TSTP Solution File: SET762+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET762+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 15:26:20 EDT 2023
% Result : Theorem 11.12s 2.20s
% Output : Proof 13.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET762+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n009.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 10:54:50 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.53/0.62 ________ _____
% 0.53/0.62 ___ __ \_________(_)________________________________
% 0.53/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.53/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.53/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.53/0.62
% 0.53/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.53/0.62 (2023-06-19)
% 0.53/0.62
% 0.53/0.62 (c) Philipp Rümmer, 2009-2023
% 0.53/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.53/0.62 Amanda Stjerna.
% 0.53/0.62 Free software under BSD-3-Clause.
% 0.53/0.62
% 0.53/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.53/0.62
% 0.53/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.64 Running up to 7 provers in parallel.
% 0.69/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.69/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.53/1.17 Prover 4: Preprocessing ...
% 3.53/1.17 Prover 1: Preprocessing ...
% 3.78/1.21 Prover 6: Preprocessing ...
% 3.78/1.21 Prover 2: Preprocessing ...
% 3.78/1.21 Prover 3: Preprocessing ...
% 3.78/1.21 Prover 0: Preprocessing ...
% 3.78/1.21 Prover 5: Preprocessing ...
% 8.75/1.86 Prover 5: Proving ...
% 8.75/1.88 Prover 2: Proving ...
% 9.32/1.93 Prover 6: Proving ...
% 9.79/2.03 Prover 1: Constructing countermodel ...
% 9.79/2.04 Prover 3: Constructing countermodel ...
% 11.12/2.19 Prover 3: proved (1549ms)
% 11.12/2.20
% 11.12/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.12/2.20
% 11.12/2.20 Prover 2: stopped
% 11.12/2.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.12/2.21 Prover 6: stopped
% 11.12/2.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.12/2.21 Prover 5: stopped
% 11.12/2.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.70/2.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.70/2.25 Prover 7: Preprocessing ...
% 11.70/2.27 Prover 8: Preprocessing ...
% 11.70/2.28 Prover 10: Preprocessing ...
% 12.15/2.29 Prover 11: Preprocessing ...
% 12.15/2.32 Prover 1: Found proof (size 33)
% 12.15/2.32 Prover 1: proved (1674ms)
% 12.15/2.32 Prover 7: stopped
% 12.15/2.32 Prover 10: stopped
% 12.83/2.39 Prover 4: Constructing countermodel ...
% 12.83/2.40 Prover 11: stopped
% 12.83/2.41 Prover 0: Proving ...
% 12.83/2.41 Prover 0: stopped
% 13.14/2.42 Prover 4: stopped
% 13.26/2.50 Prover 8: Warning: ignoring some quantifiers
% 13.26/2.52 Prover 8: Constructing countermodel ...
% 13.68/2.52 Prover 8: stopped
% 13.68/2.52
% 13.68/2.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.68/2.52
% 13.68/2.53 % SZS output start Proof for theBenchmark
% 13.68/2.53 Assumptions after simplification:
% 13.68/2.53 ---------------------------------
% 13.68/2.53
% 13.68/2.53 (empty_set)
% 13.68/2.56 $i(empty_set) & ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 13.68/2.56
% 13.68/2.56 (equal_set)
% 13.68/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 13.68/2.56 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 13.68/2.56 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 13.68/2.56 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 13.68/2.56 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 13.68/2.56
% 13.68/2.56 (image2)
% 13.68/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 13.68/2.56 | ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~
% 13.68/2.56 $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v5, v2) = 0) | ~ $i(v5) |
% 13.68/2.56 ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))) & ! [v0: $i] : !
% 13.68/2.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (image2(v0, v1) = v3) | ~
% 13.68/2.56 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 13.68/2.56 (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & $i(v4)))
% 13.68/2.56
% 13.68/2.56 (subset)
% 13.68/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 13.68/2.57 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 13.68/2.57 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 13.68/2.57 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 13.68/2.57 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 13.68/2.57
% 13.68/2.57 (thIIa12)
% 13.68/2.57 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 13.68/2.57 [v4: int] : ( ~ (v4 = 0) & image2(v0, empty_set) = v3 & maps(v0, v1, v2) = 0 &
% 13.68/2.57 equal_set(v3, empty_set) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.68/2.57
% 13.68/2.57 Further assumptions not needed in the proof:
% 13.68/2.57 --------------------------------------------
% 13.68/2.57 compose_function, compose_predicate, decreasing_function, difference,
% 13.68/2.57 equal_maps, identity, image3, increasing_function, injective, intersection,
% 13.68/2.57 inverse_function, inverse_image2, inverse_image3, inverse_predicate,
% 13.68/2.57 isomorphism, maps, one_to_one, power_set, product, singleton, sum, surjective,
% 13.68/2.57 union, unordered_pair
% 13.68/2.57
% 13.68/2.57 Those formulas are unsatisfiable:
% 13.68/2.57 ---------------------------------
% 13.68/2.57
% 13.68/2.57 Begin of proof
% 13.68/2.57 |
% 13.68/2.57 | ALPHA: (subset) implies:
% 13.68/2.57 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 13.68/2.57 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 13.68/2.57 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 13.68/2.57 |
% 13.68/2.57 | ALPHA: (equal_set) implies:
% 13.68/2.57 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 13.68/2.57 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 13.68/2.57 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 13.68/2.57 | 0))))
% 13.68/2.57 |
% 13.68/2.57 | ALPHA: (empty_set) implies:
% 13.68/2.58 | (3) ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 13.68/2.58 |
% 13.68/2.58 | ALPHA: (image2) implies:
% 13.68/2.58 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (image2(v0,
% 13.68/2.58 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 13.68/2.58 | $i(v0) | ? [v4: $i] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 &
% 13.68/2.58 | $i(v4)))
% 13.68/2.58 |
% 13.68/2.58 | ALPHA: (thIIa12) implies:
% 13.68/2.58 | (5) $i(empty_set)
% 13.68/2.58 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] :
% 13.68/2.58 | ( ~ (v4 = 0) & image2(v0, empty_set) = v3 & maps(v0, v1, v2) = 0 &
% 13.68/2.58 | equal_set(v3, empty_set) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.68/2.58 |
% 13.68/2.58 | DELTA: instantiating (6) with fresh symbols all_32_0, all_32_1, all_32_2,
% 13.68/2.58 | all_32_3, all_32_4 gives:
% 13.68/2.58 | (7) ~ (all_32_0 = 0) & image2(all_32_4, empty_set) = all_32_1 &
% 13.68/2.58 | maps(all_32_4, all_32_3, all_32_2) = 0 & equal_set(all_32_1, empty_set)
% 13.68/2.58 | = all_32_0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & $i(all_32_4)
% 13.68/2.58 |
% 13.68/2.58 | ALPHA: (7) implies:
% 13.68/2.58 | (8) ~ (all_32_0 = 0)
% 13.68/2.58 | (9) $i(all_32_4)
% 13.68/2.58 | (10) $i(all_32_1)
% 13.98/2.58 | (11) equal_set(all_32_1, empty_set) = all_32_0
% 13.98/2.58 | (12) image2(all_32_4, empty_set) = all_32_1
% 13.98/2.58 |
% 13.98/2.58 | GROUND_INST: instantiating (2) with all_32_1, empty_set, all_32_0, simplifying
% 13.98/2.58 | with (5), (10), (11) gives:
% 13.98/2.58 | (13) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_32_1,
% 13.98/2.58 | empty_set) = v0 & subset(empty_set, all_32_1) = v1 & ( ~ (v1 = 0)
% 13.98/2.58 | | ~ (v0 = 0)))
% 13.98/2.58 |
% 13.98/2.58 | BETA: splitting (13) gives:
% 13.98/2.58 |
% 13.98/2.58 | Case 1:
% 13.98/2.58 | |
% 13.98/2.58 | | (14) all_32_0 = 0
% 13.98/2.58 | |
% 13.98/2.58 | | REDUCE: (8), (14) imply:
% 13.98/2.58 | | (15) $false
% 13.98/2.58 | |
% 13.98/2.58 | | CLOSE: (15) is inconsistent.
% 13.98/2.58 | |
% 13.98/2.58 | Case 2:
% 13.98/2.58 | |
% 13.98/2.58 | | (16) ? [v0: any] : ? [v1: any] : (subset(all_32_1, empty_set) = v0 &
% 13.98/2.58 | | subset(empty_set, all_32_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.98/2.58 | |
% 13.98/2.58 | | DELTA: instantiating (16) with fresh symbols all_44_0, all_44_1 gives:
% 13.98/2.59 | | (17) subset(all_32_1, empty_set) = all_44_1 & subset(empty_set, all_32_1)
% 13.98/2.59 | | = all_44_0 & ( ~ (all_44_0 = 0) | ~ (all_44_1 = 0))
% 13.98/2.59 | |
% 13.98/2.59 | | ALPHA: (17) implies:
% 13.98/2.59 | | (18) subset(empty_set, all_32_1) = all_44_0
% 13.98/2.59 | | (19) subset(all_32_1, empty_set) = all_44_1
% 13.98/2.59 | | (20) ~ (all_44_0 = 0) | ~ (all_44_1 = 0)
% 13.98/2.59 | |
% 13.98/2.59 | | GROUND_INST: instantiating (1) with empty_set, all_32_1, all_44_0,
% 13.98/2.59 | | simplifying with (5), (10), (18) gives:
% 13.98/2.59 | | (21) all_44_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.98/2.59 | | member(v0, all_32_1) = v1 & member(v0, empty_set) = 0 & $i(v0))
% 13.98/2.59 | |
% 13.98/2.59 | | GROUND_INST: instantiating (1) with all_32_1, empty_set, all_44_1,
% 13.98/2.59 | | simplifying with (5), (10), (19) gives:
% 13.98/2.59 | | (22) all_44_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.98/2.59 | | member(v0, all_32_1) = 0 & member(v0, empty_set) = v1 & $i(v0))
% 13.98/2.59 | |
% 13.98/2.59 | | BETA: splitting (20) gives:
% 13.98/2.59 | |
% 13.98/2.59 | | Case 1:
% 13.98/2.59 | | |
% 13.98/2.59 | | | (23) ~ (all_44_0 = 0)
% 13.98/2.59 | | |
% 13.98/2.59 | | | BETA: splitting (21) gives:
% 13.98/2.59 | | |
% 13.98/2.59 | | | Case 1:
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | (24) all_44_0 = 0
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | REDUCE: (23), (24) imply:
% 13.98/2.59 | | | | (25) $false
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | CLOSE: (25) is inconsistent.
% 13.98/2.59 | | | |
% 13.98/2.59 | | | Case 2:
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1)
% 13.98/2.59 | | | | = v1 & member(v0, empty_set) = 0 & $i(v0))
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | DELTA: instantiating (26) with fresh symbols all_57_0, all_57_1 gives:
% 13.98/2.59 | | | | (27) ~ (all_57_0 = 0) & member(all_57_1, all_32_1) = all_57_0 &
% 13.98/2.59 | | | | member(all_57_1, empty_set) = 0 & $i(all_57_1)
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | ALPHA: (27) implies:
% 13.98/2.59 | | | | (28) $i(all_57_1)
% 13.98/2.59 | | | | (29) member(all_57_1, empty_set) = 0
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | GROUND_INST: instantiating (3) with all_57_1, simplifying with (28),
% 13.98/2.59 | | | | (29) gives:
% 13.98/2.59 | | | | (30) $false
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | CLOSE: (30) is inconsistent.
% 13.98/2.59 | | | |
% 13.98/2.59 | | | End of split
% 13.98/2.59 | | |
% 13.98/2.59 | | Case 2:
% 13.98/2.59 | | |
% 13.98/2.59 | | | (31) ~ (all_44_1 = 0)
% 13.98/2.59 | | |
% 13.98/2.59 | | | BETA: splitting (22) gives:
% 13.98/2.59 | | |
% 13.98/2.59 | | | Case 1:
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | (32) all_44_1 = 0
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | REDUCE: (31), (32) imply:
% 13.98/2.59 | | | | (33) $false
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | CLOSE: (33) is inconsistent.
% 13.98/2.59 | | | |
% 13.98/2.59 | | | Case 2:
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1)
% 13.98/2.59 | | | | = 0 & member(v0, empty_set) = v1 & $i(v0))
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | DELTA: instantiating (34) with fresh symbols all_57_0, all_57_1 gives:
% 13.98/2.59 | | | | (35) ~ (all_57_0 = 0) & member(all_57_1, all_32_1) = 0 &
% 13.98/2.59 | | | | member(all_57_1, empty_set) = all_57_0 & $i(all_57_1)
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | ALPHA: (35) implies:
% 13.98/2.59 | | | | (36) $i(all_57_1)
% 13.98/2.59 | | | | (37) member(all_57_1, all_32_1) = 0
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | GROUND_INST: instantiating (4) with all_32_4, empty_set, all_57_1,
% 13.98/2.59 | | | | all_32_1, simplifying with (5), (9), (12), (36), (37)
% 13.98/2.59 | | | | gives:
% 13.98/2.59 | | | | (38) ? [v0: $i] : (apply(all_32_4, v0, all_57_1) = 0 & member(v0,
% 13.98/2.59 | | | | empty_set) = 0 & $i(v0))
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | DELTA: instantiating (38) with fresh symbol all_65_0 gives:
% 13.98/2.59 | | | | (39) apply(all_32_4, all_65_0, all_57_1) = 0 & member(all_65_0,
% 13.98/2.59 | | | | empty_set) = 0 & $i(all_65_0)
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | ALPHA: (39) implies:
% 13.98/2.59 | | | | (40) $i(all_65_0)
% 13.98/2.59 | | | | (41) member(all_65_0, empty_set) = 0
% 13.98/2.59 | | | |
% 13.98/2.59 | | | | GROUND_INST: instantiating (3) with all_65_0, simplifying with (40),
% 13.98/2.59 | | | | (41) gives:
% 13.98/2.60 | | | | (42) $false
% 13.98/2.60 | | | |
% 13.98/2.60 | | | | CLOSE: (42) is inconsistent.
% 13.98/2.60 | | | |
% 13.98/2.60 | | | End of split
% 13.98/2.60 | | |
% 13.98/2.60 | | End of split
% 13.98/2.60 | |
% 13.98/2.60 | End of split
% 13.98/2.60 |
% 13.98/2.60 End of proof
% 13.98/2.60 % SZS output end Proof for theBenchmark
% 13.98/2.60
% 13.98/2.60 1970ms
%------------------------------------------------------------------------------