TSTP Solution File: SET624+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET624+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 : n021.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 15:25:42 EDT 2023
% Result : Theorem 5.02s 1.48s
% Output : Proof 7.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET624+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n021.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 13:57:12 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.15/0.96 Prover 1: Preprocessing ...
% 2.15/0.96 Prover 4: Preprocessing ...
% 2.15/1.00 Prover 2: Preprocessing ...
% 2.15/1.00 Prover 0: Preprocessing ...
% 2.15/1.00 Prover 6: Preprocessing ...
% 2.15/1.00 Prover 3: Preprocessing ...
% 2.15/1.00 Prover 5: Preprocessing ...
% 3.57/1.18 Prover 5: Proving ...
% 3.57/1.19 Prover 2: Proving ...
% 3.57/1.19 Prover 3: Warning: ignoring some quantifiers
% 3.57/1.20 Prover 1: Warning: ignoring some quantifiers
% 3.57/1.20 Prover 3: Constructing countermodel ...
% 3.57/1.21 Prover 1: Constructing countermodel ...
% 3.57/1.22 Prover 6: Proving ...
% 3.57/1.22 Prover 4: Warning: ignoring some quantifiers
% 3.99/1.23 Prover 4: Constructing countermodel ...
% 3.99/1.25 Prover 0: Proving ...
% 5.02/1.48 Prover 0: proved (851ms)
% 5.02/1.48
% 5.02/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.02/1.48
% 5.02/1.48 Prover 3: stopped
% 5.02/1.48 Prover 5: stopped
% 5.02/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.02/1.48 Prover 2: stopped
% 5.02/1.49 Prover 6: stopped
% 5.02/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.02/1.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.02/1.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.02/1.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.98/1.51 Prover 13: Preprocessing ...
% 5.98/1.51 Prover 10: Preprocessing ...
% 5.98/1.51 Prover 7: Preprocessing ...
% 5.98/1.51 Prover 8: Preprocessing ...
% 5.98/1.52 Prover 11: Preprocessing ...
% 5.98/1.54 Prover 10: Warning: ignoring some quantifiers
% 5.98/1.54 Prover 10: Constructing countermodel ...
% 5.98/1.55 Prover 8: Warning: ignoring some quantifiers
% 5.98/1.56 Prover 8: Constructing countermodel ...
% 5.98/1.56 Prover 7: Warning: ignoring some quantifiers
% 5.98/1.56 Prover 7: Constructing countermodel ...
% 5.98/1.56 Prover 13: Warning: ignoring some quantifiers
% 5.98/1.56 Prover 13: Constructing countermodel ...
% 6.53/1.61 Prover 11: Warning: ignoring some quantifiers
% 6.53/1.62 Prover 11: Constructing countermodel ...
% 6.53/1.65 Prover 1: Found proof (size 91)
% 6.53/1.66 Prover 1: proved (1027ms)
% 6.53/1.66 Prover 13: stopped
% 6.53/1.66 Prover 11: stopped
% 6.53/1.66 Prover 10: stopped
% 6.53/1.66 Prover 8: stopped
% 6.53/1.66 Prover 7: stopped
% 6.53/1.66 Prover 4: stopped
% 6.53/1.66
% 6.53/1.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.53/1.66
% 7.17/1.67 % SZS output start Proof for theBenchmark
% 7.17/1.68 Assumptions after simplification:
% 7.17/1.68 ---------------------------------
% 7.17/1.68
% 7.17/1.68 (commutativity_of_union)
% 7.27/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1)
% 7.27/1.70 | ~ $i(v0) | (union(v1, v0) = v2 & $i(v2)))
% 7.27/1.70
% 7.27/1.70 (intersect_defn)
% 7.27/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) =
% 7.27/1.71 v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3, v0) = 0) | ~
% 7.27/1.71 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))) & ! [v0:
% 7.27/1.71 $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 7.27/1.71 [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2)))
% 7.27/1.71
% 7.27/1.71 (prove_intersect_with_union)
% 7.27/1.71 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5:
% 7.27/1.71 any] : ? [v6: any] : (intersect(v0, v3) = v4 & intersect(v0, v2) = v6 &
% 7.27/1.71 intersect(v0, v1) = v5 & union(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) &
% 7.27/1.71 $i(v0) & ((v4 = 0 & ~ (v6 = 0) & ~ (v5 = 0)) | ( ~ (v4 = 0) & (v6 = 0 | v5
% 7.27/1.71 = 0))))
% 7.27/1.71
% 7.27/1.71 (union_defn)
% 7.27/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.27/1.71 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 7.27/1.71 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 7.27/1.71 member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 7.27/1.71 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0)
% 7.27/1.71 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 7.27/1.71 (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 7.27/1.71
% 7.27/1.71 (function-axioms)
% 7.27/1.72 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.27/1.72 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) =
% 7.27/1.72 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 7.27/1.72 ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0:
% 7.27/1.72 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.27/1.72 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 7.27/1.72
% 7.27/1.72 Further assumptions not needed in the proof:
% 7.27/1.72 --------------------------------------------
% 7.27/1.72 equal_member_defn, symmetry_of_intersect
% 7.27/1.72
% 7.27/1.72 Those formulas are unsatisfiable:
% 7.27/1.72 ---------------------------------
% 7.27/1.72
% 7.27/1.72 Begin of proof
% 7.27/1.72 |
% 7.27/1.72 | ALPHA: (union_defn) implies:
% 7.44/1.72 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0,
% 7.44/1.72 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 7.44/1.72 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v2, v1) = v5 &
% 7.44/1.72 | member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 7.44/1.72 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 7.44/1.72 | (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~
% 7.44/1.72 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 7.44/1.72 | (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) =
% 7.44/1.72 | v5))
% 7.44/1.72 |
% 7.44/1.72 | ALPHA: (intersect_defn) implies:
% 7.44/1.73 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) |
% 7.44/1.73 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 &
% 7.44/1.73 | $i(v2)))
% 7.48/1.73 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0,
% 7.48/1.73 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3,
% 7.48/1.73 | v0) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3,
% 7.48/1.73 | v1) = v4)))
% 7.48/1.73 |
% 7.48/1.73 | ALPHA: (function-axioms) implies:
% 7.48/1.73 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.48/1.73 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 7.48/1.73 | = v0))
% 7.48/1.73 |
% 7.48/1.73 | DELTA: instantiating (prove_intersect_with_union) with fresh symbols all_8_0,
% 7.48/1.73 | all_8_1, all_8_2, all_8_3, all_8_4, all_8_5, all_8_6 gives:
% 7.48/1.73 | (6) intersect(all_8_6, all_8_3) = all_8_2 & intersect(all_8_6, all_8_4) =
% 7.48/1.73 | all_8_0 & intersect(all_8_6, all_8_5) = all_8_1 & union(all_8_5,
% 7.48/1.73 | all_8_4) = all_8_3 & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) &
% 7.48/1.73 | $i(all_8_6) & ((all_8_2 = 0 & ~ (all_8_0 = 0) & ~ (all_8_1 = 0)) | (
% 7.48/1.73 | ~ (all_8_2 = 0) & (all_8_0 = 0 | all_8_1 = 0)))
% 7.48/1.73 |
% 7.48/1.73 | ALPHA: (6) implies:
% 7.48/1.73 | (7) $i(all_8_6)
% 7.48/1.73 | (8) $i(all_8_5)
% 7.48/1.73 | (9) $i(all_8_4)
% 7.48/1.73 | (10) union(all_8_5, all_8_4) = all_8_3
% 7.48/1.73 | (11) intersect(all_8_6, all_8_5) = all_8_1
% 7.48/1.73 | (12) intersect(all_8_6, all_8_4) = all_8_0
% 7.48/1.73 | (13) intersect(all_8_6, all_8_3) = all_8_2
% 7.48/1.73 | (14) (all_8_2 = 0 & ~ (all_8_0 = 0) & ~ (all_8_1 = 0)) | ( ~ (all_8_2 =
% 7.48/1.74 | 0) & (all_8_0 = 0 | all_8_1 = 0))
% 7.48/1.74 |
% 7.48/1.74 | GROUND_INST: instantiating (commutativity_of_union) with all_8_5, all_8_4,
% 7.48/1.74 | all_8_3, simplifying with (8), (9), (10) gives:
% 7.48/1.74 | (15) union(all_8_4, all_8_5) = all_8_3 & $i(all_8_3)
% 7.48/1.74 |
% 7.48/1.74 | ALPHA: (15) implies:
% 7.48/1.74 | (16) $i(all_8_3)
% 7.48/1.74 | (17) union(all_8_4, all_8_5) = all_8_3
% 7.48/1.74 |
% 7.48/1.74 | GROUND_INST: instantiating (4) with all_8_6, all_8_5, all_8_1, simplifying
% 7.48/1.74 | with (7), (8), (11) gives:
% 7.48/1.74 | (18) all_8_1 = 0 | ! [v0: $i] : ( ~ (member(v0, all_8_6) = 0) | ~ $i(v0)
% 7.48/1.74 | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_5) = v1))
% 7.48/1.74 |
% 7.48/1.74 | GROUND_INST: instantiating (4) with all_8_6, all_8_4, all_8_0, simplifying
% 7.48/1.74 | with (7), (9), (12) gives:
% 7.48/1.74 | (19) all_8_0 = 0 | ! [v0: $i] : ( ~ (member(v0, all_8_6) = 0) | ~ $i(v0)
% 7.48/1.74 | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_4) = v1))
% 7.48/1.74 |
% 7.48/1.74 | GROUND_INST: instantiating (4) with all_8_6, all_8_3, all_8_2, simplifying
% 7.48/1.74 | with (7), (13), (16) gives:
% 7.48/1.74 | (20) all_8_2 = 0 | ! [v0: $i] : ( ~ (member(v0, all_8_6) = 0) | ~ $i(v0)
% 7.48/1.74 | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_3) = v1))
% 7.48/1.74 |
% 7.48/1.74 | BETA: splitting (14) gives:
% 7.48/1.74 |
% 7.48/1.74 | Case 1:
% 7.48/1.74 | |
% 7.48/1.74 | | (21) all_8_2 = 0 & ~ (all_8_0 = 0) & ~ (all_8_1 = 0)
% 7.48/1.74 | |
% 7.48/1.74 | | ALPHA: (21) implies:
% 7.48/1.74 | | (22) all_8_2 = 0
% 7.48/1.74 | | (23) ~ (all_8_1 = 0)
% 7.48/1.74 | | (24) ~ (all_8_0 = 0)
% 7.48/1.74 | |
% 7.48/1.74 | | REDUCE: (13), (22) imply:
% 7.48/1.74 | | (25) intersect(all_8_6, all_8_3) = 0
% 7.48/1.74 | |
% 7.48/1.74 | | BETA: splitting (19) gives:
% 7.48/1.74 | |
% 7.48/1.74 | | Case 1:
% 7.48/1.74 | | |
% 7.48/1.74 | | | (26) all_8_0 = 0
% 7.48/1.74 | | |
% 7.48/1.74 | | | REDUCE: (24), (26) imply:
% 7.48/1.74 | | | (27) $false
% 7.48/1.75 | | |
% 7.48/1.75 | | | CLOSE: (27) is inconsistent.
% 7.48/1.75 | | |
% 7.48/1.75 | | Case 2:
% 7.48/1.75 | | |
% 7.48/1.75 | | | (28) ! [v0: $i] : ( ~ (member(v0, all_8_6) = 0) | ~ $i(v0) | ? [v1:
% 7.48/1.75 | | | int] : ( ~ (v1 = 0) & member(v0, all_8_4) = v1))
% 7.48/1.75 | | |
% 7.48/1.75 | | | BETA: splitting (18) gives:
% 7.48/1.75 | | |
% 7.48/1.75 | | | Case 1:
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | (29) all_8_1 = 0
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | REDUCE: (23), (29) imply:
% 7.48/1.75 | | | | (30) $false
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | CLOSE: (30) is inconsistent.
% 7.48/1.75 | | | |
% 7.48/1.75 | | | Case 2:
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | (31) ! [v0: $i] : ( ~ (member(v0, all_8_6) = 0) | ~ $i(v0) | ?
% 7.48/1.75 | | | | [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_5) = v1))
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | GROUND_INST: instantiating (3) with all_8_6, all_8_3, simplifying with
% 7.48/1.75 | | | | (7), (16), (25) gives:
% 7.48/1.75 | | | | (32) ? [v0: $i] : (member(v0, all_8_3) = 0 & member(v0, all_8_6) = 0
% 7.48/1.75 | | | | & $i(v0))
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | DELTA: instantiating (32) with fresh symbol all_45_0 gives:
% 7.48/1.75 | | | | (33) member(all_45_0, all_8_3) = 0 & member(all_45_0, all_8_6) = 0 &
% 7.48/1.75 | | | | $i(all_45_0)
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | ALPHA: (33) implies:
% 7.48/1.75 | | | | (34) $i(all_45_0)
% 7.48/1.75 | | | | (35) member(all_45_0, all_8_6) = 0
% 7.48/1.75 | | | | (36) member(all_45_0, all_8_3) = 0
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | GROUND_INST: instantiating (28) with all_45_0, simplifying with (34),
% 7.48/1.75 | | | | (35) gives:
% 7.48/1.75 | | | | (37) ? [v0: int] : ( ~ (v0 = 0) & member(all_45_0, all_8_4) = v0)
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | GROUND_INST: instantiating (31) with all_45_0, simplifying with (34),
% 7.48/1.75 | | | | (35) gives:
% 7.48/1.75 | | | | (38) ? [v0: int] : ( ~ (v0 = 0) & member(all_45_0, all_8_5) = v0)
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | GROUND_INST: instantiating (1) with all_8_4, all_8_5, all_45_0, all_8_3,
% 7.48/1.75 | | | | simplifying with (8), (9), (17), (34), (36) gives:
% 7.48/1.75 | | | | (39) ? [v0: any] : ? [v1: any] : (member(all_45_0, all_8_4) = v0 &
% 7.48/1.75 | | | | member(all_45_0, all_8_5) = v1 & (v1 = 0 | v0 = 0))
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | GROUND_INST: instantiating (1) with all_8_5, all_8_4, all_45_0, all_8_3,
% 7.48/1.75 | | | | simplifying with (8), (9), (10), (34), (36) gives:
% 7.48/1.75 | | | | (40) ? [v0: any] : ? [v1: any] : (member(all_45_0, all_8_4) = v1 &
% 7.48/1.75 | | | | member(all_45_0, all_8_5) = v0 & (v1 = 0 | v0 = 0))
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | DELTA: instantiating (38) with fresh symbol all_52_0 gives:
% 7.48/1.75 | | | | (41) ~ (all_52_0 = 0) & member(all_45_0, all_8_5) = all_52_0
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | ALPHA: (41) implies:
% 7.48/1.75 | | | | (42) ~ (all_52_0 = 0)
% 7.48/1.75 | | | | (43) member(all_45_0, all_8_5) = all_52_0
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | DELTA: instantiating (37) with fresh symbol all_54_0 gives:
% 7.48/1.75 | | | | (44) ~ (all_54_0 = 0) & member(all_45_0, all_8_4) = all_54_0
% 7.48/1.75 | | | |
% 7.48/1.75 | | | | ALPHA: (44) implies:
% 7.48/1.75 | | | | (45) ~ (all_54_0 = 0)
% 7.48/1.76 | | | | (46) member(all_45_0, all_8_4) = all_54_0
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | DELTA: instantiating (40) with fresh symbols all_58_0, all_58_1 gives:
% 7.48/1.76 | | | | (47) member(all_45_0, all_8_4) = all_58_0 & member(all_45_0, all_8_5)
% 7.48/1.76 | | | | = all_58_1 & (all_58_0 = 0 | all_58_1 = 0)
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | ALPHA: (47) implies:
% 7.48/1.76 | | | | (48) member(all_45_0, all_8_5) = all_58_1
% 7.48/1.76 | | | | (49) member(all_45_0, all_8_4) = all_58_0
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | DELTA: instantiating (39) with fresh symbols all_60_0, all_60_1 gives:
% 7.48/1.76 | | | | (50) member(all_45_0, all_8_4) = all_60_1 & member(all_45_0, all_8_5)
% 7.48/1.76 | | | | = all_60_0 & (all_60_0 = 0 | all_60_1 = 0)
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | ALPHA: (50) implies:
% 7.48/1.76 | | | | (51) member(all_45_0, all_8_5) = all_60_0
% 7.48/1.76 | | | | (52) member(all_45_0, all_8_4) = all_60_1
% 7.48/1.76 | | | | (53) all_60_0 = 0 | all_60_1 = 0
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | GROUND_INST: instantiating (5) with all_58_1, all_60_0, all_8_5,
% 7.48/1.76 | | | | all_45_0, simplifying with (48), (51) gives:
% 7.48/1.76 | | | | (54) all_60_0 = all_58_1
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | GROUND_INST: instantiating (5) with all_52_0, all_60_0, all_8_5,
% 7.48/1.76 | | | | all_45_0, simplifying with (43), (51) gives:
% 7.48/1.76 | | | | (55) all_60_0 = all_52_0
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | GROUND_INST: instantiating (5) with all_58_0, all_60_1, all_8_4,
% 7.48/1.76 | | | | all_45_0, simplifying with (49), (52) gives:
% 7.48/1.76 | | | | (56) all_60_1 = all_58_0
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | GROUND_INST: instantiating (5) with all_54_0, all_60_1, all_8_4,
% 7.48/1.76 | | | | all_45_0, simplifying with (46), (52) gives:
% 7.48/1.76 | | | | (57) all_60_1 = all_54_0
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | COMBINE_EQS: (54), (55) imply:
% 7.48/1.76 | | | | (58) all_58_1 = all_52_0
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | COMBINE_EQS: (56), (57) imply:
% 7.48/1.76 | | | | (59) all_58_0 = all_54_0
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | BETA: splitting (53) gives:
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | Case 1:
% 7.48/1.76 | | | | |
% 7.48/1.76 | | | | | (60) all_60_0 = 0
% 7.48/1.76 | | | | |
% 7.48/1.76 | | | | | COMBINE_EQS: (55), (60) imply:
% 7.48/1.76 | | | | | (61) all_52_0 = 0
% 7.48/1.76 | | | | |
% 7.48/1.76 | | | | | REDUCE: (42), (61) imply:
% 7.48/1.76 | | | | | (62) $false
% 7.48/1.76 | | | | |
% 7.48/1.76 | | | | | CLOSE: (62) is inconsistent.
% 7.48/1.76 | | | | |
% 7.48/1.76 | | | | Case 2:
% 7.48/1.76 | | | | |
% 7.48/1.76 | | | | | (63) all_60_1 = 0
% 7.48/1.76 | | | | |
% 7.48/1.76 | | | | | COMBINE_EQS: (57), (63) imply:
% 7.48/1.76 | | | | | (64) all_54_0 = 0
% 7.48/1.76 | | | | |
% 7.48/1.76 | | | | | SIMP: (64) implies:
% 7.48/1.76 | | | | | (65) all_54_0 = 0
% 7.48/1.76 | | | | |
% 7.48/1.76 | | | | | REDUCE: (45), (65) imply:
% 7.48/1.76 | | | | | (66) $false
% 7.48/1.76 | | | | |
% 7.48/1.76 | | | | | CLOSE: (66) is inconsistent.
% 7.48/1.76 | | | | |
% 7.48/1.76 | | | | End of split
% 7.48/1.76 | | | |
% 7.48/1.76 | | | End of split
% 7.48/1.76 | | |
% 7.48/1.76 | | End of split
% 7.48/1.76 | |
% 7.48/1.76 | Case 2:
% 7.48/1.76 | |
% 7.48/1.76 | | (67) ~ (all_8_2 = 0) & (all_8_0 = 0 | all_8_1 = 0)
% 7.48/1.76 | |
% 7.48/1.76 | | ALPHA: (67) implies:
% 7.48/1.76 | | (68) ~ (all_8_2 = 0)
% 7.48/1.76 | | (69) all_8_0 = 0 | all_8_1 = 0
% 7.48/1.76 | |
% 7.48/1.76 | | BETA: splitting (20) gives:
% 7.48/1.76 | |
% 7.48/1.76 | | Case 1:
% 7.48/1.76 | | |
% 7.48/1.76 | | | (70) all_8_2 = 0
% 7.48/1.76 | | |
% 7.48/1.76 | | | REDUCE: (68), (70) imply:
% 7.48/1.76 | | | (71) $false
% 7.48/1.76 | | |
% 7.48/1.76 | | | CLOSE: (71) is inconsistent.
% 7.48/1.76 | | |
% 7.48/1.76 | | Case 2:
% 7.48/1.76 | | |
% 7.48/1.76 | | | (72) ! [v0: $i] : ( ~ (member(v0, all_8_6) = 0) | ~ $i(v0) | ? [v1:
% 7.48/1.76 | | | int] : ( ~ (v1 = 0) & member(v0, all_8_3) = v1))
% 7.48/1.76 | | |
% 7.48/1.76 | | | BETA: splitting (18) gives:
% 7.48/1.76 | | |
% 7.48/1.76 | | | Case 1:
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | (73) all_8_1 = 0
% 7.48/1.76 | | | |
% 7.48/1.76 | | | | REDUCE: (11), (73) imply:
% 7.48/1.77 | | | | (74) intersect(all_8_6, all_8_5) = 0
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | GROUND_INST: instantiating (3) with all_8_6, all_8_5, simplifying with
% 7.48/1.77 | | | | (7), (8), (74) gives:
% 7.48/1.77 | | | | (75) ? [v0: $i] : (member(v0, all_8_5) = 0 & member(v0, all_8_6) = 0
% 7.48/1.77 | | | | & $i(v0))
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | DELTA: instantiating (75) with fresh symbol all_48_0 gives:
% 7.48/1.77 | | | | (76) member(all_48_0, all_8_5) = 0 & member(all_48_0, all_8_6) = 0 &
% 7.48/1.77 | | | | $i(all_48_0)
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | ALPHA: (76) implies:
% 7.48/1.77 | | | | (77) $i(all_48_0)
% 7.48/1.77 | | | | (78) member(all_48_0, all_8_6) = 0
% 7.48/1.77 | | | | (79) member(all_48_0, all_8_5) = 0
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | GROUND_INST: instantiating (72) with all_48_0, simplifying with (77),
% 7.48/1.77 | | | | (78) gives:
% 7.48/1.77 | | | | (80) ? [v0: int] : ( ~ (v0 = 0) & member(all_48_0, all_8_3) = v0)
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | DELTA: instantiating (80) with fresh symbol all_55_0 gives:
% 7.48/1.77 | | | | (81) ~ (all_55_0 = 0) & member(all_48_0, all_8_3) = all_55_0
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | ALPHA: (81) implies:
% 7.48/1.77 | | | | (82) ~ (all_55_0 = 0)
% 7.48/1.77 | | | | (83) member(all_48_0, all_8_3) = all_55_0
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | GROUND_INST: instantiating (2) with all_8_5, all_8_4, all_48_0, all_8_3,
% 7.48/1.77 | | | | all_55_0, simplifying with (8), (9), (10), (77), (83)
% 7.48/1.77 | | | | gives:
% 7.48/1.77 | | | | (84) all_55_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 7.48/1.77 | | | | (v0 = 0) & member(all_48_0, all_8_4) = v1 & member(all_48_0,
% 7.48/1.77 | | | | all_8_5) = v0)
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | BETA: splitting (84) gives:
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | Case 1:
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | (85) all_55_0 = 0
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | REDUCE: (82), (85) imply:
% 7.48/1.77 | | | | | (86) $false
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | CLOSE: (86) is inconsistent.
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | Case 2:
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | (87) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 7.48/1.77 | | | | | member(all_48_0, all_8_4) = v1 & member(all_48_0, all_8_5) =
% 7.48/1.77 | | | | | v0)
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | DELTA: instantiating (87) with fresh symbols all_70_0, all_70_1 gives:
% 7.48/1.77 | | | | | (88) ~ (all_70_0 = 0) & ~ (all_70_1 = 0) & member(all_48_0,
% 7.48/1.77 | | | | | all_8_4) = all_70_0 & member(all_48_0, all_8_5) = all_70_1
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | ALPHA: (88) implies:
% 7.48/1.77 | | | | | (89) ~ (all_70_1 = 0)
% 7.48/1.77 | | | | | (90) member(all_48_0, all_8_5) = all_70_1
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | GROUND_INST: instantiating (5) with 0, all_70_1, all_8_5, all_48_0,
% 7.48/1.77 | | | | | simplifying with (79), (90) gives:
% 7.48/1.77 | | | | | (91) all_70_1 = 0
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | REDUCE: (89), (91) imply:
% 7.48/1.77 | | | | | (92) $false
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | CLOSE: (92) is inconsistent.
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | End of split
% 7.48/1.77 | | | |
% 7.48/1.77 | | | Case 2:
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | (93) ~ (all_8_1 = 0)
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | BETA: splitting (69) gives:
% 7.48/1.77 | | | |
% 7.48/1.77 | | | | Case 1:
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | (94) all_8_0 = 0
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | REDUCE: (12), (94) imply:
% 7.48/1.77 | | | | | (95) intersect(all_8_6, all_8_4) = 0
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | GROUND_INST: instantiating (3) with all_8_6, all_8_4, simplifying with
% 7.48/1.77 | | | | | (7), (9), (95) gives:
% 7.48/1.77 | | | | | (96) ? [v0: $i] : (member(v0, all_8_4) = 0 & member(v0, all_8_6) =
% 7.48/1.77 | | | | | 0 & $i(v0))
% 7.48/1.77 | | | | |
% 7.48/1.77 | | | | | DELTA: instantiating (96) with fresh symbol all_53_0 gives:
% 7.48/1.78 | | | | | (97) member(all_53_0, all_8_4) = 0 & member(all_53_0, all_8_6) = 0
% 7.48/1.78 | | | | | & $i(all_53_0)
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | | ALPHA: (97) implies:
% 7.48/1.78 | | | | | (98) $i(all_53_0)
% 7.48/1.78 | | | | | (99) member(all_53_0, all_8_6) = 0
% 7.48/1.78 | | | | | (100) member(all_53_0, all_8_4) = 0
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | | GROUND_INST: instantiating (72) with all_53_0, simplifying with (98),
% 7.48/1.78 | | | | | (99) gives:
% 7.48/1.78 | | | | | (101) ? [v0: int] : ( ~ (v0 = 0) & member(all_53_0, all_8_3) = v0)
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | | DELTA: instantiating (101) with fresh symbol all_62_0 gives:
% 7.48/1.78 | | | | | (102) ~ (all_62_0 = 0) & member(all_53_0, all_8_3) = all_62_0
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | | ALPHA: (102) implies:
% 7.48/1.78 | | | | | (103) ~ (all_62_0 = 0)
% 7.48/1.78 | | | | | (104) member(all_53_0, all_8_3) = all_62_0
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | | GROUND_INST: instantiating (2) with all_8_4, all_8_5, all_53_0,
% 7.48/1.78 | | | | | all_8_3, all_62_0, simplifying with (8), (9), (17), (98),
% 7.48/1.78 | | | | | (104) gives:
% 7.48/1.78 | | | | | (105) all_62_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) &
% 7.48/1.78 | | | | | ~ (v0 = 0) & member(all_53_0, all_8_4) = v0 &
% 7.48/1.78 | | | | | member(all_53_0, all_8_5) = v1)
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | | BETA: splitting (105) gives:
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | | Case 1:
% 7.48/1.78 | | | | | |
% 7.48/1.78 | | | | | | (106) all_62_0 = 0
% 7.48/1.78 | | | | | |
% 7.48/1.78 | | | | | | REDUCE: (103), (106) imply:
% 7.48/1.78 | | | | | | (107) $false
% 7.48/1.78 | | | | | |
% 7.48/1.78 | | | | | | CLOSE: (107) is inconsistent.
% 7.48/1.78 | | | | | |
% 7.48/1.78 | | | | | Case 2:
% 7.48/1.78 | | | | | |
% 7.48/1.78 | | | | | | (108) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 7.48/1.78 | | | | | | member(all_53_0, all_8_4) = v0 & member(all_53_0,
% 7.48/1.78 | | | | | | all_8_5) = v1)
% 7.48/1.78 | | | | | |
% 7.48/1.78 | | | | | | DELTA: instantiating (108) with fresh symbols all_79_0, all_79_1
% 7.48/1.78 | | | | | | gives:
% 7.48/1.78 | | | | | | (109) ~ (all_79_0 = 0) & ~ (all_79_1 = 0) & member(all_53_0,
% 7.48/1.78 | | | | | | all_8_4) = all_79_1 & member(all_53_0, all_8_5) =
% 7.48/1.78 | | | | | | all_79_0
% 7.48/1.78 | | | | | |
% 7.48/1.78 | | | | | | ALPHA: (109) implies:
% 7.48/1.78 | | | | | | (110) ~ (all_79_1 = 0)
% 7.48/1.78 | | | | | | (111) member(all_53_0, all_8_4) = all_79_1
% 7.48/1.78 | | | | | |
% 7.48/1.78 | | | | | | GROUND_INST: instantiating (5) with 0, all_79_1, all_8_4, all_53_0,
% 7.48/1.78 | | | | | | simplifying with (100), (111) gives:
% 7.48/1.78 | | | | | | (112) all_79_1 = 0
% 7.48/1.78 | | | | | |
% 7.48/1.78 | | | | | | REDUCE: (110), (112) imply:
% 7.48/1.78 | | | | | | (113) $false
% 7.48/1.78 | | | | | |
% 7.48/1.78 | | | | | | CLOSE: (113) is inconsistent.
% 7.48/1.78 | | | | | |
% 7.48/1.78 | | | | | End of split
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | Case 2:
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | | (114) all_8_1 = 0
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | | REDUCE: (93), (114) imply:
% 7.48/1.78 | | | | | (115) $false
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | | CLOSE: (115) is inconsistent.
% 7.48/1.78 | | | | |
% 7.48/1.78 | | | | End of split
% 7.48/1.78 | | | |
% 7.48/1.78 | | | End of split
% 7.48/1.78 | | |
% 7.48/1.78 | | End of split
% 7.48/1.78 | |
% 7.48/1.78 | End of split
% 7.48/1.78 |
% 7.48/1.78 End of proof
% 7.48/1.78 % SZS output end Proof for theBenchmark
% 7.48/1.78
% 7.48/1.78 1173ms
%------------------------------------------------------------------------------