TSTP Solution File: SET047+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.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 15:23:25 EDT 2023
% Result : Theorem 4.21s 1.36s
% Output : Proof 5.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 13:17:17 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.64 ________ _____
% 0.21/0.64 ___ __ \_________(_)________________________________
% 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.64
% 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.64 (2023-06-19)
% 0.21/0.64
% 0.21/0.64 (c) Philipp Rümmer, 2009-2023
% 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.64 Amanda Stjerna.
% 0.21/0.64 Free software under BSD-3-Clause.
% 0.21/0.64
% 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.64
% 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.82/1.01 Prover 4: Preprocessing ...
% 1.82/1.01 Prover 1: Preprocessing ...
% 2.18/1.06 Prover 0: Preprocessing ...
% 2.18/1.06 Prover 2: Preprocessing ...
% 2.18/1.06 Prover 3: Preprocessing ...
% 2.27/1.06 Prover 6: Preprocessing ...
% 2.27/1.06 Prover 5: Preprocessing ...
% 2.70/1.15 Prover 5: Proving ...
% 2.70/1.15 Prover 2: Proving ...
% 2.97/1.16 Prover 6: Proving ...
% 2.97/1.16 Prover 3: Constructing countermodel ...
% 2.97/1.17 Prover 1: Constructing countermodel ...
% 2.97/1.19 Prover 0: Proving ...
% 2.97/1.20 Prover 4: Constructing countermodel ...
% 4.21/1.36 Prover 3: proved (695ms)
% 4.21/1.36
% 4.21/1.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.21/1.36
% 4.21/1.37 Prover 2: stopped
% 4.21/1.37 Prover 6: stopped
% 4.21/1.37 Prover 0: stopped
% 4.21/1.37 Prover 5: stopped
% 4.21/1.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.21/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.21/1.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.21/1.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.21/1.38 Prover 10: Preprocessing ...
% 4.21/1.38 Prover 7: Preprocessing ...
% 4.21/1.38 Prover 8: Preprocessing ...
% 4.21/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.21/1.38 Prover 11: Preprocessing ...
% 4.21/1.39 Prover 13: Preprocessing ...
% 4.21/1.41 Prover 10: Warning: ignoring some quantifiers
% 4.21/1.41 Prover 10: Constructing countermodel ...
% 4.21/1.41 Prover 13: Warning: ignoring some quantifiers
% 4.21/1.41 Prover 7: Warning: ignoring some quantifiers
% 4.21/1.41 Prover 13: Constructing countermodel ...
% 4.21/1.42 Prover 7: Constructing countermodel ...
% 4.21/1.43 Prover 13: gave up
% 4.21/1.43 Prover 10: gave up
% 4.21/1.45 Prover 8: Warning: ignoring some quantifiers
% 4.21/1.45 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.21/1.45 Prover 8: Constructing countermodel ...
% 4.21/1.45 Prover 16: Preprocessing ...
% 4.21/1.45 Prover 7: gave up
% 4.21/1.45 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.21/1.45 Prover 11: Constructing countermodel ...
% 4.21/1.45 Prover 19: Preprocessing ...
% 4.21/1.47 Prover 1: Found proof (size 63)
% 4.21/1.47 Prover 1: proved (811ms)
% 4.21/1.47 Prover 8: stopped
% 4.21/1.47 Prover 11: stopped
% 4.21/1.47 Prover 4: Found proof (size 69)
% 4.21/1.47 Prover 4: proved (806ms)
% 4.21/1.47 Prover 16: Warning: ignoring some quantifiers
% 4.21/1.47 Prover 16: Constructing countermodel ...
% 4.21/1.47 Prover 16: stopped
% 4.59/1.51 Prover 19: Warning: ignoring some quantifiers
% 4.59/1.51 Prover 19: Constructing countermodel ...
% 4.59/1.51 Prover 19: stopped
% 4.59/1.51
% 4.59/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.59/1.51
% 4.59/1.52 % SZS output start Proof for theBenchmark
% 4.59/1.52 Assumptions after simplification:
% 4.59/1.52 ---------------------------------
% 4.59/1.52
% 4.59/1.52 (pel43)
% 5.41/1.55 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (set_equal(v1, v0) =
% 5.41/1.55 v3 & set_equal(v0, v1) = v2 & $i(v1) & $i(v0) & ((v3 = 0 & ~ (v2 = 0)) |
% 5.41/1.55 (v2 = 0 & ~ (v3 = 0))))
% 5.41/1.55
% 5.41/1.55 (pel43_1)
% 5.41/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (set_equal(v0, v1) =
% 5.41/1.56 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] :
% 5.41/1.56 (element(v3, v1) = v5 & element(v3, v0) = v4 & $i(v3) & ( ~ (v5 = 0) | ~
% 5.41/1.56 (v4 = 0)) & (v5 = 0 | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 5.41/1.56 (set_equal(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3:
% 5.41/1.56 int] : (v3 = 0 | ~ (element(v2, v0) = v3) | ~ $i(v2) | ? [v4: int] :
% 5.41/1.56 ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2: $i] : ( ~ (element(v2,
% 5.41/1.56 v0) = 0) | ~ $i(v2) | element(v2, v1) = 0)))
% 5.41/1.56
% 5.41/1.56 (function-axioms)
% 5.41/1.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 5.41/1.56 [v3: $i] : (v1 = v0 | ~ (set_equal(v3, v2) = v1) | ~ (set_equal(v3, v2) =
% 5.41/1.56 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 5.41/1.56 $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 5.41/1.56 v2) = v0))
% 5.41/1.56
% 5.41/1.56 Those formulas are unsatisfiable:
% 5.41/1.56 ---------------------------------
% 5.41/1.56
% 5.41/1.56 Begin of proof
% 5.41/1.56 |
% 5.41/1.56 | ALPHA: (pel43_1) implies:
% 5.41/1.57 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (set_equal(v0, v1) = 0) | ~ $i(v1) |
% 5.41/1.57 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (element(v2,
% 5.41/1.57 | v0) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 5.41/1.57 | element(v2, v1) = v4)) & ! [v2: $i] : ( ~ (element(v2, v0) =
% 5.41/1.57 | 0) | ~ $i(v2) | element(v2, v1) = 0)))
% 5.41/1.57 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (set_equal(v0,
% 5.41/1.57 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 5.41/1.57 | ? [v5: any] : (element(v3, v1) = v5 & element(v3, v0) = v4 & $i(v3) &
% 5.41/1.57 | ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 5.41/1.57 |
% 5.41/1.57 | ALPHA: (function-axioms) implies:
% 5.41/1.57 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.41/1.57 | ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 5.41/1.57 | v2) = v0))
% 5.41/1.57 |
% 5.41/1.57 | DELTA: instantiating (pel43) with fresh symbols all_4_0, all_4_1, all_4_2,
% 5.41/1.57 | all_4_3 gives:
% 5.41/1.57 | (4) set_equal(all_4_2, all_4_3) = all_4_0 & set_equal(all_4_3, all_4_2) =
% 5.41/1.57 | all_4_1 & $i(all_4_2) & $i(all_4_3) & ((all_4_0 = 0 & ~ (all_4_1 = 0))
% 5.41/1.57 | | (all_4_1 = 0 & ~ (all_4_0 = 0)))
% 5.41/1.57 |
% 5.41/1.57 | ALPHA: (4) implies:
% 5.41/1.57 | (5) $i(all_4_3)
% 5.41/1.58 | (6) $i(all_4_2)
% 5.41/1.58 | (7) set_equal(all_4_3, all_4_2) = all_4_1
% 5.41/1.58 | (8) set_equal(all_4_2, all_4_3) = all_4_0
% 5.41/1.58 | (9) (all_4_0 = 0 & ~ (all_4_1 = 0)) | (all_4_1 = 0 & ~ (all_4_0 = 0))
% 5.41/1.58 |
% 5.41/1.58 | GROUND_INST: instantiating (2) with all_4_3, all_4_2, all_4_1, simplifying
% 5.41/1.58 | with (5), (6), (7) gives:
% 5.41/1.58 | (10) all_4_1 = 0 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (element(v0,
% 5.41/1.58 | all_4_2) = v2 & element(v0, all_4_3) = v1 & $i(v0) & ( ~ (v2 = 0)
% 5.41/1.58 | | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 5.41/1.58 |
% 5.41/1.58 | GROUND_INST: instantiating (2) with all_4_2, all_4_3, all_4_0, simplifying
% 5.41/1.58 | with (5), (6), (8) gives:
% 5.41/1.58 | (11) all_4_0 = 0 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (element(v0,
% 5.41/1.58 | all_4_2) = v1 & element(v0, all_4_3) = v2 & $i(v0) & ( ~ (v2 = 0)
% 5.41/1.58 | | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 5.41/1.58 |
% 5.41/1.58 | BETA: splitting (9) gives:
% 5.41/1.58 |
% 5.41/1.58 | Case 1:
% 5.41/1.58 | |
% 5.41/1.58 | | (12) all_4_0 = 0 & ~ (all_4_1 = 0)
% 5.41/1.58 | |
% 5.41/1.58 | | ALPHA: (12) implies:
% 5.58/1.58 | | (13) all_4_0 = 0
% 5.58/1.58 | | (14) ~ (all_4_1 = 0)
% 5.58/1.58 | |
% 5.58/1.58 | | REDUCE: (8), (13) imply:
% 5.58/1.58 | | (15) set_equal(all_4_2, all_4_3) = 0
% 5.58/1.58 | |
% 5.58/1.58 | | BETA: splitting (10) gives:
% 5.58/1.58 | |
% 5.58/1.58 | | Case 1:
% 5.58/1.58 | | |
% 5.58/1.58 | | | (16) all_4_1 = 0
% 5.58/1.58 | | |
% 5.58/1.58 | | | REDUCE: (14), (16) imply:
% 5.58/1.58 | | | (17) $false
% 5.58/1.59 | | |
% 5.58/1.59 | | | CLOSE: (17) is inconsistent.
% 5.58/1.59 | | |
% 5.58/1.59 | | Case 2:
% 5.58/1.59 | | |
% 5.58/1.59 | | | (18) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (element(v0, all_4_2)
% 5.58/1.59 | | | = v2 & element(v0, all_4_3) = v1 & $i(v0) & ( ~ (v2 = 0) | ~
% 5.58/1.59 | | | (v1 = 0)) & (v2 = 0 | v1 = 0))
% 5.58/1.59 | | |
% 5.58/1.59 | | | DELTA: instantiating (18) with fresh symbols all_17_0, all_17_1, all_17_2
% 5.58/1.59 | | | gives:
% 5.58/1.59 | | | (19) element(all_17_2, all_4_2) = all_17_0 & element(all_17_2, all_4_3)
% 5.58/1.59 | | | = all_17_1 & $i(all_17_2) & ( ~ (all_17_0 = 0) | ~ (all_17_1 =
% 5.58/1.59 | | | 0)) & (all_17_0 = 0 | all_17_1 = 0)
% 5.58/1.59 | | |
% 5.58/1.59 | | | ALPHA: (19) implies:
% 5.58/1.59 | | | (20) $i(all_17_2)
% 5.58/1.59 | | | (21) element(all_17_2, all_4_3) = all_17_1
% 5.58/1.59 | | | (22) element(all_17_2, all_4_2) = all_17_0
% 5.58/1.59 | | | (23) all_17_0 = 0 | all_17_1 = 0
% 5.58/1.59 | | | (24) ~ (all_17_0 = 0) | ~ (all_17_1 = 0)
% 5.58/1.59 | | |
% 5.58/1.59 | | | GROUND_INST: instantiating (1) with all_4_2, all_4_3, simplifying with
% 5.58/1.59 | | | (5), (6), (15) gives:
% 5.58/1.59 | | | (25) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (element(v0, all_4_2) =
% 5.58/1.59 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & element(v0,
% 5.58/1.59 | | | all_4_3) = v2)) & ! [v0: $i] : ( ~ (element(v0, all_4_2) =
% 5.58/1.59 | | | 0) | ~ $i(v0) | element(v0, all_4_3) = 0)
% 5.58/1.59 | | |
% 5.58/1.59 | | | ALPHA: (25) implies:
% 5.58/1.59 | | | (26) ! [v0: $i] : ( ~ (element(v0, all_4_2) = 0) | ~ $i(v0) |
% 5.58/1.59 | | | element(v0, all_4_3) = 0)
% 5.58/1.59 | | | (27) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (element(v0, all_4_2) =
% 5.58/1.59 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & element(v0,
% 5.58/1.59 | | | all_4_3) = v2))
% 5.58/1.59 | | |
% 5.58/1.59 | | | GROUND_INST: instantiating (27) with all_17_2, all_17_0, simplifying with
% 5.58/1.59 | | | (20), (22) gives:
% 5.58/1.59 | | | (28) all_17_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2,
% 5.58/1.59 | | | all_4_3) = v0)
% 5.58/1.59 | | |
% 5.58/1.59 | | | BETA: splitting (23) gives:
% 5.58/1.59 | | |
% 5.58/1.59 | | | Case 1:
% 5.58/1.59 | | | |
% 5.58/1.59 | | | | (29) all_17_0 = 0
% 5.58/1.59 | | | |
% 5.58/1.59 | | | | REDUCE: (22), (29) imply:
% 5.58/1.60 | | | | (30) element(all_17_2, all_4_2) = 0
% 5.58/1.60 | | | |
% 5.58/1.60 | | | | BETA: splitting (24) gives:
% 5.58/1.60 | | | |
% 5.58/1.60 | | | | Case 1:
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | (31) ~ (all_17_0 = 0)
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | REDUCE: (29), (31) imply:
% 5.58/1.60 | | | | | (32) $false
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | CLOSE: (32) is inconsistent.
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | Case 2:
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | (33) ~ (all_17_1 = 0)
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | GROUND_INST: instantiating (26) with all_17_2, simplifying with (20),
% 5.58/1.60 | | | | | (30) gives:
% 5.58/1.60 | | | | | (34) element(all_17_2, all_4_3) = 0
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | GROUND_INST: instantiating (3) with all_17_1, 0, all_4_3, all_17_2,
% 5.58/1.60 | | | | | simplifying with (21), (34) gives:
% 5.58/1.60 | | | | | (35) all_17_1 = 0
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | REDUCE: (33), (35) imply:
% 5.58/1.60 | | | | | (36) $false
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | CLOSE: (36) is inconsistent.
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | End of split
% 5.58/1.60 | | | |
% 5.58/1.60 | | | Case 2:
% 5.58/1.60 | | | |
% 5.58/1.60 | | | | (37) all_17_1 = 0
% 5.58/1.60 | | | | (38) ~ (all_17_0 = 0)
% 5.58/1.60 | | | |
% 5.58/1.60 | | | | REDUCE: (21), (37) imply:
% 5.58/1.60 | | | | (39) element(all_17_2, all_4_3) = 0
% 5.58/1.60 | | | |
% 5.58/1.60 | | | | BETA: splitting (28) gives:
% 5.58/1.60 | | | |
% 5.58/1.60 | | | | Case 1:
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | (40) all_17_0 = 0
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | REDUCE: (38), (40) imply:
% 5.58/1.60 | | | | | (41) $false
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | CLOSE: (41) is inconsistent.
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | Case 2:
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | (42) ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2, all_4_3) = v0)
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | DELTA: instantiating (42) with fresh symbol all_33_0 gives:
% 5.58/1.60 | | | | | (43) ~ (all_33_0 = 0) & element(all_17_2, all_4_3) = all_33_0
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | ALPHA: (43) implies:
% 5.58/1.60 | | | | | (44) ~ (all_33_0 = 0)
% 5.58/1.60 | | | | | (45) element(all_17_2, all_4_3) = all_33_0
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | GROUND_INST: instantiating (3) with 0, all_33_0, all_4_3, all_17_2,
% 5.58/1.60 | | | | | simplifying with (39), (45) gives:
% 5.58/1.60 | | | | | (46) all_33_0 = 0
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | REDUCE: (44), (46) imply:
% 5.58/1.60 | | | | | (47) $false
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | | CLOSE: (47) is inconsistent.
% 5.58/1.60 | | | | |
% 5.58/1.60 | | | | End of split
% 5.58/1.60 | | | |
% 5.58/1.60 | | | End of split
% 5.58/1.60 | | |
% 5.58/1.60 | | End of split
% 5.58/1.60 | |
% 5.58/1.60 | Case 2:
% 5.58/1.60 | |
% 5.58/1.60 | | (48) all_4_1 = 0 & ~ (all_4_0 = 0)
% 5.58/1.60 | |
% 5.58/1.60 | | ALPHA: (48) implies:
% 5.58/1.60 | | (49) all_4_1 = 0
% 5.58/1.60 | | (50) ~ (all_4_0 = 0)
% 5.58/1.60 | |
% 5.58/1.60 | | REDUCE: (7), (49) imply:
% 5.58/1.60 | | (51) set_equal(all_4_3, all_4_2) = 0
% 5.58/1.60 | |
% 5.58/1.60 | | BETA: splitting (11) gives:
% 5.58/1.60 | |
% 5.58/1.60 | | Case 1:
% 5.58/1.60 | | |
% 5.58/1.60 | | | (52) all_4_0 = 0
% 5.58/1.60 | | |
% 5.58/1.60 | | | REDUCE: (50), (52) imply:
% 5.58/1.60 | | | (53) $false
% 5.58/1.60 | | |
% 5.58/1.60 | | | CLOSE: (53) is inconsistent.
% 5.58/1.60 | | |
% 5.58/1.60 | | Case 2:
% 5.58/1.60 | | |
% 5.58/1.60 | | | (54) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (element(v0, all_4_2)
% 5.58/1.60 | | | = v1 & element(v0, all_4_3) = v2 & $i(v0) & ( ~ (v2 = 0) | ~
% 5.58/1.60 | | | (v1 = 0)) & (v2 = 0 | v1 = 0))
% 5.58/1.60 | | |
% 5.58/1.60 | | | DELTA: instantiating (54) with fresh symbols all_17_0, all_17_1, all_17_2
% 5.58/1.60 | | | gives:
% 5.58/1.61 | | | (55) element(all_17_2, all_4_2) = all_17_1 & element(all_17_2, all_4_3)
% 5.58/1.61 | | | = all_17_0 & $i(all_17_2) & ( ~ (all_17_0 = 0) | ~ (all_17_1 =
% 5.58/1.61 | | | 0)) & (all_17_0 = 0 | all_17_1 = 0)
% 5.58/1.61 | | |
% 5.58/1.61 | | | ALPHA: (55) implies:
% 5.58/1.61 | | | (56) $i(all_17_2)
% 5.58/1.61 | | | (57) element(all_17_2, all_4_3) = all_17_0
% 5.58/1.61 | | | (58) element(all_17_2, all_4_2) = all_17_1
% 5.58/1.61 | | | (59) all_17_0 = 0 | all_17_1 = 0
% 5.58/1.61 | | | (60) ~ (all_17_0 = 0) | ~ (all_17_1 = 0)
% 5.58/1.61 | | |
% 5.58/1.61 | | | GROUND_INST: instantiating (1) with all_4_3, all_4_2, simplifying with
% 5.58/1.61 | | | (5), (6), (51) gives:
% 5.58/1.61 | | | (61) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (element(v0, all_4_3) =
% 5.58/1.61 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & element(v0,
% 5.58/1.61 | | | all_4_2) = v2)) & ! [v0: $i] : ( ~ (element(v0, all_4_3) =
% 5.58/1.61 | | | 0) | ~ $i(v0) | element(v0, all_4_2) = 0)
% 5.58/1.61 | | |
% 5.58/1.61 | | | ALPHA: (61) implies:
% 5.58/1.61 | | | (62) ! [v0: $i] : ( ~ (element(v0, all_4_3) = 0) | ~ $i(v0) |
% 5.58/1.61 | | | element(v0, all_4_2) = 0)
% 5.58/1.61 | | | (63) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (element(v0, all_4_3) =
% 5.58/1.61 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & element(v0,
% 5.58/1.61 | | | all_4_2) = v2))
% 5.58/1.61 | | |
% 5.58/1.61 | | | GROUND_INST: instantiating (63) with all_17_2, all_17_0, simplifying with
% 5.58/1.61 | | | (56), (57) gives:
% 5.58/1.61 | | | (64) all_17_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2,
% 5.58/1.61 | | | all_4_2) = v0)
% 5.58/1.61 | | |
% 5.58/1.61 | | | BETA: splitting (59) gives:
% 5.58/1.61 | | |
% 5.58/1.61 | | | Case 1:
% 5.58/1.61 | | | |
% 5.58/1.61 | | | | (65) all_17_0 = 0
% 5.58/1.61 | | | |
% 5.58/1.61 | | | | REDUCE: (57), (65) imply:
% 5.58/1.61 | | | | (66) element(all_17_2, all_4_3) = 0
% 5.58/1.61 | | | |
% 5.58/1.61 | | | | BETA: splitting (60) gives:
% 5.58/1.61 | | | |
% 5.58/1.61 | | | | Case 1:
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | (67) ~ (all_17_0 = 0)
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | REDUCE: (65), (67) imply:
% 5.58/1.61 | | | | | (68) $false
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | CLOSE: (68) is inconsistent.
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | Case 2:
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | (69) ~ (all_17_1 = 0)
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | GROUND_INST: instantiating (62) with all_17_2, simplifying with (56),
% 5.58/1.61 | | | | | (66) gives:
% 5.58/1.61 | | | | | (70) element(all_17_2, all_4_2) = 0
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | GROUND_INST: instantiating (3) with all_17_1, 0, all_4_2, all_17_2,
% 5.58/1.61 | | | | | simplifying with (58), (70) gives:
% 5.58/1.61 | | | | | (71) all_17_1 = 0
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | REDUCE: (69), (71) imply:
% 5.58/1.61 | | | | | (72) $false
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | CLOSE: (72) is inconsistent.
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | End of split
% 5.58/1.61 | | | |
% 5.58/1.61 | | | Case 2:
% 5.58/1.61 | | | |
% 5.58/1.61 | | | | (73) all_17_1 = 0
% 5.58/1.61 | | | | (74) ~ (all_17_0 = 0)
% 5.58/1.61 | | | |
% 5.58/1.61 | | | | REDUCE: (58), (73) imply:
% 5.58/1.61 | | | | (75) element(all_17_2, all_4_2) = 0
% 5.58/1.61 | | | |
% 5.58/1.61 | | | | BETA: splitting (64) gives:
% 5.58/1.61 | | | |
% 5.58/1.61 | | | | Case 1:
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | (76) all_17_0 = 0
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | REDUCE: (74), (76) imply:
% 5.58/1.61 | | | | | (77) $false
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | CLOSE: (77) is inconsistent.
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | Case 2:
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | (78) ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2, all_4_2) = v0)
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | DELTA: instantiating (78) with fresh symbol all_33_0 gives:
% 5.58/1.61 | | | | | (79) ~ (all_33_0 = 0) & element(all_17_2, all_4_2) = all_33_0
% 5.58/1.61 | | | | |
% 5.58/1.61 | | | | | ALPHA: (79) implies:
% 5.58/1.61 | | | | | (80) ~ (all_33_0 = 0)
% 5.58/1.62 | | | | | (81) element(all_17_2, all_4_2) = all_33_0
% 5.58/1.62 | | | | |
% 5.58/1.62 | | | | | GROUND_INST: instantiating (3) with 0, all_33_0, all_4_2, all_17_2,
% 5.58/1.62 | | | | | simplifying with (75), (81) gives:
% 5.58/1.62 | | | | | (82) all_33_0 = 0
% 5.58/1.62 | | | | |
% 5.58/1.62 | | | | | REDUCE: (80), (82) imply:
% 5.58/1.62 | | | | | (83) $false
% 5.58/1.62 | | | | |
% 5.58/1.62 | | | | | CLOSE: (83) is inconsistent.
% 5.58/1.62 | | | | |
% 5.58/1.62 | | | | End of split
% 5.58/1.62 | | | |
% 5.58/1.62 | | | End of split
% 5.58/1.62 | | |
% 5.58/1.62 | | End of split
% 5.58/1.62 | |
% 5.58/1.62 | End of split
% 5.58/1.62 |
% 5.58/1.62 End of proof
% 5.58/1.62 % SZS output end Proof for theBenchmark
% 5.58/1.62
% 5.58/1.62 979ms
%------------------------------------------------------------------------------