TSTP Solution File: SYN941+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN941+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n015.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 : Fri Sep 1 03:29:18 EDT 2023
% Result : Theorem 3.54s 1.27s
% Output : Proof 4.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN941+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n015.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 21:28:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.66 ________ _____
% 0.19/0.66 ___ __ \_________(_)________________________________
% 0.19/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.66
% 0.19/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.66 (2023-06-19)
% 0.19/0.66
% 0.19/0.66 (c) Philipp Rümmer, 2009-2023
% 0.19/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.66 Amanda Stjerna.
% 0.19/0.66 Free software under BSD-3-Clause.
% 0.19/0.66
% 0.19/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.66
% 0.19/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.68 Running up to 7 provers in parallel.
% 0.19/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.65/0.99 Prover 4: Preprocessing ...
% 1.65/0.99 Prover 1: Preprocessing ...
% 2.18/1.04 Prover 0: Preprocessing ...
% 2.18/1.04 Prover 5: Preprocessing ...
% 2.18/1.04 Prover 3: Preprocessing ...
% 2.18/1.04 Prover 6: Preprocessing ...
% 2.18/1.04 Prover 2: Preprocessing ...
% 2.63/1.13 Prover 1: Constructing countermodel ...
% 2.63/1.13 Prover 3: Constructing countermodel ...
% 2.63/1.14 Prover 2: Proving ...
% 2.63/1.14 Prover 5: Proving ...
% 2.63/1.14 Prover 6: Proving ...
% 3.21/1.17 Prover 0: Proving ...
% 3.32/1.18 Prover 4: Constructing countermodel ...
% 3.54/1.25 Prover 3: gave up
% 3.54/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.54/1.26 Prover 0: proved (576ms)
% 3.54/1.26
% 3.54/1.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.54/1.27
% 3.54/1.27 Prover 5: stopped
% 3.54/1.27 Prover 2: stopped
% 3.54/1.28 Prover 7: Preprocessing ...
% 3.54/1.28 Prover 6: stopped
% 3.54/1.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.54/1.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.54/1.29 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.54/1.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.54/1.29 Prover 8: Preprocessing ...
% 3.54/1.29 Prover 10: Preprocessing ...
% 3.54/1.29 Prover 13: Preprocessing ...
% 3.54/1.29 Prover 11: Preprocessing ...
% 3.54/1.30 Prover 7: Constructing countermodel ...
% 3.54/1.32 Prover 1: gave up
% 3.54/1.32 Prover 8: Warning: ignoring some quantifiers
% 3.54/1.32 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 3.54/1.33 Prover 8: Constructing countermodel ...
% 3.54/1.33 Prover 4: Found proof (size 25)
% 3.54/1.33 Prover 4: proved (641ms)
% 3.54/1.33 Prover 8: stopped
% 3.54/1.33 Prover 7: stopped
% 3.54/1.34 Prover 10: Constructing countermodel ...
% 3.54/1.34 Prover 10: stopped
% 3.54/1.34 Prover 16: Preprocessing ...
% 4.22/1.35 Prover 13: Warning: ignoring some quantifiers
% 4.22/1.35 Prover 13: Constructing countermodel ...
% 4.22/1.35 Prover 13: stopped
% 4.22/1.36 Prover 16: Warning: ignoring some quantifiers
% 4.22/1.36 Prover 16: Constructing countermodel ...
% 4.22/1.36 Prover 16: stopped
% 4.22/1.37 Prover 11: Constructing countermodel ...
% 4.22/1.38 Prover 11: stopped
% 4.22/1.38
% 4.22/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.22/1.38
% 4.22/1.38 % SZS output start Proof for theBenchmark
% 4.22/1.39 Assumptions after simplification:
% 4.22/1.39 ---------------------------------
% 4.22/1.39
% 4.22/1.39 (prove_this)
% 4.73/1.43 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : (f(v0)
% 4.73/1.43 = v2 & q(v2) = 0 & r(v1) = v4 & r(v0) = v3 & $i(v2) & $i(v1) & $i(v0) & !
% 4.73/1.43 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: any] : ! [v9: any] : ( ~
% 4.73/1.43 (f(v6) = v7) | ~ (p(v7) = v8) | ~ (p(v5) = v9) | ~ $i(v6) | ~ $i(v5) |
% 4.73/1.43 ? [v10: any] : ? [v11: any] : (q(v5) = v11 & r(v6) = v10 & ( ~ (v11 = 0)
% 4.73/1.43 | (v8 = 0 & ( ~ (v9 = 0) | (v10 = 0 & ( ~ (v4 = 0) | ~ (v3 =
% 4.73/1.43 0)))))))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 4.73/1.43 [v8: int] : (v8 = 0 | ~ (f(v6) = v7) | ~ (q(v5) = 0) | ~ (p(v7) = v8) |
% 4.73/1.43 ~ $i(v6) | ~ $i(v5)) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 4.73/1.43 MultipleValueBool] : ( ~ (f(v6) = v7) | ~ (q(v5) = 0) | ~ (p(v7) = v8) |
% 4.73/1.43 ~ $i(v6) | ~ $i(v5) | ? [v9: any] : ? [v10: any] : (p(v5) = v9 & r(v6)
% 4.73/1.43 = v10 & ( ~ (v9 = 0) | (v10 = 0 & ( ~ (v4 = 0) | ~ (v3 = 0)))))) & !
% 4.73/1.43 [v5: $i] : ! [v6: $i] : ! [v7: any] : ! [v8: any] : ( ~ (p(v5) = v7) | ~
% 4.73/1.43 (r(v6) = v8) | ~ $i(v6) | ~ $i(v5) | ? [v9: $i] : ? [v10: any] : ?
% 4.73/1.43 [v11: any] : (f(v6) = v9 & q(v5) = v11 & p(v9) = v10 & $i(v9) & ( ~ (v11 =
% 4.73/1.43 0) | (v10 = 0 & ( ~ (v7 = 0) | (v8 = 0 & ( ~ (v4 = 0) | ~ (v3 =
% 4.73/1.43 0)))))))) & ! [v5: $i] : ! [v6: $i] : ! [v7: any] : ( ~
% 4.73/1.43 (q(v5) = 0) | ~ (r(v6) = v7) | ~ $i(v6) | ~ $i(v5) | ? [v8: $i] : ?
% 4.73/1.43 [v9: any] : (f(v6) = v8 & p(v8) = 0 & p(v5) = v9 & $i(v8) & ( ~ (v9 = 0) |
% 4.73/1.43 (v7 = 0 & ( ~ (v4 = 0) | ~ (v3 = 0)))))))
% 4.73/1.43
% 4.73/1.43 (function-axioms)
% 4.73/1.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (f(v2) = v1) | ~
% 4.73/1.44 (f(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : !
% 4.73/1.44 [v2: $i] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) & ! [v0:
% 4.73/1.44 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 4.73/1.44 ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 4.73/1.44 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (r(v2) = v1) | ~ (r(v2) =
% 4.73/1.44 v0))
% 4.73/1.44
% 4.73/1.44 Those formulas are unsatisfiable:
% 4.73/1.44 ---------------------------------
% 4.73/1.44
% 4.73/1.44 Begin of proof
% 4.73/1.44 |
% 4.73/1.44 | ALPHA: (function-axioms) implies:
% 4.73/1.44 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.73/1.44 | (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 4.73/1.44 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (f(v2) = v1) |
% 4.73/1.44 | ~ (f(v2) = v0))
% 4.73/1.44 |
% 4.73/1.44 | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1,
% 4.73/1.44 | all_3_2, all_3_3, all_3_4 gives:
% 4.73/1.45 | (3) f(all_3_4) = all_3_2 & q(all_3_2) = 0 & r(all_3_3) = all_3_0 &
% 4.73/1.45 | r(all_3_4) = all_3_1 & $i(all_3_2) & $i(all_3_3) & $i(all_3_4) & !
% 4.73/1.45 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : (
% 4.73/1.45 | ~ (f(v1) = v2) | ~ (p(v2) = v3) | ~ (p(v0) = v4) | ~ $i(v1) | ~
% 4.73/1.45 | $i(v0) | ? [v5: any] : ? [v6: any] : (q(v0) = v6 & r(v1) = v5 & ( ~
% 4.73/1.45 | (v6 = 0) | (v3 = 0 & ( ~ (v4 = 0) | (v5 = 0 & ( ~ (all_3_0 = 0) |
% 4.73/1.45 | ~ (all_3_1 = 0)))))))) & ! [v0: $i] : ! [v1: $i] : !
% 4.73/1.45 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (f(v1) = v2) | ~ (q(v0) = 0) |
% 4.73/1.45 | ~ (p(v2) = v3) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] :
% 4.73/1.45 | ! [v2: $i] : ! [v3: MultipleValueBool] : ( ~ (f(v1) = v2) | ~ (q(v0)
% 4.73/1.45 | = 0) | ~ (p(v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 4.73/1.45 | [v5: any] : (p(v0) = v4 & r(v1) = v5 & ( ~ (v4 = 0) | (v5 = 0 & ( ~
% 4.73/1.45 | (all_3_0 = 0) | ~ (all_3_1 = 0)))))) & ! [v0: $i] : ! [v1:
% 4.73/1.45 | $i] : ! [v2: any] : ! [v3: any] : ( ~ (p(v0) = v2) | ~ (r(v1) =
% 4.73/1.45 | v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6:
% 4.73/1.45 | any] : (f(v1) = v4 & q(v0) = v6 & p(v4) = v5 & $i(v4) & ( ~ (v6 =
% 4.73/1.45 | 0) | (v5 = 0 & ( ~ (v2 = 0) | (v3 = 0 & ( ~ (all_3_0 = 0) | ~
% 4.73/1.45 | (all_3_1 = 0)))))))) & ! [v0: $i] : ! [v1: $i] : !
% 4.73/1.45 | [v2: any] : ( ~ (q(v0) = 0) | ~ (r(v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 4.73/1.45 | ? [v3: $i] : ? [v4: any] : (f(v1) = v3 & p(v3) = 0 & p(v0) = v4 &
% 4.73/1.45 | $i(v3) & ( ~ (v4 = 0) | (v2 = 0 & ( ~ (all_3_0 = 0) | ~ (all_3_1 =
% 4.73/1.45 | 0))))))
% 4.73/1.45 |
% 4.73/1.45 | ALPHA: (3) implies:
% 4.73/1.45 | (4) $i(all_3_4)
% 4.73/1.45 | (5) $i(all_3_3)
% 4.73/1.45 | (6) $i(all_3_2)
% 4.73/1.45 | (7) r(all_3_4) = all_3_1
% 4.73/1.45 | (8) r(all_3_3) = all_3_0
% 4.73/1.45 | (9) q(all_3_2) = 0
% 4.73/1.45 | (10) f(all_3_4) = all_3_2
% 4.73/1.46 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (q(v0) = 0) | ~ (r(v1)
% 4.73/1.46 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 4.73/1.46 | (f(v1) = v3 & p(v3) = 0 & p(v0) = v4 & $i(v3) & ( ~ (v4 = 0) | (v2 =
% 4.73/1.46 | 0 & ( ~ (all_3_0 = 0) | ~ (all_3_1 = 0))))))
% 4.73/1.46 |
% 4.73/1.46 | GROUND_INST: instantiating (11) with all_3_2, all_3_3, all_3_0, simplifying
% 4.73/1.46 | with (5), (6), (8), (9) gives:
% 4.73/1.46 | (12) ? [v0: $i] : ? [v1: any] : (f(all_3_3) = v0 & p(v0) = 0 & p(all_3_2)
% 4.73/1.46 | = v1 & $i(v0) & ( ~ (v1 = 0) | (all_3_0 = 0 & ~ (all_3_1 = 0))))
% 4.73/1.46 |
% 4.73/1.46 | GROUND_INST: instantiating (11) with all_3_2, all_3_4, all_3_1, simplifying
% 4.73/1.46 | with (4), (6), (7), (9) gives:
% 4.73/1.46 | (13) ? [v0: $i] : ? [v1: any] : (f(all_3_4) = v0 & p(v0) = 0 & p(all_3_2)
% 4.73/1.46 | = v1 & $i(v0) & ( ~ (v1 = 0) | (all_3_1 = 0 & ~ (all_3_0 = 0))))
% 4.73/1.46 |
% 4.73/1.46 | DELTA: instantiating (13) with fresh symbols all_11_0, all_11_1 gives:
% 4.73/1.46 | (14) f(all_3_4) = all_11_1 & p(all_11_1) = 0 & p(all_3_2) = all_11_0 &
% 4.73/1.46 | $i(all_11_1) & ( ~ (all_11_0 = 0) | (all_3_1 = 0 & ~ (all_3_0 = 0)))
% 4.73/1.46 |
% 4.73/1.46 | ALPHA: (14) implies:
% 4.73/1.46 | (15) p(all_3_2) = all_11_0
% 4.73/1.46 | (16) p(all_11_1) = 0
% 4.73/1.46 | (17) f(all_3_4) = all_11_1
% 4.73/1.46 | (18) ~ (all_11_0 = 0) | (all_3_1 = 0 & ~ (all_3_0 = 0))
% 4.73/1.46 |
% 4.73/1.46 | DELTA: instantiating (12) with fresh symbols all_13_0, all_13_1 gives:
% 4.73/1.46 | (19) f(all_3_3) = all_13_1 & p(all_13_1) = 0 & p(all_3_2) = all_13_0 &
% 4.73/1.46 | $i(all_13_1) & ( ~ (all_13_0 = 0) | (all_3_0 = 0 & ~ (all_3_1 = 0)))
% 4.73/1.46 |
% 4.73/1.46 | ALPHA: (19) implies:
% 4.73/1.46 | (20) p(all_3_2) = all_13_0
% 4.73/1.46 | (21) ~ (all_13_0 = 0) | (all_3_0 = 0 & ~ (all_3_1 = 0))
% 4.73/1.46 |
% 4.73/1.46 | GROUND_INST: instantiating (1) with all_11_0, all_13_0, all_3_2, simplifying
% 4.73/1.46 | with (15), (20) gives:
% 4.73/1.46 | (22) all_13_0 = all_11_0
% 4.73/1.46 |
% 4.73/1.46 | GROUND_INST: instantiating (2) with all_3_2, all_11_1, all_3_4, simplifying
% 4.73/1.46 | with (10), (17) gives:
% 4.73/1.46 | (23) all_11_1 = all_3_2
% 4.73/1.46 |
% 4.73/1.47 | REDUCE: (16), (23) imply:
% 4.73/1.47 | (24) p(all_3_2) = 0
% 4.73/1.47 |
% 4.73/1.47 | GROUND_INST: instantiating (1) with all_11_0, 0, all_3_2, simplifying with
% 4.73/1.47 | (15), (24) gives:
% 4.73/1.47 | (25) all_11_0 = 0
% 4.73/1.47 |
% 4.73/1.47 | COMBINE_EQS: (22), (25) imply:
% 4.73/1.47 | (26) all_13_0 = 0
% 4.73/1.47 |
% 4.73/1.47 | BETA: splitting (18) gives:
% 4.73/1.47 |
% 4.73/1.47 | Case 1:
% 4.73/1.47 | |
% 4.73/1.47 | | (27) ~ (all_11_0 = 0)
% 4.73/1.47 | |
% 4.73/1.47 | | REDUCE: (25), (27) imply:
% 4.73/1.47 | | (28) $false
% 4.73/1.47 | |
% 4.73/1.47 | | CLOSE: (28) is inconsistent.
% 4.73/1.47 | |
% 4.73/1.47 | Case 2:
% 4.73/1.47 | |
% 4.73/1.47 | | (29) all_3_1 = 0 & ~ (all_3_0 = 0)
% 4.73/1.47 | |
% 4.73/1.47 | | ALPHA: (29) implies:
% 4.73/1.47 | | (30) all_3_1 = 0
% 4.73/1.47 | |
% 4.73/1.47 | | BETA: splitting (21) gives:
% 4.73/1.47 | |
% 4.73/1.47 | | Case 1:
% 4.73/1.47 | | |
% 4.73/1.47 | | | (31) ~ (all_13_0 = 0)
% 4.73/1.47 | | |
% 4.73/1.47 | | | REDUCE: (26), (31) imply:
% 4.73/1.47 | | | (32) $false
% 4.73/1.47 | | |
% 4.73/1.47 | | | CLOSE: (32) is inconsistent.
% 4.73/1.47 | | |
% 4.73/1.47 | | Case 2:
% 4.73/1.47 | | |
% 4.73/1.47 | | | (33) all_3_0 = 0 & ~ (all_3_1 = 0)
% 4.73/1.47 | | |
% 4.73/1.47 | | | ALPHA: (33) implies:
% 4.73/1.47 | | | (34) ~ (all_3_1 = 0)
% 4.73/1.47 | | |
% 4.73/1.47 | | | REDUCE: (30), (34) imply:
% 4.73/1.47 | | | (35) $false
% 4.73/1.47 | | |
% 4.73/1.47 | | | CLOSE: (35) is inconsistent.
% 4.73/1.47 | | |
% 4.73/1.47 | | End of split
% 4.73/1.47 | |
% 4.73/1.47 | End of split
% 4.73/1.47 |
% 4.73/1.47 End of proof
% 4.73/1.47 % SZS output end Proof for theBenchmark
% 4.73/1.47
% 4.73/1.47 811ms
%------------------------------------------------------------------------------