TSTP Solution File: SET931+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET931+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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:27:06 EDT 2023
% Result : Theorem 5.16s 1.40s
% Output : Proof 6.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET931+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 14:00:05 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.59/0.62 ________ _____
% 0.59/0.62 ___ __ \_________(_)________________________________
% 0.59/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.59/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.59/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.59/0.62
% 0.59/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.59/0.62 (2023-06-19)
% 0.59/0.62
% 0.59/0.62 (c) Philipp Rümmer, 2009-2023
% 0.59/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.59/0.62 Amanda Stjerna.
% 0.59/0.62 Free software under BSD-3-Clause.
% 0.59/0.62
% 0.59/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.59/0.62
% 0.59/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.64 Running up to 7 provers in parallel.
% 0.70/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.70/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.70/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.70/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.70/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.70/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.70/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.95/0.97 Prover 4: Preprocessing ...
% 1.95/0.97 Prover 1: Preprocessing ...
% 2.37/1.01 Prover 6: Preprocessing ...
% 2.37/1.01 Prover 3: Preprocessing ...
% 2.37/1.01 Prover 0: Preprocessing ...
% 2.37/1.01 Prover 5: Preprocessing ...
% 2.37/1.01 Prover 2: Preprocessing ...
% 3.71/1.21 Prover 1: Warning: ignoring some quantifiers
% 3.71/1.21 Prover 3: Warning: ignoring some quantifiers
% 3.89/1.23 Prover 4: Constructing countermodel ...
% 3.89/1.24 Prover 3: Constructing countermodel ...
% 3.89/1.24 Prover 5: Proving ...
% 3.89/1.24 Prover 6: Proving ...
% 3.89/1.24 Prover 1: Constructing countermodel ...
% 3.89/1.25 Prover 0: Proving ...
% 3.89/1.25 Prover 2: Proving ...
% 5.16/1.40 Prover 3: proved (752ms)
% 5.16/1.40
% 5.16/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.16/1.40
% 5.16/1.40 Prover 0: stopped
% 5.16/1.40 Prover 2: stopped
% 5.16/1.40 Prover 5: stopped
% 5.16/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.16/1.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.16/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.16/1.42 Prover 6: proved (768ms)
% 5.16/1.42
% 5.16/1.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.16/1.42
% 5.16/1.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.16/1.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.16/1.43 Prover 10: Preprocessing ...
% 5.16/1.44 Prover 7: Preprocessing ...
% 5.16/1.44 Prover 8: Preprocessing ...
% 5.16/1.45 Prover 13: Preprocessing ...
% 5.16/1.46 Prover 11: Preprocessing ...
% 5.68/1.48 Prover 10: Warning: ignoring some quantifiers
% 5.68/1.49 Prover 8: Warning: ignoring some quantifiers
% 5.68/1.50 Prover 10: Constructing countermodel ...
% 5.90/1.50 Prover 8: Constructing countermodel ...
% 5.90/1.51 Prover 13: Warning: ignoring some quantifiers
% 5.90/1.51 Prover 13: Constructing countermodel ...
% 5.90/1.51 Prover 7: Warning: ignoring some quantifiers
% 5.90/1.52 Prover 7: Constructing countermodel ...
% 6.14/1.53 Prover 11: Constructing countermodel ...
% 6.14/1.53 Prover 1: Found proof (size 65)
% 6.14/1.53 Prover 1: proved (885ms)
% 6.14/1.53 Prover 8: stopped
% 6.14/1.53 Prover 7: stopped
% 6.14/1.53 Prover 4: stopped
% 6.14/1.53 Prover 13: stopped
% 6.14/1.54 Prover 10: stopped
% 6.14/1.54 Prover 11: stopped
% 6.14/1.54
% 6.14/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.14/1.54
% 6.14/1.55 % SZS output start Proof for theBenchmark
% 6.14/1.55 Assumptions after simplification:
% 6.14/1.55 ---------------------------------
% 6.14/1.55
% 6.14/1.55 (commutativity_k2_tarski)
% 6.14/1.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) |
% 6.14/1.58 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 6.14/1.58
% 6.14/1.58 (l46_zfmisc_1)
% 6.14/1.59 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 6.14/1.59 [v4: int] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (unordered_pair(v1, v2) =
% 6.14/1.59 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v3 = v0) & ~ (v0 =
% 6.14/1.59 empty_set) & ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v0) & ~ (v5 = v0) &
% 6.14/1.59 singleton(v2) = v6 & singleton(v1) = v5 & $i(v6) & $i(v5)))) & ! [v0:
% 6.14/1.59 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v0 = empty_set |
% 6.14/1.59 ~ (subset(v0, v3) = 0) | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~
% 6.14/1.59 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (singleton(v2) = v5 &
% 6.14/1.59 singleton(v1) = v4 & $i(v5) & $i(v4) & (v5 = v0 | v4 = v0)))
% 6.14/1.59
% 6.14/1.59 (t37_xboole_1)
% 6.14/1.59 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 6.14/1.59 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~
% 6.14/1.59 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 6.14/1.59 (set_difference(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | subset(v0,
% 6.14/1.59 v1) = 0)
% 6.14/1.59
% 6.14/1.59 (t75_zfmisc_1)
% 6.14/1.60 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 6.14/1.60 [v4: $i] : ? [v5: $i] : ? [v6: $i] : (set_difference(v0, v3) = v4 &
% 6.14/1.60 singleton(v2) = v6 & singleton(v1) = v5 & unordered_pair(v1, v2) = v3 &
% 6.14/1.60 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 =
% 6.14/1.60 empty_set & ~ (v6 = v0) & ~ (v5 = v0) & ~ (v3 = v0) & ~ (v0 =
% 6.14/1.60 empty_set)) | ( ~ (v4 = empty_set) & (v6 = v0 | v5 = v0 | v3 = v0 | v0
% 6.14/1.60 = empty_set))))
% 6.14/1.60
% 6.14/1.60 (function-axioms)
% 6.14/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.14/1.60 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 6.14/1.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 6.14/1.60 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 6.14/1.60 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.14/1.60 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 6.14/1.60 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 6.14/1.60 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.14/1.60 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 6.14/1.60 (empty(v2) = v0))
% 6.14/1.60
% 6.14/1.60 Further assumptions not needed in the proof:
% 6.14/1.60 --------------------------------------------
% 6.14/1.60 fc1_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 6.14/1.60
% 6.14/1.60 Those formulas are unsatisfiable:
% 6.14/1.60 ---------------------------------
% 6.14/1.60
% 6.14/1.60 Begin of proof
% 6.14/1.60 |
% 6.14/1.60 | ALPHA: (l46_zfmisc_1) implies:
% 6.14/1.61 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v0 =
% 6.14/1.61 | empty_set | ~ (subset(v0, v3) = 0) | ~ (unordered_pair(v1, v2) =
% 6.14/1.61 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i]
% 6.14/1.61 | : (singleton(v2) = v5 & singleton(v1) = v4 & $i(v5) & $i(v4) & (v5 =
% 6.14/1.61 | v0 | v4 = v0)))
% 6.14/1.61 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 6.14/1.61 | (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (unordered_pair(v1, v2) = v3) |
% 6.14/1.61 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v3 = v0) & ~ (v0 =
% 6.14/1.61 | empty_set) & ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v0) & ~ (v5 =
% 6.14/1.61 | v0) & singleton(v2) = v6 & singleton(v1) = v5 & $i(v6) &
% 6.14/1.61 | $i(v5))))
% 6.14/1.61 |
% 6.14/1.61 | ALPHA: (t37_xboole_1) implies:
% 6.14/1.61 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) |
% 6.14/1.61 | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = 0)
% 6.14/1.61 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 6.14/1.61 | (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 6.14/1.61 | : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 6.14/1.61 |
% 6.14/1.61 | ALPHA: (t75_zfmisc_1) implies:
% 6.14/1.62 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 6.14/1.62 | ? [v5: $i] : ? [v6: $i] : (set_difference(v0, v3) = v4 & singleton(v2)
% 6.14/1.62 | = v6 & singleton(v1) = v5 & unordered_pair(v1, v2) = v3 & $i(v6) &
% 6.14/1.62 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 =
% 6.14/1.62 | empty_set & ~ (v6 = v0) & ~ (v5 = v0) & ~ (v3 = v0) & ~ (v0 =
% 6.14/1.62 | empty_set)) | ( ~ (v4 = empty_set) & (v6 = v0 | v5 = v0 | v3 =
% 6.14/1.62 | v0 | v0 = empty_set))))
% 6.14/1.62 |
% 6.14/1.62 | ALPHA: (function-axioms) implies:
% 6.14/1.62 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 6.14/1.62 | = v1) | ~ (singleton(v2) = v0))
% 6.14/1.62 |
% 6.14/1.62 | DELTA: instantiating (5) with fresh symbols all_13_0, all_13_1, all_13_2,
% 6.14/1.62 | all_13_3, all_13_4, all_13_5, all_13_6 gives:
% 6.14/1.62 | (7) set_difference(all_13_6, all_13_3) = all_13_2 & singleton(all_13_4) =
% 6.14/1.62 | all_13_0 & singleton(all_13_5) = all_13_1 & unordered_pair(all_13_5,
% 6.14/1.62 | all_13_4) = all_13_3 & $i(all_13_0) & $i(all_13_1) & $i(all_13_2) &
% 6.14/1.62 | $i(all_13_3) & $i(all_13_4) & $i(all_13_5) & $i(all_13_6) & ((all_13_2
% 6.14/1.62 | = empty_set & ~ (all_13_0 = all_13_6) & ~ (all_13_1 = all_13_6) &
% 6.14/1.62 | ~ (all_13_3 = all_13_6) & ~ (all_13_6 = empty_set)) | ( ~
% 6.14/1.62 | (all_13_2 = empty_set) & (all_13_0 = all_13_6 | all_13_1 = all_13_6
% 6.14/1.62 | | all_13_3 = all_13_6 | all_13_6 = empty_set)))
% 6.14/1.62 |
% 6.14/1.62 | ALPHA: (7) implies:
% 6.14/1.62 | (8) $i(all_13_6)
% 6.14/1.62 | (9) $i(all_13_5)
% 6.14/1.62 | (10) $i(all_13_4)
% 6.14/1.62 | (11) unordered_pair(all_13_5, all_13_4) = all_13_3
% 6.14/1.62 | (12) singleton(all_13_5) = all_13_1
% 6.14/1.62 | (13) singleton(all_13_4) = all_13_0
% 6.14/1.62 | (14) set_difference(all_13_6, all_13_3) = all_13_2
% 6.14/1.62 | (15) (all_13_2 = empty_set & ~ (all_13_0 = all_13_6) & ~ (all_13_1 =
% 6.14/1.62 | all_13_6) & ~ (all_13_3 = all_13_6) & ~ (all_13_6 = empty_set))
% 6.14/1.62 | | ( ~ (all_13_2 = empty_set) & (all_13_0 = all_13_6 | all_13_1 =
% 6.14/1.62 | all_13_6 | all_13_3 = all_13_6 | all_13_6 = empty_set))
% 6.14/1.62 |
% 6.64/1.63 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_13_5, all_13_4,
% 6.64/1.63 | all_13_3, simplifying with (9), (10), (11) gives:
% 6.64/1.63 | (16) unordered_pair(all_13_4, all_13_5) = all_13_3 & $i(all_13_3)
% 6.64/1.63 |
% 6.64/1.63 | ALPHA: (16) implies:
% 6.64/1.63 | (17) $i(all_13_3)
% 6.64/1.63 |
% 6.64/1.63 | GROUND_INST: instantiating (4) with all_13_6, all_13_3, all_13_2, simplifying
% 6.64/1.63 | with (8), (14), (17) gives:
% 6.64/1.63 | (18) all_13_2 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(all_13_6,
% 6.64/1.63 | all_13_3) = v0)
% 6.64/1.63 |
% 6.64/1.63 | BETA: splitting (15) gives:
% 6.64/1.63 |
% 6.64/1.63 | Case 1:
% 6.64/1.63 | |
% 6.64/1.63 | | (19) all_13_2 = empty_set & ~ (all_13_0 = all_13_6) & ~ (all_13_1 =
% 6.64/1.63 | | all_13_6) & ~ (all_13_3 = all_13_6) & ~ (all_13_6 = empty_set)
% 6.64/1.63 | |
% 6.64/1.63 | | ALPHA: (19) implies:
% 6.64/1.63 | | (20) all_13_2 = empty_set
% 6.64/1.63 | | (21) ~ (all_13_6 = empty_set)
% 6.64/1.63 | | (22) ~ (all_13_3 = all_13_6)
% 6.64/1.63 | | (23) ~ (all_13_1 = all_13_6)
% 6.64/1.63 | | (24) ~ (all_13_0 = all_13_6)
% 6.64/1.63 | |
% 6.64/1.63 | | REDUCE: (14), (20) imply:
% 6.64/1.63 | | (25) set_difference(all_13_6, all_13_3) = empty_set
% 6.64/1.63 | |
% 6.64/1.63 | | GROUND_INST: instantiating (3) with all_13_6, all_13_3, simplifying with
% 6.64/1.63 | | (8), (17), (25) gives:
% 6.64/1.63 | | (26) subset(all_13_6, all_13_3) = 0
% 6.64/1.63 | |
% 6.64/1.63 | | GROUND_INST: instantiating (1) with all_13_6, all_13_5, all_13_4, all_13_3,
% 6.64/1.63 | | simplifying with (8), (9), (10), (11), (26) gives:
% 6.64/1.63 | | (27) all_13_3 = all_13_6 | all_13_6 = empty_set | ? [v0: $i] : ? [v1:
% 6.64/1.63 | | $i] : (singleton(all_13_4) = v1 & singleton(all_13_5) = v0 &
% 6.64/1.63 | | $i(v1) & $i(v0) & (v1 = all_13_6 | v0 = all_13_6))
% 6.64/1.63 | |
% 6.64/1.63 | | BETA: splitting (27) gives:
% 6.64/1.63 | |
% 6.64/1.63 | | Case 1:
% 6.64/1.63 | | |
% 6.64/1.63 | | | (28) all_13_6 = empty_set
% 6.64/1.63 | | |
% 6.64/1.63 | | | REDUCE: (21), (28) imply:
% 6.64/1.63 | | | (29) $false
% 6.64/1.63 | | |
% 6.64/1.63 | | | CLOSE: (29) is inconsistent.
% 6.64/1.63 | | |
% 6.64/1.63 | | Case 2:
% 6.64/1.63 | | |
% 6.64/1.64 | | | (30) all_13_3 = all_13_6 | ? [v0: $i] : ? [v1: $i] :
% 6.64/1.64 | | | (singleton(all_13_4) = v1 & singleton(all_13_5) = v0 & $i(v1) &
% 6.64/1.64 | | | $i(v0) & (v1 = all_13_6 | v0 = all_13_6))
% 6.64/1.64 | | |
% 6.64/1.64 | | | BETA: splitting (30) gives:
% 6.64/1.64 | | |
% 6.64/1.64 | | | Case 1:
% 6.64/1.64 | | | |
% 6.64/1.64 | | | | (31) all_13_3 = all_13_6
% 6.64/1.64 | | | |
% 6.64/1.64 | | | | REDUCE: (22), (31) imply:
% 6.64/1.64 | | | | (32) $false
% 6.64/1.64 | | | |
% 6.64/1.64 | | | | CLOSE: (32) is inconsistent.
% 6.64/1.64 | | | |
% 6.64/1.64 | | | Case 2:
% 6.64/1.64 | | | |
% 6.64/1.64 | | | | (33) ? [v0: $i] : ? [v1: $i] : (singleton(all_13_4) = v1 &
% 6.64/1.64 | | | | singleton(all_13_5) = v0 & $i(v1) & $i(v0) & (v1 = all_13_6 |
% 6.64/1.64 | | | | v0 = all_13_6))
% 6.64/1.64 | | | |
% 6.64/1.64 | | | | DELTA: instantiating (33) with fresh symbols all_45_0, all_45_1 gives:
% 6.64/1.64 | | | | (34) singleton(all_13_4) = all_45_0 & singleton(all_13_5) = all_45_1
% 6.64/1.64 | | | | & $i(all_45_0) & $i(all_45_1) & (all_45_0 = all_13_6 | all_45_1
% 6.64/1.64 | | | | = all_13_6)
% 6.64/1.64 | | | |
% 6.64/1.64 | | | | ALPHA: (34) implies:
% 6.64/1.64 | | | | (35) singleton(all_13_5) = all_45_1
% 6.64/1.64 | | | | (36) singleton(all_13_4) = all_45_0
% 6.64/1.64 | | | | (37) all_45_0 = all_13_6 | all_45_1 = all_13_6
% 6.64/1.64 | | | |
% 6.64/1.64 | | | | GROUND_INST: instantiating (6) with all_13_1, all_45_1, all_13_5,
% 6.64/1.64 | | | | simplifying with (12), (35) gives:
% 6.64/1.64 | | | | (38) all_45_1 = all_13_1
% 6.64/1.64 | | | |
% 6.64/1.64 | | | | GROUND_INST: instantiating (6) with all_13_0, all_45_0, all_13_4,
% 6.64/1.64 | | | | simplifying with (13), (36) gives:
% 6.64/1.64 | | | | (39) all_45_0 = all_13_0
% 6.64/1.64 | | | |
% 6.64/1.64 | | | | BETA: splitting (37) gives:
% 6.64/1.64 | | | |
% 6.64/1.64 | | | | Case 1:
% 6.64/1.64 | | | | |
% 6.64/1.64 | | | | | (40) all_45_0 = all_13_6
% 6.64/1.64 | | | | |
% 6.64/1.64 | | | | | COMBINE_EQS: (39), (40) imply:
% 6.64/1.64 | | | | | (41) all_13_0 = all_13_6
% 6.64/1.64 | | | | |
% 6.64/1.64 | | | | | REDUCE: (24), (41) imply:
% 6.64/1.64 | | | | | (42) $false
% 6.64/1.64 | | | | |
% 6.64/1.64 | | | | | CLOSE: (42) is inconsistent.
% 6.64/1.64 | | | | |
% 6.64/1.64 | | | | Case 2:
% 6.64/1.64 | | | | |
% 6.64/1.64 | | | | | (43) all_45_1 = all_13_6
% 6.64/1.64 | | | | |
% 6.64/1.64 | | | | | COMBINE_EQS: (38), (43) imply:
% 6.64/1.64 | | | | | (44) all_13_1 = all_13_6
% 6.64/1.64 | | | | |
% 6.64/1.64 | | | | | SIMP: (44) implies:
% 6.64/1.64 | | | | | (45) all_13_1 = all_13_6
% 6.64/1.64 | | | | |
% 6.64/1.64 | | | | | REDUCE: (23), (45) imply:
% 6.64/1.64 | | | | | (46) $false
% 6.64/1.64 | | | | |
% 6.64/1.64 | | | | | CLOSE: (46) is inconsistent.
% 6.64/1.64 | | | | |
% 6.64/1.64 | | | | End of split
% 6.64/1.64 | | | |
% 6.64/1.64 | | | End of split
% 6.64/1.64 | | |
% 6.64/1.64 | | End of split
% 6.64/1.64 | |
% 6.64/1.64 | Case 2:
% 6.64/1.64 | |
% 6.64/1.64 | | (47) ~ (all_13_2 = empty_set) & (all_13_0 = all_13_6 | all_13_1 =
% 6.64/1.64 | | all_13_6 | all_13_3 = all_13_6 | all_13_6 = empty_set)
% 6.64/1.64 | |
% 6.64/1.64 | | ALPHA: (47) implies:
% 6.64/1.64 | | (48) ~ (all_13_2 = empty_set)
% 6.64/1.64 | | (49) all_13_0 = all_13_6 | all_13_1 = all_13_6 | all_13_3 = all_13_6 |
% 6.64/1.64 | | all_13_6 = empty_set
% 6.64/1.64 | |
% 6.64/1.64 | | BETA: splitting (18) gives:
% 6.64/1.64 | |
% 6.64/1.64 | | Case 1:
% 6.64/1.64 | | |
% 6.64/1.64 | | | (50) all_13_2 = empty_set
% 6.64/1.64 | | |
% 6.64/1.64 | | | REDUCE: (48), (50) imply:
% 6.64/1.64 | | | (51) $false
% 6.64/1.64 | | |
% 6.64/1.64 | | | CLOSE: (51) is inconsistent.
% 6.64/1.64 | | |
% 6.64/1.64 | | Case 2:
% 6.64/1.64 | | |
% 6.64/1.64 | | | (52) ? [v0: int] : ( ~ (v0 = 0) & subset(all_13_6, all_13_3) = v0)
% 6.64/1.64 | | |
% 6.64/1.64 | | | DELTA: instantiating (52) with fresh symbol all_32_0 gives:
% 6.64/1.64 | | | (53) ~ (all_32_0 = 0) & subset(all_13_6, all_13_3) = all_32_0
% 6.64/1.64 | | |
% 6.64/1.64 | | | ALPHA: (53) implies:
% 6.64/1.64 | | | (54) ~ (all_32_0 = 0)
% 6.64/1.64 | | | (55) subset(all_13_6, all_13_3) = all_32_0
% 6.64/1.64 | | |
% 6.64/1.64 | | | GROUND_INST: instantiating (2) with all_13_6, all_13_5, all_13_4,
% 6.64/1.65 | | | all_13_3, all_32_0, simplifying with (8), (9), (10), (11),
% 6.64/1.65 | | | (55) gives:
% 6.64/1.65 | | | (56) all_32_0 = 0 | ( ~ (all_13_3 = all_13_6) & ~ (all_13_6 =
% 6.64/1.65 | | | empty_set) & ? [v0: any] : ? [v1: any] : ( ~ (v1 = all_13_6)
% 6.64/1.65 | | | & ~ (v0 = all_13_6) & singleton(all_13_4) = v1 &
% 6.64/1.65 | | | singleton(all_13_5) = v0 & $i(v1) & $i(v0)))
% 6.64/1.65 | | |
% 6.64/1.65 | | | BETA: splitting (49) gives:
% 6.64/1.65 | | |
% 6.64/1.65 | | | Case 1:
% 6.64/1.65 | | | |
% 6.64/1.65 | | | | (57) all_13_6 = empty_set
% 6.64/1.65 | | | |
% 6.64/1.65 | | | | BETA: splitting (56) gives:
% 6.64/1.65 | | | |
% 6.64/1.65 | | | | Case 1:
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | (58) all_32_0 = 0
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | REDUCE: (54), (58) imply:
% 6.64/1.65 | | | | | (59) $false
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | CLOSE: (59) is inconsistent.
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | Case 2:
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | (60) ~ (all_13_3 = all_13_6) & ~ (all_13_6 = empty_set) & ? [v0:
% 6.64/1.65 | | | | | any] : ? [v1: any] : ( ~ (v1 = all_13_6) & ~ (v0 =
% 6.64/1.65 | | | | | all_13_6) & singleton(all_13_4) = v1 & singleton(all_13_5)
% 6.64/1.65 | | | | | = v0 & $i(v1) & $i(v0))
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | ALPHA: (60) implies:
% 6.64/1.65 | | | | | (61) ~ (all_13_6 = empty_set)
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | REDUCE: (57), (61) imply:
% 6.64/1.65 | | | | | (62) $false
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | CLOSE: (62) is inconsistent.
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | End of split
% 6.64/1.65 | | | |
% 6.64/1.65 | | | Case 2:
% 6.64/1.65 | | | |
% 6.64/1.65 | | | | (63) all_13_0 = all_13_6 | all_13_1 = all_13_6 | all_13_3 = all_13_6
% 6.64/1.65 | | | |
% 6.64/1.65 | | | | BETA: splitting (56) gives:
% 6.64/1.65 | | | |
% 6.64/1.65 | | | | Case 1:
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | (64) all_32_0 = 0
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | REDUCE: (54), (64) imply:
% 6.64/1.65 | | | | | (65) $false
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | CLOSE: (65) is inconsistent.
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | Case 2:
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | (66) ~ (all_13_3 = all_13_6) & ~ (all_13_6 = empty_set) & ? [v0:
% 6.64/1.65 | | | | | any] : ? [v1: any] : ( ~ (v1 = all_13_6) & ~ (v0 =
% 6.64/1.65 | | | | | all_13_6) & singleton(all_13_4) = v1 & singleton(all_13_5)
% 6.64/1.65 | | | | | = v0 & $i(v1) & $i(v0))
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | ALPHA: (66) implies:
% 6.64/1.65 | | | | | (67) ~ (all_13_3 = all_13_6)
% 6.64/1.65 | | | | | (68) ? [v0: any] : ? [v1: any] : ( ~ (v1 = all_13_6) & ~ (v0 =
% 6.64/1.65 | | | | | all_13_6) & singleton(all_13_4) = v1 & singleton(all_13_5)
% 6.64/1.65 | | | | | = v0 & $i(v1) & $i(v0))
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | DELTA: instantiating (68) with fresh symbols all_45_0, all_45_1 gives:
% 6.64/1.65 | | | | | (69) ~ (all_45_0 = all_13_6) & ~ (all_45_1 = all_13_6) &
% 6.64/1.65 | | | | | singleton(all_13_4) = all_45_0 & singleton(all_13_5) =
% 6.64/1.65 | | | | | all_45_1 & $i(all_45_0) & $i(all_45_1)
% 6.64/1.65 | | | | |
% 6.64/1.65 | | | | | ALPHA: (69) implies:
% 6.64/1.65 | | | | | (70) ~ (all_45_1 = all_13_6)
% 6.64/1.65 | | | | | (71) ~ (all_45_0 = all_13_6)
% 6.64/1.65 | | | | | (72) singleton(all_13_5) = all_45_1
% 6.64/1.65 | | | | | (73) singleton(all_13_4) = all_45_0
% 6.64/1.65 | | | | |
% 6.64/1.66 | | | | | GROUND_INST: instantiating (6) with all_13_1, all_45_1, all_13_5,
% 6.64/1.66 | | | | | simplifying with (12), (72) gives:
% 6.64/1.66 | | | | | (74) all_45_1 = all_13_1
% 6.64/1.66 | | | | |
% 6.64/1.66 | | | | | GROUND_INST: instantiating (6) with all_13_0, all_45_0, all_13_4,
% 6.64/1.66 | | | | | simplifying with (13), (73) gives:
% 6.64/1.66 | | | | | (75) all_45_0 = all_13_0
% 6.64/1.66 | | | | |
% 6.64/1.66 | | | | | REDUCE: (71), (75) imply:
% 6.64/1.66 | | | | | (76) ~ (all_13_0 = all_13_6)
% 6.64/1.66 | | | | |
% 6.64/1.66 | | | | | REDUCE: (70), (74) imply:
% 6.64/1.66 | | | | | (77) ~ (all_13_1 = all_13_6)
% 6.64/1.66 | | | | |
% 6.64/1.66 | | | | | BETA: splitting (63) gives:
% 6.64/1.66 | | | | |
% 6.64/1.66 | | | | | Case 1:
% 6.64/1.66 | | | | | |
% 6.64/1.66 | | | | | | (78) all_13_0 = all_13_6
% 6.64/1.66 | | | | | |
% 6.64/1.66 | | | | | | REDUCE: (76), (78) imply:
% 6.64/1.66 | | | | | | (79) $false
% 6.64/1.66 | | | | | |
% 6.64/1.66 | | | | | | CLOSE: (79) is inconsistent.
% 6.64/1.66 | | | | | |
% 6.64/1.66 | | | | | Case 2:
% 6.64/1.66 | | | | | |
% 6.64/1.66 | | | | | | (80) all_13_1 = all_13_6 | all_13_3 = all_13_6
% 6.64/1.66 | | | | | |
% 6.64/1.66 | | | | | | BETA: splitting (80) gives:
% 6.64/1.66 | | | | | |
% 6.64/1.66 | | | | | | Case 1:
% 6.64/1.66 | | | | | | |
% 6.64/1.66 | | | | | | | (81) all_13_1 = all_13_6
% 6.64/1.66 | | | | | | |
% 6.64/1.66 | | | | | | | REDUCE: (77), (81) imply:
% 6.64/1.66 | | | | | | | (82) $false
% 6.64/1.66 | | | | | | |
% 6.64/1.66 | | | | | | | CLOSE: (82) is inconsistent.
% 6.64/1.66 | | | | | | |
% 6.64/1.66 | | | | | | Case 2:
% 6.64/1.66 | | | | | | |
% 6.64/1.66 | | | | | | | (83) all_13_3 = all_13_6
% 6.64/1.66 | | | | | | |
% 6.64/1.66 | | | | | | | REDUCE: (67), (83) imply:
% 6.64/1.66 | | | | | | | (84) $false
% 6.64/1.66 | | | | | | |
% 6.64/1.66 | | | | | | | CLOSE: (84) is inconsistent.
% 6.64/1.66 | | | | | | |
% 6.64/1.66 | | | | | | End of split
% 6.64/1.66 | | | | | |
% 6.64/1.66 | | | | | End of split
% 6.64/1.66 | | | | |
% 6.64/1.66 | | | | End of split
% 6.64/1.66 | | | |
% 6.64/1.66 | | | End of split
% 6.64/1.66 | | |
% 6.64/1.66 | | End of split
% 6.64/1.66 | |
% 6.64/1.66 | End of split
% 6.64/1.66 |
% 6.64/1.66 End of proof
% 6.64/1.66 % SZS output end Proof for theBenchmark
% 6.64/1.66
% 6.64/1.66 1039ms
%------------------------------------------------------------------------------