201+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 15:24:17 EDT 2023
% Result : Theorem 6.10s 1.62s
% Output : Proof 7.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET201+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.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 08:43:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.66 ________ _____
% 0.20/0.66 ___ __ \_________(_)________________________________
% 0.20/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.66
% 0.20/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.66 (2023-06-19)
% 0.20/0.66
% 0.20/0.66 (c) Philipp Rümmer, 2009-2023
% 0.20/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.66 Amanda Stjerna.
% 0.20/0.66 Free software under BSD-3-Clause.
% 0.20/0.66
% 0.20/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.66
% 0.20/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.68 Running up to 7 provers in parallel.
% 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.98/1.07 Prover 1: Preprocessing ...
% 1.98/1.07 Prover 4: Preprocessing ...
% 2.65/1.12 Prover 5: Preprocessing ...
% 2.65/1.12 Prover 0: Preprocessing ...
% 2.65/1.12 Prover 6: Preprocessing ...
% 2.65/1.12 Prover 3: Preprocessing ...
% 2.65/1.12 Prover 2: Preprocessing ...
% 4.06/1.37 Prover 5: Proving ...
% 4.06/1.37 Prover 3: Warning: ignoring some quantifiers
% 4.06/1.37 Prover 2: Proving ...
% 4.06/1.38 Prover 1: Warning: ignoring some quantifiers
% 4.06/1.39 Prover 3: Constructing countermodel ...
% 4.06/1.39 Prover 1: Constructing countermodel ...
% 4.75/1.40 Prover 4: Warning: ignoring some quantifiers
% 4.75/1.41 Prover 0: Proving ...
% 4.75/1.42 Prover 6: Proving ...
% 4.75/1.42 Prover 4: Constructing countermodel ...
% 6.10/1.61 Prover 3: proved (925ms)
% 6.10/1.62
% 6.10/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.10/1.62
% 6.10/1.62 Prover 0: proved (935ms)
% 6.10/1.62
% 6.10/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.10/1.62
% 6.10/1.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.10/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.10/1.62 Prover 5: stopped
% 6.10/1.63 Prover 2: stopped
% 6.10/1.63 Prover 6: stopped
% 6.10/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.10/1.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.10/1.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.10/1.66 Prover 7: Preprocessing ...
% 6.10/1.66 Prover 8: Preprocessing ...
% 6.10/1.66 Prover 13: Preprocessing ...
% 6.10/1.67 Prover 11: Preprocessing ...
% 6.10/1.67 Prover 10: Preprocessing ...
% 6.10/1.71 Prover 10: Warning: ignoring some quantifiers
% 6.10/1.71 Prover 10: Constructing countermodel ...
% 6.10/1.73 Prover 7: Warning: ignoring some quantifiers
% 6.10/1.73 Prover 7: Constructing countermodel ...
% 6.10/1.75 Prover 1: Found proof (size 44)
% 6.10/1.75 Prover 1: proved (1064ms)
% 6.10/1.75 Prover 10: stopped
% 6.10/1.75 Prover 7: stopped
% 6.10/1.75 Prover 4: stopped
% 6.10/1.75 Prover 13: Warning: ignoring some quantifiers
% 6.10/1.76 Prover 13: Constructing countermodel ...
% 6.10/1.76 Prover 13: stopped
% 6.10/1.77 Prover 8: Warning: ignoring some quantifiers
% 7.22/1.78 Prover 8: Constructing countermodel ...
% 7.22/1.78 Prover 8: stopped
% 7.22/1.79 Prover 11: Warning: ignoring some quantifiers
% 7.22/1.80 Prover 11: Constructing countermodel ...
% 7.22/1.80 Prover 11: stopped
% 7.22/1.80
% 7.22/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.22/1.80
% 7.22/1.81 % SZS output start Proof for theBenchmark
% 7.22/1.82 Assumptions after simplification:
% 7.22/1.82 ---------------------------------
% 7.22/1.82
% 7.22/1.82 (commutativity_of_intersection)
% 7.22/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~
% 7.22/1.86 $i(v1) | ~ $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 7.22/1.86
% 7.22/1.86 (intersection_defn)
% 7.22/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.22/1.87 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~
% 7.22/1.87 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 &
% 7.22/1.87 member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 7.22/1.87 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) | ~
% 7.22/1.87 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) =
% 7.22/1.87 0 & member(v2, v0) = 0))
% 7.22/1.87
% 7.22/1.87 (prove_th41)
% 7.22/1.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.22/1.87 $i] : ? [v6: int] : ( ~ (v6 = 0) & subset(v4, v5) = v6 & subset(v2, v3) = 0
% 7.74/1.87 & subset(v0, v1) = 0 & intersection(v1, v3) = v5 & intersection(v0, v2) = v4
% 7.74/1.87 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.74/1.87
% 7.74/1.87 (subset_defn)
% 7.74/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 7.74/1.88 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 7.74/1.88 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 7.74/1.88 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 7.74/1.88 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 7.74/1.88
% 7.74/1.88 (function-axioms)
% 7.74/1.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.74/1.88 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 7.74/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.74/1.88 (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0:
% 7.74/1.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.74/1.88 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 7.74/1.88
% 7.74/1.88 Further assumptions not needed in the proof:
% 7.74/1.88 --------------------------------------------
% 7.74/1.88 equal_member_defn, reflexivity_of_subset
% 7.74/1.88
% 7.74/1.88 Those formulas are unsatisfiable:
% 7.74/1.88 ---------------------------------
% 7.74/1.88
% 7.74/1.88 Begin of proof
% 7.74/1.88 |
% 7.74/1.88 | ALPHA: (intersection_defn) implies:
% 7.74/1.89 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.74/1.89 | (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) |
% 7.74/1.89 | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 7.74/1.89 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 7.74/1.89 | (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) |
% 7.74/1.89 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 7.74/1.89 | (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 7.74/1.89 | 0))))
% 7.74/1.89 |
% 7.74/1.89 | ALPHA: (subset_defn) implies:
% 7.74/1.89 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 7.74/1.89 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 7.74/1.89 | member(v2, v1) = 0))
% 7.74/1.89 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 7.74/1.89 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 7.74/1.89 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 7.74/1.90 |
% 7.74/1.90 | ALPHA: (function-axioms) implies:
% 7.74/1.90 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.74/1.90 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 7.74/1.90 | = v0))
% 7.74/1.90 |
% 7.74/1.90 | DELTA: instantiating (prove_th41) with fresh symbols all_8_0, all_8_1,
% 7.74/1.90 | all_8_2, all_8_3, all_8_4, all_8_5, all_8_6 gives:
% 7.74/1.90 | (6) ~ (all_8_0 = 0) & subset(all_8_2, all_8_1) = all_8_0 & subset(all_8_4,
% 7.74/1.90 | all_8_3) = 0 & subset(all_8_6, all_8_5) = 0 & intersection(all_8_5,
% 7.74/1.90 | all_8_3) = all_8_1 & intersection(all_8_6, all_8_4) = all_8_2 &
% 7.74/1.90 | $i(all_8_1) & $i(all_8_2) & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) &
% 7.74/1.90 | $i(all_8_6)
% 7.74/1.90 |
% 7.74/1.90 | ALPHA: (6) implies:
% 7.74/1.90 | (7) ~ (all_8_0 = 0)
% 7.74/1.90 | (8) $i(all_8_6)
% 7.74/1.90 | (9) $i(all_8_5)
% 7.74/1.90 | (10) $i(all_8_4)
% 7.74/1.90 | (11) $i(all_8_3)
% 7.74/1.90 | (12) intersection(all_8_6, all_8_4) = all_8_2
% 7.74/1.90 | (13) intersection(all_8_5, all_8_3) = all_8_1
% 7.74/1.90 | (14) subset(all_8_6, all_8_5) = 0
% 7.74/1.90 | (15) subset(all_8_4, all_8_3) = 0
% 7.74/1.90 | (16) subset(all_8_2, all_8_1) = all_8_0
% 7.74/1.90 |
% 7.74/1.90 | GROUND_INST: instantiating (commutativity_of_intersection) with all_8_6,
% 7.74/1.90 | all_8_4, all_8_2, simplifying with (8), (10), (12) gives:
% 7.74/1.90 | (17) intersection(all_8_4, all_8_6) = all_8_2 & $i(all_8_2)
% 7.74/1.90 |
% 7.74/1.90 | ALPHA: (17) implies:
% 7.74/1.91 | (18) $i(all_8_2)
% 7.74/1.91 | (19) intersection(all_8_4, all_8_6) = all_8_2
% 7.74/1.91 |
% 7.74/1.91 | GROUND_INST: instantiating (commutativity_of_intersection) with all_8_5,
% 7.74/1.91 | all_8_3, all_8_1, simplifying with (9), (11), (13) gives:
% 7.74/1.91 | (20) intersection(all_8_3, all_8_5) = all_8_1 & $i(all_8_1)
% 7.74/1.91 |
% 7.74/1.91 | ALPHA: (20) implies:
% 7.74/1.91 | (21) $i(all_8_1)
% 7.74/1.91 | (22) intersection(all_8_3, all_8_5) = all_8_1
% 7.74/1.91 |
% 7.74/1.91 | GROUND_INST: instantiating (3) with all_8_6, all_8_5, simplifying with (8),
% 7.74/1.91 | (9), (14) gives:
% 7.74/1.91 | (23) ! [v0: $i] : ( ~ (member(v0, all_8_6) = 0) | ~ $i(v0) | member(v0,
% 7.74/1.91 | all_8_5) = 0)
% 7.74/1.91 |
% 7.74/1.91 | GROUND_INST: instantiating (3) with all_8_4, all_8_3, simplifying with (10),
% 7.74/1.91 | (11), (15) gives:
% 7.74/1.91 | (24) ! [v0: $i] : ( ~ (member(v0, all_8_4) = 0) | ~ $i(v0) | member(v0,
% 7.74/1.91 | all_8_3) = 0)
% 7.74/1.91 |
% 7.74/1.91 | GROUND_INST: instantiating (4) with all_8_2, all_8_1, all_8_0, simplifying
% 7.74/1.91 | with (16), (18), (21) gives:
% 7.74/1.91 | (25) all_8_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 7.74/1.91 | all_8_1) = v1 & member(v0, all_8_2) = 0 & $i(v0))
% 7.74/1.91 |
% 7.74/1.91 | BETA: splitting (25) gives:
% 7.74/1.91 |
% 7.74/1.91 | Case 1:
% 7.74/1.91 | |
% 7.74/1.91 | | (26) all_8_0 = 0
% 7.74/1.91 | |
% 7.74/1.91 | | REDUCE: (7), (26) imply:
% 7.74/1.91 | | (27) $false
% 7.74/1.91 | |
% 7.74/1.91 | | CLOSE: (27) is inconsistent.
% 7.74/1.91 | |
% 7.74/1.91 | Case 2:
% 7.74/1.91 | |
% 7.74/1.91 | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_1) = v1
% 7.74/1.92 | | & member(v0, all_8_2) = 0 & $i(v0))
% 7.74/1.92 | |
% 7.74/1.92 | | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1 gives:
% 7.74/1.92 | | (29) ~ (all_22_0 = 0) & member(all_22_1, all_8_1) = all_22_0 &
% 7.74/1.92 | | member(all_22_1, all_8_2) = 0 & $i(all_22_1)
% 7.74/1.92 | |
% 7.74/1.92 | | ALPHA: (29) implies:
% 7.74/1.92 | | (30) ~ (all_22_0 = 0)
% 7.74/1.92 | | (31) $i(all_22_1)
% 7.74/1.92 | | (32) member(all_22_1, all_8_2) = 0
% 7.74/1.92 | | (33) member(all_22_1, all_8_1) = all_22_0
% 7.74/1.92 | |
% 7.74/1.92 | | GROUND_INST: instantiating (2) with all_8_5, all_8_3, all_22_1, all_8_1,
% 7.74/1.92 | | all_22_0, simplifying with (9), (11), (13), (31), (33) gives:
% 7.74/1.92 | | (34) all_22_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_22_1,
% 7.74/1.92 | | all_8_3) = v1 & member(all_22_1, all_8_5) = v0 & ( ~ (v1 = 0) |
% 7.74/1.92 | | ~ (v0 = 0)))
% 7.74/1.92 | |
% 7.74/1.92 | | GROUND_INST: instantiating (1) with all_8_4, all_8_6, all_22_1, all_8_2,
% 7.74/1.92 | | simplifying with (8), (10), (19), (31), (32) gives:
% 7.74/1.92 | | (35) member(all_22_1, all_8_4) = 0 & member(all_22_1, all_8_6) = 0
% 7.74/1.92 | |
% 7.74/1.92 | | ALPHA: (35) implies:
% 7.74/1.92 | | (36) member(all_22_1, all_8_6) = 0
% 7.74/1.92 | | (37) member(all_22_1, all_8_4) = 0
% 7.74/1.92 | |
% 7.74/1.92 | | GROUND_INST: instantiating (2) with all_8_3, all_8_5, all_22_1, all_8_1,
% 7.74/1.92 | | all_22_0, simplifying with (9), (11), (22), (31), (33) gives:
% 7.74/1.92 | | (38) all_22_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_22_1,
% 7.74/1.92 | | all_8_3) = v0 & member(all_22_1, all_8_5) = v1 & ( ~ (v1 = 0) |
% 7.74/1.92 | | ~ (v0 = 0)))
% 7.74/1.92 | |
% 7.74/1.92 | | BETA: splitting (38) gives:
% 7.74/1.92 | |
% 7.74/1.92 | | Case 1:
% 7.74/1.92 | | |
% 7.74/1.92 | | | (39) all_22_0 = 0
% 7.74/1.92 | | |
% 7.74/1.92 | | | REDUCE: (30), (39) imply:
% 7.74/1.92 | | | (40) $false
% 7.74/1.92 | | |
% 7.74/1.92 | | | CLOSE: (40) is inconsistent.
% 7.74/1.92 | | |
% 7.74/1.92 | | Case 2:
% 7.74/1.92 | | |
% 7.74/1.93 | | | (41) ? [v0: any] : ? [v1: any] : (member(all_22_1, all_8_3) = v0 &
% 7.74/1.93 | | | member(all_22_1, all_8_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.74/1.93 | | |
% 7.74/1.93 | | | DELTA: instantiating (41) with fresh symbols all_34_0, all_34_1 gives:
% 7.74/1.93 | | | (42) member(all_22_1, all_8_3) = all_34_1 & member(all_22_1, all_8_5) =
% 7.74/1.93 | | | all_34_0 & ( ~ (all_34_0 = 0) | ~ (all_34_1 = 0))
% 7.74/1.93 | | |
% 7.74/1.93 | | | ALPHA: (42) implies:
% 7.74/1.93 | | | (43) member(all_22_1, all_8_5) = all_34_0
% 7.74/1.93 | | | (44) member(all_22_1, all_8_3) = all_34_1
% 7.74/1.93 | | | (45) ~ (all_34_0 = 0) | ~ (all_34_1 = 0)
% 7.74/1.93 | | |
% 7.74/1.93 | | | BETA: splitting (34) gives:
% 7.74/1.93 | | |
% 7.74/1.93 | | | Case 1:
% 7.74/1.93 | | | |
% 7.74/1.93 | | | | (46) all_22_0 = 0
% 7.74/1.93 | | | |
% 7.74/1.93 | | | | REDUCE: (30), (46) imply:
% 7.74/1.93 | | | | (47) $false
% 7.74/1.93 | | | |
% 7.74/1.93 | | | | CLOSE: (47) is inconsistent.
% 7.74/1.93 | | | |
% 7.74/1.93 | | | Case 2:
% 7.74/1.93 | | | |
% 7.74/1.93 | | | | (48) ? [v0: any] : ? [v1: any] : (member(all_22_1, all_8_3) = v1 &
% 7.74/1.93 | | | | member(all_22_1, all_8_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.74/1.93 | | | |
% 7.74/1.93 | | | | DELTA: instantiating (48) with fresh symbols all_39_0, all_39_1 gives:
% 7.74/1.93 | | | | (49) member(all_22_1, all_8_3) = all_39_0 & member(all_22_1, all_8_5)
% 7.74/1.93 | | | | = all_39_1 & ( ~ (all_39_0 = 0) | ~ (all_39_1 = 0))
% 7.74/1.93 | | | |
% 7.74/1.93 | | | | ALPHA: (49) implies:
% 7.74/1.93 | | | | (50) member(all_22_1, all_8_5) = all_39_1
% 7.74/1.93 | | | | (51) member(all_22_1, all_8_3) = all_39_0
% 7.74/1.93 | | | |
% 7.74/1.93 | | | | GROUND_INST: instantiating (5) with all_34_0, all_39_1, all_8_5,
% 7.74/1.93 | | | | all_22_1, simplifying with (43), (50) gives:
% 7.74/1.93 | | | | (52) all_39_1 = all_34_0
% 7.74/1.93 | | | |
% 7.74/1.93 | | | | GROUND_INST: instantiating (5) with all_34_1, all_39_0, all_8_3,
% 7.74/1.93 | | | | all_22_1, simplifying with (44), (51) gives:
% 7.74/1.93 | | | | (53) all_39_0 = all_34_1
% 7.74/1.93 | | | |
% 7.74/1.93 | | | | GROUND_INST: instantiating (23) with all_22_1, simplifying with (31),
% 7.74/1.93 | | | | (36) gives:
% 7.74/1.93 | | | | (54) member(all_22_1, all_8_5) = 0
% 7.74/1.93 | | | |
% 7.74/1.93 | | | | GROUND_INST: instantiating (24) with all_22_1, simplifying with (31),
% 7.74/1.93 | | | | (37) gives:
% 7.74/1.93 | | | | (55) member(all_22_1, all_8_3) = 0
% 7.74/1.93 | | | |
% 7.74/1.93 | | | | GROUND_INST: instantiating (5) with all_34_0, 0, all_8_5, all_22_1,
% 7.74/1.93 | | | | simplifying with (43), (54) gives:
% 7.74/1.94 | | | | (56) all_34_0 = 0
% 7.74/1.94 | | | |
% 7.74/1.94 | | | | GROUND_INST: instantiating (5) with all_34_1, 0, all_8_3, all_22_1,
% 7.74/1.94 | | | | simplifying with (44), (55) gives:
% 7.74/1.94 | | | | (57) all_34_1 = 0
% 7.74/1.94 | | | |
% 7.74/1.94 | | | | BETA: splitting (45) gives:
% 7.74/1.94 | | | |
% 7.74/1.94 | | | | Case 1:
% 7.74/1.94 | | | | |
% 7.74/1.94 | | | | | (58) ~ (all_34_0 = 0)
% 7.74/1.94 | | | | |
% 7.74/1.94 | | | | | REDUCE: (56), (58) imply:
% 7.74/1.94 | | | | | (59) $false
% 7.74/1.94 | | | | |
% 7.74/1.94 | | | | | CLOSE: (59) is inconsistent.
% 7.74/1.94 | | | | |
% 7.74/1.94 | | | | Case 2:
% 7.74/1.94 | | | | |
% 7.74/1.94 | | | | | (60) ~ (all_34_1 = 0)
% 7.74/1.94 | | | | |
% 7.74/1.94 | | | | | REDUCE: (57), (60) imply:
% 7.74/1.94 | | | | | (61) $false
% 7.74/1.94 | | | | |
% 7.74/1.94 | | | | | CLOSE: (61) is inconsistent.
% 7.74/1.94 | | | | |
% 7.74/1.94 | | | | End of split
% 7.74/1.94 | | | |
% 7.74/1.94 | | | End of split
% 7.74/1.94 | | |
% 7.74/1.94 | | End of split
% 7.74/1.94 | |
% 7.74/1.94 | End of split
% 7.74/1.94 |
% 7.74/1.94 End of proof
% 7.74/1.94 % SZS output end Proof for theBenchmark
% 7.74/1.94
% 7.74/1.94 1275ms
%------------------------------------------------------------------------------