TSTP Solution File: SET882+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET882+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 15:26:54 EDT 2023
% Result : Theorem 4.82s 1.49s
% Output : Proof 6.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET882+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 16:13:44 EDT 2023
% 0.13/0.35 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 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 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 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
% 1.96/1.02 Prover 1: Preprocessing ...
% 1.96/1.02 Prover 4: Preprocessing ...
% 1.96/1.06 Prover 5: Preprocessing ...
% 1.96/1.06 Prover 3: Preprocessing ...
% 1.96/1.06 Prover 2: Preprocessing ...
% 1.96/1.06 Prover 6: Preprocessing ...
% 1.96/1.06 Prover 0: Preprocessing ...
% 3.58/1.23 Prover 4: Warning: ignoring some quantifiers
% 3.58/1.23 Prover 1: Warning: ignoring some quantifiers
% 3.58/1.24 Prover 3: Warning: ignoring some quantifiers
% 3.58/1.25 Prover 3: Constructing countermodel ...
% 3.58/1.25 Prover 1: Constructing countermodel ...
% 3.58/1.25 Prover 6: Proving ...
% 3.58/1.25 Prover 4: Constructing countermodel ...
% 3.58/1.27 Prover 5: Proving ...
% 3.58/1.27 Prover 0: Proving ...
% 4.07/1.30 Prover 2: Proving ...
% 4.82/1.49 Prover 5: proved (834ms)
% 4.82/1.49
% 4.82/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.82/1.49
% 4.82/1.49 Prover 6: stopped
% 4.82/1.50 Prover 2: stopped
% 4.82/1.51 Prover 3: stopped
% 4.82/1.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.82/1.51 Prover 0: stopped
% 4.82/1.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.82/1.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.82/1.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.82/1.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.82/1.53 Prover 13: Preprocessing ...
% 4.82/1.54 Prover 7: Preprocessing ...
% 4.82/1.54 Prover 10: Preprocessing ...
% 5.56/1.55 Prover 11: Preprocessing ...
% 5.56/1.55 Prover 8: Preprocessing ...
% 5.81/1.58 Prover 7: Warning: ignoring some quantifiers
% 5.81/1.59 Prover 7: Constructing countermodel ...
% 5.81/1.59 Prover 1: Found proof (size 35)
% 5.81/1.59 Prover 1: proved (950ms)
% 5.81/1.59 Prover 4: stopped
% 5.81/1.59 Prover 10: Warning: ignoring some quantifiers
% 5.81/1.59 Prover 7: stopped
% 5.81/1.60 Prover 10: Constructing countermodel ...
% 5.81/1.60 Prover 10: stopped
% 5.81/1.60 Prover 8: Warning: ignoring some quantifiers
% 5.81/1.61 Prover 11: Warning: ignoring some quantifiers
% 5.81/1.61 Prover 8: Constructing countermodel ...
% 5.81/1.61 Prover 11: Constructing countermodel ...
% 5.81/1.62 Prover 11: stopped
% 5.81/1.62 Prover 8: stopped
% 5.81/1.62 Prover 13: Warning: ignoring some quantifiers
% 5.81/1.63 Prover 13: Constructing countermodel ...
% 5.81/1.63 Prover 13: stopped
% 5.81/1.63
% 5.81/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.81/1.63
% 6.35/1.64 % SZS output start Proof for theBenchmark
% 6.35/1.65 Assumptions after simplification:
% 6.35/1.65 ---------------------------------
% 6.35/1.65
% 6.35/1.65 (d1_tarski)
% 6.55/1.68 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) |
% 6.55/1.68 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 &
% 6.55/1.68 $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0: $i]
% 6.55/1.68 : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2:
% 6.55/1.68 $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & ! [v2: int] : (v2 =
% 6.55/1.68 0 | ~ (in(v0, v1) = v2))))
% 6.55/1.68
% 6.55/1.68 (l39_zfmisc_1)
% 6.55/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 6.55/1.69 (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ $i(v2)
% 6.55/1.69 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] :
% 6.55/1.69 (singleton(v0) = v7 & in(v1, v2) = v6 & in(v0, v2) = v5 & $i(v7) & (v7 = v4
% 6.55/1.69 | v5 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0))))) & ! [v0: $i] : ! [v1: $i] :
% 6.55/1.69 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (set_difference(v3, v2) = v4) |
% 6.55/1.69 ~ (unordered_pair(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 6.55/1.69 [v5: $i] : ? [v6: any] : ? [v7: any] : (singleton(v0) = v5 & in(v1, v2) =
% 6.55/1.69 v7 & in(v0, v2) = v6 & $i(v5) & ( ~ (v5 = v4) | ( ~ (v6 = 0) & (v7 = 0 |
% 6.55/1.69 v1 = v0)))))
% 6.55/1.69
% 6.55/1.69 (t23_zfmisc_1)
% 6.55/1.69 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 6.55/1.69 $i] : ( ~ (v5 = v4) & ~ (v1 = v0) & set_difference(v2, v3) = v4 &
% 6.55/1.69 singleton(v1) = v3 & singleton(v0) = v5 & unordered_pair(v0, v1) = v2 &
% 6.55/1.69 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 6.55/1.69
% 6.55/1.69 (function-axioms)
% 6.55/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.55/1.70 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 6.55/1.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.55/1.70 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 6.55/1.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 6.55/1.70 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 6.55/1.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 6.55/1.70 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 6.55/1.70 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.55/1.70
% 6.55/1.70 Further assumptions not needed in the proof:
% 6.55/1.70 --------------------------------------------
% 6.55/1.70 antisymmetry_r2_hidden, commutativity_k2_tarski, rc1_xboole_0, rc2_xboole_0
% 6.55/1.70
% 6.55/1.70 Those formulas are unsatisfiable:
% 6.55/1.70 ---------------------------------
% 6.55/1.70
% 6.55/1.70 Begin of proof
% 6.55/1.70 |
% 6.55/1.70 | ALPHA: (d1_tarski) implies:
% 6.55/1.70 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~
% 6.55/1.70 | $i(v0) | ( ! [v2: $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) &
% 6.55/1.70 | ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2))))
% 6.55/1.70 |
% 6.55/1.70 | ALPHA: (l39_zfmisc_1) implies:
% 6.55/1.71 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 6.55/1.71 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) |
% 6.55/1.71 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: any] : ?
% 6.55/1.71 | [v7: any] : (singleton(v0) = v5 & in(v1, v2) = v7 & in(v0, v2) = v6 &
% 6.55/1.71 | $i(v5) & ( ~ (v5 = v4) | ( ~ (v6 = 0) & (v7 = 0 | v1 = v0)))))
% 6.55/1.71 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 6.55/1.71 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) |
% 6.55/1.71 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ?
% 6.55/1.71 | [v7: $i] : (singleton(v0) = v7 & in(v1, v2) = v6 & in(v0, v2) = v5 &
% 6.55/1.71 | $i(v7) & (v7 = v4 | v5 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0)))))
% 6.55/1.71 |
% 6.55/1.71 | ALPHA: (function-axioms) implies:
% 6.55/1.71 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 6.55/1.71 | = v1) | ~ (singleton(v2) = v0))
% 6.55/1.71 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.55/1.71 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.55/1.71 |
% 6.55/1.71 | DELTA: instantiating (t23_zfmisc_1) with fresh symbols all_13_0, all_13_1,
% 6.55/1.71 | all_13_2, all_13_3, all_13_4, all_13_5 gives:
% 6.55/1.71 | (6) ~ (all_13_0 = all_13_1) & ~ (all_13_4 = all_13_5) &
% 6.55/1.71 | set_difference(all_13_3, all_13_2) = all_13_1 & singleton(all_13_4) =
% 6.55/1.71 | all_13_2 & singleton(all_13_5) = all_13_0 & unordered_pair(all_13_5,
% 6.55/1.71 | all_13_4) = all_13_3 & $i(all_13_0) & $i(all_13_1) & $i(all_13_2) &
% 6.55/1.71 | $i(all_13_3) & $i(all_13_4) & $i(all_13_5)
% 6.55/1.71 |
% 6.55/1.71 | ALPHA: (6) implies:
% 6.55/1.72 | (7) ~ (all_13_4 = all_13_5)
% 6.55/1.72 | (8) ~ (all_13_0 = all_13_1)
% 6.55/1.72 | (9) $i(all_13_5)
% 6.55/1.72 | (10) $i(all_13_4)
% 6.55/1.72 | (11) $i(all_13_2)
% 6.55/1.72 | (12) unordered_pair(all_13_5, all_13_4) = all_13_3
% 6.55/1.72 | (13) singleton(all_13_5) = all_13_0
% 6.55/1.72 | (14) singleton(all_13_4) = all_13_2
% 6.55/1.72 | (15) set_difference(all_13_3, all_13_2) = all_13_1
% 6.55/1.72 |
% 6.55/1.72 | GROUND_INST: instantiating (1) with all_13_4, all_13_2, simplifying with (10),
% 6.55/1.72 | (11), (14) gives:
% 6.55/1.72 | (16) ! [v0: any] : (v0 = all_13_4 | ~ (in(v0, all_13_2) = 0) | ~ $i(v0))
% 6.55/1.72 | & ! [v0: int] : (v0 = 0 | ~ (in(all_13_4, all_13_2) = v0))
% 6.55/1.72 |
% 6.55/1.72 | ALPHA: (16) implies:
% 6.55/1.72 | (17) ! [v0: int] : (v0 = 0 | ~ (in(all_13_4, all_13_2) = v0))
% 6.55/1.72 | (18) ! [v0: any] : (v0 = all_13_4 | ~ (in(v0, all_13_2) = 0) | ~ $i(v0))
% 6.55/1.72 |
% 6.55/1.72 | GROUND_INST: instantiating (3) with all_13_5, all_13_4, all_13_2, all_13_3,
% 6.55/1.72 | all_13_1, simplifying with (9), (10), (11), (12), (15) gives:
% 6.55/1.72 | (19) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (singleton(all_13_5) = v2
% 6.55/1.72 | & in(all_13_4, all_13_2) = v1 & in(all_13_5, all_13_2) = v0 & $i(v2)
% 6.55/1.72 | & (v2 = all_13_1 | v0 = 0 | ( ~ (v1 = 0) & ~ (all_13_4 =
% 6.55/1.72 | all_13_5))))
% 6.55/1.72 |
% 6.55/1.72 | GROUND_INST: instantiating (2) with all_13_5, all_13_4, all_13_2, all_13_3,
% 6.55/1.72 | all_13_1, simplifying with (9), (10), (11), (12), (15) gives:
% 6.55/1.73 | (20) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (singleton(all_13_5) = v0
% 6.55/1.73 | & in(all_13_4, all_13_2) = v2 & in(all_13_5, all_13_2) = v1 & $i(v0)
% 6.55/1.73 | & ( ~ (v0 = all_13_1) | ( ~ (v1 = 0) & (v2 = 0 | all_13_4 =
% 6.55/1.73 | all_13_5))))
% 6.55/1.73 |
% 6.55/1.73 | DELTA: instantiating (19) with fresh symbols all_23_0, all_23_1, all_23_2
% 6.55/1.73 | gives:
% 6.55/1.73 | (21) singleton(all_13_5) = all_23_0 & in(all_13_4, all_13_2) = all_23_1 &
% 6.55/1.73 | in(all_13_5, all_13_2) = all_23_2 & $i(all_23_0) & (all_23_0 =
% 6.55/1.73 | all_13_1 | all_23_2 = 0 | ( ~ (all_23_1 = 0) & ~ (all_13_4 =
% 6.55/1.73 | all_13_5)))
% 6.55/1.73 |
% 6.55/1.73 | ALPHA: (21) implies:
% 6.55/1.73 | (22) in(all_13_5, all_13_2) = all_23_2
% 6.55/1.73 | (23) in(all_13_4, all_13_2) = all_23_1
% 6.55/1.73 | (24) singleton(all_13_5) = all_23_0
% 6.55/1.73 | (25) all_23_0 = all_13_1 | all_23_2 = 0 | ( ~ (all_23_1 = 0) & ~ (all_13_4
% 6.55/1.73 | = all_13_5))
% 6.55/1.73 |
% 6.55/1.73 | DELTA: instantiating (20) with fresh symbols all_25_0, all_25_1, all_25_2
% 6.55/1.73 | gives:
% 6.55/1.73 | (26) singleton(all_13_5) = all_25_2 & in(all_13_4, all_13_2) = all_25_0 &
% 6.55/1.73 | in(all_13_5, all_13_2) = all_25_1 & $i(all_25_2) & ( ~ (all_25_2 =
% 6.55/1.73 | all_13_1) | ( ~ (all_25_1 = 0) & (all_25_0 = 0 | all_13_4 =
% 6.55/1.73 | all_13_5)))
% 6.55/1.73 |
% 6.55/1.73 | ALPHA: (26) implies:
% 6.55/1.73 | (27) in(all_13_5, all_13_2) = all_25_1
% 6.55/1.73 | (28) in(all_13_4, all_13_2) = all_25_0
% 6.55/1.73 | (29) singleton(all_13_5) = all_25_2
% 6.55/1.73 |
% 6.55/1.73 | GROUND_INST: instantiating (5) with all_23_2, all_25_1, all_13_2, all_13_5,
% 6.55/1.73 | simplifying with (22), (27) gives:
% 6.55/1.73 | (30) all_25_1 = all_23_2
% 6.55/1.73 |
% 6.55/1.73 | GROUND_INST: instantiating (5) with all_23_1, all_25_0, all_13_2, all_13_4,
% 6.55/1.73 | simplifying with (23), (28) gives:
% 6.55/1.73 | (31) all_25_0 = all_23_1
% 6.55/1.73 |
% 6.55/1.73 | GROUND_INST: instantiating (17) with all_25_0, simplifying with (28) gives:
% 6.55/1.73 | (32) all_25_0 = 0
% 6.55/1.73 |
% 6.55/1.73 | GROUND_INST: instantiating (4) with all_13_0, all_25_2, all_13_5, simplifying
% 6.55/1.73 | with (13), (29) gives:
% 6.55/1.73 | (33) all_25_2 = all_13_0
% 6.55/1.73 |
% 6.55/1.73 | GROUND_INST: instantiating (4) with all_23_0, all_25_2, all_13_5, simplifying
% 6.55/1.73 | with (24), (29) gives:
% 6.55/1.73 | (34) all_25_2 = all_23_0
% 6.55/1.73 |
% 6.55/1.73 | COMBINE_EQS: (31), (32) imply:
% 6.55/1.73 | (35) all_23_1 = 0
% 6.55/1.73 |
% 6.55/1.73 | SIMP: (35) implies:
% 6.55/1.73 | (36) all_23_1 = 0
% 6.55/1.73 |
% 6.55/1.73 | COMBINE_EQS: (33), (34) imply:
% 6.55/1.73 | (37) all_23_0 = all_13_0
% 6.55/1.73 |
% 6.55/1.73 | SIMP: (37) implies:
% 6.55/1.73 | (38) all_23_0 = all_13_0
% 6.55/1.73 |
% 6.55/1.73 | BETA: splitting (25) gives:
% 6.55/1.73 |
% 6.55/1.73 | Case 1:
% 6.55/1.73 | |
% 6.55/1.73 | | (39) all_23_2 = 0
% 6.55/1.73 | |
% 6.55/1.73 | | REDUCE: (22), (39) imply:
% 6.55/1.74 | | (40) in(all_13_5, all_13_2) = 0
% 6.55/1.74 | |
% 6.55/1.74 | | GROUND_INST: instantiating (18) with all_13_5, simplifying with (9), (40)
% 6.55/1.74 | | gives:
% 6.55/1.74 | | (41) all_13_4 = all_13_5
% 6.55/1.74 | |
% 6.55/1.74 | | REDUCE: (7), (41) imply:
% 6.84/1.74 | | (42) $false
% 6.84/1.74 | |
% 6.84/1.74 | | CLOSE: (42) is inconsistent.
% 6.84/1.74 | |
% 6.84/1.74 | Case 2:
% 6.84/1.74 | |
% 6.84/1.74 | | (43) all_23_0 = all_13_1 | ( ~ (all_23_1 = 0) & ~ (all_13_4 = all_13_5))
% 6.84/1.74 | |
% 6.84/1.74 | | BETA: splitting (43) gives:
% 6.84/1.74 | |
% 6.84/1.74 | | Case 1:
% 6.84/1.74 | | |
% 6.84/1.74 | | | (44) all_23_0 = all_13_1
% 6.84/1.74 | | |
% 6.84/1.74 | | | COMBINE_EQS: (38), (44) imply:
% 6.84/1.74 | | | (45) all_13_0 = all_13_1
% 6.84/1.74 | | |
% 6.84/1.74 | | | REDUCE: (8), (45) imply:
% 6.84/1.74 | | | (46) $false
% 6.84/1.74 | | |
% 6.84/1.74 | | | CLOSE: (46) is inconsistent.
% 6.84/1.74 | | |
% 6.84/1.74 | | Case 2:
% 6.84/1.74 | | |
% 6.84/1.74 | | | (47) ~ (all_23_1 = 0) & ~ (all_13_4 = all_13_5)
% 6.84/1.74 | | |
% 6.84/1.74 | | | ALPHA: (47) implies:
% 6.84/1.74 | | | (48) ~ (all_23_1 = 0)
% 6.84/1.74 | | |
% 6.84/1.74 | | | REDUCE: (36), (48) imply:
% 6.84/1.74 | | | (49) $false
% 6.84/1.74 | | |
% 6.84/1.74 | | | CLOSE: (49) is inconsistent.
% 6.84/1.74 | | |
% 6.84/1.74 | | End of split
% 6.84/1.74 | |
% 6.84/1.74 | End of split
% 6.84/1.74 |
% 6.84/1.74 End of proof
% 6.84/1.74 % SZS output end Proof for theBenchmark
% 6.84/1.74
% 6.84/1.74 1117ms
%------------------------------------------------------------------------------