TSTP Solution File: SET930+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET930+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 15:27:06 EDT 2023
% Result : Theorem 4.61s 1.40s
% Output : Proof 7.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 09:16:29 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 ________ _____
% 0.20/0.56 ___ __ \_________(_)________________________________
% 0.20/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.56
% 0.20/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.56 (2023-06-19)
% 0.20/0.56
% 0.20/0.56 (c) Philipp Rümmer, 2009-2023
% 0.20/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.56 Amanda Stjerna.
% 0.20/0.56 Free software under BSD-3-Clause.
% 0.20/0.56
% 0.20/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.56
% 0.20/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.57 Running up to 7 provers in parallel.
% 0.20/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.16/0.96 Prover 4: Preprocessing ...
% 2.16/0.96 Prover 1: Preprocessing ...
% 2.43/1.00 Prover 5: Preprocessing ...
% 2.43/1.00 Prover 0: Preprocessing ...
% 2.43/1.00 Prover 6: Preprocessing ...
% 2.43/1.00 Prover 3: Preprocessing ...
% 2.43/1.00 Prover 2: Preprocessing ...
% 4.33/1.25 Prover 6: Constructing countermodel ...
% 4.33/1.25 Prover 1: Constructing countermodel ...
% 4.33/1.25 Prover 4: Constructing countermodel ...
% 4.33/1.25 Prover 3: Constructing countermodel ...
% 4.33/1.26 Prover 5: Proving ...
% 4.33/1.26 Prover 0: Proving ...
% 4.61/1.29 Prover 2: Proving ...
% 4.61/1.40 Prover 3: proved (822ms)
% 4.61/1.40
% 4.61/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.61/1.40
% 4.61/1.42 Prover 2: stopped
% 4.61/1.42 Prover 0: stopped
% 4.61/1.42 Prover 6: stopped
% 4.61/1.42 Prover 5: stopped
% 4.61/1.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.61/1.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.61/1.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.61/1.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.61/1.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.28/1.44 Prover 8: Preprocessing ...
% 5.77/1.45 Prover 11: Preprocessing ...
% 5.77/1.46 Prover 10: Preprocessing ...
% 5.77/1.46 Prover 7: Preprocessing ...
% 5.77/1.47 Prover 13: Preprocessing ...
% 5.77/1.49 Prover 8: Warning: ignoring some quantifiers
% 5.77/1.50 Prover 8: Constructing countermodel ...
% 6.25/1.52 Prover 11: Constructing countermodel ...
% 6.25/1.52 Prover 7: Constructing countermodel ...
% 6.25/1.55 Prover 10: Constructing countermodel ...
% 6.25/1.55 Prover 13: Warning: ignoring some quantifiers
% 6.60/1.56 Prover 13: Constructing countermodel ...
% 6.60/1.59 Prover 1: Found proof (size 85)
% 6.60/1.59 Prover 1: proved (1004ms)
% 6.60/1.59 Prover 4: Found proof (size 86)
% 6.60/1.59 Prover 4: proved (1005ms)
% 6.60/1.59 Prover 13: stopped
% 6.60/1.59 Prover 11: stopped
% 6.60/1.59 Prover 10: stopped
% 6.60/1.59 Prover 8: stopped
% 6.60/1.59 Prover 7: stopped
% 6.60/1.59
% 6.60/1.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.60/1.59
% 6.60/1.61 % SZS output start Proof for theBenchmark
% 6.60/1.62 Assumptions after simplification:
% 6.60/1.62 ---------------------------------
% 6.60/1.62
% 6.60/1.62 (commutativity_k2_tarski)
% 6.60/1.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) |
% 6.60/1.64 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 6.60/1.64
% 6.60/1.64 (l39_zfmisc_1)
% 7.11/1.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 7.11/1.65 (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ $i(v2)
% 7.11/1.65 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] :
% 7.11/1.65 (singleton(v0) = v7 & in(v1, v2) = v6 & in(v0, v2) = v5 & $i(v7) & (v7 = v4
% 7.11/1.65 | v5 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0))))) & ! [v0: $i] : ! [v1: $i] :
% 7.11/1.65 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (set_difference(v3, v2) = v4) |
% 7.11/1.65 ~ (unordered_pair(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 7.11/1.65 [v5: $i] : ? [v6: any] : ? [v7: any] : (singleton(v0) = v5 & in(v1, v2) =
% 7.11/1.65 v7 & in(v0, v2) = v6 & $i(v5) & ( ~ (v5 = v4) | ( ~ (v6 = 0) & (v7 = 0 |
% 7.11/1.65 v1 = v0)))))
% 7.11/1.65
% 7.11/1.65 (t72_zfmisc_1)
% 7.11/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3
% 7.11/1.66 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~
% 7.11/1.66 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v1, v2) =
% 7.11/1.66 v6 & in(v0, v2) = v5 & (v6 = 0 | v5 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 7.11/1.66 ! [v2: $i] : ! [v3: $i] : ( ~ (set_difference(v3, v2) = v3) | ~
% 7.11/1.66 (unordered_pair(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 7.11/1.66 int] : ? [v5: int] : ( ~ (v5 = 0) & ~ (v4 = 0) & in(v1, v2) = v5 &
% 7.11/1.66 in(v0, v2) = v4))
% 7.11/1.66
% 7.11/1.66 (t73_zfmisc_1)
% 7.11/1.66 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 7.11/1.66 [v4: $i] : (v4 = empty_set | ~ (set_difference(v3, v2) = v4) | ~
% 7.11/1.66 (unordered_pair(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 7.11/1.66 any] : ? [v6: any] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) |
% 7.11/1.66 ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 7.11/1.66 ( ~ (set_difference(v3, v2) = empty_set) | ~ (unordered_pair(v0, v1) = v3) |
% 7.11/1.66 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 7.11/1.66
% 7.11/1.66 (t74_zfmisc_1)
% 7.11/1.66 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 7.11/1.66 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & ~ (v5 = v4) & ~ (v4 =
% 7.11/1.66 v3) & ~ (v4 = empty_set) & set_difference(v3, v2) = v4 & singleton(v1) =
% 7.11/1.66 v6 & singleton(v0) = v5 & unordered_pair(v0, v1) = v3 & $i(v6) & $i(v5) &
% 7.11/1.66 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.11/1.66
% 7.11/1.67 (function-axioms)
% 7.11/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.11/1.67 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 7.11/1.67 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.11/1.67 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 7.11/1.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.11/1.67 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 7.11/1.67 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 7.11/1.67 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.11/1.67 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 7.11/1.67 (empty(v2) = v0))
% 7.11/1.67
% 7.11/1.67 Further assumptions not needed in the proof:
% 7.11/1.67 --------------------------------------------
% 7.11/1.67 antisymmetry_r2_hidden, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0
% 7.11/1.67
% 7.11/1.67 Those formulas are unsatisfiable:
% 7.11/1.67 ---------------------------------
% 7.11/1.67
% 7.11/1.67 Begin of proof
% 7.11/1.67 |
% 7.11/1.67 | ALPHA: (l39_zfmisc_1) implies:
% 7.11/1.68 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 7.11/1.68 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) |
% 7.11/1.68 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: any] : ?
% 7.11/1.68 | [v7: any] : (singleton(v0) = v5 & in(v1, v2) = v7 & in(v0, v2) = v6 &
% 7.11/1.68 | $i(v5) & ( ~ (v5 = v4) | ( ~ (v6 = 0) & (v7 = 0 | v1 = v0)))))
% 7.11/1.68 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 7.11/1.68 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) |
% 7.11/1.68 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ?
% 7.11/1.68 | [v7: $i] : (singleton(v0) = v7 & in(v1, v2) = v6 & in(v0, v2) = v5 &
% 7.11/1.68 | $i(v7) & (v7 = v4 | v5 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0)))))
% 7.11/1.68 |
% 7.11/1.68 | ALPHA: (t72_zfmisc_1) implies:
% 7.11/1.68 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 7.11/1.68 | (v4 = v3 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0,
% 7.11/1.68 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ?
% 7.11/1.68 | [v6: any] : (in(v1, v2) = v6 & in(v0, v2) = v5 & (v6 = 0 | v5 = 0)))
% 7.11/1.68 |
% 7.11/1.68 | ALPHA: (t73_zfmisc_1) implies:
% 7.11/1.68 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 7.11/1.68 | (v4 = empty_set | ~ (set_difference(v3, v2) = v4) | ~
% 7.11/1.68 | (unordered_pair(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 7.11/1.68 | ? [v5: any] : ? [v6: any] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~
% 7.11/1.68 | (v6 = 0) | ~ (v5 = 0))))
% 7.11/1.68 |
% 7.11/1.68 | ALPHA: (t74_zfmisc_1) implies:
% 7.11/1.68 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 7.11/1.68 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & ~ (v5 = v4) & ~ (v4 = v3)
% 7.11/1.68 | & ~ (v4 = empty_set) & set_difference(v3, v2) = v4 & singleton(v1) =
% 7.11/1.68 | v6 & singleton(v0) = v5 & unordered_pair(v0, v1) = v3 & $i(v6) &
% 7.31/1.68 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.31/1.68 |
% 7.31/1.68 | ALPHA: (function-axioms) implies:
% 7.31/1.69 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 7.31/1.69 | = v1) | ~ (singleton(v2) = v0))
% 7.31/1.69 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.31/1.69 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 7.31/1.69 |
% 7.31/1.69 | DELTA: instantiating (5) with fresh symbols all_13_0, all_13_1, all_13_2,
% 7.31/1.69 | all_13_3, all_13_4, all_13_5, all_13_6 gives:
% 7.31/1.69 | (8) ~ (all_13_0 = all_13_2) & ~ (all_13_1 = all_13_2) & ~ (all_13_2 =
% 7.31/1.69 | all_13_3) & ~ (all_13_2 = empty_set) & set_difference(all_13_3,
% 7.31/1.69 | all_13_4) = all_13_2 & singleton(all_13_5) = all_13_0 &
% 7.31/1.69 | singleton(all_13_6) = all_13_1 & unordered_pair(all_13_6, all_13_5) =
% 7.31/1.69 | all_13_3 & $i(all_13_0) & $i(all_13_1) & $i(all_13_2) & $i(all_13_3) &
% 7.31/1.69 | $i(all_13_4) & $i(all_13_5) & $i(all_13_6)
% 7.31/1.69 |
% 7.31/1.69 | ALPHA: (8) implies:
% 7.31/1.69 | (9) ~ (all_13_2 = empty_set)
% 7.31/1.69 | (10) ~ (all_13_2 = all_13_3)
% 7.31/1.69 | (11) ~ (all_13_1 = all_13_2)
% 7.31/1.69 | (12) ~ (all_13_0 = all_13_2)
% 7.31/1.69 | (13) $i(all_13_6)
% 7.31/1.69 | (14) $i(all_13_5)
% 7.31/1.69 | (15) $i(all_13_4)
% 7.31/1.69 | (16) unordered_pair(all_13_6, all_13_5) = all_13_3
% 7.31/1.69 | (17) singleton(all_13_6) = all_13_1
% 7.31/1.69 | (18) singleton(all_13_5) = all_13_0
% 7.31/1.69 | (19) set_difference(all_13_3, all_13_4) = all_13_2
% 7.31/1.69 |
% 7.31/1.69 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_13_6, all_13_5,
% 7.31/1.69 | all_13_3, simplifying with (13), (14), (16) gives:
% 7.31/1.69 | (20) unordered_pair(all_13_5, all_13_6) = all_13_3 & $i(all_13_3)
% 7.31/1.69 |
% 7.31/1.69 | ALPHA: (20) implies:
% 7.31/1.69 | (21) unordered_pair(all_13_5, all_13_6) = all_13_3
% 7.31/1.69 |
% 7.31/1.69 | GROUND_INST: instantiating (3) with all_13_6, all_13_5, all_13_4, all_13_3,
% 7.31/1.69 | all_13_2, simplifying with (13), (14), (15), (16), (19) gives:
% 7.31/1.69 | (22) all_13_2 = all_13_3 | ? [v0: any] : ? [v1: any] : (in(all_13_5,
% 7.31/1.69 | all_13_4) = v1 & in(all_13_6, all_13_4) = v0 & (v1 = 0 | v0 = 0))
% 7.31/1.69 |
% 7.31/1.69 | GROUND_INST: instantiating (4) with all_13_6, all_13_5, all_13_4, all_13_3,
% 7.31/1.69 | all_13_2, simplifying with (13), (14), (15), (16), (19) gives:
% 7.31/1.70 | (23) all_13_2 = empty_set | ? [v0: any] : ? [v1: any] : (in(all_13_5,
% 7.31/1.70 | all_13_4) = v1 & in(all_13_6, all_13_4) = v0 & ( ~ (v1 = 0) | ~
% 7.31/1.70 | (v0 = 0)))
% 7.31/1.70 |
% 7.31/1.70 | GROUND_INST: instantiating (2) with all_13_6, all_13_5, all_13_4, all_13_3,
% 7.31/1.70 | all_13_2, simplifying with (13), (14), (15), (16), (19) gives:
% 7.31/1.70 | (24) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (singleton(all_13_6) = v2
% 7.31/1.70 | & in(all_13_5, all_13_4) = v1 & in(all_13_6, all_13_4) = v0 & $i(v2)
% 7.31/1.70 | & (v2 = all_13_2 | v0 = 0 | ( ~ (v1 = 0) & ~ (all_13_5 =
% 7.31/1.70 | all_13_6))))
% 7.31/1.70 |
% 7.31/1.70 | GROUND_INST: instantiating (1) with all_13_6, all_13_5, all_13_4, all_13_3,
% 7.31/1.70 | all_13_2, simplifying with (13), (14), (15), (16), (19) gives:
% 7.31/1.70 | (25) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (singleton(all_13_6) = v0
% 7.31/1.70 | & in(all_13_5, all_13_4) = v2 & in(all_13_6, all_13_4) = v1 & $i(v0)
% 7.31/1.70 | & ( ~ (v0 = all_13_2) | ( ~ (v1 = 0) & (v2 = 0 | all_13_5 =
% 7.31/1.70 | all_13_6))))
% 7.31/1.70 |
% 7.31/1.70 | DELTA: instantiating (25) with fresh symbols all_21_0, all_21_1, all_21_2
% 7.31/1.70 | gives:
% 7.31/1.70 | (26) singleton(all_13_6) = all_21_2 & in(all_13_5, all_13_4) = all_21_0 &
% 7.31/1.70 | in(all_13_6, all_13_4) = all_21_1 & $i(all_21_2) & ( ~ (all_21_2 =
% 7.31/1.70 | all_13_2) | ( ~ (all_21_1 = 0) & (all_21_0 = 0 | all_13_5 =
% 7.31/1.70 | all_13_6)))
% 7.31/1.70 |
% 7.31/1.70 | ALPHA: (26) implies:
% 7.31/1.70 | (27) in(all_13_6, all_13_4) = all_21_1
% 7.31/1.70 | (28) in(all_13_5, all_13_4) = all_21_0
% 7.31/1.70 | (29) singleton(all_13_6) = all_21_2
% 7.31/1.70 |
% 7.31/1.70 | DELTA: instantiating (24) with fresh symbols all_23_0, all_23_1, all_23_2
% 7.31/1.70 | gives:
% 7.31/1.70 | (30) singleton(all_13_6) = all_23_0 & in(all_13_5, all_13_4) = all_23_1 &
% 7.31/1.70 | in(all_13_6, all_13_4) = all_23_2 & $i(all_23_0) & (all_23_0 =
% 7.31/1.70 | all_13_2 | all_23_2 = 0 | ( ~ (all_23_1 = 0) & ~ (all_13_5 =
% 7.31/1.70 | all_13_6)))
% 7.31/1.70 |
% 7.31/1.70 | ALPHA: (30) implies:
% 7.31/1.70 | (31) in(all_13_6, all_13_4) = all_23_2
% 7.31/1.70 | (32) in(all_13_5, all_13_4) = all_23_1
% 7.31/1.70 | (33) singleton(all_13_6) = all_23_0
% 7.31/1.70 | (34) all_23_0 = all_13_2 | all_23_2 = 0 | ( ~ (all_23_1 = 0) & ~ (all_13_5
% 7.31/1.70 | = all_13_6))
% 7.31/1.70 |
% 7.31/1.70 | GROUND_INST: instantiating (7) with all_21_1, all_23_2, all_13_4, all_13_6,
% 7.31/1.70 | simplifying with (27), (31) gives:
% 7.31/1.70 | (35) all_23_2 = all_21_1
% 7.31/1.70 |
% 7.31/1.70 | GROUND_INST: instantiating (7) with all_21_0, all_23_1, all_13_4, all_13_5,
% 7.31/1.70 | simplifying with (28), (32) gives:
% 7.31/1.70 | (36) all_23_1 = all_21_0
% 7.31/1.70 |
% 7.31/1.70 | GROUND_INST: instantiating (6) with all_13_1, all_23_0, all_13_6, simplifying
% 7.31/1.70 | with (17), (33) gives:
% 7.31/1.70 | (37) all_23_0 = all_13_1
% 7.31/1.70 |
% 7.31/1.71 | GROUND_INST: instantiating (6) with all_21_2, all_23_0, all_13_6, simplifying
% 7.31/1.71 | with (29), (33) gives:
% 7.31/1.71 | (38) all_23_0 = all_21_2
% 7.31/1.71 |
% 7.31/1.71 | COMBINE_EQS: (37), (38) imply:
% 7.31/1.71 | (39) all_21_2 = all_13_1
% 7.31/1.71 |
% 7.31/1.71 | GROUND_INST: instantiating (2) with all_13_5, all_13_6, all_13_4, all_13_3,
% 7.31/1.71 | all_13_2, simplifying with (13), (14), (15), (19), (21) gives:
% 7.31/1.71 | (40) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (singleton(all_13_5) = v2
% 7.31/1.71 | & in(all_13_5, all_13_4) = v0 & in(all_13_6, all_13_4) = v1 & $i(v2)
% 7.31/1.71 | & (v2 = all_13_2 | v0 = 0 | ( ~ (v1 = 0) & ~ (all_13_5 =
% 7.31/1.71 | all_13_6))))
% 7.31/1.71 |
% 7.31/1.71 | DELTA: instantiating (40) with fresh symbols all_34_0, all_34_1, all_34_2
% 7.31/1.71 | gives:
% 7.31/1.71 | (41) singleton(all_13_5) = all_34_0 & in(all_13_5, all_13_4) = all_34_2 &
% 7.31/1.71 | in(all_13_6, all_13_4) = all_34_1 & $i(all_34_0) & (all_34_0 =
% 7.31/1.71 | all_13_2 | all_34_2 = 0 | ( ~ (all_34_1 = 0) & ~ (all_13_5 =
% 7.31/1.71 | all_13_6)))
% 7.31/1.71 |
% 7.31/1.71 | ALPHA: (41) implies:
% 7.31/1.71 | (42) in(all_13_6, all_13_4) = all_34_1
% 7.31/1.71 | (43) in(all_13_5, all_13_4) = all_34_2
% 7.31/1.71 | (44) singleton(all_13_5) = all_34_0
% 7.31/1.71 | (45) all_34_0 = all_13_2 | all_34_2 = 0 | ( ~ (all_34_1 = 0) & ~ (all_13_5
% 7.31/1.71 | = all_13_6))
% 7.31/1.71 |
% 7.31/1.71 | GROUND_INST: instantiating (7) with all_21_1, all_34_1, all_13_4, all_13_6,
% 7.31/1.71 | simplifying with (27), (42) gives:
% 7.31/1.71 | (46) all_34_1 = all_21_1
% 7.31/1.71 |
% 7.31/1.71 | GROUND_INST: instantiating (7) with all_21_0, all_34_2, all_13_4, all_13_5,
% 7.31/1.71 | simplifying with (28), (43) gives:
% 7.31/1.71 | (47) all_34_2 = all_21_0
% 7.31/1.71 |
% 7.31/1.71 | GROUND_INST: instantiating (6) with all_13_0, all_34_0, all_13_5, simplifying
% 7.31/1.71 | with (18), (44) gives:
% 7.31/1.71 | (48) all_34_0 = all_13_0
% 7.31/1.71 |
% 7.31/1.71 | BETA: splitting (23) gives:
% 7.31/1.71 |
% 7.31/1.71 | Case 1:
% 7.31/1.71 | |
% 7.31/1.71 | | (49) all_13_2 = empty_set
% 7.31/1.71 | |
% 7.31/1.71 | | REDUCE: (9), (49) imply:
% 7.31/1.71 | | (50) $false
% 7.31/1.71 | |
% 7.31/1.71 | | CLOSE: (50) is inconsistent.
% 7.31/1.71 | |
% 7.31/1.71 | Case 2:
% 7.31/1.71 | |
% 7.31/1.71 | | (51) ? [v0: any] : ? [v1: any] : (in(all_13_5, all_13_4) = v1 &
% 7.31/1.71 | | in(all_13_6, all_13_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.31/1.71 | |
% 7.31/1.71 | | DELTA: instantiating (51) with fresh symbols all_47_0, all_47_1 gives:
% 7.31/1.72 | | (52) in(all_13_5, all_13_4) = all_47_0 & in(all_13_6, all_13_4) =
% 7.31/1.72 | | all_47_1 & ( ~ (all_47_0 = 0) | ~ (all_47_1 = 0))
% 7.31/1.72 | |
% 7.31/1.72 | | ALPHA: (52) implies:
% 7.31/1.72 | | (53) in(all_13_6, all_13_4) = all_47_1
% 7.31/1.72 | | (54) in(all_13_5, all_13_4) = all_47_0
% 7.31/1.72 | | (55) ~ (all_47_0 = 0) | ~ (all_47_1 = 0)
% 7.31/1.72 | |
% 7.31/1.72 | | GROUND_INST: instantiating (7) with all_21_1, all_47_1, all_13_4, all_13_6,
% 7.31/1.72 | | simplifying with (27), (53) gives:
% 7.31/1.72 | | (56) all_47_1 = all_21_1
% 7.31/1.72 | |
% 7.31/1.72 | | GROUND_INST: instantiating (7) with all_21_0, all_47_0, all_13_4, all_13_5,
% 7.31/1.72 | | simplifying with (28), (54) gives:
% 7.31/1.72 | | (57) all_47_0 = all_21_0
% 7.31/1.72 | |
% 7.31/1.72 | | BETA: splitting (22) gives:
% 7.31/1.72 | |
% 7.31/1.72 | | Case 1:
% 7.31/1.72 | | |
% 7.31/1.72 | | | (58) all_13_2 = all_13_3
% 7.31/1.72 | | |
% 7.31/1.72 | | | REDUCE: (10), (58) imply:
% 7.31/1.72 | | | (59) $false
% 7.31/1.72 | | |
% 7.31/1.72 | | | CLOSE: (59) is inconsistent.
% 7.31/1.72 | | |
% 7.31/1.72 | | Case 2:
% 7.31/1.72 | | |
% 7.31/1.72 | | | (60) ? [v0: any] : ? [v1: any] : (in(all_13_5, all_13_4) = v1 &
% 7.31/1.72 | | | in(all_13_6, all_13_4) = v0 & (v1 = 0 | v0 = 0))
% 7.31/1.72 | | |
% 7.31/1.72 | | | DELTA: instantiating (60) with fresh symbols all_60_0, all_60_1 gives:
% 7.31/1.72 | | | (61) in(all_13_5, all_13_4) = all_60_0 & in(all_13_6, all_13_4) =
% 7.31/1.72 | | | all_60_1 & (all_60_0 = 0 | all_60_1 = 0)
% 7.31/1.72 | | |
% 7.31/1.72 | | | ALPHA: (61) implies:
% 7.31/1.72 | | | (62) in(all_13_6, all_13_4) = all_60_1
% 7.31/1.72 | | | (63) in(all_13_5, all_13_4) = all_60_0
% 7.31/1.72 | | | (64) all_60_0 = 0 | all_60_1 = 0
% 7.31/1.72 | | |
% 7.31/1.72 | | | GROUND_INST: instantiating (7) with all_21_1, all_60_1, all_13_4,
% 7.31/1.72 | | | all_13_6, simplifying with (27), (62) gives:
% 7.31/1.72 | | | (65) all_60_1 = all_21_1
% 7.31/1.72 | | |
% 7.31/1.72 | | | GROUND_INST: instantiating (7) with all_21_0, all_60_0, all_13_4,
% 7.31/1.72 | | | all_13_5, simplifying with (28), (63) gives:
% 7.31/1.72 | | | (66) all_60_0 = all_21_0
% 7.31/1.72 | | |
% 7.31/1.72 | | | BETA: splitting (34) gives:
% 7.31/1.72 | | |
% 7.31/1.72 | | | Case 1:
% 7.31/1.72 | | | |
% 7.31/1.72 | | | | (67) all_23_2 = 0
% 7.31/1.72 | | | |
% 7.31/1.72 | | | | COMBINE_EQS: (35), (67) imply:
% 7.31/1.72 | | | | (68) all_21_1 = 0
% 7.31/1.72 | | | |
% 7.31/1.72 | | | | COMBINE_EQS: (46), (68) imply:
% 7.31/1.72 | | | | (69) all_34_1 = 0
% 7.31/1.72 | | | |
% 7.31/1.72 | | | | COMBINE_EQS: (56), (68) imply:
% 7.31/1.72 | | | | (70) all_47_1 = 0
% 7.31/1.72 | | | |
% 7.31/1.72 | | | | BETA: splitting (55) gives:
% 7.31/1.72 | | | |
% 7.31/1.72 | | | | Case 1:
% 7.31/1.72 | | | | |
% 7.31/1.72 | | | | | (71) ~ (all_47_0 = 0)
% 7.31/1.72 | | | | |
% 7.31/1.72 | | | | | REDUCE: (57), (71) imply:
% 7.31/1.72 | | | | | (72) ~ (all_21_0 = 0)
% 7.31/1.72 | | | | |
% 7.31/1.72 | | | | | BETA: splitting (45) gives:
% 7.31/1.72 | | | | |
% 7.31/1.72 | | | | | Case 1:
% 7.31/1.72 | | | | | |
% 7.31/1.72 | | | | | | (73) all_34_2 = 0
% 7.31/1.72 | | | | | |
% 7.31/1.72 | | | | | | COMBINE_EQS: (47), (73) imply:
% 7.31/1.72 | | | | | | (74) all_21_0 = 0
% 7.31/1.72 | | | | | |
% 7.31/1.72 | | | | | | SIMP: (74) implies:
% 7.31/1.72 | | | | | | (75) all_21_0 = 0
% 7.31/1.72 | | | | | |
% 7.31/1.72 | | | | | | REDUCE: (72), (75) imply:
% 7.31/1.72 | | | | | | (76) $false
% 7.31/1.72 | | | | | |
% 7.31/1.72 | | | | | | CLOSE: (76) is inconsistent.
% 7.31/1.72 | | | | | |
% 7.31/1.72 | | | | | Case 2:
% 7.31/1.72 | | | | | |
% 7.31/1.72 | | | | | | (77) all_34_0 = all_13_2 | ( ~ (all_34_1 = 0) & ~ (all_13_5 =
% 7.31/1.72 | | | | | | all_13_6))
% 7.31/1.72 | | | | | |
% 7.31/1.72 | | | | | | BETA: splitting (77) gives:
% 7.31/1.72 | | | | | |
% 7.31/1.72 | | | | | | Case 1:
% 7.31/1.72 | | | | | | |
% 7.31/1.72 | | | | | | | (78) all_34_0 = all_13_2
% 7.31/1.72 | | | | | | |
% 7.31/1.72 | | | | | | | COMBINE_EQS: (48), (78) imply:
% 7.31/1.73 | | | | | | | (79) all_13_0 = all_13_2
% 7.31/1.73 | | | | | | |
% 7.31/1.73 | | | | | | | REDUCE: (12), (79) imply:
% 7.31/1.73 | | | | | | | (80) $false
% 7.31/1.73 | | | | | | |
% 7.31/1.73 | | | | | | | CLOSE: (80) is inconsistent.
% 7.31/1.73 | | | | | | |
% 7.31/1.73 | | | | | | Case 2:
% 7.31/1.73 | | | | | | |
% 7.31/1.73 | | | | | | | (81) ~ (all_34_1 = 0) & ~ (all_13_5 = all_13_6)
% 7.31/1.73 | | | | | | |
% 7.31/1.73 | | | | | | | ALPHA: (81) implies:
% 7.31/1.73 | | | | | | | (82) ~ (all_34_1 = 0)
% 7.31/1.73 | | | | | | |
% 7.31/1.73 | | | | | | | REDUCE: (69), (82) imply:
% 7.31/1.73 | | | | | | | (83) $false
% 7.31/1.73 | | | | | | |
% 7.31/1.73 | | | | | | | CLOSE: (83) is inconsistent.
% 7.31/1.73 | | | | | | |
% 7.31/1.73 | | | | | | End of split
% 7.31/1.73 | | | | | |
% 7.31/1.73 | | | | | End of split
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | Case 2:
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | (84) ~ (all_47_1 = 0)
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | REDUCE: (70), (84) imply:
% 7.31/1.73 | | | | | (85) $false
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | CLOSE: (85) is inconsistent.
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | End of split
% 7.31/1.73 | | | |
% 7.31/1.73 | | | Case 2:
% 7.31/1.73 | | | |
% 7.31/1.73 | | | | (86) ~ (all_23_2 = 0)
% 7.31/1.73 | | | | (87) all_23_0 = all_13_2 | ( ~ (all_23_1 = 0) & ~ (all_13_5 =
% 7.31/1.73 | | | | all_13_6))
% 7.31/1.73 | | | |
% 7.31/1.73 | | | | REDUCE: (35), (86) imply:
% 7.31/1.73 | | | | (88) ~ (all_21_1 = 0)
% 7.31/1.73 | | | |
% 7.31/1.73 | | | | BETA: splitting (87) gives:
% 7.31/1.73 | | | |
% 7.31/1.73 | | | | Case 1:
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | (89) all_23_0 = all_13_2
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | COMBINE_EQS: (37), (89) imply:
% 7.31/1.73 | | | | | (90) all_13_1 = all_13_2
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | REDUCE: (11), (90) imply:
% 7.31/1.73 | | | | | (91) $false
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | CLOSE: (91) is inconsistent.
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | Case 2:
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | (92) ~ (all_23_1 = 0) & ~ (all_13_5 = all_13_6)
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | ALPHA: (92) implies:
% 7.31/1.73 | | | | | (93) ~ (all_23_1 = 0)
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | REDUCE: (36), (93) imply:
% 7.31/1.73 | | | | | (94) ~ (all_21_0 = 0)
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | BETA: splitting (64) gives:
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | | Case 1:
% 7.31/1.73 | | | | | |
% 7.31/1.73 | | | | | | (95) all_60_0 = 0
% 7.31/1.73 | | | | | |
% 7.31/1.73 | | | | | | COMBINE_EQS: (66), (95) imply:
% 7.31/1.73 | | | | | | (96) all_21_0 = 0
% 7.31/1.73 | | | | | |
% 7.31/1.73 | | | | | | REDUCE: (94), (96) imply:
% 7.31/1.73 | | | | | | (97) $false
% 7.31/1.73 | | | | | |
% 7.31/1.73 | | | | | | CLOSE: (97) is inconsistent.
% 7.31/1.73 | | | | | |
% 7.31/1.73 | | | | | Case 2:
% 7.31/1.73 | | | | | |
% 7.31/1.73 | | | | | | (98) all_60_1 = 0
% 7.31/1.73 | | | | | |
% 7.31/1.73 | | | | | | COMBINE_EQS: (65), (98) imply:
% 7.31/1.73 | | | | | | (99) all_21_1 = 0
% 7.31/1.73 | | | | | |
% 7.31/1.73 | | | | | | REDUCE: (88), (99) imply:
% 7.31/1.73 | | | | | | (100) $false
% 7.31/1.73 | | | | | |
% 7.31/1.73 | | | | | | CLOSE: (100) is inconsistent.
% 7.31/1.73 | | | | | |
% 7.31/1.73 | | | | | End of split
% 7.31/1.73 | | | | |
% 7.31/1.73 | | | | End of split
% 7.31/1.73 | | | |
% 7.31/1.73 | | | End of split
% 7.31/1.73 | | |
% 7.31/1.73 | | End of split
% 7.31/1.73 | |
% 7.31/1.73 | End of split
% 7.31/1.73 |
% 7.31/1.73 End of proof
% 7.31/1.73 % SZS output end Proof for theBenchmark
% 7.31/1.73
% 7.31/1.73 1171ms
%------------------------------------------------------------------------------