TSTP Solution File: SET707+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET707+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 : n008.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 15:26:04 EDT 2023
% Result : Theorem 10.92s 2.24s
% Output : Proof 11.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET707+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Sat Aug 26 10:07:02 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.09/1.01 Prover 1: Preprocessing ...
% 2.09/1.01 Prover 4: Preprocessing ...
% 2.61/1.05 Prover 0: Preprocessing ...
% 2.61/1.05 Prover 3: Preprocessing ...
% 2.61/1.05 Prover 6: Preprocessing ...
% 2.61/1.05 Prover 2: Preprocessing ...
% 2.61/1.05 Prover 5: Preprocessing ...
% 4.73/1.41 Prover 1: Constructing countermodel ...
% 4.73/1.41 Prover 6: Proving ...
% 4.73/1.46 Prover 3: Constructing countermodel ...
% 4.73/1.47 Prover 5: Proving ...
% 5.80/1.49 Prover 4: Constructing countermodel ...
% 5.80/1.50 Prover 2: Proving ...
% 5.80/1.53 Prover 0: Proving ...
% 5.80/1.53 Prover 3: gave up
% 5.80/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.43/1.57 Prover 7: Preprocessing ...
% 6.64/1.60 Prover 1: gave up
% 6.64/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.90/1.64 Prover 8: Preprocessing ...
% 6.90/1.66 Prover 7: Warning: ignoring some quantifiers
% 6.90/1.67 Prover 7: Constructing countermodel ...
% 7.45/1.71 Prover 4: gave up
% 7.45/1.72 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 7.45/1.74 Prover 9: Preprocessing ...
% 7.92/1.78 Prover 8: Warning: ignoring some quantifiers
% 7.92/1.79 Prover 8: Constructing countermodel ...
% 8.66/1.89 Prover 8: gave up
% 8.86/1.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.86/1.91 Prover 10: Preprocessing ...
% 9.13/1.97 Prover 10: Warning: ignoring some quantifiers
% 9.13/1.97 Prover 10: Constructing countermodel ...
% 9.13/2.03 Prover 9: Constructing countermodel ...
% 10.92/2.23 Prover 10: Found proof (size 116)
% 10.92/2.23 Prover 10: proved (338ms)
% 10.92/2.24 Prover 9: stopped
% 10.92/2.24 Prover 6: stopped
% 10.92/2.24 Prover 5: stopped
% 10.92/2.24 Prover 0: stopped
% 10.92/2.24 Prover 2: stopped
% 10.92/2.24 Prover 7: stopped
% 10.92/2.24
% 10.92/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.92/2.24
% 10.92/2.26 % SZS output start Proof for theBenchmark
% 10.92/2.26 Assumptions after simplification:
% 10.92/2.26 ---------------------------------
% 10.92/2.26
% 10.92/2.26 (equal_set)
% 10.92/2.27 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ equal_set(v0, v1) |
% 10.92/2.27 subset(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 10.92/2.27 equal_set(v0, v1) | subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1)
% 10.92/2.27 | ~ $i(v0) | ~ subset(v1, v0) | ~ subset(v0, v1) | equal_set(v0, v1))
% 10.92/2.27
% 10.92/2.27 (singleton)
% 11.55/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1) = v2) |
% 11.55/2.29 ~ $i(v1) | ~ $i(v0) | ~ member(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.55/2.29 (singleton(v0) = v1) | ~ $i(v0) | member(v0, v1))
% 11.55/2.29
% 11.55/2.29 (subset)
% 11.55/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 11.55/2.29 ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ? [v0: $i] : ?
% 11.55/2.29 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | subset(v0, v1) | ? [v2: $i] : ($i(v2) &
% 11.55/2.29 member(v2, v0) & ~ member(v2, v1)))
% 11.55/2.29
% 11.55/2.29 (thI50)
% 11.55/2.29 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 11.55/2.29 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 11.55/2.29 (unordered_pair(v7, v8) = v9 & unordered_pair(v4, v5) = v6 &
% 11.55/2.29 unordered_pair(v2, v3) = v8 & unordered_pair(v0, v1) = v5 & singleton(v2) =
% 11.55/2.29 v7 & singleton(v0) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 11.55/2.29 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & equal_set(v6, v9) & ( ~ (v3 =
% 11.55/2.29 v1) | ~ (v2 = v0)))
% 11.55/2.29
% 11.55/2.29 (unordered_pair)
% 11.59/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = v0 |
% 11.59/2.30 ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 11.59/2.30 member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 11.59/2.30 (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | member(v0, v2)) & !
% 11.59/2.30 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~
% 11.59/2.30 $i(v1) | ~ $i(v0) | member(v0, v2))
% 11.59/2.30
% 11.59/2.30 Further assumptions not needed in the proof:
% 11.59/2.30 --------------------------------------------
% 11.59/2.30 difference, empty_set, intersection, power_set, product, sum, union
% 11.59/2.30
% 11.59/2.30 Those formulas are unsatisfiable:
% 11.59/2.30 ---------------------------------
% 11.59/2.30
% 11.59/2.30 Begin of proof
% 11.59/2.30 |
% 11.59/2.30 | ALPHA: (subset) implies:
% 11.59/2.30 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 11.59/2.30 | $i(v0) | ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1))
% 11.59/2.30 |
% 11.59/2.30 | ALPHA: (equal_set) implies:
% 11.59/2.30 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ equal_set(v0,
% 11.59/2.30 | v1) | subset(v0, v1))
% 11.59/2.30 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ equal_set(v0,
% 11.59/2.30 | v1) | subset(v1, v0))
% 11.59/2.30 |
% 11.59/2.30 | ALPHA: (singleton) implies:
% 11.59/2.30 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 11.59/2.30 | member(v0, v1))
% 11.59/2.30 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1)
% 11.59/2.30 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, v2))
% 11.59/2.30 |
% 11.59/2.30 | ALPHA: (unordered_pair) implies:
% 11.59/2.30 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 11.59/2.30 | v2) | ~ $i(v1) | ~ $i(v0) | member(v0, v2))
% 11.59/2.31 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 11.64/2.31 | v2) | ~ $i(v1) | ~ $i(v0) | member(v0, v2))
% 11.64/2.31 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 =
% 11.64/2.31 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 11.64/2.31 | $i(v0) | ~ member(v0, v3))
% 11.64/2.31 |
% 11.65/2.31 | DELTA: instantiating (thI50) with fresh symbols all_18_0, all_18_1, all_18_2,
% 11.65/2.31 | all_18_3, all_18_4, all_18_5, all_18_6, all_18_7, all_18_8, all_18_9
% 11.65/2.31 | gives:
% 11.65/2.31 | (9) unordered_pair(all_18_2, all_18_1) = all_18_0 &
% 11.65/2.31 | unordered_pair(all_18_5, all_18_4) = all_18_3 &
% 11.65/2.31 | unordered_pair(all_18_7, all_18_6) = all_18_1 &
% 11.65/2.31 | unordered_pair(all_18_9, all_18_8) = all_18_4 & singleton(all_18_7) =
% 11.65/2.31 | all_18_2 & singleton(all_18_9) = all_18_5 & $i(all_18_0) & $i(all_18_1)
% 11.65/2.31 | & $i(all_18_2) & $i(all_18_3) & $i(all_18_4) & $i(all_18_5) &
% 11.65/2.31 | $i(all_18_6) & $i(all_18_7) & $i(all_18_8) & $i(all_18_9) &
% 11.65/2.31 | equal_set(all_18_3, all_18_0) & ( ~ (all_18_6 = all_18_8) | ~
% 11.65/2.31 | (all_18_7 = all_18_9))
% 11.65/2.31 |
% 11.65/2.31 | ALPHA: (9) implies:
% 11.65/2.31 | (10) equal_set(all_18_3, all_18_0)
% 11.65/2.31 | (11) $i(all_18_9)
% 11.65/2.31 | (12) $i(all_18_8)
% 11.65/2.31 | (13) $i(all_18_7)
% 11.65/2.31 | (14) $i(all_18_6)
% 11.65/2.31 | (15) $i(all_18_5)
% 11.65/2.31 | (16) $i(all_18_4)
% 11.65/2.31 | (17) $i(all_18_3)
% 11.65/2.31 | (18) $i(all_18_2)
% 11.65/2.31 | (19) $i(all_18_1)
% 11.65/2.31 | (20) $i(all_18_0)
% 11.65/2.31 | (21) singleton(all_18_9) = all_18_5
% 11.65/2.31 | (22) singleton(all_18_7) = all_18_2
% 11.65/2.31 | (23) unordered_pair(all_18_9, all_18_8) = all_18_4
% 11.65/2.31 | (24) unordered_pair(all_18_7, all_18_6) = all_18_1
% 11.65/2.31 | (25) unordered_pair(all_18_5, all_18_4) = all_18_3
% 11.65/2.31 | (26) unordered_pair(all_18_2, all_18_1) = all_18_0
% 11.65/2.31 | (27) ~ (all_18_6 = all_18_8) | ~ (all_18_7 = all_18_9)
% 11.65/2.31 |
% 11.65/2.31 | GROUND_INST: instantiating (3) with all_18_3, all_18_0, simplifying with (10),
% 11.65/2.31 | (17), (20) gives:
% 11.65/2.31 | (28) subset(all_18_0, all_18_3)
% 11.65/2.31 |
% 11.65/2.31 | GROUND_INST: instantiating (2) with all_18_3, all_18_0, simplifying with (10),
% 11.65/2.31 | (17), (20) gives:
% 11.65/2.31 | (29) subset(all_18_3, all_18_0)
% 11.65/2.31 |
% 11.65/2.31 | GROUND_INST: instantiating (4) with all_18_9, all_18_5, simplifying with (11),
% 11.65/2.31 | (21) gives:
% 11.65/2.31 | (30) member(all_18_9, all_18_5)
% 11.65/2.31 |
% 11.65/2.31 | GROUND_INST: instantiating (7) with all_18_8, all_18_9, all_18_4, simplifying
% 11.65/2.31 | with (11), (12), (23) gives:
% 11.65/2.31 | (31) member(all_18_8, all_18_4)
% 11.65/2.31 |
% 11.65/2.31 | GROUND_INST: instantiating (6) with all_18_9, all_18_8, all_18_4, simplifying
% 11.65/2.31 | with (11), (12), (23) gives:
% 11.65/2.31 | (32) member(all_18_9, all_18_4)
% 11.65/2.31 |
% 11.65/2.31 | GROUND_INST: instantiating (7) with all_18_6, all_18_7, all_18_1, simplifying
% 11.65/2.31 | with (13), (14), (24) gives:
% 11.65/2.31 | (33) member(all_18_6, all_18_1)
% 11.65/2.31 |
% 11.65/2.32 | GROUND_INST: instantiating (6) with all_18_7, all_18_6, all_18_1, simplifying
% 11.65/2.32 | with (13), (14), (24) gives:
% 11.65/2.32 | (34) member(all_18_7, all_18_1)
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (7) with all_18_4, all_18_5, all_18_3, simplifying
% 11.65/2.32 | with (15), (16), (25) gives:
% 11.65/2.32 | (35) member(all_18_4, all_18_3)
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (6) with all_18_5, all_18_4, all_18_3, simplifying
% 11.65/2.32 | with (15), (16), (25) gives:
% 11.65/2.32 | (36) member(all_18_5, all_18_3)
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (7) with all_18_1, all_18_2, all_18_0, simplifying
% 11.65/2.32 | with (18), (19), (26) gives:
% 11.65/2.32 | (37) member(all_18_1, all_18_0)
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (6) with all_18_2, all_18_1, all_18_0, simplifying
% 11.65/2.32 | with (18), (19), (26) gives:
% 11.65/2.32 | (38) member(all_18_2, all_18_0)
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (1) with all_18_3, all_18_0, all_18_5, simplifying
% 11.65/2.32 | with (15), (17), (20), (29), (36) gives:
% 11.65/2.32 | (39) member(all_18_5, all_18_0)
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (1) with all_18_3, all_18_0, all_18_4, simplifying
% 11.65/2.32 | with (16), (17), (20), (29), (35) gives:
% 11.65/2.32 | (40) member(all_18_4, all_18_0)
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (1) with all_18_0, all_18_3, all_18_2, simplifying
% 11.65/2.32 | with (17), (18), (20), (28), (38) gives:
% 11.65/2.32 | (41) member(all_18_2, all_18_3)
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (1) with all_18_0, all_18_3, all_18_1, simplifying
% 11.65/2.32 | with (17), (19), (20), (28), (37) gives:
% 11.65/2.32 | (42) member(all_18_1, all_18_3)
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (8) with all_18_5, all_18_2, all_18_1, all_18_0,
% 11.65/2.32 | simplifying with (15), (18), (19), (26), (39) gives:
% 11.65/2.32 | (43) all_18_1 = all_18_5 | all_18_2 = all_18_5
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (8) with all_18_4, all_18_2, all_18_1, all_18_0,
% 11.65/2.32 | simplifying with (16), (18), (19), (26), (40) gives:
% 11.65/2.32 | (44) all_18_1 = all_18_4 | all_18_2 = all_18_4
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (8) with all_18_2, all_18_5, all_18_4, all_18_3,
% 11.65/2.32 | simplifying with (15), (16), (18), (25), (41) gives:
% 11.65/2.32 | (45) all_18_2 = all_18_4 | all_18_2 = all_18_5
% 11.65/2.32 |
% 11.65/2.32 | GROUND_INST: instantiating (8) with all_18_1, all_18_5, all_18_4, all_18_3,
% 11.65/2.32 | simplifying with (15), (16), (19), (25), (42) gives:
% 11.65/2.32 | (46) all_18_1 = all_18_4 | all_18_1 = all_18_5
% 11.65/2.32 |
% 11.65/2.32 | BETA: splitting (27) gives:
% 11.65/2.32 |
% 11.65/2.32 | Case 1:
% 11.65/2.32 | |
% 11.65/2.32 | | (47) ~ (all_18_6 = all_18_8)
% 11.65/2.32 | |
% 11.65/2.32 | | BETA: splitting (44) gives:
% 11.65/2.32 | |
% 11.65/2.32 | | Case 1:
% 11.65/2.32 | | |
% 11.65/2.32 | | | (48) all_18_1 = all_18_4
% 11.65/2.32 | | |
% 11.65/2.32 | | | REDUCE: (24), (48) imply:
% 11.65/2.32 | | | (49) unordered_pair(all_18_7, all_18_6) = all_18_4
% 11.65/2.32 | | |
% 11.65/2.32 | | | REDUCE: (33), (48) imply:
% 11.65/2.32 | | | (50) member(all_18_6, all_18_4)
% 11.65/2.32 | | |
% 11.65/2.32 | | | GROUND_INST: instantiating (8) with all_18_6, all_18_9, all_18_8,
% 11.65/2.32 | | | all_18_4, simplifying with (11), (12), (14), (23), (50)
% 11.65/2.32 | | | gives:
% 11.65/2.33 | | | (51) all_18_6 = all_18_8 | all_18_6 = all_18_9
% 11.65/2.33 | | |
% 11.65/2.33 | | | GROUND_INST: instantiating (8) with all_18_8, all_18_7, all_18_6,
% 11.65/2.33 | | | all_18_4, simplifying with (12), (13), (14), (31), (49)
% 11.65/2.33 | | | gives:
% 11.65/2.33 | | | (52) all_18_6 = all_18_8 | all_18_7 = all_18_8
% 11.65/2.33 | | |
% 11.65/2.33 | | | BETA: splitting (43) gives:
% 11.65/2.33 | | |
% 11.65/2.33 | | | Case 1:
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | (53) all_18_1 = all_18_5
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | COMBINE_EQS: (48), (53) imply:
% 11.65/2.33 | | | | (54) all_18_4 = all_18_5
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | REDUCE: (50), (54) imply:
% 11.65/2.33 | | | | (55) member(all_18_6, all_18_5)
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | BETA: splitting (45) gives:
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | Case 1:
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | (56) all_18_2 = all_18_4
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | COMBINE_EQS: (54), (56) imply:
% 11.65/2.33 | | | | | (57) all_18_2 = all_18_5
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | REDUCE: (22), (57) imply:
% 11.65/2.33 | | | | | (58) singleton(all_18_7) = all_18_5
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | BETA: splitting (51) gives:
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | Case 1:
% 11.65/2.33 | | | | | |
% 11.65/2.33 | | | | | | (59) all_18_6 = all_18_8
% 11.65/2.33 | | | | | |
% 11.65/2.33 | | | | | | REDUCE: (47), (59) imply:
% 11.65/2.33 | | | | | | (60) $false
% 11.65/2.33 | | | | | |
% 11.65/2.33 | | | | | | CLOSE: (60) is inconsistent.
% 11.65/2.33 | | | | | |
% 11.65/2.33 | | | | | Case 2:
% 11.65/2.33 | | | | | |
% 11.65/2.33 | | | | | | (61) all_18_6 = all_18_9
% 11.65/2.33 | | | | | |
% 11.65/2.33 | | | | | | REDUCE: (47), (61) imply:
% 11.65/2.33 | | | | | | (62) ~ (all_18_8 = all_18_9)
% 11.65/2.33 | | | | | |
% 11.65/2.33 | | | | | | SIMP: (62) implies:
% 11.65/2.33 | | | | | | (63) ~ (all_18_8 = all_18_9)
% 11.65/2.33 | | | | | |
% 11.65/2.33 | | | | | | REF_CLOSE: (5), (11), (13), (30), (52), (58), (61), (63) are
% 11.65/2.33 | | | | | | inconsistent by sub-proof #1.
% 11.65/2.33 | | | | | |
% 11.65/2.33 | | | | | End of split
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | Case 2:
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | (64) all_18_2 = all_18_5
% 11.65/2.33 | | | | | (65) ~ (all_18_2 = all_18_4)
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | REDUCE: (54), (64), (65) imply:
% 11.65/2.33 | | | | | (66) $false
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | CLOSE: (66) is inconsistent.
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | End of split
% 11.65/2.33 | | | |
% 11.65/2.33 | | | Case 2:
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | (67) all_18_2 = all_18_5
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | REDUCE: (22), (67) imply:
% 11.65/2.33 | | | | (68) singleton(all_18_7) = all_18_5
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | BETA: splitting (51) gives:
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | Case 1:
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | (69) all_18_6 = all_18_8
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | REDUCE: (47), (69) imply:
% 11.65/2.33 | | | | | (70) $false
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | CLOSE: (70) is inconsistent.
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | Case 2:
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | (71) all_18_6 = all_18_9
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | REDUCE: (47), (71) imply:
% 11.65/2.33 | | | | | (72) ~ (all_18_8 = all_18_9)
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | SIMP: (72) implies:
% 11.65/2.33 | | | | | (73) ~ (all_18_8 = all_18_9)
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | | REF_CLOSE: (5), (11), (13), (30), (52), (68), (71), (73) are
% 11.65/2.33 | | | | | inconsistent by sub-proof #1.
% 11.65/2.33 | | | | |
% 11.65/2.33 | | | | End of split
% 11.65/2.33 | | | |
% 11.65/2.33 | | | End of split
% 11.65/2.33 | | |
% 11.65/2.33 | | Case 2:
% 11.65/2.33 | | |
% 11.65/2.33 | | | (74) all_18_2 = all_18_4
% 11.65/2.33 | | | (75) ~ (all_18_1 = all_18_4)
% 11.65/2.33 | | |
% 11.65/2.33 | | | REDUCE: (22), (74) imply:
% 11.65/2.33 | | | (76) singleton(all_18_7) = all_18_4
% 11.65/2.33 | | |
% 11.65/2.33 | | | BETA: splitting (46) gives:
% 11.65/2.33 | | |
% 11.65/2.33 | | | Case 1:
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | (77) all_18_1 = all_18_4
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | REDUCE: (75), (77) imply:
% 11.65/2.33 | | | | (78) $false
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | CLOSE: (78) is inconsistent.
% 11.65/2.33 | | | |
% 11.65/2.33 | | | Case 2:
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | (79) all_18_1 = all_18_5
% 11.65/2.33 | | | |
% 11.65/2.33 | | | | REDUCE: (33), (79) imply:
% 11.65/2.33 | | | | (80) member(all_18_6, all_18_5)
% 11.65/2.33 | | | |
% 11.65/2.34 | | | | GROUND_INST: instantiating (5) with all_18_6, all_18_9, all_18_5,
% 11.65/2.34 | | | | simplifying with (11), (14), (21), (80) gives:
% 11.65/2.34 | | | | (81) all_18_6 = all_18_9
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | GROUND_INST: instantiating (5) with all_18_8, all_18_7, all_18_4,
% 11.65/2.34 | | | | simplifying with (12), (13), (31), (76) gives:
% 11.65/2.34 | | | | (82) all_18_7 = all_18_8
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | GROUND_INST: instantiating (5) with all_18_9, all_18_7, all_18_4,
% 11.65/2.34 | | | | simplifying with (11), (13), (32), (76) gives:
% 11.65/2.34 | | | | (83) all_18_7 = all_18_9
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | COMBINE_EQS: (82), (83) imply:
% 11.65/2.34 | | | | (84) all_18_8 = all_18_9
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | SIMP: (84) implies:
% 11.65/2.34 | | | | (85) all_18_8 = all_18_9
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | REDUCE: (47), (81), (85) imply:
% 11.65/2.34 | | | | (86) $false
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | CLOSE: (86) is inconsistent.
% 11.65/2.34 | | | |
% 11.65/2.34 | | | End of split
% 11.65/2.34 | | |
% 11.65/2.34 | | End of split
% 11.65/2.34 | |
% 11.65/2.34 | Case 2:
% 11.65/2.34 | |
% 11.65/2.34 | | (87) all_18_6 = all_18_8
% 11.65/2.34 | | (88) ~ (all_18_7 = all_18_9)
% 11.65/2.34 | |
% 11.65/2.34 | | REDUCE: (24), (87) imply:
% 11.65/2.34 | | (89) unordered_pair(all_18_7, all_18_8) = all_18_1
% 11.65/2.34 | |
% 11.65/2.34 | | BETA: splitting (44) gives:
% 11.65/2.34 | |
% 11.65/2.34 | | Case 1:
% 11.65/2.34 | | |
% 11.65/2.34 | | | (90) all_18_1 = all_18_4
% 11.65/2.34 | | |
% 11.65/2.34 | | | REDUCE: (89), (90) imply:
% 11.65/2.34 | | | (91) unordered_pair(all_18_7, all_18_8) = all_18_4
% 11.65/2.34 | | |
% 11.65/2.34 | | | REDUCE: (34), (90) imply:
% 11.65/2.34 | | | (92) member(all_18_7, all_18_4)
% 11.65/2.34 | | |
% 11.65/2.34 | | | GROUND_INST: instantiating (8) with all_18_7, all_18_9, all_18_8,
% 11.65/2.34 | | | all_18_4, simplifying with (11), (12), (13), (23), (92)
% 11.65/2.34 | | | gives:
% 11.65/2.34 | | | (93) all_18_7 = all_18_8 | all_18_7 = all_18_9
% 11.65/2.34 | | |
% 11.65/2.34 | | | GROUND_INST: instantiating (8) with all_18_9, all_18_7, all_18_8,
% 11.65/2.34 | | | all_18_4, simplifying with (11), (12), (13), (32), (91)
% 11.65/2.34 | | | gives:
% 11.65/2.34 | | | (94) all_18_7 = all_18_9 | all_18_8 = all_18_9
% 11.65/2.34 | | |
% 11.65/2.34 | | | BETA: splitting (94) gives:
% 11.65/2.34 | | |
% 11.65/2.34 | | | Case 1:
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | (95) all_18_7 = all_18_9
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | REDUCE: (88), (95) imply:
% 11.65/2.34 | | | | (96) $false
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | CLOSE: (96) is inconsistent.
% 11.65/2.34 | | | |
% 11.65/2.34 | | | Case 2:
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | (97) all_18_8 = all_18_9
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | BETA: splitting (93) gives:
% 11.65/2.34 | | | |
% 11.65/2.34 | | | | Case 1:
% 11.65/2.34 | | | | |
% 11.65/2.34 | | | | | (98) all_18_7 = all_18_8
% 11.65/2.34 | | | | |
% 11.65/2.34 | | | | | COMBINE_EQS: (97), (98) imply:
% 11.65/2.34 | | | | | (99) all_18_7 = all_18_9
% 11.65/2.34 | | | | |
% 11.65/2.34 | | | | | REDUCE: (88), (99) imply:
% 11.65/2.34 | | | | | (100) $false
% 11.65/2.34 | | | | |
% 11.65/2.34 | | | | | CLOSE: (100) is inconsistent.
% 11.65/2.34 | | | | |
% 11.65/2.34 | | | | Case 2:
% 11.65/2.34 | | | | |
% 11.65/2.34 | | | | | (101) all_18_7 = all_18_9
% 11.65/2.34 | | | | |
% 11.65/2.34 | | | | | REDUCE: (88), (101) imply:
% 11.65/2.34 | | | | | (102) $false
% 11.65/2.34 | | | | |
% 11.65/2.34 | | | | | CLOSE: (102) is inconsistent.
% 11.65/2.34 | | | | |
% 11.65/2.34 | | | | End of split
% 11.65/2.34 | | | |
% 11.65/2.34 | | | End of split
% 11.65/2.34 | | |
% 11.65/2.34 | | Case 2:
% 11.65/2.34 | | |
% 11.65/2.34 | | | (103) all_18_2 = all_18_4
% 11.65/2.34 | | |
% 11.65/2.34 | | | REDUCE: (22), (103) imply:
% 11.65/2.34 | | | (104) singleton(all_18_7) = all_18_4
% 11.65/2.34 | | |
% 11.65/2.34 | | | GROUND_INST: instantiating (5) with all_18_8, all_18_7, all_18_4,
% 11.65/2.34 | | | simplifying with (12), (13), (31), (104) gives:
% 11.65/2.34 | | | (105) all_18_7 = all_18_8
% 11.65/2.34 | | |
% 11.65/2.34 | | | GROUND_INST: instantiating (5) with all_18_9, all_18_7, all_18_4,
% 11.65/2.34 | | | simplifying with (11), (13), (32), (104) gives:
% 11.65/2.34 | | | (106) all_18_7 = all_18_9
% 11.65/2.34 | | |
% 11.65/2.34 | | | COMBINE_EQS: (105), (106) imply:
% 11.65/2.34 | | | (107) all_18_8 = all_18_9
% 11.65/2.34 | | |
% 11.65/2.34 | | | REDUCE: (88), (106) imply:
% 11.65/2.34 | | | (108) $false
% 11.65/2.34 | | |
% 11.65/2.34 | | | CLOSE: (108) is inconsistent.
% 11.65/2.34 | | |
% 11.65/2.34 | | End of split
% 11.65/2.34 | |
% 11.65/2.34 | End of split
% 11.65/2.34 |
% 11.65/2.34 End of proof
% 11.65/2.34
% 11.65/2.34 Sub-proof #1 shows that the following formulas are inconsistent:
% 11.65/2.34 ----------------------------------------------------------------
% 11.65/2.34 (1) member(all_18_9, all_18_5)
% 11.65/2.34 (2) all_18_6 = all_18_8 | all_18_7 = all_18_8
% 11.65/2.34 (3) singleton(all_18_7) = all_18_5
% 11.65/2.35 (4) $i(all_18_7)
% 11.65/2.35 (5) all_18_6 = all_18_9
% 11.65/2.35 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1) =
% 11.65/2.35 v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, v2))
% 11.65/2.35 (7) ~ (all_18_8 = all_18_9)
% 11.65/2.35 (8) $i(all_18_9)
% 11.65/2.35
% 11.65/2.35 Begin of proof
% 11.65/2.35 |
% 11.65/2.35 | BETA: splitting (2) gives:
% 11.65/2.35 |
% 11.65/2.35 | Case 1:
% 11.65/2.35 | |
% 11.65/2.35 | | (9) all_18_6 = all_18_8
% 11.65/2.35 | |
% 11.65/2.35 | | COMBINE_EQS: (5), (9) imply:
% 11.65/2.35 | | (10) all_18_8 = all_18_9
% 11.65/2.35 | |
% 11.65/2.35 | | SIMP: (10) implies:
% 11.65/2.35 | | (11) all_18_8 = all_18_9
% 11.65/2.35 | |
% 11.65/2.35 | | REDUCE: (7), (11) imply:
% 11.65/2.35 | | (12) $false
% 11.65/2.35 | |
% 11.65/2.35 | | CLOSE: (12) is inconsistent.
% 11.65/2.35 | |
% 11.65/2.35 | Case 2:
% 11.65/2.35 | |
% 11.65/2.35 | | (13) all_18_7 = all_18_8
% 11.65/2.35 | | (14) ~ (all_18_6 = all_18_8)
% 11.65/2.35 | |
% 11.65/2.35 | | REDUCE: (5), (14) imply:
% 11.65/2.35 | | (15) ~ (all_18_8 = all_18_9)
% 11.65/2.35 | |
% 11.65/2.35 | | REDUCE: (3), (13) imply:
% 11.65/2.35 | | (16) singleton(all_18_8) = all_18_5
% 11.65/2.35 | |
% 11.65/2.35 | | REDUCE: (4), (13) imply:
% 11.65/2.35 | | (17) $i(all_18_8)
% 11.65/2.35 | |
% 11.65/2.35 | | GROUND_INST: instantiating (6) with all_18_9, all_18_8, all_18_5,
% 11.65/2.35 | | simplifying with (1), (8), (16), (17) gives:
% 11.65/2.35 | | (18) all_18_8 = all_18_9
% 11.65/2.35 | |
% 11.65/2.35 | | REDUCE: (7), (18) imply:
% 11.65/2.35 | | (19) $false
% 11.65/2.35 | |
% 11.65/2.35 | | CLOSE: (19) is inconsistent.
% 11.65/2.35 | |
% 11.65/2.35 | End of split
% 11.65/2.35 |
% 11.65/2.35 End of proof
% 11.65/2.35 % SZS output end Proof for theBenchmark
% 11.65/2.35
% 11.65/2.35 1741ms
%------------------------------------------------------------------------------