TSTP Solution File: SET703+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET703+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n009.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 15:26:03 EDT 2023
% Result : Theorem 8.04s 1.79s
% Output : Proof 8.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET703+4 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 15:37:50 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.54/0.59 ________ _____
% 0.54/0.59 ___ __ \_________(_)________________________________
% 0.54/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.54/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.54/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.54/0.59
% 0.54/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.54/0.59 (2023-06-19)
% 0.54/0.59
% 0.54/0.59 (c) Philipp Rümmer, 2009-2023
% 0.54/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.54/0.59 Amanda Stjerna.
% 0.54/0.59 Free software under BSD-3-Clause.
% 0.54/0.59
% 0.54/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.54/0.59
% 0.54/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.54/0.60 Running up to 7 provers in parallel.
% 0.54/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.54/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.54/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.54/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.54/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.54/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.54/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.58/1.05 Prover 4: Preprocessing ...
% 2.58/1.05 Prover 1: Preprocessing ...
% 2.88/1.09 Prover 5: Preprocessing ...
% 2.88/1.09 Prover 0: Preprocessing ...
% 2.88/1.09 Prover 2: Preprocessing ...
% 2.88/1.09 Prover 3: Preprocessing ...
% 2.88/1.09 Prover 6: Preprocessing ...
% 4.92/1.43 Prover 6: Proving ...
% 4.92/1.44 Prover 1: Constructing countermodel ...
% 5.55/1.45 Prover 3: Constructing countermodel ...
% 5.55/1.45 Prover 5: Proving ...
% 5.79/1.48 Prover 2: Proving ...
% 5.79/1.49 Prover 4: Constructing countermodel ...
% 5.79/1.51 Prover 0: Proving ...
% 7.91/1.77 Prover 1: Found proof (size 63)
% 7.91/1.77 Prover 1: proved (1157ms)
% 7.91/1.77 Prover 4: stopped
% 7.91/1.77 Prover 3: stopped
% 7.91/1.77 Prover 5: stopped
% 7.91/1.77 Prover 0: stopped
% 7.91/1.77 Prover 2: stopped
% 8.04/1.79 Prover 6: proved (1172ms)
% 8.04/1.79
% 8.04/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.04/1.79
% 8.04/1.80 % SZS output start Proof for theBenchmark
% 8.04/1.80 Assumptions after simplification:
% 8.04/1.80 ---------------------------------
% 8.04/1.80
% 8.04/1.80 (equal_set)
% 8.22/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 8.22/1.83 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 8.22/1.83 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 8.22/1.83 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.22/1.83 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 8.22/1.83
% 8.22/1.83 (singleton)
% 8.22/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) |
% 8.22/1.83 ~ (member(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 8.22/1.83 $i] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0) | ~
% 8.22/1.83 $i(v1) | ~ $i(v0))
% 8.22/1.83
% 8.22/1.83 (subset)
% 8.30/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 8.30/1.84 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 8.30/1.84 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 8.30/1.84 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 8.30/1.84 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 8.30/1.84
% 8.30/1.84 (thI41)
% 8.30/1.84 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.30/1.84 $i] : ? [v6: int] : ( ~ (v6 = 0) & unordered_pair(v0, v1) = v5 &
% 8.30/1.84 singleton(v1) = v3 & singleton(v0) = v2 & union(v2, v3) = v4 & equal_set(v4,
% 8.30/1.84 v5) = v6 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.30/1.84
% 8.30/1.84 (union)
% 8.30/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 8.30/1.84 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 8.30/1.84 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 8.30/1.84 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 8.30/1.84 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0)
% 8.30/1.84 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 8.30/1.84 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 8.30/1.84
% 8.30/1.84 (unordered_pair)
% 8.30/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 8.30/1.84 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) |
% 8.30/1.85 ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0))) & ! [v0: $i] : !
% 8.30/1.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = v0 | ~
% 8.30/1.85 (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~
% 8.30/1.85 $i(v1) | ~ $i(v0))
% 8.30/1.85
% 8.30/1.85 Further assumptions not needed in the proof:
% 8.30/1.85 --------------------------------------------
% 8.30/1.85 difference, empty_set, intersection, power_set, product, sum
% 8.30/1.85
% 8.30/1.85 Those formulas are unsatisfiable:
% 8.30/1.85 ---------------------------------
% 8.30/1.85
% 8.30/1.85 Begin of proof
% 8.30/1.85 |
% 8.30/1.85 | ALPHA: (subset) implies:
% 8.30/1.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.30/1.85 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.30/1.85 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 8.30/1.85 |
% 8.30/1.85 | ALPHA: (equal_set) implies:
% 8.30/1.85 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 8.30/1.85 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 8.30/1.85 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 8.30/1.85 | 0))))
% 8.30/1.85 |
% 8.30/1.85 | ALPHA: (union) implies:
% 8.30/1.85 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1,
% 8.30/1.85 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 8.30/1.85 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 &
% 8.30/1.85 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 8.30/1.85 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 8.30/1.85 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~
% 8.30/1.85 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 8.30/1.86 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) =
% 8.30/1.86 | v5))
% 8.30/1.86 |
% 8.30/1.86 | ALPHA: (singleton) implies:
% 8.30/1.86 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1)
% 8.30/1.86 | = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0))
% 8.30/1.86 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0)
% 8.30/1.86 | = v1) | ~ (member(v0, v1) = v2) | ~ $i(v0))
% 8.30/1.86 |
% 8.30/1.86 | ALPHA: (unordered_pair) implies:
% 8.30/1.86 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 =
% 8.30/1.86 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~
% 8.30/1.86 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 8.30/1.86 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 8.30/1.86 | (v4 = 0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) |
% 8.30/1.86 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0)))
% 8.30/1.86 |
% 8.30/1.86 | DELTA: instantiating (thI41) with fresh symbols all_15_0, all_15_1, all_15_2,
% 8.30/1.86 | all_15_3, all_15_4, all_15_5, all_15_6 gives:
% 8.30/1.86 | (9) ~ (all_15_0 = 0) & unordered_pair(all_15_6, all_15_5) = all_15_1 &
% 8.30/1.86 | singleton(all_15_5) = all_15_3 & singleton(all_15_6) = all_15_4 &
% 8.30/1.86 | union(all_15_4, all_15_3) = all_15_2 & equal_set(all_15_2, all_15_1) =
% 8.30/1.86 | all_15_0 & $i(all_15_1) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) &
% 8.30/1.86 | $i(all_15_5) & $i(all_15_6)
% 8.30/1.86 |
% 8.30/1.86 | ALPHA: (9) implies:
% 8.30/1.86 | (10) ~ (all_15_0 = 0)
% 8.30/1.86 | (11) $i(all_15_6)
% 8.30/1.86 | (12) $i(all_15_5)
% 8.30/1.86 | (13) $i(all_15_4)
% 8.30/1.86 | (14) $i(all_15_3)
% 8.30/1.86 | (15) $i(all_15_2)
% 8.30/1.86 | (16) $i(all_15_1)
% 8.30/1.86 | (17) equal_set(all_15_2, all_15_1) = all_15_0
% 8.30/1.86 | (18) union(all_15_4, all_15_3) = all_15_2
% 8.30/1.86 | (19) singleton(all_15_6) = all_15_4
% 8.30/1.86 | (20) singleton(all_15_5) = all_15_3
% 8.30/1.86 | (21) unordered_pair(all_15_6, all_15_5) = all_15_1
% 8.30/1.86 |
% 8.30/1.86 | GROUND_INST: instantiating (2) with all_15_2, all_15_1, all_15_0, simplifying
% 8.30/1.86 | with (15), (16), (17) gives:
% 8.30/1.87 | (22) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1,
% 8.30/1.87 | all_15_2) = v1 & subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) |
% 8.30/1.87 | ~ (v0 = 0)))
% 8.30/1.87 |
% 8.30/1.87 | BETA: splitting (22) gives:
% 8.30/1.87 |
% 8.30/1.87 | Case 1:
% 8.30/1.87 | |
% 8.30/1.87 | | (23) all_15_0 = 0
% 8.30/1.87 | |
% 8.30/1.87 | | REDUCE: (10), (23) imply:
% 8.30/1.87 | | (24) $false
% 8.30/1.87 | |
% 8.30/1.87 | | CLOSE: (24) is inconsistent.
% 8.30/1.87 | |
% 8.30/1.87 | Case 2:
% 8.30/1.87 | |
% 8.30/1.87 | | (25) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_2) = v1 &
% 8.30/1.87 | | subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.30/1.87 | |
% 8.30/1.87 | | DELTA: instantiating (25) with fresh symbols all_24_0, all_24_1 gives:
% 8.30/1.87 | | (26) subset(all_15_1, all_15_2) = all_24_0 & subset(all_15_2, all_15_1) =
% 8.30/1.87 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0))
% 8.30/1.87 | |
% 8.30/1.87 | | ALPHA: (26) implies:
% 8.30/1.87 | | (27) subset(all_15_2, all_15_1) = all_24_1
% 8.30/1.87 | | (28) subset(all_15_1, all_15_2) = all_24_0
% 8.30/1.87 | | (29) ~ (all_24_0 = 0) | ~ (all_24_1 = 0)
% 8.30/1.87 | |
% 8.30/1.87 | | GROUND_INST: instantiating (1) with all_15_2, all_15_1, all_24_1,
% 8.30/1.87 | | simplifying with (15), (16), (27) gives:
% 8.30/1.87 | | (30) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.30/1.87 | | member(v0, all_15_1) = v1 & member(v0, all_15_2) = 0 & $i(v0))
% 8.30/1.87 | |
% 8.30/1.87 | | GROUND_INST: instantiating (1) with all_15_1, all_15_2, all_24_0,
% 8.30/1.87 | | simplifying with (15), (16), (28) gives:
% 8.30/1.87 | | (31) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.30/1.87 | | member(v0, all_15_1) = 0 & member(v0, all_15_2) = v1 & $i(v0))
% 8.30/1.87 | |
% 8.30/1.87 | | BETA: splitting (29) gives:
% 8.30/1.87 | |
% 8.30/1.87 | | Case 1:
% 8.30/1.87 | | |
% 8.30/1.87 | | | (32) ~ (all_24_0 = 0)
% 8.30/1.87 | | |
% 8.30/1.87 | | | BETA: splitting (31) gives:
% 8.30/1.87 | | |
% 8.30/1.87 | | | Case 1:
% 8.30/1.87 | | | |
% 8.30/1.87 | | | | (33) all_24_0 = 0
% 8.30/1.87 | | | |
% 8.30/1.87 | | | | REDUCE: (32), (33) imply:
% 8.30/1.87 | | | | (34) $false
% 8.30/1.87 | | | |
% 8.30/1.87 | | | | CLOSE: (34) is inconsistent.
% 8.30/1.87 | | | |
% 8.30/1.87 | | | Case 2:
% 8.30/1.87 | | | |
% 8.30/1.87 | | | | (35) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 8.30/1.87 | | | | = 0 & member(v0, all_15_2) = v1 & $i(v0))
% 8.30/1.87 | | | |
% 8.30/1.87 | | | | DELTA: instantiating (35) with fresh symbols all_37_0, all_37_1 gives:
% 8.30/1.87 | | | | (36) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 &
% 8.30/1.87 | | | | member(all_37_1, all_15_2) = all_37_0 & $i(all_37_1)
% 8.30/1.87 | | | |
% 8.30/1.87 | | | | ALPHA: (36) implies:
% 8.30/1.87 | | | | (37) ~ (all_37_0 = 0)
% 8.30/1.87 | | | | (38) $i(all_37_1)
% 8.30/1.87 | | | | (39) member(all_37_1, all_15_2) = all_37_0
% 8.30/1.87 | | | | (40) member(all_37_1, all_15_1) = 0
% 8.30/1.87 | | | |
% 8.30/1.87 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_4, all_15_3,
% 8.30/1.87 | | | | all_15_2, all_37_0, simplifying with (13), (14), (18),
% 8.30/1.87 | | | | (38), (39) gives:
% 8.30/1.87 | | | | (41) all_37_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 8.30/1.87 | | | | (v0 = 0) & member(all_37_1, all_15_3) = v1 & member(all_37_1,
% 8.30/1.87 | | | | all_15_4) = v0)
% 8.30/1.87 | | | |
% 8.30/1.88 | | | | GROUND_INST: instantiating (7) with all_37_1, all_15_6, all_15_5,
% 8.30/1.88 | | | | all_15_1, simplifying with (11), (12), (21), (38), (40)
% 8.30/1.88 | | | | gives:
% 8.30/1.88 | | | | (42) all_37_1 = all_15_5 | all_37_1 = all_15_6
% 8.30/1.88 | | | |
% 8.30/1.88 | | | | BETA: splitting (41) gives:
% 8.30/1.88 | | | |
% 8.30/1.88 | | | | Case 1:
% 8.30/1.88 | | | | |
% 8.30/1.88 | | | | | (43) all_37_0 = 0
% 8.30/1.88 | | | | |
% 8.30/1.88 | | | | | REDUCE: (37), (43) imply:
% 8.30/1.88 | | | | | (44) $false
% 8.30/1.88 | | | | |
% 8.30/1.88 | | | | | CLOSE: (44) is inconsistent.
% 8.30/1.88 | | | | |
% 8.30/1.88 | | | | Case 2:
% 8.30/1.88 | | | | |
% 8.30/1.88 | | | | | (45) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 8.30/1.88 | | | | | member(all_37_1, all_15_3) = v1 & member(all_37_1, all_15_4)
% 8.30/1.88 | | | | | = v0)
% 8.30/1.88 | | | | |
% 8.30/1.88 | | | | | DELTA: instantiating (45) with fresh symbols all_52_0, all_52_1 gives:
% 8.30/1.88 | | | | | (46) ~ (all_52_0 = 0) & ~ (all_52_1 = 0) & member(all_37_1,
% 8.30/1.88 | | | | | all_15_3) = all_52_0 & member(all_37_1, all_15_4) = all_52_1
% 8.30/1.88 | | | | |
% 8.30/1.88 | | | | | ALPHA: (46) implies:
% 8.30/1.88 | | | | | (47) ~ (all_52_1 = 0)
% 8.30/1.88 | | | | | (48) ~ (all_52_0 = 0)
% 8.30/1.88 | | | | | (49) member(all_37_1, all_15_4) = all_52_1
% 8.30/1.88 | | | | | (50) member(all_37_1, all_15_3) = all_52_0
% 8.30/1.88 | | | | |
% 8.30/1.88 | | | | | BETA: splitting (42) gives:
% 8.30/1.88 | | | | |
% 8.30/1.88 | | | | | Case 1:
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | | (51) all_37_1 = all_15_5
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | | REDUCE: (50), (51) imply:
% 8.30/1.88 | | | | | | (52) member(all_15_5, all_15_3) = all_52_0
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | | GROUND_INST: instantiating (6) with all_15_5, all_15_3, all_52_0,
% 8.30/1.88 | | | | | | simplifying with (12), (20), (52) gives:
% 8.30/1.88 | | | | | | (53) all_52_0 = 0
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | | REDUCE: (48), (53) imply:
% 8.30/1.88 | | | | | | (54) $false
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | | CLOSE: (54) is inconsistent.
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | Case 2:
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | | (55) all_37_1 = all_15_6
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | | REDUCE: (49), (55) imply:
% 8.30/1.88 | | | | | | (56) member(all_15_6, all_15_4) = all_52_1
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | | GROUND_INST: instantiating (6) with all_15_6, all_15_4, all_52_1,
% 8.30/1.88 | | | | | | simplifying with (11), (19), (56) gives:
% 8.30/1.88 | | | | | | (57) all_52_1 = 0
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | | REDUCE: (47), (57) imply:
% 8.30/1.88 | | | | | | (58) $false
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | | CLOSE: (58) is inconsistent.
% 8.30/1.88 | | | | | |
% 8.30/1.88 | | | | | End of split
% 8.30/1.88 | | | | |
% 8.30/1.88 | | | | End of split
% 8.30/1.88 | | | |
% 8.30/1.88 | | | End of split
% 8.30/1.88 | | |
% 8.30/1.88 | | Case 2:
% 8.30/1.88 | | |
% 8.30/1.88 | | | (59) ~ (all_24_1 = 0)
% 8.30/1.88 | | |
% 8.30/1.88 | | | BETA: splitting (30) gives:
% 8.30/1.88 | | |
% 8.30/1.88 | | | Case 1:
% 8.30/1.88 | | | |
% 8.30/1.88 | | | | (60) all_24_1 = 0
% 8.30/1.88 | | | |
% 8.30/1.88 | | | | REDUCE: (59), (60) imply:
% 8.30/1.88 | | | | (61) $false
% 8.30/1.88 | | | |
% 8.30/1.88 | | | | CLOSE: (61) is inconsistent.
% 8.30/1.88 | | | |
% 8.30/1.88 | | | Case 2:
% 8.30/1.88 | | | |
% 8.30/1.88 | | | | (62) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 8.30/1.88 | | | | = v1 & member(v0, all_15_2) = 0 & $i(v0))
% 8.30/1.88 | | | |
% 8.30/1.88 | | | | DELTA: instantiating (62) with fresh symbols all_37_0, all_37_1 gives:
% 8.30/1.88 | | | | (63) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 &
% 8.30/1.88 | | | | member(all_37_1, all_15_2) = 0 & $i(all_37_1)
% 8.30/1.88 | | | |
% 8.30/1.88 | | | | ALPHA: (63) implies:
% 8.30/1.88 | | | | (64) ~ (all_37_0 = 0)
% 8.30/1.88 | | | | (65) $i(all_37_1)
% 8.30/1.88 | | | | (66) member(all_37_1, all_15_2) = 0
% 8.30/1.88 | | | | (67) member(all_37_1, all_15_1) = all_37_0
% 8.30/1.88 | | | |
% 8.30/1.88 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_4, all_15_3,
% 8.30/1.88 | | | | all_15_2, simplifying with (13), (14), (18), (65), (66)
% 8.30/1.88 | | | | gives:
% 8.30/1.89 | | | | (68) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_3) = v1 &
% 8.30/1.89 | | | | member(all_37_1, all_15_4) = v0 & (v1 = 0 | v0 = 0))
% 8.30/1.89 | | | |
% 8.30/1.89 | | | | GROUND_INST: instantiating (8) with all_37_1, all_15_6, all_15_5,
% 8.30/1.89 | | | | all_15_1, all_37_0, simplifying with (11), (12), (21),
% 8.30/1.89 | | | | (65), (67) gives:
% 8.30/1.89 | | | | (69) all_37_0 = 0 | ( ~ (all_37_1 = all_15_5) & ~ (all_37_1 =
% 8.30/1.89 | | | | all_15_6))
% 8.30/1.89 | | | |
% 8.30/1.89 | | | | DELTA: instantiating (68) with fresh symbols all_45_0, all_45_1 gives:
% 8.30/1.89 | | | | (70) member(all_37_1, all_15_3) = all_45_0 & member(all_37_1,
% 8.30/1.89 | | | | all_15_4) = all_45_1 & (all_45_0 = 0 | all_45_1 = 0)
% 8.30/1.89 | | | |
% 8.30/1.89 | | | | ALPHA: (70) implies:
% 8.30/1.89 | | | | (71) member(all_37_1, all_15_4) = all_45_1
% 8.30/1.89 | | | | (72) member(all_37_1, all_15_3) = all_45_0
% 8.30/1.89 | | | | (73) all_45_0 = 0 | all_45_1 = 0
% 8.30/1.89 | | | |
% 8.30/1.89 | | | | BETA: splitting (69) gives:
% 8.30/1.89 | | | |
% 8.30/1.89 | | | | Case 1:
% 8.30/1.89 | | | | |
% 8.30/1.89 | | | | | (74) all_37_0 = 0
% 8.30/1.89 | | | | |
% 8.30/1.89 | | | | | REDUCE: (64), (74) imply:
% 8.30/1.89 | | | | | (75) $false
% 8.30/1.89 | | | | |
% 8.30/1.89 | | | | | CLOSE: (75) is inconsistent.
% 8.30/1.89 | | | | |
% 8.30/1.89 | | | | Case 2:
% 8.30/1.89 | | | | |
% 8.30/1.89 | | | | | (76) ~ (all_37_1 = all_15_5) & ~ (all_37_1 = all_15_6)
% 8.30/1.89 | | | | |
% 8.30/1.89 | | | | | ALPHA: (76) implies:
% 8.30/1.89 | | | | | (77) ~ (all_37_1 = all_15_6)
% 8.30/1.89 | | | | | (78) ~ (all_37_1 = all_15_5)
% 8.30/1.89 | | | | |
% 8.30/1.89 | | | | | BETA: splitting (73) gives:
% 8.30/1.89 | | | | |
% 8.30/1.89 | | | | | Case 1:
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | | (79) all_45_0 = 0
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | | REDUCE: (72), (79) imply:
% 8.30/1.89 | | | | | | (80) member(all_37_1, all_15_3) = 0
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_5, all_15_3,
% 8.30/1.89 | | | | | | simplifying with (12), (20), (65), (80) gives:
% 8.30/1.89 | | | | | | (81) all_37_1 = all_15_5
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | | REDUCE: (78), (81) imply:
% 8.30/1.89 | | | | | | (82) $false
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | | CLOSE: (82) is inconsistent.
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | Case 2:
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | | (83) all_45_1 = 0
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | | REDUCE: (71), (83) imply:
% 8.30/1.89 | | | | | | (84) member(all_37_1, all_15_4) = 0
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_6, all_15_4,
% 8.30/1.89 | | | | | | simplifying with (11), (19), (65), (84) gives:
% 8.30/1.89 | | | | | | (85) all_37_1 = all_15_6
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | | REDUCE: (77), (85) imply:
% 8.30/1.89 | | | | | | (86) $false
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | | CLOSE: (86) is inconsistent.
% 8.30/1.89 | | | | | |
% 8.30/1.89 | | | | | End of split
% 8.30/1.89 | | | | |
% 8.30/1.89 | | | | End of split
% 8.30/1.89 | | | |
% 8.30/1.89 | | | End of split
% 8.30/1.89 | | |
% 8.30/1.89 | | End of split
% 8.30/1.89 | |
% 8.30/1.89 | End of split
% 8.30/1.89 |
% 8.30/1.89 End of proof
% 8.30/1.89 % SZS output end Proof for theBenchmark
% 8.30/1.89
% 8.30/1.89 1300ms
%------------------------------------------------------------------------------