TSTP Solution File: SET764+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET764+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 : n026.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 11.83s 2.45s
% Output : Proof 13.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET764+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 15:20:03 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.64 ________ _____
% 0.21/0.64 ___ __ \_________(_)________________________________
% 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.64
% 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.64 (2023-06-19)
% 0.21/0.64
% 0.21/0.64 (c) Philipp Rümmer, 2009-2023
% 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.64 Amanda Stjerna.
% 0.21/0.64 Free software under BSD-3-Clause.
% 0.21/0.64
% 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.64
% 0.21/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.14/1.25 Prover 1: Preprocessing ...
% 3.14/1.25 Prover 4: Preprocessing ...
% 3.67/1.27 Prover 5: Preprocessing ...
% 3.67/1.27 Prover 2: Preprocessing ...
% 3.67/1.27 Prover 3: Preprocessing ...
% 3.67/1.27 Prover 6: Preprocessing ...
% 3.67/1.27 Prover 0: Preprocessing ...
% 9.14/2.09 Prover 5: Proving ...
% 9.14/2.15 Prover 2: Proving ...
% 9.14/2.21 Prover 6: Proving ...
% 9.93/2.27 Prover 3: Constructing countermodel ...
% 10.86/2.29 Prover 1: Constructing countermodel ...
% 11.83/2.45 Prover 3: proved (1777ms)
% 11.83/2.45
% 11.83/2.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.83/2.45
% 11.83/2.45 Prover 2: stopped
% 11.83/2.45 Prover 5: stopped
% 11.83/2.45 Prover 6: stopped
% 11.83/2.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.83/2.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.83/2.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.83/2.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.28/2.53 Prover 8: Preprocessing ...
% 12.28/2.53 Prover 1: Found proof (size 33)
% 12.28/2.53 Prover 1: proved (1875ms)
% 12.28/2.55 Prover 7: Preprocessing ...
% 12.88/2.57 Prover 10: Preprocessing ...
% 13.02/2.60 Prover 11: Preprocessing ...
% 13.32/2.64 Prover 7: stopped
% 13.32/2.64 Prover 10: stopped
% 13.32/2.68 Prover 4: Constructing countermodel ...
% 13.32/2.71 Prover 4: stopped
% 13.90/2.72 Prover 11: stopped
% 13.90/2.76 Prover 0: Proving ...
% 13.90/2.76 Prover 0: stopped
% 13.90/2.81 Prover 8: Warning: ignoring some quantifiers
% 13.90/2.82 Prover 8: Constructing countermodel ...
% 13.90/2.83 Prover 8: stopped
% 13.90/2.83
% 13.90/2.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.90/2.83
% 13.90/2.84 % SZS output start Proof for theBenchmark
% 13.90/2.84 Assumptions after simplification:
% 13.90/2.84 ---------------------------------
% 13.90/2.84
% 13.90/2.84 (empty_set)
% 13.90/2.86 $i(empty_set) & ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 13.90/2.86
% 13.90/2.86 (equal_set)
% 13.90/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 13.90/2.87 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 13.90/2.87 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 13.90/2.87 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 13.90/2.87 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 13.90/2.87
% 13.90/2.87 (inverse_image2)
% 13.90/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 13.90/2.87 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) |
% 13.90/2.87 ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v2, v5) = 0) | ~ $i(v5)
% 13.90/2.87 | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))) & ! [v0: $i] : !
% 13.90/2.87 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (inverse_image2(v0, v1) = v3) | ~
% 13.90/2.87 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 13.90/2.87 (apply(v0, v2, v4) = 0 & member(v4, v1) = 0 & $i(v4)))
% 13.90/2.87
% 13.90/2.87 (subset)
% 13.90/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 13.90/2.87 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 13.90/2.87 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 13.90/2.87 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 13.90/2.87 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 13.90/2.87
% 13.90/2.87 (thIIa14)
% 13.90/2.88 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 13.90/2.88 [v4: int] : ( ~ (v4 = 0) & inverse_image2(v0, empty_set) = v3 & maps(v0, v1,
% 13.90/2.88 v2) = 0 & equal_set(v3, empty_set) = v4 & $i(v3) & $i(v2) & $i(v1) &
% 13.90/2.88 $i(v0))
% 13.90/2.88
% 13.90/2.88 Further assumptions not needed in the proof:
% 13.90/2.88 --------------------------------------------
% 13.90/2.88 compose_function, compose_predicate, decreasing_function, difference,
% 13.90/2.88 equal_maps, identity, image2, image3, increasing_function, injective,
% 13.90/2.88 intersection, inverse_function, inverse_image3, inverse_predicate, isomorphism,
% 13.90/2.88 maps, one_to_one, power_set, product, singleton, sum, surjective, union,
% 13.90/2.88 unordered_pair
% 13.90/2.88
% 13.90/2.88 Those formulas are unsatisfiable:
% 13.90/2.88 ---------------------------------
% 13.90/2.88
% 13.90/2.88 Begin of proof
% 13.90/2.88 |
% 13.90/2.88 | ALPHA: (subset) implies:
% 13.90/2.88 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 13.90/2.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 13.90/2.88 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 13.90/2.88 |
% 13.90/2.88 | ALPHA: (equal_set) implies:
% 13.90/2.88 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 13.90/2.88 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 13.90/2.88 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 13.90/2.88 | 0))))
% 13.90/2.88 |
% 13.90/2.88 | ALPHA: (empty_set) implies:
% 13.90/2.88 | (3) ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 13.90/2.88 |
% 13.90/2.88 | ALPHA: (inverse_image2) implies:
% 13.90/2.88 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 13.90/2.88 | (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) |
% 13.90/2.88 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v2, v4) = 0 &
% 13.90/2.88 | member(v4, v1) = 0 & $i(v4)))
% 13.90/2.88 |
% 13.90/2.88 | ALPHA: (thIIa14) implies:
% 13.90/2.88 | (5) $i(empty_set)
% 13.90/2.88 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] :
% 13.90/2.88 | ( ~ (v4 = 0) & inverse_image2(v0, empty_set) = v3 & maps(v0, v1, v2) =
% 13.90/2.88 | 0 & equal_set(v3, empty_set) = v4 & $i(v3) & $i(v2) & $i(v1) &
% 13.90/2.88 | $i(v0))
% 13.90/2.88 |
% 13.90/2.88 | DELTA: instantiating (6) with fresh symbols all_32_0, all_32_1, all_32_2,
% 13.90/2.88 | all_32_3, all_32_4 gives:
% 13.90/2.88 | (7) ~ (all_32_0 = 0) & inverse_image2(all_32_4, empty_set) = all_32_1 &
% 13.90/2.88 | maps(all_32_4, all_32_3, all_32_2) = 0 & equal_set(all_32_1, empty_set)
% 13.90/2.88 | = all_32_0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & $i(all_32_4)
% 13.90/2.88 |
% 13.90/2.88 | ALPHA: (7) implies:
% 13.90/2.88 | (8) ~ (all_32_0 = 0)
% 13.90/2.89 | (9) $i(all_32_4)
% 13.90/2.89 | (10) $i(all_32_1)
% 13.90/2.89 | (11) equal_set(all_32_1, empty_set) = all_32_0
% 13.90/2.89 | (12) inverse_image2(all_32_4, empty_set) = all_32_1
% 13.90/2.89 |
% 13.90/2.89 | GROUND_INST: instantiating (2) with all_32_1, empty_set, all_32_0, simplifying
% 13.90/2.89 | with (5), (10), (11) gives:
% 13.90/2.89 | (13) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_32_1,
% 13.90/2.89 | empty_set) = v0 & subset(empty_set, all_32_1) = v1 & ( ~ (v1 = 0)
% 13.90/2.89 | | ~ (v0 = 0)))
% 13.90/2.89 |
% 13.90/2.89 | BETA: splitting (13) gives:
% 13.90/2.89 |
% 13.90/2.89 | Case 1:
% 13.90/2.89 | |
% 13.90/2.89 | | (14) all_32_0 = 0
% 13.90/2.89 | |
% 13.90/2.89 | | REDUCE: (8), (14) imply:
% 13.90/2.89 | | (15) $false
% 13.90/2.89 | |
% 13.90/2.89 | | CLOSE: (15) is inconsistent.
% 13.90/2.89 | |
% 13.90/2.89 | Case 2:
% 13.90/2.89 | |
% 13.90/2.89 | | (16) ? [v0: any] : ? [v1: any] : (subset(all_32_1, empty_set) = v0 &
% 13.90/2.89 | | subset(empty_set, all_32_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.90/2.89 | |
% 13.90/2.89 | | DELTA: instantiating (16) with fresh symbols all_44_0, all_44_1 gives:
% 13.90/2.89 | | (17) subset(all_32_1, empty_set) = all_44_1 & subset(empty_set, all_32_1)
% 13.90/2.89 | | = all_44_0 & ( ~ (all_44_0 = 0) | ~ (all_44_1 = 0))
% 13.90/2.89 | |
% 13.90/2.89 | | ALPHA: (17) implies:
% 13.90/2.89 | | (18) subset(empty_set, all_32_1) = all_44_0
% 13.90/2.89 | | (19) subset(all_32_1, empty_set) = all_44_1
% 13.90/2.89 | | (20) ~ (all_44_0 = 0) | ~ (all_44_1 = 0)
% 13.90/2.89 | |
% 13.90/2.89 | | GROUND_INST: instantiating (1) with empty_set, all_32_1, all_44_0,
% 13.90/2.89 | | simplifying with (5), (10), (18) gives:
% 13.90/2.89 | | (21) all_44_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.90/2.89 | | member(v0, all_32_1) = v1 & member(v0, empty_set) = 0 & $i(v0))
% 13.90/2.89 | |
% 13.90/2.89 | | GROUND_INST: instantiating (1) with all_32_1, empty_set, all_44_1,
% 13.90/2.89 | | simplifying with (5), (10), (19) gives:
% 13.90/2.89 | | (22) all_44_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.90/2.89 | | member(v0, all_32_1) = 0 & member(v0, empty_set) = v1 & $i(v0))
% 13.90/2.89 | |
% 13.90/2.89 | | BETA: splitting (20) gives:
% 13.90/2.89 | |
% 13.90/2.89 | | Case 1:
% 13.90/2.89 | | |
% 13.90/2.89 | | | (23) ~ (all_44_0 = 0)
% 13.90/2.89 | | |
% 13.90/2.89 | | | BETA: splitting (21) gives:
% 13.90/2.89 | | |
% 13.90/2.89 | | | Case 1:
% 13.90/2.89 | | | |
% 13.90/2.89 | | | | (24) all_44_0 = 0
% 13.90/2.89 | | | |
% 13.90/2.89 | | | | REDUCE: (23), (24) imply:
% 13.90/2.89 | | | | (25) $false
% 13.90/2.89 | | | |
% 13.90/2.89 | | | | CLOSE: (25) is inconsistent.
% 13.90/2.89 | | | |
% 13.90/2.89 | | | Case 2:
% 13.90/2.89 | | | |
% 13.90/2.89 | | | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1)
% 13.90/2.89 | | | | = v1 & member(v0, empty_set) = 0 & $i(v0))
% 13.90/2.89 | | | |
% 13.90/2.89 | | | | DELTA: instantiating (26) with fresh symbols all_57_0, all_57_1 gives:
% 13.90/2.89 | | | | (27) ~ (all_57_0 = 0) & member(all_57_1, all_32_1) = all_57_0 &
% 13.90/2.89 | | | | member(all_57_1, empty_set) = 0 & $i(all_57_1)
% 13.90/2.89 | | | |
% 13.90/2.89 | | | | ALPHA: (27) implies:
% 13.90/2.89 | | | | (28) $i(all_57_1)
% 13.90/2.89 | | | | (29) member(all_57_1, empty_set) = 0
% 13.90/2.89 | | | |
% 13.90/2.89 | | | | GROUND_INST: instantiating (3) with all_57_1, simplifying with (28),
% 13.90/2.89 | | | | (29) gives:
% 13.90/2.90 | | | | (30) $false
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | CLOSE: (30) is inconsistent.
% 13.90/2.90 | | | |
% 13.90/2.90 | | | End of split
% 13.90/2.90 | | |
% 13.90/2.90 | | Case 2:
% 13.90/2.90 | | |
% 13.90/2.90 | | | (31) ~ (all_44_1 = 0)
% 13.90/2.90 | | |
% 13.90/2.90 | | | BETA: splitting (22) gives:
% 13.90/2.90 | | |
% 13.90/2.90 | | | Case 1:
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | (32) all_44_1 = 0
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | REDUCE: (31), (32) imply:
% 13.90/2.90 | | | | (33) $false
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | CLOSE: (33) is inconsistent.
% 13.90/2.90 | | | |
% 13.90/2.90 | | | Case 2:
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1)
% 13.90/2.90 | | | | = 0 & member(v0, empty_set) = v1 & $i(v0))
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | DELTA: instantiating (34) with fresh symbols all_57_0, all_57_1 gives:
% 13.90/2.90 | | | | (35) ~ (all_57_0 = 0) & member(all_57_1, all_32_1) = 0 &
% 13.90/2.90 | | | | member(all_57_1, empty_set) = all_57_0 & $i(all_57_1)
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | ALPHA: (35) implies:
% 13.90/2.90 | | | | (36) $i(all_57_1)
% 13.90/2.90 | | | | (37) member(all_57_1, all_32_1) = 0
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | GROUND_INST: instantiating (4) with all_32_4, empty_set, all_57_1,
% 13.90/2.90 | | | | all_32_1, simplifying with (5), (9), (12), (36), (37)
% 13.90/2.90 | | | | gives:
% 13.90/2.90 | | | | (38) ? [v0: $i] : (apply(all_32_4, all_57_1, v0) = 0 & member(v0,
% 13.90/2.90 | | | | empty_set) = 0 & $i(v0))
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | DELTA: instantiating (38) with fresh symbol all_65_0 gives:
% 13.90/2.90 | | | | (39) apply(all_32_4, all_57_1, all_65_0) = 0 & member(all_65_0,
% 13.90/2.90 | | | | empty_set) = 0 & $i(all_65_0)
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | ALPHA: (39) implies:
% 13.90/2.90 | | | | (40) $i(all_65_0)
% 13.90/2.90 | | | | (41) member(all_65_0, empty_set) = 0
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | GROUND_INST: instantiating (3) with all_65_0, simplifying with (40),
% 13.90/2.90 | | | | (41) gives:
% 13.90/2.90 | | | | (42) $false
% 13.90/2.90 | | | |
% 13.90/2.90 | | | | CLOSE: (42) is inconsistent.
% 13.90/2.90 | | | |
% 13.90/2.90 | | | End of split
% 13.90/2.90 | | |
% 13.90/2.90 | | End of split
% 13.90/2.90 | |
% 13.90/2.90 | End of split
% 13.90/2.90 |
% 13.90/2.90 End of proof
% 13.90/2.90 % SZS output end Proof for theBenchmark
% 13.90/2.90
% 13.90/2.90 2259ms
%------------------------------------------------------------------------------