TSTP Solution File: SEU165+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU165+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n012.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 17:42:58 EDT 2023
% Result : Theorem 4.53s 1.36s
% Output : Proof 6.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU165+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 22:05:57 EDT 2023
% 0.12/0.34 % 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
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.97/0.97 Prover 4: Preprocessing ...
% 1.97/0.98 Prover 1: Preprocessing ...
% 2.38/1.02 Prover 2: Preprocessing ...
% 2.38/1.02 Prover 5: Preprocessing ...
% 2.38/1.02 Prover 3: Preprocessing ...
% 2.38/1.02 Prover 6: Preprocessing ...
% 2.38/1.02 Prover 0: Preprocessing ...
% 3.72/1.21 Prover 6: Constructing countermodel ...
% 3.72/1.21 Prover 4: Constructing countermodel ...
% 3.72/1.22 Prover 3: Constructing countermodel ...
% 3.72/1.22 Prover 5: Proving ...
% 3.72/1.22 Prover 1: Constructing countermodel ...
% 3.72/1.23 Prover 2: Proving ...
% 3.72/1.24 Prover 0: Proving ...
% 4.53/1.36 Prover 3: proved (728ms)
% 4.53/1.36
% 4.53/1.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.53/1.36
% 4.53/1.36 Prover 0: stopped
% 4.53/1.36 Prover 5: stopped
% 4.53/1.36 Prover 2: stopped
% 4.53/1.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.53/1.36 Prover 6: stopped
% 4.53/1.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.53/1.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.53/1.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.53/1.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.53/1.38 Prover 11: Preprocessing ...
% 4.53/1.40 Prover 13: Preprocessing ...
% 4.53/1.40 Prover 10: Preprocessing ...
% 4.53/1.41 Prover 7: Preprocessing ...
% 4.53/1.41 Prover 8: Preprocessing ...
% 4.53/1.45 Prover 10: Constructing countermodel ...
% 4.53/1.46 Prover 13: Warning: ignoring some quantifiers
% 4.53/1.47 Prover 13: Constructing countermodel ...
% 4.53/1.47 Prover 7: Constructing countermodel ...
% 5.32/1.48 Prover 1: Found proof (size 32)
% 5.32/1.48 Prover 1: proved (858ms)
% 5.32/1.48 Prover 13: stopped
% 5.32/1.48 Prover 4: stopped
% 5.32/1.48 Prover 10: stopped
% 5.32/1.48 Prover 7: stopped
% 5.32/1.49 Prover 8: Warning: ignoring some quantifiers
% 5.32/1.49 Prover 8: Constructing countermodel ...
% 5.32/1.49 Prover 8: stopped
% 5.32/1.50 Prover 11: Constructing countermodel ...
% 5.32/1.51 Prover 11: stopped
% 5.32/1.51
% 5.32/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.32/1.51
% 5.32/1.51 % SZS output start Proof for theBenchmark
% 5.32/1.52 Assumptions after simplification:
% 5.32/1.52 ---------------------------------
% 5.32/1.52
% 5.32/1.52 (l55_zfmisc_1)
% 5.32/1.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 5.32/1.55 $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~
% 5.32/1.55 (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) |
% 5.32/1.55 ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (in(v1, v3) = v8 &
% 5.32/1.55 in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1:
% 5.32/1.55 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 5.32/1.55 (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~
% 5.32/1.55 (in(v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1,
% 5.32/1.55 v3) = 0 & in(v0, v2) = 0))
% 5.32/1.55
% 5.32/1.55 (t106_zfmisc_1)
% 5.32/1.55 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 5.32/1.56 $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : (cartesian_product2(v2,
% 5.32/1.56 v3) = v5 & ordered_pair(v0, v1) = v4 & in(v4, v5) = v6 & in(v1, v3) = v8 &
% 5.32/1.56 in(v0, v2) = v7 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v8
% 5.32/1.56 = 0 & v7 = 0 & ~ (v6 = 0)) | (v6 = 0 & ( ~ (v8 = 0) | ~ (v7 = 0)))))
% 5.32/1.56
% 5.32/1.56 (function-axioms)
% 5.32/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.32/1.56 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 5.32/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.32/1.56 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0:
% 5.32/1.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 5.32/1.56 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 5.32/1.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) =
% 5.32/1.56 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 5.32/1.56 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & !
% 5.32/1.56 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 5.32/1.56 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 5.32/1.56
% 5.32/1.56 Further assumptions not needed in the proof:
% 5.32/1.56 --------------------------------------------
% 5.32/1.56 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, fc1_zfmisc_1,
% 5.32/1.56 rc1_xboole_0, rc2_xboole_0
% 5.32/1.56
% 5.32/1.56 Those formulas are unsatisfiable:
% 5.32/1.56 ---------------------------------
% 5.32/1.56
% 5.32/1.56 Begin of proof
% 5.32/1.56 |
% 5.32/1.56 | ALPHA: (l55_zfmisc_1) implies:
% 5.32/1.57 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 5.32/1.57 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~
% 5.32/1.57 | (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | ~ $i(v3) | ~
% 5.32/1.57 | $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 6.12/1.57 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 6.12/1.57 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) =
% 6.12/1.57 | v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~
% 6.12/1.57 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8:
% 6.12/1.57 | any] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 =
% 6.12/1.57 | 0))))
% 6.12/1.57 |
% 6.12/1.57 | ALPHA: (function-axioms) implies:
% 6.12/1.57 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.12/1.57 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.12/1.57 |
% 6.12/1.57 | DELTA: instantiating (t106_zfmisc_1) with fresh symbols all_12_0, all_12_1,
% 6.12/1.57 | all_12_2, all_12_3, all_12_4, all_12_5, all_12_6, all_12_7, all_12_8
% 6.12/1.57 | gives:
% 6.12/1.58 | (4) cartesian_product2(all_12_6, all_12_5) = all_12_3 &
% 6.12/1.58 | ordered_pair(all_12_8, all_12_7) = all_12_4 & in(all_12_4, all_12_3) =
% 6.12/1.58 | all_12_2 & in(all_12_7, all_12_5) = all_12_0 & in(all_12_8, all_12_6) =
% 6.12/1.58 | all_12_1 & $i(all_12_3) & $i(all_12_4) & $i(all_12_5) & $i(all_12_6) &
% 6.12/1.58 | $i(all_12_7) & $i(all_12_8) & ((all_12_0 = 0 & all_12_1 = 0 & ~
% 6.12/1.58 | (all_12_2 = 0)) | (all_12_2 = 0 & ( ~ (all_12_0 = 0) | ~ (all_12_1
% 6.12/1.58 | = 0))))
% 6.12/1.58 |
% 6.12/1.58 | ALPHA: (4) implies:
% 6.12/1.58 | (5) $i(all_12_8)
% 6.12/1.58 | (6) $i(all_12_7)
% 6.12/1.58 | (7) $i(all_12_6)
% 6.12/1.58 | (8) $i(all_12_5)
% 6.12/1.58 | (9) in(all_12_8, all_12_6) = all_12_1
% 6.12/1.58 | (10) in(all_12_7, all_12_5) = all_12_0
% 6.12/1.58 | (11) in(all_12_4, all_12_3) = all_12_2
% 6.12/1.58 | (12) ordered_pair(all_12_8, all_12_7) = all_12_4
% 6.12/1.58 | (13) cartesian_product2(all_12_6, all_12_5) = all_12_3
% 6.12/1.58 | (14) (all_12_0 = 0 & all_12_1 = 0 & ~ (all_12_2 = 0)) | (all_12_2 = 0 & (
% 6.12/1.58 | ~ (all_12_0 = 0) | ~ (all_12_1 = 0)))
% 6.12/1.58 |
% 6.12/1.58 | GROUND_INST: instantiating (2) with all_12_8, all_12_7, all_12_6, all_12_5,
% 6.12/1.58 | all_12_4, all_12_3, all_12_2, simplifying with (5), (6), (7),
% 6.12/1.58 | (8), (11), (12), (13) gives:
% 6.12/1.58 | (15) all_12_2 = 0 | ? [v0: any] : ? [v1: any] : (in(all_12_7, all_12_5) =
% 6.12/1.58 | v1 & in(all_12_8, all_12_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.12/1.58 |
% 6.12/1.58 | BETA: splitting (14) gives:
% 6.12/1.58 |
% 6.12/1.58 | Case 1:
% 6.12/1.58 | |
% 6.12/1.58 | | (16) all_12_0 = 0 & all_12_1 = 0 & ~ (all_12_2 = 0)
% 6.12/1.58 | |
% 6.12/1.58 | | ALPHA: (16) implies:
% 6.12/1.58 | | (17) all_12_1 = 0
% 6.12/1.58 | | (18) all_12_0 = 0
% 6.12/1.58 | | (19) ~ (all_12_2 = 0)
% 6.12/1.58 | |
% 6.12/1.58 | | REDUCE: (10), (18) imply:
% 6.12/1.59 | | (20) in(all_12_7, all_12_5) = 0
% 6.12/1.59 | |
% 6.12/1.59 | | REDUCE: (9), (17) imply:
% 6.12/1.59 | | (21) in(all_12_8, all_12_6) = 0
% 6.12/1.59 | |
% 6.12/1.59 | | BETA: splitting (15) gives:
% 6.12/1.59 | |
% 6.12/1.59 | | Case 1:
% 6.12/1.59 | | |
% 6.12/1.59 | | | (22) all_12_2 = 0
% 6.12/1.59 | | |
% 6.12/1.59 | | | REDUCE: (19), (22) imply:
% 6.12/1.59 | | | (23) $false
% 6.12/1.59 | | |
% 6.12/1.59 | | | CLOSE: (23) is inconsistent.
% 6.12/1.59 | | |
% 6.12/1.59 | | Case 2:
% 6.12/1.59 | | |
% 6.12/1.59 | | | (24) ? [v0: any] : ? [v1: any] : (in(all_12_7, all_12_5) = v1 &
% 6.12/1.59 | | | in(all_12_8, all_12_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.12/1.59 | | |
% 6.12/1.59 | | | DELTA: instantiating (24) with fresh symbols all_32_0, all_32_1 gives:
% 6.12/1.59 | | | (25) in(all_12_7, all_12_5) = all_32_0 & in(all_12_8, all_12_6) =
% 6.12/1.59 | | | all_32_1 & ( ~ (all_32_0 = 0) | ~ (all_32_1 = 0))
% 6.12/1.59 | | |
% 6.12/1.59 | | | ALPHA: (25) implies:
% 6.12/1.59 | | | (26) in(all_12_8, all_12_6) = all_32_1
% 6.12/1.59 | | | (27) in(all_12_7, all_12_5) = all_32_0
% 6.12/1.59 | | | (28) ~ (all_32_0 = 0) | ~ (all_32_1 = 0)
% 6.12/1.59 | | |
% 6.12/1.59 | | | GROUND_INST: instantiating (3) with 0, all_32_1, all_12_6, all_12_8,
% 6.12/1.59 | | | simplifying with (21), (26) gives:
% 6.12/1.59 | | | (29) all_32_1 = 0
% 6.12/1.59 | | |
% 6.12/1.59 | | | GROUND_INST: instantiating (3) with 0, all_32_0, all_12_5, all_12_7,
% 6.12/1.59 | | | simplifying with (20), (27) gives:
% 6.12/1.59 | | | (30) all_32_0 = 0
% 6.12/1.59 | | |
% 6.12/1.59 | | | BETA: splitting (28) gives:
% 6.12/1.59 | | |
% 6.12/1.59 | | | Case 1:
% 6.12/1.59 | | | |
% 6.12/1.59 | | | | (31) ~ (all_32_0 = 0)
% 6.12/1.59 | | | |
% 6.12/1.59 | | | | REDUCE: (30), (31) imply:
% 6.12/1.59 | | | | (32) $false
% 6.12/1.59 | | | |
% 6.12/1.59 | | | | CLOSE: (32) is inconsistent.
% 6.12/1.59 | | | |
% 6.12/1.59 | | | Case 2:
% 6.12/1.59 | | | |
% 6.12/1.59 | | | | (33) ~ (all_32_1 = 0)
% 6.12/1.59 | | | |
% 6.12/1.59 | | | | REDUCE: (29), (33) imply:
% 6.12/1.59 | | | | (34) $false
% 6.12/1.59 | | | |
% 6.12/1.59 | | | | CLOSE: (34) is inconsistent.
% 6.12/1.59 | | | |
% 6.12/1.59 | | | End of split
% 6.12/1.59 | | |
% 6.12/1.59 | | End of split
% 6.12/1.59 | |
% 6.12/1.59 | Case 2:
% 6.12/1.59 | |
% 6.12/1.59 | | (35) all_12_2 = 0 & ( ~ (all_12_0 = 0) | ~ (all_12_1 = 0))
% 6.12/1.59 | |
% 6.12/1.59 | | ALPHA: (35) implies:
% 6.12/1.59 | | (36) all_12_2 = 0
% 6.12/1.59 | | (37) ~ (all_12_0 = 0) | ~ (all_12_1 = 0)
% 6.12/1.59 | |
% 6.12/1.59 | | REDUCE: (11), (36) imply:
% 6.12/1.59 | | (38) in(all_12_4, all_12_3) = 0
% 6.12/1.59 | |
% 6.12/1.60 | | GROUND_INST: instantiating (1) with all_12_8, all_12_7, all_12_6, all_12_5,
% 6.12/1.60 | | all_12_4, all_12_3, simplifying with (5), (6), (7), (8), (12),
% 6.12/1.60 | | (13), (38) gives:
% 6.12/1.60 | | (39) in(all_12_7, all_12_5) = 0 & in(all_12_8, all_12_6) = 0
% 6.12/1.60 | |
% 6.12/1.60 | | ALPHA: (39) implies:
% 6.12/1.60 | | (40) in(all_12_8, all_12_6) = 0
% 6.12/1.60 | | (41) in(all_12_7, all_12_5) = 0
% 6.12/1.60 | |
% 6.12/1.60 | | GROUND_INST: instantiating (3) with all_12_1, 0, all_12_6, all_12_8,
% 6.12/1.60 | | simplifying with (9), (40) gives:
% 6.12/1.60 | | (42) all_12_1 = 0
% 6.12/1.60 | |
% 6.12/1.60 | | GROUND_INST: instantiating (3) with all_12_0, 0, all_12_5, all_12_7,
% 6.12/1.60 | | simplifying with (10), (41) gives:
% 6.12/1.60 | | (43) all_12_0 = 0
% 6.12/1.60 | |
% 6.12/1.60 | | BETA: splitting (37) gives:
% 6.12/1.60 | |
% 6.12/1.60 | | Case 1:
% 6.12/1.60 | | |
% 6.12/1.60 | | | (44) ~ (all_12_0 = 0)
% 6.12/1.60 | | |
% 6.12/1.60 | | | REDUCE: (43), (44) imply:
% 6.12/1.60 | | | (45) $false
% 6.12/1.60 | | |
% 6.12/1.60 | | | CLOSE: (45) is inconsistent.
% 6.12/1.60 | | |
% 6.12/1.60 | | Case 2:
% 6.12/1.60 | | |
% 6.12/1.60 | | | (46) ~ (all_12_1 = 0)
% 6.12/1.60 | | |
% 6.12/1.60 | | | REDUCE: (42), (46) imply:
% 6.12/1.60 | | | (47) $false
% 6.12/1.60 | | |
% 6.12/1.60 | | | CLOSE: (47) is inconsistent.
% 6.12/1.60 | | |
% 6.12/1.60 | | End of split
% 6.12/1.60 | |
% 6.12/1.60 | End of split
% 6.12/1.60 |
% 6.12/1.60 End of proof
% 6.12/1.60 % SZS output end Proof for theBenchmark
% 6.12/1.60
% 6.12/1.60 996ms
%------------------------------------------------------------------------------