TSTP Solution File: SYN954+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN954+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 : 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 : Fri Sep 1 03:29:21 EDT 2023
% Result : Theorem 3.32s 1.21s
% Output : Proof 4.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN954+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 18:04:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.75/0.94 Prover 4: Preprocessing ...
% 1.75/0.94 Prover 1: Preprocessing ...
% 1.96/0.99 Prover 3: Preprocessing ...
% 1.96/0.99 Prover 5: Preprocessing ...
% 1.96/0.99 Prover 6: Preprocessing ...
% 1.96/0.99 Prover 2: Preprocessing ...
% 1.96/0.99 Prover 0: Preprocessing ...
% 2.46/1.07 Prover 5: Proving ...
% 2.46/1.07 Prover 3: Constructing countermodel ...
% 2.46/1.07 Prover 1: Constructing countermodel ...
% 2.46/1.07 Prover 2: Proving ...
% 2.46/1.07 Prover 6: Proving ...
% 2.76/1.08 Prover 4: Constructing countermodel ...
% 2.76/1.09 Prover 0: Proving ...
% 3.32/1.17 Prover 1: gave up
% 3.32/1.17 Prover 3: gave up
% 3.32/1.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.32/1.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.32/1.18 Prover 7: Preprocessing ...
% 3.32/1.19 Prover 8: Preprocessing ...
% 3.32/1.19 Prover 7: Warning: ignoring some quantifiers
% 3.32/1.19 Prover 7: Constructing countermodel ...
% 3.32/1.20 Prover 0: proved (573ms)
% 3.32/1.21
% 3.32/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.32/1.21
% 3.66/1.21 Prover 2: stopped
% 3.66/1.22 Prover 6: stopped
% 3.66/1.23 Prover 5: stopped
% 3.66/1.24 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.66/1.24 Prover 8: Warning: ignoring some quantifiers
% 3.66/1.24 Prover 8: Constructing countermodel ...
% 3.66/1.24 Prover 10: Preprocessing ...
% 3.66/1.24 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.66/1.24 Prover 11: Preprocessing ...
% 3.66/1.24 Prover 10: Warning: ignoring some quantifiers
% 3.66/1.24 Prover 10: Constructing countermodel ...
% 3.66/1.24 Prover 7: gave up
% 3.92/1.25 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.92/1.25 Prover 13: Preprocessing ...
% 3.92/1.25 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 3.92/1.25 Prover 8: gave up
% 3.92/1.25 Prover 16: Preprocessing ...
% 3.92/1.26 Prover 13: Warning: ignoring some quantifiers
% 3.92/1.26 Prover 13: Constructing countermodel ...
% 3.92/1.26 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 3.92/1.26 Prover 10: gave up
% 3.92/1.26 Prover 19: Preprocessing ...
% 3.92/1.26 Prover 16: Warning: ignoring some quantifiers
% 3.92/1.27 Prover 16: Constructing countermodel ...
% 3.92/1.28 Prover 11: Constructing countermodel ...
% 3.92/1.29 Prover 13: gave up
% 3.92/1.30 Prover 4: Found proof (size 52)
% 3.92/1.30 Prover 4: proved (667ms)
% 3.92/1.30 Prover 11: stopped
% 3.92/1.30 Prover 16: stopped
% 3.92/1.30 Prover 19: Warning: ignoring some quantifiers
% 3.92/1.30 Prover 19: Constructing countermodel ...
% 3.92/1.30 Prover 19: stopped
% 3.92/1.30
% 3.92/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.92/1.30
% 3.92/1.31 % SZS output start Proof for theBenchmark
% 3.92/1.31 Assumptions after simplification:
% 3.92/1.31 ---------------------------------
% 3.92/1.31
% 3.92/1.31 (prove_this)
% 4.43/1.35 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (p(v1) = v3 & p(v0)
% 4.43/1.35 = v2 & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: MultipleValueBool] : ( ~ (v3
% 4.43/1.35 = 0) | ~ (v2 = 0) | ~ (p(v4) = v5) | ~ $i(v4)) & ! [v4: $i] : !
% 4.43/1.35 [v5: MultipleValueBool] : ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (q(v4) = v5) | ~
% 4.43/1.35 $i(v4)) & ! [v4: $i] : ! [v5: int] : ( ~ (v3 = 0) | v5 = 0 | ~ (p(v4) =
% 4.43/1.35 v5) | ~ $i(v4)) & ! [v4: $i] : ! [v5: MultipleValueBool] : ( ~ (v3 =
% 4.43/1.35 0) | ~ (q(v4) = v5) | ~ $i(v4) | p(v4) = 0) & ! [v4: $i] : ! [v5:
% 4.43/1.35 int] : ( ~ (v2 = 0) | v5 = 0 | ~ (q(v4) = v5) | ~ $i(v4)) & ! [v4: $i]
% 4.43/1.35 : ! [v5: MultipleValueBool] : ( ~ (v2 = 0) | ~ (p(v4) = v5) | ~ $i(v4) |
% 4.43/1.35 q(v4) = 0) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (p(v4) = v5) | ~
% 4.43/1.35 $i(v4) | q(v4) = 0) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (p(v4) =
% 4.43/1.35 v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & q(v4) = v6)) & ! [v4:
% 4.43/1.35 $i] : ! [v5: int] : (v5 = 0 | ~ (q(v4) = v5) | ~ $i(v4) | p(v4) = 0) &
% 4.43/1.35 ! [v4: $i] : ( ~ (q(v4) = 0) | ~ $i(v4) | p(v4) = 0))
% 4.43/1.35
% 4.43/1.35 (function-axioms)
% 4.43/1.35 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 4.43/1.35 v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 4.43/1.35 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2)
% 4.43/1.35 = v0))
% 4.43/1.35
% 4.43/1.35 Those formulas are unsatisfiable:
% 4.43/1.35 ---------------------------------
% 4.43/1.35
% 4.43/1.35 Begin of proof
% 4.43/1.35 |
% 4.43/1.35 | ALPHA: (function-axioms) implies:
% 4.43/1.36 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.43/1.36 | (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0))
% 4.43/1.36 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.43/1.36 | (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 4.43/1.36 |
% 4.43/1.36 | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1,
% 4.43/1.36 | all_3_2, all_3_3 gives:
% 4.43/1.36 | (3) p(all_3_2) = all_3_0 & p(all_3_3) = all_3_1 & $i(all_3_2) & $i(all_3_3)
% 4.43/1.36 | & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (all_3_0 = 0) | ~
% 4.43/1.36 | (all_3_1 = 0) | ~ (p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1:
% 4.43/1.36 | MultipleValueBool] : ( ~ (all_3_0 = 0) | ~ (all_3_1 = 0) | ~ (q(v0)
% 4.43/1.36 | = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: int] : ( ~ (all_3_0 = 0)
% 4.43/1.36 | | v1 = 0 | ~ (p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1:
% 4.43/1.36 | MultipleValueBool] : ( ~ (all_3_0 = 0) | ~ (q(v0) = v1) | ~ $i(v0)
% 4.43/1.36 | | p(v0) = 0) & ! [v0: $i] : ! [v1: int] : ( ~ (all_3_1 = 0) | v1 =
% 4.43/1.36 | 0 | ~ (q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1:
% 4.43/1.36 | MultipleValueBool] : ( ~ (all_3_1 = 0) | ~ (p(v0) = v1) | ~ $i(v0)
% 4.43/1.37 | | q(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1)
% 4.43/1.37 | | ~ $i(v0) | q(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 4.43/1.37 | (p(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & q(v0) = v2))
% 4.43/1.37 | & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (q(v0) = v1) | ~ $i(v0) |
% 4.43/1.37 | p(v0) = 0) & ! [v0: $i] : ( ~ (q(v0) = 0) | ~ $i(v0) | p(v0) = 0)
% 4.43/1.37 |
% 4.43/1.37 | ALPHA: (3) implies:
% 4.43/1.37 | (4) $i(all_3_3)
% 4.43/1.37 | (5) $i(all_3_2)
% 4.43/1.37 | (6) p(all_3_3) = all_3_1
% 4.43/1.37 | (7) p(all_3_2) = all_3_0
% 4.43/1.37 | (8) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | ~ $i(v0) | ?
% 4.43/1.37 | [v2: int] : ( ~ (v2 = 0) & q(v0) = v2))
% 4.43/1.37 | (9) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | ~ $i(v0) |
% 4.43/1.37 | q(v0) = 0)
% 4.43/1.37 | (10) ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (all_3_1 = 0) | ~
% 4.43/1.37 | (p(v0) = v1) | ~ $i(v0) | q(v0) = 0)
% 4.43/1.37 | (11) ! [v0: $i] : ! [v1: int] : ( ~ (all_3_0 = 0) | v1 = 0 | ~ (p(v0) =
% 4.43/1.37 | v1) | ~ $i(v0))
% 4.43/1.37 | (12) ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (all_3_0 = 0) | ~
% 4.43/1.37 | (all_3_1 = 0) | ~ (p(v0) = v1) | ~ $i(v0))
% 4.43/1.37 |
% 4.43/1.37 | GROUND_INST: instantiating (11) with all_3_3, all_3_1, simplifying with (4),
% 4.43/1.37 | (6) gives:
% 4.43/1.37 | (13) ~ (all_3_0 = 0) | all_3_1 = 0
% 4.43/1.37 |
% 4.43/1.37 | GROUND_INST: instantiating (12) with all_3_2, 0, simplifying with (5) gives:
% 4.43/1.37 | (14) ~ (all_3_0 = 0) | ~ (all_3_1 = 0) | ~ (p(all_3_2) = 0)
% 4.43/1.37 |
% 4.43/1.37 | GROUND_INST: instantiating (10) with all_3_2, all_3_0, simplifying with (5),
% 4.43/1.37 | (7) gives:
% 4.43/1.37 | (15) ~ (all_3_1 = 0) | q(all_3_2) = 0
% 4.43/1.37 |
% 4.43/1.37 | GROUND_INST: instantiating (9) with all_3_2, all_3_0, simplifying with (5),
% 4.43/1.37 | (7) gives:
% 4.43/1.37 | (16) all_3_0 = 0 | q(all_3_2) = 0
% 4.43/1.37 |
% 4.43/1.37 | GROUND_INST: instantiating (8) with all_3_2, all_3_0, simplifying with (5),
% 4.43/1.37 | (7) gives:
% 4.43/1.37 | (17) all_3_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & q(all_3_2) = v0)
% 4.43/1.37 |
% 4.43/1.37 | BETA: splitting (16) gives:
% 4.43/1.37 |
% 4.43/1.37 | Case 1:
% 4.43/1.37 | |
% 4.43/1.37 | | (18) q(all_3_2) = 0
% 4.43/1.37 | |
% 4.43/1.37 | | BETA: splitting (17) gives:
% 4.43/1.37 | |
% 4.43/1.37 | | Case 1:
% 4.43/1.37 | | |
% 4.43/1.37 | | | (19) all_3_0 = 0
% 4.43/1.38 | | |
% 4.43/1.38 | | | REDUCE: (7), (19) imply:
% 4.43/1.38 | | | (20) p(all_3_2) = 0
% 4.43/1.38 | | |
% 4.43/1.38 | | | BETA: splitting (13) gives:
% 4.43/1.38 | | |
% 4.43/1.38 | | | Case 1:
% 4.43/1.38 | | | |
% 4.43/1.38 | | | | (21) ~ (all_3_0 = 0)
% 4.43/1.38 | | | |
% 4.43/1.38 | | | | REF_CLOSE: (2), (7), (20), (21) are inconsistent by sub-proof #2.
% 4.43/1.38 | | | |
% 4.43/1.38 | | | Case 2:
% 4.43/1.38 | | | |
% 4.43/1.38 | | | | (22) all_3_1 = 0
% 4.43/1.38 | | | |
% 4.43/1.38 | | | | BETA: splitting (14) gives:
% 4.43/1.38 | | | |
% 4.43/1.38 | | | | Case 1:
% 4.43/1.38 | | | | |
% 4.43/1.38 | | | | | (23) ~ (p(all_3_2) = 0)
% 4.43/1.38 | | | | |
% 4.43/1.38 | | | | | BETA: splitting (17) gives:
% 4.43/1.38 | | | | |
% 4.43/1.38 | | | | | Case 1:
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | | PRED_UNIFY: (20), (23) imply:
% 4.43/1.38 | | | | | | (24) $false
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | | CLOSE: (24) is inconsistent.
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | Case 2:
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | | (25) ? [v0: int] : ( ~ (v0 = 0) & q(all_3_2) = v0)
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | | DELTA: instantiating (25) with fresh symbol all_37_0 gives:
% 4.43/1.38 | | | | | | (26) ~ (all_37_0 = 0) & q(all_3_2) = all_37_0
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | | REF_CLOSE: (1), (18), (26) are inconsistent by sub-proof #1.
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | End of split
% 4.43/1.38 | | | | |
% 4.43/1.38 | | | | Case 2:
% 4.43/1.38 | | | | |
% 4.43/1.38 | | | | | (27) ~ (all_3_0 = 0) | ~ (all_3_1 = 0)
% 4.43/1.38 | | | | |
% 4.43/1.38 | | | | | BETA: splitting (27) gives:
% 4.43/1.38 | | | | |
% 4.43/1.38 | | | | | Case 1:
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | | (28) ~ (all_3_0 = 0)
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | | REF_CLOSE: (2), (7), (20), (28) are inconsistent by sub-proof #2.
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | Case 2:
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | | (29) ~ (all_3_1 = 0)
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | | REDUCE: (22), (29) imply:
% 4.43/1.38 | | | | | | (30) $false
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | | CLOSE: (30) is inconsistent.
% 4.43/1.38 | | | | | |
% 4.43/1.38 | | | | | End of split
% 4.43/1.38 | | | | |
% 4.43/1.38 | | | | End of split
% 4.43/1.38 | | | |
% 4.43/1.38 | | | End of split
% 4.43/1.38 | | |
% 4.43/1.38 | | Case 2:
% 4.43/1.38 | | |
% 4.43/1.38 | | | (31) ? [v0: int] : ( ~ (v0 = 0) & q(all_3_2) = v0)
% 4.43/1.38 | | |
% 4.43/1.38 | | | DELTA: instantiating (31) with fresh symbol all_37_0 gives:
% 4.43/1.38 | | | (32) ~ (all_37_0 = 0) & q(all_3_2) = all_37_0
% 4.43/1.38 | | |
% 4.43/1.38 | | | REF_CLOSE: (1), (18), (32) are inconsistent by sub-proof #1.
% 4.43/1.38 | | |
% 4.43/1.38 | | End of split
% 4.43/1.38 | |
% 4.43/1.38 | Case 2:
% 4.43/1.38 | |
% 4.43/1.38 | | (33) all_3_0 = 0
% 4.43/1.38 | | (34) ~ (q(all_3_2) = 0)
% 4.43/1.38 | |
% 4.43/1.38 | | REDUCE: (7), (33) imply:
% 4.43/1.38 | | (35) p(all_3_2) = 0
% 4.43/1.38 | |
% 4.43/1.38 | | BETA: splitting (15) gives:
% 4.43/1.38 | |
% 4.43/1.38 | | Case 1:
% 4.43/1.38 | | |
% 4.43/1.38 | | | (36) q(all_3_2) = 0
% 4.43/1.38 | | |
% 4.43/1.38 | | | PRED_UNIFY: (34), (36) imply:
% 4.43/1.38 | | | (37) $false
% 4.43/1.38 | | |
% 4.43/1.38 | | | CLOSE: (37) is inconsistent.
% 4.43/1.38 | | |
% 4.43/1.38 | | Case 2:
% 4.43/1.38 | | |
% 4.43/1.38 | | | (38) ~ (all_3_1 = 0)
% 4.43/1.38 | | |
% 4.43/1.38 | | | BETA: splitting (13) gives:
% 4.43/1.38 | | |
% 4.43/1.38 | | | Case 1:
% 4.43/1.38 | | | |
% 4.43/1.38 | | | | (39) ~ (all_3_0 = 0)
% 4.43/1.38 | | | |
% 4.43/1.38 | | | | REF_CLOSE: (2), (7), (35), (39) are inconsistent by sub-proof #2.
% 4.43/1.38 | | | |
% 4.43/1.38 | | | Case 2:
% 4.43/1.38 | | | |
% 4.43/1.39 | | | | (40) all_3_1 = 0
% 4.43/1.39 | | | |
% 4.43/1.39 | | | | REDUCE: (38), (40) imply:
% 4.43/1.39 | | | | (41) $false
% 4.43/1.39 | | | |
% 4.43/1.39 | | | | CLOSE: (41) is inconsistent.
% 4.43/1.39 | | | |
% 4.43/1.39 | | | End of split
% 4.43/1.39 | | |
% 4.43/1.39 | | End of split
% 4.43/1.39 | |
% 4.43/1.39 | End of split
% 4.43/1.39 |
% 4.43/1.39 End of proof
% 4.43/1.39
% 4.43/1.39 Sub-proof #1 shows that the following formulas are inconsistent:
% 4.43/1.39 ----------------------------------------------------------------
% 4.43/1.39 (1) ~ (all_37_0 = 0) & q(all_3_2) = all_37_0
% 4.43/1.39 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.43/1.39 (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0))
% 4.43/1.39 (3) q(all_3_2) = 0
% 4.43/1.39
% 4.43/1.39 Begin of proof
% 4.43/1.39 |
% 4.43/1.39 | ALPHA: (1) implies:
% 4.43/1.39 | (4) ~ (all_37_0 = 0)
% 4.43/1.39 | (5) q(all_3_2) = all_37_0
% 4.43/1.39 |
% 4.43/1.39 | GROUND_INST: instantiating (2) with 0, all_37_0, all_3_2, simplifying with
% 4.43/1.39 | (3), (5) gives:
% 4.43/1.39 | (6) all_37_0 = 0
% 4.43/1.39 |
% 4.43/1.39 | REDUCE: (4), (6) imply:
% 4.43/1.39 | (7) $false
% 4.43/1.39 |
% 4.43/1.39 | CLOSE: (7) is inconsistent.
% 4.43/1.39 |
% 4.43/1.39 End of proof
% 4.43/1.39
% 4.43/1.39 Sub-proof #2 shows that the following formulas are inconsistent:
% 4.43/1.39 ----------------------------------------------------------------
% 4.43/1.39 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.43/1.39 (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 4.43/1.39 (2) p(all_3_2) = all_3_0
% 4.43/1.39 (3) p(all_3_2) = 0
% 4.43/1.39 (4) ~ (all_3_0 = 0)
% 4.43/1.39
% 4.43/1.39 Begin of proof
% 4.43/1.39 |
% 4.43/1.39 | GROUND_INST: instantiating (1) with all_3_0, 0, all_3_2, simplifying with (2),
% 4.43/1.39 | (3) gives:
% 4.43/1.39 | (5) all_3_0 = 0
% 4.43/1.39 |
% 4.43/1.39 | REDUCE: (4), (5) imply:
% 4.43/1.39 | (6) $false
% 4.43/1.39 |
% 4.43/1.39 | CLOSE: (6) is inconsistent.
% 4.43/1.39 |
% 4.43/1.39 End of proof
% 4.43/1.39 % SZS output end Proof for theBenchmark
% 4.43/1.39
% 4.43/1.39 785ms
%------------------------------------------------------------------------------