TSTP Solution File: SET586+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET586+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 : n023.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 15:25:25 EDT 2023
% Result : Theorem 4.68s 1.34s
% Output : Proof 6.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET586+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 16:13:41 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.58/0.61 ________ _____
% 0.58/0.61 ___ __ \_________(_)________________________________
% 0.58/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.58/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.58/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.58/0.61
% 0.58/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.58/0.61 (2023-06-19)
% 0.58/0.61
% 0.58/0.61 (c) Philipp Rümmer, 2009-2023
% 0.58/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.58/0.61 Amanda Stjerna.
% 0.58/0.61 Free software under BSD-3-Clause.
% 0.58/0.61
% 0.58/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.58/0.61
% 0.58/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.58/0.62 Running up to 7 provers in parallel.
% 0.69/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.69/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.08/0.95 Prover 4: Preprocessing ...
% 2.08/0.95 Prover 1: Preprocessing ...
% 2.08/0.99 Prover 5: Preprocessing ...
% 2.08/0.99 Prover 6: Preprocessing ...
% 2.08/0.99 Prover 3: Preprocessing ...
% 2.08/0.99 Prover 0: Preprocessing ...
% 2.08/0.99 Prover 2: Preprocessing ...
% 2.98/1.16 Prover 3: Warning: ignoring some quantifiers
% 2.98/1.16 Prover 5: Proving ...
% 2.98/1.16 Prover 1: Warning: ignoring some quantifiers
% 3.60/1.17 Prover 2: Proving ...
% 3.60/1.17 Prover 3: Constructing countermodel ...
% 3.60/1.17 Prover 1: Constructing countermodel ...
% 3.60/1.17 Prover 4: Warning: ignoring some quantifiers
% 3.60/1.17 Prover 6: Proving ...
% 3.60/1.18 Prover 4: Constructing countermodel ...
% 3.79/1.20 Prover 0: Proving ...
% 4.68/1.33 Prover 3: proved (701ms)
% 4.68/1.33
% 4.68/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.68/1.34
% 4.68/1.34 Prover 5: stopped
% 4.68/1.34 Prover 6: stopped
% 4.68/1.34 Prover 2: stopped
% 4.68/1.35 Prover 0: stopped
% 4.68/1.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.68/1.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.68/1.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.68/1.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.68/1.37 Prover 8: Preprocessing ...
% 4.68/1.37 Prover 11: Preprocessing ...
% 4.68/1.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.68/1.37 Prover 7: Preprocessing ...
% 5.17/1.38 Prover 10: Preprocessing ...
% 5.17/1.39 Prover 13: Preprocessing ...
% 5.17/1.40 Prover 4: Found proof (size 44)
% 5.17/1.40 Prover 4: proved (774ms)
% 5.17/1.41 Prover 7: Warning: ignoring some quantifiers
% 5.17/1.41 Prover 13: stopped
% 5.17/1.41 Prover 1: stopped
% 5.17/1.41 Prover 10: Warning: ignoring some quantifiers
% 5.17/1.41 Prover 11: stopped
% 5.17/1.41 Prover 7: Constructing countermodel ...
% 5.17/1.41 Prover 10: Constructing countermodel ...
% 5.17/1.41 Prover 7: stopped
% 5.17/1.42 Prover 10: stopped
% 5.17/1.43 Prover 8: Warning: ignoring some quantifiers
% 5.17/1.44 Prover 8: Constructing countermodel ...
% 5.17/1.44 Prover 8: stopped
% 5.17/1.44
% 5.17/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.17/1.44
% 5.17/1.45 % SZS output start Proof for theBenchmark
% 5.17/1.45 Assumptions after simplification:
% 5.17/1.45 ---------------------------------
% 5.17/1.45
% 5.17/1.45 (commutativity_of_intersection)
% 5.87/1.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) | ~
% 5.87/1.49 $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) & ! [v0: $i] :
% 5.87/1.49 ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ $i(v1) | ~
% 5.87/1.49 $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 5.87/1.49
% 5.87/1.49 (intersection_defn)
% 5.87/1.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 5.87/1.50 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~
% 5.87/1.50 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 &
% 5.87/1.50 member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 5.87/1.50 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) | ~
% 5.87/1.50 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) =
% 5.87/1.50 0 & member(v2, v0) = 0))
% 5.87/1.50
% 5.87/1.50 (prove_intersection_of_subset)
% 5.87/1.50 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 5.87/1.50 int] : ( ~ (v5 = 0) & subset(v3, v4) = v5 & subset(v0, v1) = 0 &
% 5.87/1.50 intersection(v1, v2) = v4 & intersection(v0, v2) = v3 & $i(v4) & $i(v3) &
% 5.87/1.50 $i(v2) & $i(v1) & $i(v0))
% 5.87/1.50
% 5.87/1.50 (subset_defn)
% 5.87/1.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 5.87/1.50 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 5.87/1.50 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 5.87/1.50 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 5.87/1.50 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 5.87/1.50 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 5.87/1.50 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 5.87/1.50 ~ $i(v0) | member(v2, v1) = 0)
% 5.87/1.50
% 5.87/1.50 (function-axioms)
% 5.87/1.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 5.87/1.51 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 5.87/1.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.87/1.51 (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0:
% 5.87/1.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 5.87/1.51 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 5.87/1.51
% 5.87/1.51 Further assumptions not needed in the proof:
% 5.87/1.51 --------------------------------------------
% 5.87/1.51 equal_member_defn, reflexivity_of_subset
% 5.87/1.51
% 5.87/1.51 Those formulas are unsatisfiable:
% 5.87/1.51 ---------------------------------
% 5.87/1.51
% 5.87/1.51 Begin of proof
% 5.87/1.51 |
% 5.87/1.51 | ALPHA: (intersection_defn) implies:
% 5.87/1.51 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 5.87/1.51 | (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) |
% 5.87/1.51 | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 5.87/1.51 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 5.87/1.51 | (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) |
% 5.87/1.51 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 5.87/1.51 | (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 5.87/1.51 | 0))))
% 5.87/1.51 |
% 5.87/1.51 | ALPHA: (subset_defn) implies:
% 5.87/1.52 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 5.87/1.52 | (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v2,
% 5.87/1.52 | v1) = 0)
% 5.87/1.52 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 5.87/1.52 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 5.87/1.52 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 5.87/1.52 |
% 5.87/1.52 | ALPHA: (commutativity_of_intersection) implies:
% 5.87/1.52 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) =
% 5.87/1.52 | v2) | ~ $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2)))
% 5.87/1.52 |
% 5.87/1.52 | ALPHA: (function-axioms) implies:
% 5.87/1.52 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.87/1.52 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 5.87/1.52 | = v0))
% 5.87/1.52 |
% 5.87/1.52 | DELTA: instantiating (prove_intersection_of_subset) with fresh symbols
% 5.87/1.52 | all_8_0, all_8_1, all_8_2, all_8_3, all_8_4, all_8_5 gives:
% 6.04/1.52 | (7) ~ (all_8_0 = 0) & subset(all_8_2, all_8_1) = all_8_0 & subset(all_8_5,
% 6.04/1.52 | all_8_4) = 0 & intersection(all_8_4, all_8_3) = all_8_1 &
% 6.04/1.52 | intersection(all_8_5, all_8_3) = all_8_2 & $i(all_8_1) & $i(all_8_2) &
% 6.04/1.52 | $i(all_8_3) & $i(all_8_4) & $i(all_8_5)
% 6.04/1.52 |
% 6.04/1.52 | ALPHA: (7) implies:
% 6.04/1.52 | (8) ~ (all_8_0 = 0)
% 6.04/1.52 | (9) $i(all_8_5)
% 6.04/1.52 | (10) $i(all_8_4)
% 6.04/1.52 | (11) $i(all_8_3)
% 6.04/1.52 | (12) intersection(all_8_5, all_8_3) = all_8_2
% 6.04/1.52 | (13) intersection(all_8_4, all_8_3) = all_8_1
% 6.04/1.52 | (14) subset(all_8_5, all_8_4) = 0
% 6.04/1.52 | (15) subset(all_8_2, all_8_1) = all_8_0
% 6.04/1.52 |
% 6.04/1.53 | GROUND_INST: instantiating (5) with all_8_3, all_8_5, all_8_2, simplifying
% 6.04/1.53 | with (9), (11), (12) gives:
% 6.04/1.53 | (16) intersection(all_8_3, all_8_5) = all_8_2 & $i(all_8_2)
% 6.04/1.53 |
% 6.04/1.53 | ALPHA: (16) implies:
% 6.04/1.53 | (17) $i(all_8_2)
% 6.04/1.53 | (18) intersection(all_8_3, all_8_5) = all_8_2
% 6.04/1.53 |
% 6.04/1.53 | GROUND_INST: instantiating (5) with all_8_3, all_8_4, all_8_1, simplifying
% 6.04/1.53 | with (10), (11), (13) gives:
% 6.04/1.53 | (19) intersection(all_8_3, all_8_4) = all_8_1 & $i(all_8_1)
% 6.04/1.53 |
% 6.04/1.53 | ALPHA: (19) implies:
% 6.04/1.53 | (20) $i(all_8_1)
% 6.04/1.53 | (21) intersection(all_8_3, all_8_4) = all_8_1
% 6.04/1.53 |
% 6.04/1.53 | GROUND_INST: instantiating (4) with all_8_2, all_8_1, all_8_0, simplifying
% 6.04/1.53 | with (15), (17), (20) gives:
% 6.04/1.53 | (22) all_8_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 6.04/1.53 | all_8_1) = v1 & member(v0, all_8_2) = 0 & $i(v0))
% 6.04/1.53 |
% 6.04/1.53 | BETA: splitting (22) gives:
% 6.04/1.53 |
% 6.04/1.53 | Case 1:
% 6.04/1.53 | |
% 6.04/1.53 | | (23) all_8_0 = 0
% 6.04/1.53 | |
% 6.04/1.53 | | REDUCE: (8), (23) imply:
% 6.04/1.53 | | (24) $false
% 6.09/1.53 | |
% 6.09/1.53 | | CLOSE: (24) is inconsistent.
% 6.09/1.53 | |
% 6.09/1.53 | Case 2:
% 6.09/1.53 | |
% 6.09/1.53 | | (25) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_1) = v1
% 6.09/1.53 | | & member(v0, all_8_2) = 0 & $i(v0))
% 6.09/1.53 | |
% 6.09/1.53 | | DELTA: instantiating (25) with fresh symbols all_20_0, all_20_1 gives:
% 6.09/1.53 | | (26) ~ (all_20_0 = 0) & member(all_20_1, all_8_1) = all_20_0 &
% 6.09/1.53 | | member(all_20_1, all_8_2) = 0 & $i(all_20_1)
% 6.09/1.53 | |
% 6.09/1.53 | | ALPHA: (26) implies:
% 6.09/1.53 | | (27) ~ (all_20_0 = 0)
% 6.09/1.53 | | (28) $i(all_20_1)
% 6.09/1.53 | | (29) member(all_20_1, all_8_2) = 0
% 6.09/1.53 | | (30) member(all_20_1, all_8_1) = all_20_0
% 6.09/1.53 | |
% 6.09/1.54 | | GROUND_INST: instantiating (2) with all_8_4, all_8_3, all_20_1, all_8_1,
% 6.09/1.54 | | all_20_0, simplifying with (10), (11), (13), (28), (30) gives:
% 6.09/1.54 | | (31) all_20_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_20_1,
% 6.09/1.54 | | all_8_3) = v1 & member(all_20_1, all_8_4) = v0 & ( ~ (v1 = 0) |
% 6.09/1.54 | | ~ (v0 = 0)))
% 6.09/1.54 | |
% 6.09/1.54 | | GROUND_INST: instantiating (1) with all_8_3, all_8_5, all_20_1, all_8_2,
% 6.09/1.54 | | simplifying with (9), (11), (18), (28), (29) gives:
% 6.09/1.54 | | (32) member(all_20_1, all_8_3) = 0 & member(all_20_1, all_8_5) = 0
% 6.09/1.54 | |
% 6.09/1.54 | | ALPHA: (32) implies:
% 6.09/1.54 | | (33) member(all_20_1, all_8_5) = 0
% 6.09/1.54 | | (34) member(all_20_1, all_8_3) = 0
% 6.09/1.54 | |
% 6.09/1.54 | | GROUND_INST: instantiating (2) with all_8_3, all_8_4, all_20_1, all_8_1,
% 6.09/1.54 | | all_20_0, simplifying with (10), (11), (21), (28), (30) gives:
% 6.09/1.54 | | (35) all_20_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_20_1,
% 6.09/1.54 | | all_8_3) = v0 & member(all_20_1, all_8_4) = v1 & ( ~ (v1 = 0) |
% 6.09/1.54 | | ~ (v0 = 0)))
% 6.09/1.54 | |
% 6.09/1.54 | | BETA: splitting (35) gives:
% 6.09/1.54 | |
% 6.09/1.54 | | Case 1:
% 6.09/1.54 | | |
% 6.09/1.54 | | | (36) all_20_0 = 0
% 6.09/1.54 | | |
% 6.09/1.54 | | | REDUCE: (27), (36) imply:
% 6.09/1.54 | | | (37) $false
% 6.09/1.54 | | |
% 6.09/1.54 | | | CLOSE: (37) is inconsistent.
% 6.09/1.54 | | |
% 6.09/1.54 | | Case 2:
% 6.09/1.54 | | |
% 6.09/1.54 | | | (38) ? [v0: any] : ? [v1: any] : (member(all_20_1, all_8_3) = v0 &
% 6.09/1.54 | | | member(all_20_1, all_8_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.09/1.54 | | |
% 6.09/1.54 | | | DELTA: instantiating (38) with fresh symbols all_32_0, all_32_1 gives:
% 6.09/1.54 | | | (39) member(all_20_1, all_8_3) = all_32_1 & member(all_20_1, all_8_4) =
% 6.09/1.54 | | | all_32_0 & ( ~ (all_32_0 = 0) | ~ (all_32_1 = 0))
% 6.09/1.54 | | |
% 6.09/1.54 | | | ALPHA: (39) implies:
% 6.09/1.54 | | | (40) member(all_20_1, all_8_4) = all_32_0
% 6.09/1.54 | | | (41) member(all_20_1, all_8_3) = all_32_1
% 6.09/1.54 | | | (42) ~ (all_32_0 = 0) | ~ (all_32_1 = 0)
% 6.09/1.54 | | |
% 6.09/1.54 | | | BETA: splitting (31) gives:
% 6.09/1.54 | | |
% 6.09/1.54 | | | Case 1:
% 6.09/1.54 | | | |
% 6.09/1.54 | | | | (43) all_20_0 = 0
% 6.09/1.54 | | | |
% 6.09/1.54 | | | | REDUCE: (27), (43) imply:
% 6.09/1.54 | | | | (44) $false
% 6.09/1.54 | | | |
% 6.09/1.54 | | | | CLOSE: (44) is inconsistent.
% 6.09/1.54 | | | |
% 6.09/1.54 | | | Case 2:
% 6.09/1.54 | | | |
% 6.09/1.54 | | | | (45) ? [v0: any] : ? [v1: any] : (member(all_20_1, all_8_3) = v1 &
% 6.09/1.54 | | | | member(all_20_1, all_8_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.09/1.54 | | | |
% 6.09/1.54 | | | | DELTA: instantiating (45) with fresh symbols all_37_0, all_37_1 gives:
% 6.09/1.55 | | | | (46) member(all_20_1, all_8_3) = all_37_0 & member(all_20_1, all_8_4)
% 6.09/1.55 | | | | = all_37_1 & ( ~ (all_37_0 = 0) | ~ (all_37_1 = 0))
% 6.09/1.55 | | | |
% 6.09/1.55 | | | | ALPHA: (46) implies:
% 6.09/1.55 | | | | (47) member(all_20_1, all_8_4) = all_37_1
% 6.09/1.55 | | | | (48) member(all_20_1, all_8_3) = all_37_0
% 6.09/1.55 | | | |
% 6.09/1.55 | | | | GROUND_INST: instantiating (6) with all_32_0, all_37_1, all_8_4,
% 6.09/1.55 | | | | all_20_1, simplifying with (40), (47) gives:
% 6.09/1.55 | | | | (49) all_37_1 = all_32_0
% 6.09/1.55 | | | |
% 6.09/1.55 | | | | GROUND_INST: instantiating (6) with all_32_1, all_37_0, all_8_3,
% 6.09/1.55 | | | | all_20_1, simplifying with (41), (48) gives:
% 6.09/1.55 | | | | (50) all_37_0 = all_32_1
% 6.09/1.55 | | | |
% 6.09/1.55 | | | | GROUND_INST: instantiating (6) with 0, all_37_0, all_8_3, all_20_1,
% 6.09/1.55 | | | | simplifying with (34), (48) gives:
% 6.09/1.55 | | | | (51) all_37_0 = 0
% 6.09/1.55 | | | |
% 6.09/1.55 | | | | COMBINE_EQS: (50), (51) imply:
% 6.09/1.55 | | | | (52) all_32_1 = 0
% 6.09/1.55 | | | |
% 6.09/1.55 | | | | SIMP: (52) implies:
% 6.09/1.55 | | | | (53) all_32_1 = 0
% 6.09/1.55 | | | |
% 6.09/1.55 | | | | BETA: splitting (42) gives:
% 6.09/1.55 | | | |
% 6.09/1.55 | | | | Case 1:
% 6.09/1.55 | | | | |
% 6.09/1.55 | | | | | (54) ~ (all_32_0 = 0)
% 6.09/1.55 | | | | |
% 6.09/1.55 | | | | | GROUND_INST: instantiating (3) with all_8_5, all_8_4, all_20_1,
% 6.09/1.55 | | | | | simplifying with (9), (10), (14), (28), (33) gives:
% 6.09/1.55 | | | | | (55) member(all_20_1, all_8_4) = 0
% 6.09/1.55 | | | | |
% 6.09/1.55 | | | | | GROUND_INST: instantiating (6) with all_32_0, 0, all_8_4, all_20_1,
% 6.09/1.55 | | | | | simplifying with (40), (55) gives:
% 6.09/1.55 | | | | | (56) all_32_0 = 0
% 6.09/1.55 | | | | |
% 6.09/1.55 | | | | | REDUCE: (54), (56) imply:
% 6.09/1.55 | | | | | (57) $false
% 6.09/1.55 | | | | |
% 6.09/1.55 | | | | | CLOSE: (57) is inconsistent.
% 6.09/1.55 | | | | |
% 6.09/1.55 | | | | Case 2:
% 6.09/1.55 | | | | |
% 6.09/1.55 | | | | | (58) ~ (all_32_1 = 0)
% 6.09/1.55 | | | | |
% 6.09/1.55 | | | | | REDUCE: (53), (58) imply:
% 6.09/1.55 | | | | | (59) $false
% 6.09/1.55 | | | | |
% 6.09/1.55 | | | | | CLOSE: (59) is inconsistent.
% 6.09/1.55 | | | | |
% 6.09/1.55 | | | | End of split
% 6.09/1.55 | | | |
% 6.09/1.55 | | | End of split
% 6.09/1.55 | | |
% 6.09/1.55 | | End of split
% 6.09/1.55 | |
% 6.09/1.55 | End of split
% 6.09/1.55 |
% 6.09/1.55 End of proof
% 6.09/1.55 % SZS output end Proof for theBenchmark
% 6.09/1.55
% 6.09/1.55 943ms
%------------------------------------------------------------------------------