TSTP Solution File: SET927+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET927+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n015.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 15:27:05 EDT 2023
% Result : Theorem 4.81s 1.34s
% Output : Proof 6.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET927+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n015.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 15:45:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.01/0.96 Prover 4: Preprocessing ...
% 2.01/0.96 Prover 1: Preprocessing ...
% 2.29/1.00 Prover 2: Preprocessing ...
% 2.29/1.00 Prover 5: Preprocessing ...
% 2.29/1.00 Prover 3: Preprocessing ...
% 2.29/1.00 Prover 6: Preprocessing ...
% 2.29/1.00 Prover 0: Preprocessing ...
% 3.47/1.16 Prover 3: Constructing countermodel ...
% 3.47/1.16 Prover 6: Constructing countermodel ...
% 3.47/1.17 Prover 1: Constructing countermodel ...
% 3.47/1.17 Prover 4: Constructing countermodel ...
% 3.47/1.18 Prover 5: Proving ...
% 3.47/1.19 Prover 2: Proving ...
% 3.47/1.19 Prover 0: Proving ...
% 4.81/1.34 Prover 6: proved (689ms)
% 4.81/1.34
% 4.81/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.81/1.34
% 4.81/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.81/1.35 Prover 5: stopped
% 4.81/1.36 Prover 0: stopped
% 4.81/1.36 Prover 3: stopped
% 4.81/1.36 Prover 2: stopped
% 4.81/1.36 Prover 7: Preprocessing ...
% 4.81/1.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.81/1.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.81/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.81/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.81/1.39 Prover 11: Preprocessing ...
% 4.81/1.39 Prover 8: Preprocessing ...
% 4.81/1.40 Prover 13: Preprocessing ...
% 4.81/1.40 Prover 10: Preprocessing ...
% 4.81/1.45 Prover 8: Warning: ignoring some quantifiers
% 4.81/1.45 Prover 8: Constructing countermodel ...
% 4.81/1.45 Prover 7: Constructing countermodel ...
% 4.81/1.47 Prover 11: Constructing countermodel ...
% 5.37/1.49 Prover 10: Constructing countermodel ...
% 5.37/1.50 Prover 13: Warning: ignoring some quantifiers
% 5.37/1.51 Prover 4: Found proof (size 60)
% 5.37/1.51 Prover 4: proved (861ms)
% 5.37/1.51 Prover 7: stopped
% 5.37/1.51 Prover 11: stopped
% 5.37/1.51 Prover 10: stopped
% 5.37/1.51 Prover 13: Constructing countermodel ...
% 5.37/1.51 Prover 1: Found proof (size 60)
% 5.37/1.51 Prover 1: proved (868ms)
% 5.37/1.51 Prover 8: stopped
% 5.37/1.51 Prover 13: stopped
% 5.37/1.51
% 5.37/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.37/1.51
% 5.37/1.53 % SZS output start Proof for theBenchmark
% 6.04/1.53 Assumptions after simplification:
% 6.04/1.53 ---------------------------------
% 6.04/1.53
% 6.04/1.53 (l39_zfmisc_1)
% 6.04/1.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 6.04/1.57 (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ $i(v2)
% 6.04/1.57 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] :
% 6.04/1.57 (singleton(v0) = v7 & in(v1, v2) = v6 & in(v0, v2) = v5 & $i(v7) & (v7 = v4
% 6.04/1.57 | v5 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0))))) & ! [v0: $i] : ! [v1: $i] :
% 6.04/1.57 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (set_difference(v3, v2) = v4) |
% 6.04/1.57 ~ (unordered_pair(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 6.04/1.57 [v5: $i] : ? [v6: any] : ? [v7: any] : (singleton(v0) = v5 & in(v1, v2) =
% 6.04/1.57 v7 & in(v0, v2) = v6 & $i(v5) & ( ~ (v5 = v4) | ( ~ (v6 = 0) & (v7 = 0 |
% 6.04/1.57 v1 = v0)))))
% 6.04/1.57
% 6.04/1.57 (t70_zfmisc_1)
% 6.04/1.57 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 6.04/1.57 $i] : ? [v6: any] : ? [v7: any] : (set_difference(v3, v2) = v4 &
% 6.04/1.57 singleton(v0) = v5 & in(v1, v2) = v7 & in(v0, v2) = v6 & unordered_pair(v0,
% 6.04/1.57 v1) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v5 = v4
% 6.04/1.57 & (v6 = 0 | ( ~ (v7 = 0) & ~ (v1 = v0)))) | ( ~ (v6 = 0) & ~ (v5 = v4)
% 6.04/1.57 & (v7 = 0 | v1 = v0))))
% 6.04/1.57
% 6.04/1.57 (function-axioms)
% 6.04/1.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.04/1.58 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 6.04/1.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 6.04/1.58 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 6.04/1.58 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) =
% 6.04/1.58 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 6.04/1.58 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & !
% 6.04/1.58 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 6.04/1.58 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 6.04/1.58
% 6.04/1.58 Further assumptions not needed in the proof:
% 6.04/1.58 --------------------------------------------
% 6.04/1.58 antisymmetry_r2_hidden, commutativity_k2_tarski, rc1_xboole_0, rc2_xboole_0
% 6.04/1.58
% 6.04/1.58 Those formulas are unsatisfiable:
% 6.04/1.58 ---------------------------------
% 6.04/1.58
% 6.04/1.58 Begin of proof
% 6.30/1.58 |
% 6.30/1.58 | ALPHA: (l39_zfmisc_1) implies:
% 6.30/1.59 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 6.30/1.59 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) |
% 6.30/1.59 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: any] : ?
% 6.30/1.59 | [v7: any] : (singleton(v0) = v5 & in(v1, v2) = v7 & in(v0, v2) = v6 &
% 6.30/1.59 | $i(v5) & ( ~ (v5 = v4) | ( ~ (v6 = 0) & (v7 = 0 | v1 = v0)))))
% 6.30/1.59 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 6.30/1.59 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) |
% 6.30/1.59 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ?
% 6.30/1.59 | [v7: $i] : (singleton(v0) = v7 & in(v1, v2) = v6 & in(v0, v2) = v5 &
% 6.30/1.59 | $i(v7) & (v7 = v4 | v5 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0)))))
% 6.30/1.59 |
% 6.30/1.59 | ALPHA: (function-axioms) implies:
% 6.30/1.59 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 6.30/1.59 | = v1) | ~ (singleton(v2) = v0))
% 6.30/1.59 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.30/1.59 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.30/1.59 |
% 6.30/1.59 | DELTA: instantiating (t70_zfmisc_1) with fresh symbols all_10_0, all_10_1,
% 6.30/1.60 | all_10_2, all_10_3, all_10_4, all_10_5, all_10_6, all_10_7 gives:
% 6.30/1.60 | (5) set_difference(all_10_4, all_10_5) = all_10_3 & singleton(all_10_7) =
% 6.30/1.60 | all_10_2 & in(all_10_6, all_10_5) = all_10_0 & in(all_10_7, all_10_5) =
% 6.30/1.60 | all_10_1 & unordered_pair(all_10_7, all_10_6) = all_10_4 & $i(all_10_2)
% 6.30/1.60 | & $i(all_10_3) & $i(all_10_4) & $i(all_10_5) & $i(all_10_6) &
% 6.30/1.60 | $i(all_10_7) & ((all_10_2 = all_10_3 & (all_10_1 = 0 | ( ~ (all_10_0 =
% 6.30/1.60 | 0) & ~ (all_10_6 = all_10_7)))) | ( ~ (all_10_1 = 0) & ~
% 6.30/1.60 | (all_10_2 = all_10_3) & (all_10_0 = 0 | all_10_6 = all_10_7)))
% 6.30/1.60 |
% 6.30/1.60 | ALPHA: (5) implies:
% 6.30/1.60 | (6) $i(all_10_7)
% 6.30/1.60 | (7) $i(all_10_6)
% 6.30/1.60 | (8) $i(all_10_5)
% 6.30/1.60 | (9) unordered_pair(all_10_7, all_10_6) = all_10_4
% 6.30/1.60 | (10) in(all_10_7, all_10_5) = all_10_1
% 6.30/1.60 | (11) in(all_10_6, all_10_5) = all_10_0
% 6.30/1.60 | (12) singleton(all_10_7) = all_10_2
% 6.30/1.60 | (13) set_difference(all_10_4, all_10_5) = all_10_3
% 6.30/1.60 | (14) (all_10_2 = all_10_3 & (all_10_1 = 0 | ( ~ (all_10_0 = 0) & ~
% 6.30/1.60 | (all_10_6 = all_10_7)))) | ( ~ (all_10_1 = 0) & ~ (all_10_2 =
% 6.30/1.60 | all_10_3) & (all_10_0 = 0 | all_10_6 = all_10_7))
% 6.30/1.60 |
% 6.30/1.60 | GROUND_INST: instantiating (2) with all_10_7, all_10_6, all_10_5, all_10_4,
% 6.30/1.60 | all_10_3, simplifying with (6), (7), (8), (9), (13) gives:
% 6.30/1.61 | (15) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (singleton(all_10_7) = v2
% 6.30/1.61 | & in(all_10_6, all_10_5) = v1 & in(all_10_7, all_10_5) = v0 & $i(v2)
% 6.30/1.61 | & (v2 = all_10_3 | v0 = 0 | ( ~ (v1 = 0) & ~ (all_10_6 =
% 6.30/1.61 | all_10_7))))
% 6.30/1.61 |
% 6.30/1.61 | GROUND_INST: instantiating (1) with all_10_7, all_10_6, all_10_5, all_10_4,
% 6.30/1.61 | all_10_3, simplifying with (6), (7), (8), (9), (13) gives:
% 6.30/1.61 | (16) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (singleton(all_10_7) = v0
% 6.30/1.61 | & in(all_10_6, all_10_5) = v2 & in(all_10_7, all_10_5) = v1 & $i(v0)
% 6.30/1.61 | & ( ~ (v0 = all_10_3) | ( ~ (v1 = 0) & (v2 = 0 | all_10_6 =
% 6.30/1.61 | all_10_7))))
% 6.30/1.61 |
% 6.30/1.61 | DELTA: instantiating (16) with fresh symbols all_18_0, all_18_1, all_18_2
% 6.30/1.61 | gives:
% 6.30/1.61 | (17) singleton(all_10_7) = all_18_2 & in(all_10_6, all_10_5) = all_18_0 &
% 6.30/1.61 | in(all_10_7, all_10_5) = all_18_1 & $i(all_18_2) & ( ~ (all_18_2 =
% 6.30/1.61 | all_10_3) | ( ~ (all_18_1 = 0) & (all_18_0 = 0 | all_10_6 =
% 6.30/1.61 | all_10_7)))
% 6.30/1.61 |
% 6.30/1.61 | ALPHA: (17) implies:
% 6.30/1.61 | (18) in(all_10_7, all_10_5) = all_18_1
% 6.30/1.61 | (19) in(all_10_6, all_10_5) = all_18_0
% 6.30/1.61 | (20) singleton(all_10_7) = all_18_2
% 6.30/1.61 | (21) ~ (all_18_2 = all_10_3) | ( ~ (all_18_1 = 0) & (all_18_0 = 0 |
% 6.30/1.61 | all_10_6 = all_10_7))
% 6.30/1.61 |
% 6.30/1.61 | DELTA: instantiating (15) with fresh symbols all_20_0, all_20_1, all_20_2
% 6.30/1.61 | gives:
% 6.30/1.61 | (22) singleton(all_10_7) = all_20_0 & in(all_10_6, all_10_5) = all_20_1 &
% 6.30/1.61 | in(all_10_7, all_10_5) = all_20_2 & $i(all_20_0) & (all_20_0 =
% 6.30/1.61 | all_10_3 | all_20_2 = 0 | ( ~ (all_20_1 = 0) & ~ (all_10_6 =
% 6.30/1.61 | all_10_7)))
% 6.30/1.61 |
% 6.30/1.61 | ALPHA: (22) implies:
% 6.30/1.61 | (23) in(all_10_7, all_10_5) = all_20_2
% 6.30/1.61 | (24) in(all_10_6, all_10_5) = all_20_1
% 6.30/1.61 | (25) singleton(all_10_7) = all_20_0
% 6.30/1.61 | (26) all_20_0 = all_10_3 | all_20_2 = 0 | ( ~ (all_20_1 = 0) & ~ (all_10_6
% 6.30/1.61 | = all_10_7))
% 6.30/1.61 |
% 6.30/1.61 | GROUND_INST: instantiating (4) with all_10_1, all_20_2, all_10_5, all_10_7,
% 6.30/1.61 | simplifying with (10), (23) gives:
% 6.30/1.61 | (27) all_20_2 = all_10_1
% 6.30/1.61 |
% 6.30/1.61 | GROUND_INST: instantiating (4) with all_18_1, all_20_2, all_10_5, all_10_7,
% 6.30/1.61 | simplifying with (18), (23) gives:
% 6.30/1.61 | (28) all_20_2 = all_18_1
% 6.30/1.61 |
% 6.30/1.61 | GROUND_INST: instantiating (4) with all_10_0, all_20_1, all_10_5, all_10_6,
% 6.30/1.61 | simplifying with (11), (24) gives:
% 6.30/1.61 | (29) all_20_1 = all_10_0
% 6.30/1.61 |
% 6.30/1.62 | GROUND_INST: instantiating (4) with all_18_0, all_20_1, all_10_5, all_10_6,
% 6.30/1.62 | simplifying with (19), (24) gives:
% 6.30/1.62 | (30) all_20_1 = all_18_0
% 6.30/1.62 |
% 6.30/1.62 | GROUND_INST: instantiating (3) with all_10_2, all_20_0, all_10_7, simplifying
% 6.30/1.62 | with (12), (25) gives:
% 6.30/1.62 | (31) all_20_0 = all_10_2
% 6.30/1.62 |
% 6.30/1.62 | GROUND_INST: instantiating (3) with all_18_2, all_20_0, all_10_7, simplifying
% 6.30/1.62 | with (20), (25) gives:
% 6.30/1.62 | (32) all_20_0 = all_18_2
% 6.30/1.62 |
% 6.30/1.62 | COMBINE_EQS: (31), (32) imply:
% 6.30/1.62 | (33) all_18_2 = all_10_2
% 6.30/1.62 |
% 6.30/1.62 | COMBINE_EQS: (29), (30) imply:
% 6.30/1.62 | (34) all_18_0 = all_10_0
% 6.30/1.62 |
% 6.30/1.62 | SIMP: (34) implies:
% 6.30/1.62 | (35) all_18_0 = all_10_0
% 6.30/1.62 |
% 6.30/1.62 | COMBINE_EQS: (27), (28) imply:
% 6.30/1.62 | (36) all_18_1 = all_10_1
% 6.30/1.62 |
% 6.30/1.62 | BETA: splitting (14) gives:
% 6.30/1.62 |
% 6.30/1.62 | Case 1:
% 6.30/1.62 | |
% 6.30/1.62 | | (37) all_10_2 = all_10_3 & (all_10_1 = 0 | ( ~ (all_10_0 = 0) & ~
% 6.30/1.62 | | (all_10_6 = all_10_7)))
% 6.30/1.62 | |
% 6.30/1.62 | | ALPHA: (37) implies:
% 6.30/1.62 | | (38) all_10_2 = all_10_3
% 6.30/1.62 | | (39) all_10_1 = 0 | ( ~ (all_10_0 = 0) & ~ (all_10_6 = all_10_7))
% 6.30/1.62 | |
% 6.30/1.62 | | COMBINE_EQS: (33), (38) imply:
% 6.30/1.62 | | (40) all_18_2 = all_10_3
% 6.30/1.62 | |
% 6.30/1.62 | | BETA: splitting (21) gives:
% 6.30/1.62 | |
% 6.30/1.62 | | Case 1:
% 6.30/1.62 | | |
% 6.30/1.62 | | | (41) ~ (all_18_2 = all_10_3)
% 6.30/1.62 | | |
% 6.30/1.62 | | | REDUCE: (40), (41) imply:
% 6.30/1.62 | | | (42) $false
% 6.30/1.62 | | |
% 6.30/1.62 | | | CLOSE: (42) is inconsistent.
% 6.30/1.62 | | |
% 6.30/1.62 | | Case 2:
% 6.30/1.62 | | |
% 6.30/1.62 | | | (43) ~ (all_18_1 = 0) & (all_18_0 = 0 | all_10_6 = all_10_7)
% 6.30/1.62 | | |
% 6.30/1.62 | | | ALPHA: (43) implies:
% 6.30/1.62 | | | (44) ~ (all_18_1 = 0)
% 6.30/1.62 | | | (45) all_18_0 = 0 | all_10_6 = all_10_7
% 6.30/1.62 | | |
% 6.30/1.62 | | | REDUCE: (36), (44) imply:
% 6.30/1.62 | | | (46) ~ (all_10_1 = 0)
% 6.30/1.62 | | |
% 6.30/1.62 | | | BETA: splitting (39) gives:
% 6.30/1.62 | | |
% 6.30/1.62 | | | Case 1:
% 6.30/1.62 | | | |
% 6.30/1.62 | | | | (47) all_10_1 = 0
% 6.30/1.62 | | | |
% 6.30/1.62 | | | | REDUCE: (46), (47) imply:
% 6.30/1.62 | | | | (48) $false
% 6.30/1.62 | | | |
% 6.30/1.62 | | | | CLOSE: (48) is inconsistent.
% 6.30/1.62 | | | |
% 6.30/1.62 | | | Case 2:
% 6.30/1.62 | | | |
% 6.30/1.62 | | | | (49) ~ (all_10_0 = 0) & ~ (all_10_6 = all_10_7)
% 6.30/1.62 | | | |
% 6.30/1.62 | | | | ALPHA: (49) implies:
% 6.30/1.62 | | | | (50) ~ (all_10_6 = all_10_7)
% 6.30/1.62 | | | | (51) ~ (all_10_0 = 0)
% 6.30/1.62 | | | |
% 6.30/1.62 | | | | BETA: splitting (45) gives:
% 6.30/1.62 | | | |
% 6.30/1.62 | | | | Case 1:
% 6.30/1.62 | | | | |
% 6.30/1.62 | | | | | (52) all_18_0 = 0
% 6.30/1.62 | | | | |
% 6.30/1.62 | | | | | COMBINE_EQS: (35), (52) imply:
% 6.30/1.63 | | | | | (53) all_10_0 = 0
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | SIMP: (53) implies:
% 6.30/1.63 | | | | | (54) all_10_0 = 0
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | REDUCE: (51), (54) imply:
% 6.30/1.63 | | | | | (55) $false
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | CLOSE: (55) is inconsistent.
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | Case 2:
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | (56) all_10_6 = all_10_7
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | REDUCE: (50), (56) imply:
% 6.30/1.63 | | | | | (57) $false
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | CLOSE: (57) is inconsistent.
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | End of split
% 6.30/1.63 | | | |
% 6.30/1.63 | | | End of split
% 6.30/1.63 | | |
% 6.30/1.63 | | End of split
% 6.30/1.63 | |
% 6.30/1.63 | Case 2:
% 6.30/1.63 | |
% 6.30/1.63 | | (58) ~ (all_10_1 = 0) & ~ (all_10_2 = all_10_3) & (all_10_0 = 0 |
% 6.30/1.63 | | all_10_6 = all_10_7)
% 6.30/1.63 | |
% 6.30/1.63 | | ALPHA: (58) implies:
% 6.30/1.63 | | (59) ~ (all_10_2 = all_10_3)
% 6.30/1.63 | | (60) ~ (all_10_1 = 0)
% 6.30/1.63 | | (61) all_10_0 = 0 | all_10_6 = all_10_7
% 6.30/1.63 | |
% 6.30/1.63 | | BETA: splitting (26) gives:
% 6.30/1.63 | |
% 6.30/1.63 | | Case 1:
% 6.30/1.63 | | |
% 6.30/1.63 | | | (62) all_20_2 = 0
% 6.30/1.63 | | |
% 6.30/1.63 | | | COMBINE_EQS: (27), (62) imply:
% 6.30/1.63 | | | (63) all_10_1 = 0
% 6.30/1.63 | | |
% 6.30/1.63 | | | SIMP: (63) implies:
% 6.30/1.63 | | | (64) all_10_1 = 0
% 6.30/1.63 | | |
% 6.30/1.63 | | | REDUCE: (60), (64) imply:
% 6.30/1.63 | | | (65) $false
% 6.30/1.63 | | |
% 6.30/1.63 | | | CLOSE: (65) is inconsistent.
% 6.30/1.63 | | |
% 6.30/1.63 | | Case 2:
% 6.30/1.63 | | |
% 6.30/1.63 | | | (66) all_20_0 = all_10_3 | ( ~ (all_20_1 = 0) & ~ (all_10_6 =
% 6.30/1.63 | | | all_10_7))
% 6.30/1.63 | | |
% 6.30/1.63 | | | BETA: splitting (66) gives:
% 6.30/1.63 | | |
% 6.30/1.63 | | | Case 1:
% 6.30/1.63 | | | |
% 6.30/1.63 | | | | (67) all_20_0 = all_10_3
% 6.30/1.63 | | | |
% 6.30/1.63 | | | | COMBINE_EQS: (31), (67) imply:
% 6.30/1.63 | | | | (68) all_10_2 = all_10_3
% 6.30/1.63 | | | |
% 6.30/1.63 | | | | SIMP: (68) implies:
% 6.30/1.63 | | | | (69) all_10_2 = all_10_3
% 6.30/1.63 | | | |
% 6.30/1.63 | | | | REDUCE: (59), (69) imply:
% 6.30/1.63 | | | | (70) $false
% 6.30/1.63 | | | |
% 6.30/1.63 | | | | CLOSE: (70) is inconsistent.
% 6.30/1.63 | | | |
% 6.30/1.63 | | | Case 2:
% 6.30/1.63 | | | |
% 6.30/1.63 | | | | (71) ~ (all_20_1 = 0) & ~ (all_10_6 = all_10_7)
% 6.30/1.63 | | | |
% 6.30/1.63 | | | | ALPHA: (71) implies:
% 6.30/1.63 | | | | (72) ~ (all_10_6 = all_10_7)
% 6.30/1.63 | | | | (73) ~ (all_20_1 = 0)
% 6.30/1.63 | | | |
% 6.30/1.63 | | | | REDUCE: (29), (73) imply:
% 6.30/1.63 | | | | (74) ~ (all_10_0 = 0)
% 6.30/1.63 | | | |
% 6.30/1.63 | | | | BETA: splitting (61) gives:
% 6.30/1.63 | | | |
% 6.30/1.63 | | | | Case 1:
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | (75) all_10_0 = 0
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | REDUCE: (74), (75) imply:
% 6.30/1.63 | | | | | (76) $false
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | CLOSE: (76) is inconsistent.
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | Case 2:
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | (77) all_10_6 = all_10_7
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | REDUCE: (72), (77) imply:
% 6.30/1.63 | | | | | (78) $false
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | | CLOSE: (78) is inconsistent.
% 6.30/1.63 | | | | |
% 6.30/1.63 | | | | End of split
% 6.30/1.63 | | | |
% 6.30/1.63 | | | End of split
% 6.30/1.63 | | |
% 6.30/1.63 | | End of split
% 6.30/1.63 | |
% 6.30/1.63 | End of split
% 6.30/1.63 |
% 6.30/1.63 End of proof
% 6.30/1.63 % SZS output end Proof for theBenchmark
% 6.30/1.63
% 6.30/1.63 1008ms
%------------------------------------------------------------------------------