TSTP Solution File: SET788+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET788+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 : n001.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 15:26:27 EDT 2023
% Result : Theorem 4.08s 1.23s
% Output : Proof 5.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET788+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n001.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 16:23:16 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.61 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.50/0.91 Prover 4: Preprocessing ...
% 1.50/0.91 Prover 1: Preprocessing ...
% 2.06/0.95 Prover 3: Preprocessing ...
% 2.06/0.95 Prover 5: Preprocessing ...
% 2.06/0.95 Prover 0: Preprocessing ...
% 2.06/0.95 Prover 2: Preprocessing ...
% 2.06/0.95 Prover 6: Preprocessing ...
% 2.36/1.02 Prover 5: Proving ...
% 2.36/1.02 Prover 2: Proving ...
% 2.36/1.04 Prover 6: Proving ...
% 2.36/1.04 Prover 1: Constructing countermodel ...
% 2.36/1.04 Prover 3: Constructing countermodel ...
% 2.82/1.06 Prover 0: Proving ...
% 2.82/1.06 Prover 4: Constructing countermodel ...
% 4.08/1.23 Prover 3: proved (592ms)
% 4.08/1.23
% 4.08/1.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.08/1.23
% 4.08/1.24 Prover 5: stopped
% 4.08/1.24 Prover 2: stopped
% 4.08/1.24 Prover 6: stopped
% 4.08/1.24 Prover 0: stopped
% 4.08/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.08/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.08/1.25 Prover 7: Preprocessing ...
% 4.08/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.08/1.25 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.08/1.25 Prover 8: Preprocessing ...
% 4.08/1.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.08/1.26 Prover 10: Preprocessing ...
% 4.08/1.26 Prover 13: Preprocessing ...
% 4.08/1.26 Prover 11: Preprocessing ...
% 4.08/1.27 Prover 10: Warning: ignoring some quantifiers
% 4.08/1.27 Prover 10: Constructing countermodel ...
% 4.08/1.27 Prover 13: Warning: ignoring some quantifiers
% 4.08/1.27 Prover 13: Constructing countermodel ...
% 4.08/1.27 Prover 7: Warning: ignoring some quantifiers
% 4.08/1.27 Prover 7: Constructing countermodel ...
% 4.45/1.28 Prover 8: Warning: ignoring some quantifiers
% 4.45/1.28 Prover 8: Constructing countermodel ...
% 4.45/1.29 Prover 10: gave up
% 4.45/1.29 Prover 13: gave up
% 4.45/1.30 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.45/1.30 Prover 7: gave up
% 4.45/1.30 Prover 16: Preprocessing ...
% 4.45/1.31 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.45/1.31 Prover 16: Warning: ignoring some quantifiers
% 4.45/1.31 Prover 16: Constructing countermodel ...
% 4.45/1.32 Prover 19: Preprocessing ...
% 4.45/1.33 Prover 4: Found proof (size 68)
% 4.45/1.33 Prover 4: proved (704ms)
% 4.45/1.33 Prover 1: stopped
% 4.45/1.33 Prover 8: stopped
% 4.45/1.33 Prover 16: stopped
% 4.45/1.34 Prover 11: Constructing countermodel ...
% 4.45/1.34 Prover 11: stopped
% 4.94/1.36 Prover 19: Warning: ignoring some quantifiers
% 4.94/1.36 Prover 19: Constructing countermodel ...
% 4.94/1.36 Prover 19: stopped
% 4.94/1.36
% 4.94/1.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.94/1.36
% 4.94/1.37 % SZS output start Proof for theBenchmark
% 4.94/1.37 Assumptions after simplification:
% 4.94/1.37 ---------------------------------
% 4.94/1.37
% 4.94/1.37 (prove_this)
% 4.94/1.41 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (equalish(v1, v0) =
% 4.94/1.41 v3 & equalish(v0, v1) = v2 & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] :
% 4.94/1.41 ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (equalish(v4, v5) = 0) | ~
% 4.94/1.41 (a_member_of(v6, v5) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8:
% 4.94/1.41 int] : ( ~ (v8 = 0) & a_member_of(v6, v4) = v8)) & ! [v4: $i] : ! [v5:
% 4.94/1.41 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (equalish(v4, v5) = 0) |
% 4.94/1.41 ~ (a_member_of(v6, v4) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8:
% 4.94/1.41 int] : ( ~ (v8 = 0) & a_member_of(v6, v5) = v8)) & ! [v4: $i] : ! [v5:
% 4.94/1.41 $i] : ! [v6: int] : (v6 = 0 | ~ (equalish(v4, v5) = v6) | ~ $i(v5) | ~
% 4.94/1.41 $i(v4) | ? [v7: $i] : ? [v8: any] : ? [v9: any] : (a_member_of(v7, v5)
% 4.94/1.41 = v9 & a_member_of(v7, v4) = v8 & $i(v7) & ( ~ (v9 = 0) | ~ (v8 = 0)) &
% 4.94/1.41 (v9 = 0 | v8 = 0))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 4.94/1.41 (equalish(v4, v5) = 0) | ~ (a_member_of(v6, v5) = 0) | ~ $i(v6) | ~
% 4.94/1.41 $i(v5) | ~ $i(v4) | a_member_of(v6, v4) = 0) & ! [v4: $i] : ! [v5: $i]
% 4.94/1.41 : ! [v6: $i] : ( ~ (equalish(v4, v5) = 0) | ~ (a_member_of(v6, v4) = 0) |
% 4.94/1.41 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | a_member_of(v6, v5) = 0) & ((v3 = 0 &
% 4.94/1.41 ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = 0))))
% 4.94/1.41
% 4.94/1.41 (function-axioms)
% 4.94/1.41 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.94/1.41 [v3: $i] : (v1 = v0 | ~ (equalish(v3, v2) = v1) | ~ (equalish(v3, v2) = v0))
% 4.94/1.41 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.94/1.41 [v3: $i] : (v1 = v0 | ~ (a_member_of(v3, v2) = v1) | ~ (a_member_of(v3, v2)
% 4.94/1.41 = v0))
% 4.94/1.41
% 4.94/1.41 Those formulas are unsatisfiable:
% 4.94/1.41 ---------------------------------
% 4.94/1.41
% 4.94/1.41 Begin of proof
% 4.94/1.42 |
% 4.94/1.42 | ALPHA: (function-axioms) implies:
% 4.94/1.42 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.94/1.42 | ! [v3: $i] : (v1 = v0 | ~ (a_member_of(v3, v2) = v1) | ~
% 4.94/1.42 | (a_member_of(v3, v2) = v0))
% 4.94/1.42 |
% 4.94/1.42 | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1,
% 4.94/1.42 | all_3_2, all_3_3 gives:
% 4.94/1.43 | (2) equalish(all_3_2, all_3_3) = all_3_0 & equalish(all_3_3, all_3_2) =
% 4.94/1.43 | all_3_1 & $i(all_3_2) & $i(all_3_3) & ! [v0: $i] : ! [v1: $i] : !
% 4.94/1.43 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (equalish(v0, v1) = 0) | ~
% 4.94/1.43 | (a_member_of(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 4.94/1.43 | [v4: int] : ( ~ (v4 = 0) & a_member_of(v2, v0) = v4)) & ! [v0: $i] :
% 4.94/1.43 | ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (equalish(v0,
% 4.94/1.43 | v1) = 0) | ~ (a_member_of(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1)
% 4.94/1.43 | | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & a_member_of(v2, v1) =
% 4.94/1.43 | v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 4.94/1.43 | (equalish(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 4.94/1.43 | [v4: any] : ? [v5: any] : (a_member_of(v3, v1) = v5 &
% 4.94/1.43 | a_member_of(v3, v0) = v4 & $i(v3) & ( ~ (v5 = 0) | ~ (v4 = 0)) &
% 4.94/1.43 | (v5 = 0 | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 4.94/1.43 | (equalish(v0, v1) = 0) | ~ (a_member_of(v2, v1) = 0) | ~ $i(v2) |
% 4.94/1.43 | ~ $i(v1) | ~ $i(v0) | a_member_of(v2, v0) = 0) & ! [v0: $i] : !
% 4.94/1.43 | [v1: $i] : ! [v2: $i] : ( ~ (equalish(v0, v1) = 0) | ~
% 4.94/1.43 | (a_member_of(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 4.94/1.43 | a_member_of(v2, v1) = 0) & ((all_3_0 = 0 & ~ (all_3_1 = 0)) |
% 4.94/1.43 | (all_3_1 = 0 & ~ (all_3_0 = 0)))
% 4.94/1.43 |
% 4.94/1.43 | ALPHA: (2) implies:
% 4.94/1.43 | (3) $i(all_3_3)
% 4.94/1.43 | (4) $i(all_3_2)
% 4.94/1.43 | (5) equalish(all_3_3, all_3_2) = all_3_1
% 4.94/1.43 | (6) equalish(all_3_2, all_3_3) = all_3_0
% 4.94/1.43 | (7) (all_3_0 = 0 & ~ (all_3_1 = 0)) | (all_3_1 = 0 & ~ (all_3_0 = 0))
% 4.94/1.43 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equalish(v0,
% 4.94/1.43 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 4.94/1.43 | ? [v5: any] : (a_member_of(v3, v1) = v5 & a_member_of(v3, v0) = v4 &
% 4.94/1.43 | $i(v3) & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 4.94/1.43 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.94/1.43 | (equalish(v0, v1) = 0) | ~ (a_member_of(v2, v0) = v3) | ~ $i(v2) |
% 4.94/1.43 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & a_member_of(v2,
% 4.94/1.43 | v1) = v4))
% 4.94/1.43 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.94/1.43 | (equalish(v0, v1) = 0) | ~ (a_member_of(v2, v1) = v3) | ~ $i(v2) |
% 4.94/1.44 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 4.94/1.44 | a_member_of(v2, v0) = v4))
% 4.94/1.44 |
% 4.94/1.44 | GROUND_INST: instantiating (8) with all_3_3, all_3_2, all_3_1, simplifying
% 4.94/1.44 | with (3), (4), (5) gives:
% 4.94/1.44 | (11) all_3_1 = 0 | ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 4.94/1.44 | (a_member_of(v0, all_3_2) = v2 & a_member_of(v0, all_3_3) = v1 &
% 4.94/1.44 | $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 4.94/1.44 |
% 4.94/1.44 | GROUND_INST: instantiating (8) with all_3_2, all_3_3, all_3_0, simplifying
% 4.94/1.44 | with (3), (4), (6) gives:
% 4.94/1.44 | (12) all_3_0 = 0 | ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 4.94/1.44 | (a_member_of(v0, all_3_2) = v1 & a_member_of(v0, all_3_3) = v2 &
% 4.94/1.44 | $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 4.94/1.44 |
% 4.94/1.44 | BETA: splitting (7) gives:
% 4.94/1.44 |
% 4.94/1.44 | Case 1:
% 4.94/1.44 | |
% 4.94/1.44 | | (13) all_3_0 = 0 & ~ (all_3_1 = 0)
% 4.94/1.44 | |
% 4.94/1.44 | | ALPHA: (13) implies:
% 4.94/1.44 | | (14) all_3_0 = 0
% 4.94/1.44 | | (15) ~ (all_3_1 = 0)
% 4.94/1.44 | |
% 4.94/1.44 | | REDUCE: (6), (14) imply:
% 4.94/1.44 | | (16) equalish(all_3_2, all_3_3) = 0
% 4.94/1.44 | |
% 4.94/1.44 | | BETA: splitting (11) gives:
% 4.94/1.44 | |
% 4.94/1.44 | | Case 1:
% 4.94/1.44 | | |
% 4.94/1.44 | | | (17) all_3_1 = 0
% 4.94/1.44 | | |
% 4.94/1.44 | | | REDUCE: (15), (17) imply:
% 4.94/1.44 | | | (18) $false
% 4.94/1.44 | | |
% 4.94/1.44 | | | CLOSE: (18) is inconsistent.
% 4.94/1.44 | | |
% 4.94/1.44 | | Case 2:
% 4.94/1.44 | | |
% 4.94/1.44 | | | (19) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (a_member_of(v0,
% 4.94/1.44 | | | all_3_2) = v2 & a_member_of(v0, all_3_3) = v1 & $i(v0) & ( ~
% 4.94/1.44 | | | (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 4.94/1.44 | | |
% 4.94/1.44 | | | DELTA: instantiating (19) with fresh symbols all_17_0, all_17_1, all_17_2
% 4.94/1.44 | | | gives:
% 4.94/1.44 | | | (20) a_member_of(all_17_2, all_3_2) = all_17_0 & a_member_of(all_17_2,
% 4.94/1.44 | | | all_3_3) = all_17_1 & $i(all_17_2) & ( ~ (all_17_0 = 0) | ~
% 4.94/1.44 | | | (all_17_1 = 0)) & (all_17_0 = 0 | all_17_1 = 0)
% 4.94/1.44 | | |
% 4.94/1.44 | | | ALPHA: (20) implies:
% 4.94/1.44 | | | (21) $i(all_17_2)
% 4.94/1.44 | | | (22) a_member_of(all_17_2, all_3_3) = all_17_1
% 4.94/1.44 | | | (23) a_member_of(all_17_2, all_3_2) = all_17_0
% 4.94/1.45 | | | (24) all_17_0 = 0 | all_17_1 = 0
% 4.94/1.45 | | | (25) ~ (all_17_0 = 0) | ~ (all_17_1 = 0)
% 4.94/1.45 | | |
% 4.94/1.45 | | | GROUND_INST: instantiating (9) with all_3_2, all_3_3, all_17_2, all_17_0,
% 4.94/1.45 | | | simplifying with (3), (4), (16), (21), (23) gives:
% 4.94/1.45 | | | (26) all_17_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2,
% 4.94/1.45 | | | all_3_3) = v0)
% 4.94/1.45 | | |
% 4.94/1.45 | | | GROUND_INST: instantiating (10) with all_3_2, all_3_3, all_17_2, all_17_1,
% 4.94/1.45 | | | simplifying with (3), (4), (16), (21), (22) gives:
% 4.94/1.45 | | | (27) all_17_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2,
% 4.94/1.45 | | | all_3_2) = v0)
% 4.94/1.45 | | |
% 4.94/1.45 | | | BETA: splitting (24) gives:
% 4.94/1.45 | | |
% 4.94/1.45 | | | Case 1:
% 4.94/1.45 | | | |
% 4.94/1.45 | | | | (28) all_17_0 = 0
% 4.94/1.45 | | | |
% 4.94/1.45 | | | | REDUCE: (23), (28) imply:
% 4.94/1.45 | | | | (29) a_member_of(all_17_2, all_3_2) = 0
% 4.94/1.45 | | | |
% 4.94/1.45 | | | | BETA: splitting (25) gives:
% 4.94/1.45 | | | |
% 4.94/1.45 | | | | Case 1:
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | (30) ~ (all_17_0 = 0)
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | REDUCE: (28), (30) imply:
% 4.94/1.45 | | | | | (31) $false
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | CLOSE: (31) is inconsistent.
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | Case 2:
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | (32) ~ (all_17_1 = 0)
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | BETA: splitting (27) gives:
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | Case 1:
% 4.94/1.45 | | | | | |
% 4.94/1.45 | | | | | | (33) all_17_1 = 0
% 4.94/1.45 | | | | | |
% 4.94/1.45 | | | | | | REDUCE: (32), (33) imply:
% 4.94/1.45 | | | | | | (34) $false
% 4.94/1.45 | | | | | |
% 4.94/1.45 | | | | | | CLOSE: (34) is inconsistent.
% 4.94/1.45 | | | | | |
% 4.94/1.45 | | | | | Case 2:
% 4.94/1.45 | | | | | |
% 4.94/1.45 | | | | | | (35) ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_2)
% 4.94/1.45 | | | | | | = v0)
% 4.94/1.45 | | | | | |
% 4.94/1.45 | | | | | | DELTA: instantiating (35) with fresh symbol all_34_0 gives:
% 4.94/1.45 | | | | | | (36) ~ (all_34_0 = 0) & a_member_of(all_17_2, all_3_2) =
% 4.94/1.45 | | | | | | all_34_0
% 4.94/1.45 | | | | | |
% 4.94/1.45 | | | | | | ALPHA: (36) implies:
% 4.94/1.45 | | | | | | (37) ~ (all_34_0 = 0)
% 4.94/1.45 | | | | | | (38) a_member_of(all_17_2, all_3_2) = all_34_0
% 4.94/1.45 | | | | | |
% 4.94/1.45 | | | | | | GROUND_INST: instantiating (1) with 0, all_34_0, all_3_2, all_17_2,
% 4.94/1.45 | | | | | | simplifying with (29), (38) gives:
% 4.94/1.45 | | | | | | (39) all_34_0 = 0
% 4.94/1.45 | | | | | |
% 4.94/1.45 | | | | | | REDUCE: (37), (39) imply:
% 4.94/1.45 | | | | | | (40) $false
% 4.94/1.45 | | | | | |
% 4.94/1.45 | | | | | | CLOSE: (40) is inconsistent.
% 4.94/1.45 | | | | | |
% 4.94/1.45 | | | | | End of split
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | End of split
% 4.94/1.45 | | | |
% 4.94/1.45 | | | Case 2:
% 4.94/1.45 | | | |
% 4.94/1.45 | | | | (41) all_17_1 = 0
% 4.94/1.45 | | | | (42) ~ (all_17_0 = 0)
% 4.94/1.45 | | | |
% 4.94/1.45 | | | | REDUCE: (22), (41) imply:
% 4.94/1.45 | | | | (43) a_member_of(all_17_2, all_3_3) = 0
% 4.94/1.45 | | | |
% 4.94/1.45 | | | | BETA: splitting (26) gives:
% 4.94/1.45 | | | |
% 4.94/1.45 | | | | Case 1:
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | (44) all_17_0 = 0
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | REDUCE: (42), (44) imply:
% 4.94/1.45 | | | | | (45) $false
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | CLOSE: (45) is inconsistent.
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | Case 2:
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | (46) ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_3) =
% 4.94/1.45 | | | | | v0)
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | DELTA: instantiating (46) with fresh symbol all_30_0 gives:
% 4.94/1.45 | | | | | (47) ~ (all_30_0 = 0) & a_member_of(all_17_2, all_3_3) = all_30_0
% 4.94/1.45 | | | | |
% 4.94/1.45 | | | | | ALPHA: (47) implies:
% 4.94/1.46 | | | | | (48) ~ (all_30_0 = 0)
% 4.94/1.46 | | | | | (49) a_member_of(all_17_2, all_3_3) = all_30_0
% 4.94/1.46 | | | | |
% 4.94/1.46 | | | | | GROUND_INST: instantiating (1) with 0, all_30_0, all_3_3, all_17_2,
% 4.94/1.46 | | | | | simplifying with (43), (49) gives:
% 4.94/1.46 | | | | | (50) all_30_0 = 0
% 4.94/1.46 | | | | |
% 4.94/1.46 | | | | | REDUCE: (48), (50) imply:
% 4.94/1.46 | | | | | (51) $false
% 4.94/1.46 | | | | |
% 4.94/1.46 | | | | | CLOSE: (51) is inconsistent.
% 4.94/1.46 | | | | |
% 4.94/1.46 | | | | End of split
% 4.94/1.46 | | | |
% 4.94/1.46 | | | End of split
% 4.94/1.46 | | |
% 4.94/1.46 | | End of split
% 4.94/1.46 | |
% 4.94/1.46 | Case 2:
% 4.94/1.46 | |
% 4.94/1.46 | | (52) all_3_1 = 0 & ~ (all_3_0 = 0)
% 4.94/1.46 | |
% 4.94/1.46 | | ALPHA: (52) implies:
% 4.94/1.46 | | (53) all_3_1 = 0
% 4.94/1.46 | | (54) ~ (all_3_0 = 0)
% 4.94/1.46 | |
% 4.94/1.46 | | REDUCE: (5), (53) imply:
% 4.94/1.46 | | (55) equalish(all_3_3, all_3_2) = 0
% 4.94/1.46 | |
% 4.94/1.46 | | BETA: splitting (12) gives:
% 4.94/1.46 | |
% 4.94/1.46 | | Case 1:
% 4.94/1.46 | | |
% 4.94/1.46 | | | (56) all_3_0 = 0
% 4.94/1.46 | | |
% 4.94/1.46 | | | REDUCE: (54), (56) imply:
% 4.94/1.46 | | | (57) $false
% 4.94/1.46 | | |
% 4.94/1.46 | | | CLOSE: (57) is inconsistent.
% 4.94/1.46 | | |
% 4.94/1.46 | | Case 2:
% 4.94/1.46 | | |
% 4.94/1.46 | | | (58) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (a_member_of(v0,
% 4.94/1.46 | | | all_3_2) = v1 & a_member_of(v0, all_3_3) = v2 & $i(v0) & ( ~
% 4.94/1.46 | | | (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 4.94/1.46 | | |
% 4.94/1.46 | | | DELTA: instantiating (58) with fresh symbols all_17_0, all_17_1, all_17_2
% 4.94/1.46 | | | gives:
% 4.94/1.46 | | | (59) a_member_of(all_17_2, all_3_2) = all_17_1 & a_member_of(all_17_2,
% 4.94/1.46 | | | all_3_3) = all_17_0 & $i(all_17_2) & ( ~ (all_17_0 = 0) | ~
% 4.94/1.46 | | | (all_17_1 = 0)) & (all_17_0 = 0 | all_17_1 = 0)
% 4.94/1.46 | | |
% 4.94/1.46 | | | ALPHA: (59) implies:
% 4.94/1.46 | | | (60) $i(all_17_2)
% 4.94/1.46 | | | (61) a_member_of(all_17_2, all_3_3) = all_17_0
% 4.94/1.46 | | | (62) a_member_of(all_17_2, all_3_2) = all_17_1
% 4.94/1.46 | | | (63) all_17_0 = 0 | all_17_1 = 0
% 4.94/1.46 | | | (64) ~ (all_17_0 = 0) | ~ (all_17_1 = 0)
% 4.94/1.46 | | |
% 4.94/1.46 | | | GROUND_INST: instantiating (10) with all_3_3, all_3_2, all_17_2, all_17_1,
% 4.94/1.46 | | | simplifying with (3), (4), (55), (60), (62) gives:
% 4.94/1.46 | | | (65) all_17_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2,
% 4.94/1.46 | | | all_3_3) = v0)
% 4.94/1.46 | | |
% 4.94/1.46 | | | GROUND_INST: instantiating (9) with all_3_3, all_3_2, all_17_2, all_17_0,
% 4.94/1.46 | | | simplifying with (3), (4), (55), (60), (61) gives:
% 4.94/1.46 | | | (66) all_17_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2,
% 4.94/1.46 | | | all_3_2) = v0)
% 4.94/1.46 | | |
% 4.94/1.46 | | | BETA: splitting (63) gives:
% 4.94/1.46 | | |
% 4.94/1.46 | | | Case 1:
% 4.94/1.46 | | | |
% 4.94/1.46 | | | | (67) all_17_0 = 0
% 4.94/1.46 | | | |
% 4.94/1.46 | | | | REDUCE: (61), (67) imply:
% 4.94/1.46 | | | | (68) a_member_of(all_17_2, all_3_3) = 0
% 4.94/1.46 | | | |
% 4.94/1.46 | | | | BETA: splitting (64) gives:
% 4.94/1.46 | | | |
% 4.94/1.46 | | | | Case 1:
% 4.94/1.46 | | | | |
% 4.94/1.46 | | | | | (69) ~ (all_17_0 = 0)
% 4.94/1.46 | | | | |
% 4.94/1.46 | | | | | REDUCE: (67), (69) imply:
% 4.94/1.46 | | | | | (70) $false
% 4.94/1.46 | | | | |
% 4.94/1.46 | | | | | CLOSE: (70) is inconsistent.
% 4.94/1.46 | | | | |
% 4.94/1.46 | | | | Case 2:
% 4.94/1.46 | | | | |
% 4.94/1.46 | | | | | (71) ~ (all_17_1 = 0)
% 4.94/1.46 | | | | |
% 4.94/1.46 | | | | | BETA: splitting (65) gives:
% 4.94/1.46 | | | | |
% 4.94/1.46 | | | | | Case 1:
% 4.94/1.46 | | | | | |
% 4.94/1.46 | | | | | | (72) all_17_1 = 0
% 4.94/1.46 | | | | | |
% 4.94/1.46 | | | | | | REDUCE: (71), (72) imply:
% 4.94/1.46 | | | | | | (73) $false
% 4.94/1.47 | | | | | |
% 4.94/1.47 | | | | | | CLOSE: (73) is inconsistent.
% 4.94/1.47 | | | | | |
% 4.94/1.47 | | | | | Case 2:
% 4.94/1.47 | | | | | |
% 4.94/1.47 | | | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_3)
% 4.94/1.47 | | | | | | = v0)
% 4.94/1.47 | | | | | |
% 4.94/1.47 | | | | | | DELTA: instantiating (74) with fresh symbol all_34_0 gives:
% 4.94/1.47 | | | | | | (75) ~ (all_34_0 = 0) & a_member_of(all_17_2, all_3_3) =
% 4.94/1.47 | | | | | | all_34_0
% 4.94/1.47 | | | | | |
% 4.94/1.47 | | | | | | ALPHA: (75) implies:
% 4.94/1.47 | | | | | | (76) ~ (all_34_0 = 0)
% 4.94/1.47 | | | | | | (77) a_member_of(all_17_2, all_3_3) = all_34_0
% 4.94/1.47 | | | | | |
% 4.94/1.47 | | | | | | GROUND_INST: instantiating (1) with 0, all_34_0, all_3_3, all_17_2,
% 4.94/1.47 | | | | | | simplifying with (68), (77) gives:
% 4.94/1.47 | | | | | | (78) all_34_0 = 0
% 4.94/1.47 | | | | | |
% 4.94/1.47 | | | | | | REDUCE: (76), (78) imply:
% 4.94/1.47 | | | | | | (79) $false
% 4.94/1.47 | | | | | |
% 4.94/1.47 | | | | | | CLOSE: (79) is inconsistent.
% 4.94/1.47 | | | | | |
% 4.94/1.47 | | | | | End of split
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | End of split
% 4.94/1.47 | | | |
% 4.94/1.47 | | | Case 2:
% 4.94/1.47 | | | |
% 4.94/1.47 | | | | (80) all_17_1 = 0
% 4.94/1.47 | | | | (81) ~ (all_17_0 = 0)
% 4.94/1.47 | | | |
% 4.94/1.47 | | | | REDUCE: (62), (80) imply:
% 4.94/1.47 | | | | (82) a_member_of(all_17_2, all_3_2) = 0
% 4.94/1.47 | | | |
% 4.94/1.47 | | | | BETA: splitting (66) gives:
% 4.94/1.47 | | | |
% 4.94/1.47 | | | | Case 1:
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | | (83) all_17_0 = 0
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | | REDUCE: (81), (83) imply:
% 4.94/1.47 | | | | | (84) $false
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | | CLOSE: (84) is inconsistent.
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | Case 2:
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | | (85) ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_2) =
% 4.94/1.47 | | | | | v0)
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | | DELTA: instantiating (85) with fresh symbol all_30_0 gives:
% 4.94/1.47 | | | | | (86) ~ (all_30_0 = 0) & a_member_of(all_17_2, all_3_2) = all_30_0
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | | ALPHA: (86) implies:
% 4.94/1.47 | | | | | (87) ~ (all_30_0 = 0)
% 4.94/1.47 | | | | | (88) a_member_of(all_17_2, all_3_2) = all_30_0
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | | GROUND_INST: instantiating (1) with 0, all_30_0, all_3_2, all_17_2,
% 4.94/1.47 | | | | | simplifying with (82), (88) gives:
% 4.94/1.47 | | | | | (89) all_30_0 = 0
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | | REDUCE: (87), (89) imply:
% 4.94/1.47 | | | | | (90) $false
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | | CLOSE: (90) is inconsistent.
% 4.94/1.47 | | | | |
% 4.94/1.47 | | | | End of split
% 4.94/1.47 | | | |
% 4.94/1.47 | | | End of split
% 4.94/1.47 | | |
% 4.94/1.47 | | End of split
% 4.94/1.47 | |
% 4.94/1.47 | End of split
% 4.94/1.47 |
% 4.94/1.47 End of proof
% 5.24/1.47 % SZS output end Proof for theBenchmark
% 5.24/1.47
% 5.24/1.47 869ms
%------------------------------------------------------------------------------