TSTP Solution File: SET901+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET901+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 : n020.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 15:26:57 EDT 2023
% Result : Theorem 4.49s 1.31s
% Output : Proof 6.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET901+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.34 % Computer : n020.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 12:30:29 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.99/0.96 Prover 4: Preprocessing ...
% 1.99/0.96 Prover 1: Preprocessing ...
% 2.35/1.00 Prover 0: Preprocessing ...
% 2.35/1.00 Prover 5: Preprocessing ...
% 2.35/1.00 Prover 6: Preprocessing ...
% 2.35/1.00 Prover 2: Preprocessing ...
% 2.35/1.00 Prover 3: Preprocessing ...
% 3.18/1.14 Prover 1: Warning: ignoring some quantifiers
% 3.47/1.16 Prover 4: Constructing countermodel ...
% 3.47/1.16 Prover 1: Constructing countermodel ...
% 3.47/1.16 Prover 3: Warning: ignoring some quantifiers
% 3.47/1.17 Prover 3: Constructing countermodel ...
% 3.47/1.18 Prover 6: Proving ...
% 3.47/1.19 Prover 5: Proving ...
% 3.47/1.20 Prover 2: Proving ...
% 3.47/1.20 Prover 0: Proving ...
% 4.49/1.31 Prover 3: proved (683ms)
% 4.49/1.31
% 4.49/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.49/1.31
% 4.49/1.31 Prover 6: stopped
% 4.49/1.31 Prover 5: stopped
% 4.49/1.31 Prover 0: stopped
% 4.49/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.49/1.32 Prover 2: stopped
% 4.49/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.49/1.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.49/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.49/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.49/1.34 Prover 7: Preprocessing ...
% 4.49/1.34 Prover 11: Preprocessing ...
% 4.49/1.34 Prover 8: Preprocessing ...
% 4.96/1.35 Prover 10: Preprocessing ...
% 4.96/1.35 Prover 13: Preprocessing ...
% 4.96/1.39 Prover 7: Warning: ignoring some quantifiers
% 4.96/1.39 Prover 7: Constructing countermodel ...
% 4.96/1.41 Prover 13: Warning: ignoring some quantifiers
% 4.96/1.41 Prover 13: Constructing countermodel ...
% 4.96/1.41 Prover 10: Warning: ignoring some quantifiers
% 4.96/1.42 Prover 8: Warning: ignoring some quantifiers
% 4.96/1.43 Prover 10: Constructing countermodel ...
% 4.96/1.43 Prover 8: Constructing countermodel ...
% 4.96/1.44 Prover 1: Found proof (size 51)
% 4.96/1.44 Prover 1: proved (815ms)
% 4.96/1.44 Prover 7: stopped
% 4.96/1.44 Prover 8: stopped
% 4.96/1.44 Prover 4: stopped
% 4.96/1.44 Prover 10: stopped
% 4.96/1.44 Prover 13: stopped
% 4.96/1.45 Prover 11: Constructing countermodel ...
% 4.96/1.45 Prover 11: stopped
% 4.96/1.45
% 4.96/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.96/1.45
% 4.96/1.46 % SZS output start Proof for theBenchmark
% 4.96/1.46 Assumptions after simplification:
% 4.96/1.46 ---------------------------------
% 4.96/1.46
% 4.96/1.46 (l46_zfmisc_1)
% 5.73/1.50 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 5.73/1.50 [v4: int] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (unordered_pair(v1, v2) =
% 5.73/1.50 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v3 = v0) & ~ (v0 =
% 5.73/1.50 empty_set) & ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v0) & ~ (v5 = v0) &
% 5.73/1.50 singleton(v2) = v6 & singleton(v1) = v5 & $i(v6) & $i(v5)))) & ! [v0:
% 5.73/1.50 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v0 = empty_set |
% 5.73/1.50 ~ (subset(v0, v3) = 0) | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~
% 5.73/1.50 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (singleton(v2) = v5 &
% 5.73/1.50 singleton(v1) = v4 & $i(v5) & $i(v4) & (v5 = v0 | v4 = v0)))
% 5.73/1.50
% 5.73/1.50 (t42_zfmisc_1)
% 5.73/1.50 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 5.73/1.50 [v4: any] : ? [v5: $i] : ? [v6: $i] : (singleton(v2) = v6 & singleton(v1) =
% 5.73/1.50 v5 & subset(v0, v3) = v4 & unordered_pair(v1, v2) = v3 & $i(v6) & $i(v5) &
% 5.73/1.50 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v6 = v0) & ~ (v5 = v0) &
% 5.73/1.50 ~ (v3 = v0) & ~ (v0 = empty_set)) | ( ~ (v4 = 0) & (v6 = v0 | v5 = v0
% 5.73/1.50 | v3 = v0 | v0 = empty_set))))
% 5.73/1.50
% 5.73/1.50 (function-axioms)
% 5.73/1.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 5.73/1.51 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 5.73/1.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.73/1.51 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 5.73/1.51 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 5.73/1.51 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 5.73/1.51 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 5.73/1.51 (empty(v2) = v0))
% 5.73/1.51
% 5.73/1.51 Further assumptions not needed in the proof:
% 5.73/1.51 --------------------------------------------
% 5.73/1.51 commutativity_k2_tarski, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0,
% 5.73/1.51 reflexivity_r1_tarski
% 5.73/1.51
% 5.73/1.51 Those formulas are unsatisfiable:
% 5.73/1.51 ---------------------------------
% 5.73/1.51
% 5.73/1.51 Begin of proof
% 5.73/1.51 |
% 5.73/1.51 | ALPHA: (l46_zfmisc_1) implies:
% 5.73/1.51 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v0 =
% 5.73/1.51 | empty_set | ~ (subset(v0, v3) = 0) | ~ (unordered_pair(v1, v2) =
% 5.73/1.51 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i]
% 5.73/1.51 | : (singleton(v2) = v5 & singleton(v1) = v4 & $i(v5) & $i(v4) & (v5 =
% 5.73/1.51 | v0 | v4 = v0)))
% 5.73/1.52 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 5.73/1.52 | (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (unordered_pair(v1, v2) = v3) |
% 5.73/1.52 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v3 = v0) & ~ (v0 =
% 5.73/1.52 | empty_set) & ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v0) & ~ (v5 =
% 5.73/1.52 | v0) & singleton(v2) = v6 & singleton(v1) = v5 & $i(v6) &
% 5.73/1.52 | $i(v5))))
% 5.73/1.52 |
% 5.73/1.52 | ALPHA: (t42_zfmisc_1) implies:
% 5.73/1.52 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 5.73/1.52 | ? [v5: $i] : ? [v6: $i] : (singleton(v2) = v6 & singleton(v1) = v5 &
% 5.73/1.52 | subset(v0, v3) = v4 & unordered_pair(v1, v2) = v3 & $i(v6) & $i(v5) &
% 5.73/1.52 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v6 = v0) & ~ (v5
% 5.73/1.52 | = v0) & ~ (v3 = v0) & ~ (v0 = empty_set)) | ( ~ (v4 = 0) &
% 5.73/1.52 | (v6 = v0 | v5 = v0 | v3 = v0 | v0 = empty_set))))
% 5.73/1.52 |
% 5.73/1.52 | ALPHA: (function-axioms) implies:
% 5.73/1.52 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 5.73/1.52 | = v1) | ~ (singleton(v2) = v0))
% 5.73/1.52 |
% 6.01/1.52 | DELTA: instantiating (3) with fresh symbols all_12_0, all_12_1, all_12_2,
% 6.01/1.52 | all_12_3, all_12_4, all_12_5, all_12_6 gives:
% 6.01/1.52 | (5) singleton(all_12_4) = all_12_0 & singleton(all_12_5) = all_12_1 &
% 6.01/1.52 | subset(all_12_6, all_12_3) = all_12_2 & unordered_pair(all_12_5,
% 6.01/1.52 | all_12_4) = all_12_3 & $i(all_12_0) & $i(all_12_1) & $i(all_12_3) &
% 6.01/1.52 | $i(all_12_4) & $i(all_12_5) & $i(all_12_6) & ((all_12_2 = 0 & ~
% 6.01/1.53 | (all_12_0 = all_12_6) & ~ (all_12_1 = all_12_6) & ~ (all_12_3 =
% 6.01/1.53 | all_12_6) & ~ (all_12_6 = empty_set)) | ( ~ (all_12_2 = 0) &
% 6.01/1.53 | (all_12_0 = all_12_6 | all_12_1 = all_12_6 | all_12_3 = all_12_6 |
% 6.01/1.53 | all_12_6 = empty_set)))
% 6.01/1.53 |
% 6.01/1.53 | ALPHA: (5) implies:
% 6.01/1.53 | (6) $i(all_12_6)
% 6.01/1.53 | (7) $i(all_12_5)
% 6.01/1.53 | (8) $i(all_12_4)
% 6.01/1.53 | (9) unordered_pair(all_12_5, all_12_4) = all_12_3
% 6.01/1.53 | (10) subset(all_12_6, all_12_3) = all_12_2
% 6.01/1.53 | (11) singleton(all_12_5) = all_12_1
% 6.01/1.53 | (12) singleton(all_12_4) = all_12_0
% 6.01/1.53 | (13) (all_12_2 = 0 & ~ (all_12_0 = all_12_6) & ~ (all_12_1 = all_12_6) &
% 6.01/1.53 | ~ (all_12_3 = all_12_6) & ~ (all_12_6 = empty_set)) | ( ~ (all_12_2
% 6.01/1.53 | = 0) & (all_12_0 = all_12_6 | all_12_1 = all_12_6 | all_12_3 =
% 6.01/1.53 | all_12_6 | all_12_6 = empty_set))
% 6.01/1.53 |
% 6.01/1.53 | GROUND_INST: instantiating (2) with all_12_6, all_12_5, all_12_4, all_12_3,
% 6.01/1.53 | all_12_2, simplifying with (6), (7), (8), (9), (10) gives:
% 6.01/1.53 | (14) all_12_2 = 0 | ( ~ (all_12_3 = all_12_6) & ~ (all_12_6 = empty_set) &
% 6.01/1.53 | ? [v0: any] : ? [v1: any] : ( ~ (v1 = all_12_6) & ~ (v0 =
% 6.01/1.53 | all_12_6) & singleton(all_12_4) = v1 & singleton(all_12_5) = v0
% 6.01/1.53 | & $i(v1) & $i(v0)))
% 6.01/1.53 |
% 6.01/1.53 | BETA: splitting (13) gives:
% 6.01/1.53 |
% 6.01/1.53 | Case 1:
% 6.01/1.53 | |
% 6.01/1.53 | | (15) all_12_2 = 0 & ~ (all_12_0 = all_12_6) & ~ (all_12_1 = all_12_6) &
% 6.01/1.53 | | ~ (all_12_3 = all_12_6) & ~ (all_12_6 = empty_set)
% 6.01/1.53 | |
% 6.01/1.53 | | ALPHA: (15) implies:
% 6.01/1.53 | | (16) all_12_2 = 0
% 6.01/1.53 | | (17) ~ (all_12_6 = empty_set)
% 6.01/1.53 | | (18) ~ (all_12_3 = all_12_6)
% 6.01/1.53 | | (19) ~ (all_12_1 = all_12_6)
% 6.01/1.53 | | (20) ~ (all_12_0 = all_12_6)
% 6.01/1.53 | |
% 6.01/1.53 | | REDUCE: (10), (16) imply:
% 6.01/1.54 | | (21) subset(all_12_6, all_12_3) = 0
% 6.01/1.54 | |
% 6.01/1.54 | | GROUND_INST: instantiating (1) with all_12_6, all_12_5, all_12_4, all_12_3,
% 6.01/1.54 | | simplifying with (6), (7), (8), (9), (21) gives:
% 6.01/1.54 | | (22) all_12_3 = all_12_6 | all_12_6 = empty_set | ? [v0: $i] : ? [v1:
% 6.01/1.54 | | $i] : (singleton(all_12_4) = v1 & singleton(all_12_5) = v0 &
% 6.01/1.54 | | $i(v1) & $i(v0) & (v1 = all_12_6 | v0 = all_12_6))
% 6.01/1.54 | |
% 6.01/1.54 | | BETA: splitting (22) gives:
% 6.01/1.54 | |
% 6.01/1.54 | | Case 1:
% 6.01/1.54 | | |
% 6.01/1.54 | | | (23) all_12_6 = empty_set
% 6.01/1.54 | | |
% 6.01/1.54 | | | REDUCE: (17), (23) imply:
% 6.01/1.54 | | | (24) $false
% 6.01/1.54 | | |
% 6.01/1.54 | | | CLOSE: (24) is inconsistent.
% 6.01/1.54 | | |
% 6.01/1.54 | | Case 2:
% 6.01/1.54 | | |
% 6.01/1.54 | | | (25) all_12_3 = all_12_6 | ? [v0: $i] : ? [v1: $i] :
% 6.01/1.54 | | | (singleton(all_12_4) = v1 & singleton(all_12_5) = v0 & $i(v1) &
% 6.01/1.54 | | | $i(v0) & (v1 = all_12_6 | v0 = all_12_6))
% 6.01/1.54 | | |
% 6.01/1.54 | | | BETA: splitting (25) gives:
% 6.01/1.54 | | |
% 6.01/1.54 | | | Case 1:
% 6.01/1.54 | | | |
% 6.01/1.54 | | | | (26) all_12_3 = all_12_6
% 6.01/1.54 | | | |
% 6.01/1.54 | | | | REDUCE: (18), (26) imply:
% 6.01/1.54 | | | | (27) $false
% 6.01/1.54 | | | |
% 6.01/1.54 | | | | CLOSE: (27) is inconsistent.
% 6.01/1.54 | | | |
% 6.01/1.54 | | | Case 2:
% 6.01/1.54 | | | |
% 6.01/1.54 | | | | (28) ? [v0: $i] : ? [v1: $i] : (singleton(all_12_4) = v1 &
% 6.01/1.54 | | | | singleton(all_12_5) = v0 & $i(v1) & $i(v0) & (v1 = all_12_6 |
% 6.01/1.54 | | | | v0 = all_12_6))
% 6.01/1.54 | | | |
% 6.01/1.54 | | | | DELTA: instantiating (28) with fresh symbols all_38_0, all_38_1 gives:
% 6.01/1.54 | | | | (29) singleton(all_12_4) = all_38_0 & singleton(all_12_5) = all_38_1
% 6.01/1.54 | | | | & $i(all_38_0) & $i(all_38_1) & (all_38_0 = all_12_6 | all_38_1
% 6.01/1.54 | | | | = all_12_6)
% 6.01/1.54 | | | |
% 6.01/1.54 | | | | ALPHA: (29) implies:
% 6.01/1.54 | | | | (30) singleton(all_12_5) = all_38_1
% 6.01/1.54 | | | | (31) singleton(all_12_4) = all_38_0
% 6.01/1.54 | | | | (32) all_38_0 = all_12_6 | all_38_1 = all_12_6
% 6.01/1.54 | | | |
% 6.01/1.54 | | | | GROUND_INST: instantiating (4) with all_12_1, all_38_1, all_12_5,
% 6.01/1.54 | | | | simplifying with (11), (30) gives:
% 6.01/1.54 | | | | (33) all_38_1 = all_12_1
% 6.01/1.54 | | | |
% 6.01/1.54 | | | | GROUND_INST: instantiating (4) with all_12_0, all_38_0, all_12_4,
% 6.01/1.54 | | | | simplifying with (12), (31) gives:
% 6.01/1.54 | | | | (34) all_38_0 = all_12_0
% 6.01/1.54 | | | |
% 6.01/1.54 | | | | BETA: splitting (32) gives:
% 6.01/1.54 | | | |
% 6.01/1.54 | | | | Case 1:
% 6.01/1.54 | | | | |
% 6.01/1.54 | | | | | (35) all_38_0 = all_12_6
% 6.01/1.54 | | | | |
% 6.01/1.54 | | | | | COMBINE_EQS: (34), (35) imply:
% 6.01/1.54 | | | | | (36) all_12_0 = all_12_6
% 6.01/1.54 | | | | |
% 6.01/1.54 | | | | | REDUCE: (20), (36) imply:
% 6.01/1.54 | | | | | (37) $false
% 6.01/1.54 | | | | |
% 6.01/1.54 | | | | | CLOSE: (37) is inconsistent.
% 6.01/1.54 | | | | |
% 6.01/1.54 | | | | Case 2:
% 6.01/1.54 | | | | |
% 6.01/1.54 | | | | | (38) all_38_1 = all_12_6
% 6.01/1.54 | | | | |
% 6.01/1.55 | | | | | COMBINE_EQS: (33), (38) imply:
% 6.01/1.55 | | | | | (39) all_12_1 = all_12_6
% 6.01/1.55 | | | | |
% 6.01/1.55 | | | | | SIMP: (39) implies:
% 6.01/1.55 | | | | | (40) all_12_1 = all_12_6
% 6.01/1.55 | | | | |
% 6.01/1.55 | | | | | REDUCE: (19), (40) imply:
% 6.01/1.55 | | | | | (41) $false
% 6.01/1.55 | | | | |
% 6.01/1.55 | | | | | CLOSE: (41) is inconsistent.
% 6.01/1.55 | | | | |
% 6.01/1.55 | | | | End of split
% 6.01/1.55 | | | |
% 6.01/1.55 | | | End of split
% 6.01/1.55 | | |
% 6.01/1.55 | | End of split
% 6.01/1.55 | |
% 6.01/1.55 | Case 2:
% 6.01/1.55 | |
% 6.01/1.55 | | (42) ~ (all_12_2 = 0) & (all_12_0 = all_12_6 | all_12_1 = all_12_6 |
% 6.01/1.55 | | all_12_3 = all_12_6 | all_12_6 = empty_set)
% 6.01/1.55 | |
% 6.01/1.55 | | ALPHA: (42) implies:
% 6.01/1.55 | | (43) ~ (all_12_2 = 0)
% 6.01/1.55 | | (44) all_12_0 = all_12_6 | all_12_1 = all_12_6 | all_12_3 = all_12_6 |
% 6.01/1.55 | | all_12_6 = empty_set
% 6.01/1.55 | |
% 6.01/1.55 | | BETA: splitting (14) gives:
% 6.01/1.55 | |
% 6.01/1.55 | | Case 1:
% 6.01/1.55 | | |
% 6.01/1.55 | | | (45) all_12_2 = 0
% 6.01/1.55 | | |
% 6.01/1.55 | | | REDUCE: (43), (45) imply:
% 6.01/1.55 | | | (46) $false
% 6.01/1.55 | | |
% 6.01/1.55 | | | CLOSE: (46) is inconsistent.
% 6.01/1.55 | | |
% 6.01/1.55 | | Case 2:
% 6.01/1.55 | | |
% 6.01/1.55 | | | (47) ~ (all_12_3 = all_12_6) & ~ (all_12_6 = empty_set) & ? [v0:
% 6.01/1.55 | | | any] : ? [v1: any] : ( ~ (v1 = all_12_6) & ~ (v0 = all_12_6) &
% 6.01/1.55 | | | singleton(all_12_4) = v1 & singleton(all_12_5) = v0 & $i(v1) &
% 6.01/1.55 | | | $i(v0))
% 6.01/1.55 | | |
% 6.01/1.55 | | | ALPHA: (47) implies:
% 6.01/1.55 | | | (48) ~ (all_12_6 = empty_set)
% 6.01/1.55 | | | (49) ~ (all_12_3 = all_12_6)
% 6.01/1.55 | | | (50) ? [v0: any] : ? [v1: any] : ( ~ (v1 = all_12_6) & ~ (v0 =
% 6.01/1.55 | | | all_12_6) & singleton(all_12_4) = v1 & singleton(all_12_5) =
% 6.01/1.55 | | | v0 & $i(v1) & $i(v0))
% 6.01/1.55 | | |
% 6.01/1.55 | | | DELTA: instantiating (50) with fresh symbols all_31_0, all_31_1 gives:
% 6.01/1.55 | | | (51) ~ (all_31_0 = all_12_6) & ~ (all_31_1 = all_12_6) &
% 6.01/1.55 | | | singleton(all_12_4) = all_31_0 & singleton(all_12_5) = all_31_1 &
% 6.01/1.55 | | | $i(all_31_0) & $i(all_31_1)
% 6.01/1.55 | | |
% 6.01/1.55 | | | ALPHA: (51) implies:
% 6.01/1.55 | | | (52) ~ (all_31_1 = all_12_6)
% 6.01/1.55 | | | (53) ~ (all_31_0 = all_12_6)
% 6.01/1.55 | | | (54) singleton(all_12_5) = all_31_1
% 6.01/1.55 | | | (55) singleton(all_12_4) = all_31_0
% 6.01/1.55 | | |
% 6.01/1.55 | | | GROUND_INST: instantiating (4) with all_12_1, all_31_1, all_12_5,
% 6.01/1.55 | | | simplifying with (11), (54) gives:
% 6.01/1.55 | | | (56) all_31_1 = all_12_1
% 6.01/1.55 | | |
% 6.01/1.55 | | | GROUND_INST: instantiating (4) with all_12_0, all_31_0, all_12_4,
% 6.01/1.55 | | | simplifying with (12), (55) gives:
% 6.01/1.55 | | | (57) all_31_0 = all_12_0
% 6.01/1.55 | | |
% 6.01/1.55 | | | REDUCE: (53), (57) imply:
% 6.01/1.55 | | | (58) ~ (all_12_0 = all_12_6)
% 6.01/1.55 | | |
% 6.01/1.55 | | | REDUCE: (52), (56) imply:
% 6.01/1.55 | | | (59) ~ (all_12_1 = all_12_6)
% 6.01/1.55 | | |
% 6.01/1.55 | | | BETA: splitting (44) gives:
% 6.01/1.55 | | |
% 6.01/1.55 | | | Case 1:
% 6.01/1.55 | | | |
% 6.01/1.55 | | | | (60) all_12_6 = empty_set
% 6.01/1.55 | | | |
% 6.01/1.55 | | | | REDUCE: (48), (60) imply:
% 6.01/1.55 | | | | (61) $false
% 6.01/1.55 | | | |
% 6.01/1.55 | | | | CLOSE: (61) is inconsistent.
% 6.01/1.55 | | | |
% 6.01/1.56 | | | Case 2:
% 6.01/1.56 | | | |
% 6.01/1.56 | | | | (62) all_12_0 = all_12_6 | all_12_1 = all_12_6 | all_12_3 = all_12_6
% 6.01/1.56 | | | |
% 6.01/1.56 | | | | BETA: splitting (62) gives:
% 6.01/1.56 | | | |
% 6.01/1.56 | | | | Case 1:
% 6.01/1.56 | | | | |
% 6.01/1.56 | | | | | (63) all_12_0 = all_12_6
% 6.01/1.56 | | | | |
% 6.01/1.56 | | | | | REDUCE: (58), (63) imply:
% 6.01/1.56 | | | | | (64) $false
% 6.01/1.56 | | | | |
% 6.01/1.56 | | | | | CLOSE: (64) is inconsistent.
% 6.01/1.56 | | | | |
% 6.01/1.56 | | | | Case 2:
% 6.01/1.56 | | | | |
% 6.01/1.56 | | | | | (65) all_12_1 = all_12_6 | all_12_3 = all_12_6
% 6.01/1.56 | | | | |
% 6.01/1.56 | | | | | BETA: splitting (65) gives:
% 6.01/1.56 | | | | |
% 6.01/1.56 | | | | | Case 1:
% 6.01/1.56 | | | | | |
% 6.01/1.56 | | | | | | (66) all_12_1 = all_12_6
% 6.01/1.56 | | | | | |
% 6.01/1.56 | | | | | | REDUCE: (59), (66) imply:
% 6.01/1.56 | | | | | | (67) $false
% 6.01/1.56 | | | | | |
% 6.01/1.56 | | | | | | CLOSE: (67) is inconsistent.
% 6.01/1.56 | | | | | |
% 6.01/1.56 | | | | | Case 2:
% 6.01/1.56 | | | | | |
% 6.01/1.56 | | | | | | (68) all_12_3 = all_12_6
% 6.01/1.56 | | | | | |
% 6.01/1.56 | | | | | | REDUCE: (49), (68) imply:
% 6.01/1.56 | | | | | | (69) $false
% 6.01/1.56 | | | | | |
% 6.01/1.56 | | | | | | CLOSE: (69) is inconsistent.
% 6.01/1.56 | | | | | |
% 6.01/1.56 | | | | | End of split
% 6.01/1.56 | | | | |
% 6.01/1.56 | | | | End of split
% 6.01/1.56 | | | |
% 6.01/1.56 | | | End of split
% 6.01/1.56 | | |
% 6.01/1.56 | | End of split
% 6.01/1.56 | |
% 6.01/1.56 | End of split
% 6.01/1.56 |
% 6.01/1.56 End of proof
% 6.01/1.56 % SZS output end Proof for theBenchmark
% 6.01/1.56
% 6.01/1.56 952ms
%------------------------------------------------------------------------------