TSTP Solution File: KRS134+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS134+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 : n009.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 05:51:22 EDT 2023
% Result : Theorem 4.04s 1.31s
% Output : Proof 5.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS134+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n009.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 : Mon Aug 28 01:36:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.48/0.59 ________ _____
% 0.48/0.59 ___ __ \_________(_)________________________________
% 0.48/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.48/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.48/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.48/0.60
% 0.48/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.48/0.60 (2023-06-19)
% 0.48/0.60
% 0.48/0.60 (c) Philipp Rümmer, 2009-2023
% 0.48/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.48/0.60 Amanda Stjerna.
% 0.48/0.60 Free software under BSD-3-Clause.
% 0.48/0.60
% 0.48/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.48/0.60
% 0.48/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.48/0.61 Running up to 7 provers in parallel.
% 0.48/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.48/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.48/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.48/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.48/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.48/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.48/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.03/1.00 Prover 4: Preprocessing ...
% 2.03/1.00 Prover 1: Preprocessing ...
% 2.44/1.05 Prover 5: Preprocessing ...
% 2.44/1.05 Prover 0: Preprocessing ...
% 2.44/1.05 Prover 6: Preprocessing ...
% 2.44/1.05 Prover 3: Preprocessing ...
% 2.44/1.05 Prover 2: Preprocessing ...
% 3.02/1.13 Prover 5: Proving ...
% 3.02/1.14 Prover 2: Proving ...
% 3.26/1.17 Prover 0: Proving ...
% 3.26/1.17 Prover 4: Constructing countermodel ...
% 3.26/1.17 Prover 3: Constructing countermodel ...
% 3.26/1.17 Prover 6: Constructing countermodel ...
% 3.26/1.18 Prover 1: Constructing countermodel ...
% 4.04/1.31 Prover 0: proved (695ms)
% 4.04/1.31
% 4.04/1.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.04/1.31
% 4.04/1.31 Prover 5: proved (693ms)
% 4.04/1.31
% 4.04/1.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.04/1.31
% 4.04/1.31 Prover 3: proved (694ms)
% 4.04/1.31 Prover 6: proved (691ms)
% 4.04/1.31
% 4.04/1.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.04/1.31
% 4.04/1.32
% 4.04/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.04/1.32
% 4.04/1.32 Prover 2: stopped
% 4.04/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.04/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.04/1.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.04/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.04/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.52/1.33 Prover 7: Preprocessing ...
% 4.52/1.34 Prover 8: Preprocessing ...
% 4.52/1.34 Prover 13: Preprocessing ...
% 4.52/1.34 Prover 10: Preprocessing ...
% 4.52/1.34 Prover 11: Preprocessing ...
% 4.52/1.35 Prover 1: Found proof (size 42)
% 4.52/1.35 Prover 1: proved (735ms)
% 4.52/1.35 Prover 4: stopped
% 4.52/1.35 Prover 7: Warning: ignoring some quantifiers
% 4.52/1.35 Prover 7: Constructing countermodel ...
% 4.52/1.36 Prover 13: Warning: ignoring some quantifiers
% 4.52/1.36 Prover 10: Warning: ignoring some quantifiers
% 4.52/1.36 Prover 7: stopped
% 4.52/1.36 Prover 13: Constructing countermodel ...
% 4.52/1.36 Prover 10: Constructing countermodel ...
% 4.52/1.36 Prover 13: stopped
% 4.52/1.36 Prover 10: stopped
% 4.73/1.36 Prover 11: stopped
% 4.73/1.38 Prover 8: Warning: ignoring some quantifiers
% 4.73/1.38 Prover 8: Constructing countermodel ...
% 4.73/1.39 Prover 8: stopped
% 4.73/1.39
% 4.73/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.73/1.39
% 4.73/1.40 % SZS output start Proof for theBenchmark
% 4.73/1.40 Assumptions after simplification:
% 4.73/1.40 ---------------------------------
% 4.73/1.40
% 4.73/1.40 (axiom_0)
% 5.02/1.43 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) &
% 5.02/1.43 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0))
% 5.02/1.43
% 5.02/1.43 (axiom_1)
% 5.02/1.43 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ $i(v0) |
% 5.02/1.43 xsd_integer(v0) = 0) & ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) |
% 5.02/1.43 ? [v1: int] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 5.02/1.43
% 5.02/1.43 (axiom_2)
% 5.02/1.43 ! [v0: $i] : ! [v1: $i] : ( ~ (rprop(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 5.02/1.43 cA(v1) = 0)
% 5.02/1.43
% 5.02/1.43 (the_axiom)
% 5.02/1.44 ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 &
% 5.02/1.44 xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 =
% 5.02/1.44 0)))) | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlNothing(v0) =
% 5.02/1.44 v2 & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) | ? [v0: $i] :
% 5.02/1.44 (cowlThing(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 5.02/1.44 rprop(v0, v1) = 0 & cA(v1) = v2 & $i(v1)))
% 5.02/1.44
% 5.02/1.44 (function-axioms)
% 5.02/1.44 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 5.02/1.44 [v3: $i] : (v1 = v0 | ~ (rprop(v3, v2) = v1) | ~ (rprop(v3, v2) = v0)) & !
% 5.02/1.44 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 5.02/1.44 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 5.02/1.44 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (xsd_string(v2) = v1) |
% 5.02/1.44 ~ (xsd_string(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 5.02/1.44 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~
% 5.02/1.44 (xsd_integer(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 5.02/1.44 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~
% 5.02/1.44 (cowlNothing(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 5.02/1.44 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~
% 5.02/1.44 (cowlThing(v2) = v0))
% 5.02/1.44
% 5.02/1.44 Those formulas are unsatisfiable:
% 5.02/1.44 ---------------------------------
% 5.02/1.44
% 5.02/1.44 Begin of proof
% 5.02/1.45 |
% 5.02/1.45 | ALPHA: (axiom_0) implies:
% 5.02/1.45 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0))
% 5.02/1.45 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~
% 5.02/1.45 | $i(v0))
% 5.02/1.45 |
% 5.02/1.45 | ALPHA: (axiom_1) implies:
% 5.02/1.45 | (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 5.02/1.45 | (v1 = 0) & xsd_integer(v0) = v1))
% 5.02/1.45 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~
% 5.02/1.45 | $i(v0) | xsd_integer(v0) = 0)
% 5.02/1.45 |
% 5.02/1.45 | ALPHA: (function-axioms) implies:
% 5.02/1.45 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.02/1.45 | (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 5.02/1.45 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.02/1.45 | (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0))
% 5.02/1.45 |
% 5.02/1.45 | BETA: splitting (the_axiom) gives:
% 5.02/1.45 |
% 5.02/1.45 | Case 1:
% 5.02/1.45 | |
% 5.02/1.46 | | (7) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 &
% 5.02/1.46 | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) &
% 5.02/1.46 | | ~ (v1 = 0))))
% 5.02/1.46 | |
% 5.02/1.46 | | DELTA: instantiating (7) with fresh symbols all_12_0, all_12_1, all_12_2
% 5.02/1.46 | | gives:
% 5.02/1.46 | | (8) xsd_string(all_12_2) = all_12_1 & xsd_integer(all_12_2) = all_12_0 &
% 5.18/1.46 | | $i(all_12_2) & ((all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 = 0) &
% 5.18/1.46 | | ~ (all_12_1 = 0)))
% 5.18/1.46 | |
% 5.18/1.46 | | ALPHA: (8) implies:
% 5.18/1.46 | | (9) $i(all_12_2)
% 5.18/1.46 | | (10) xsd_integer(all_12_2) = all_12_0
% 5.18/1.46 | | (11) xsd_string(all_12_2) = all_12_1
% 5.18/1.46 | | (12) (all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 = 0) & ~ (all_12_1 =
% 5.18/1.46 | | 0))
% 5.18/1.46 | |
% 5.18/1.46 | | GROUND_INST: instantiating (4) with all_12_2, all_12_1, simplifying with
% 5.18/1.46 | | (9), (11) gives:
% 5.18/1.46 | | (13) all_12_1 = 0 | xsd_integer(all_12_2) = 0
% 5.18/1.46 | |
% 5.18/1.46 | | BETA: splitting (12) gives:
% 5.18/1.46 | |
% 5.18/1.46 | | Case 1:
% 5.18/1.46 | | |
% 5.18/1.46 | | | (14) all_12_0 = 0 & all_12_1 = 0
% 5.18/1.46 | | |
% 5.18/1.46 | | | ALPHA: (14) implies:
% 5.18/1.46 | | | (15) all_12_1 = 0
% 5.18/1.46 | | | (16) all_12_0 = 0
% 5.18/1.46 | | |
% 5.18/1.46 | | | REDUCE: (11), (15) imply:
% 5.18/1.47 | | | (17) xsd_string(all_12_2) = 0
% 5.18/1.47 | | |
% 5.18/1.47 | | | REDUCE: (10), (16) imply:
% 5.18/1.47 | | | (18) xsd_integer(all_12_2) = 0
% 5.18/1.47 | | |
% 5.18/1.47 | | | GROUND_INST: instantiating (3) with all_12_2, simplifying with (9), (17)
% 5.18/1.47 | | | gives:
% 5.18/1.47 | | | (19) ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_12_2) = v0)
% 5.18/1.47 | | |
% 5.18/1.47 | | | DELTA: instantiating (19) with fresh symbol all_26_0 gives:
% 5.18/1.47 | | | (20) ~ (all_26_0 = 0) & xsd_integer(all_12_2) = all_26_0
% 5.18/1.47 | | |
% 5.18/1.47 | | | ALPHA: (20) implies:
% 5.18/1.47 | | | (21) ~ (all_26_0 = 0)
% 5.18/1.47 | | | (22) xsd_integer(all_12_2) = all_26_0
% 5.18/1.47 | | |
% 5.18/1.47 | | | GROUND_INST: instantiating (5) with 0, all_26_0, all_12_2, simplifying
% 5.18/1.47 | | | with (18), (22) gives:
% 5.18/1.47 | | | (23) all_26_0 = 0
% 5.18/1.47 | | |
% 5.18/1.47 | | | REDUCE: (21), (23) imply:
% 5.18/1.47 | | | (24) $false
% 5.18/1.47 | | |
% 5.18/1.47 | | | CLOSE: (24) is inconsistent.
% 5.18/1.47 | | |
% 5.18/1.47 | | Case 2:
% 5.18/1.47 | | |
% 5.18/1.47 | | | (25) ~ (all_12_0 = 0) & ~ (all_12_1 = 0)
% 5.18/1.47 | | |
% 5.18/1.47 | | | ALPHA: (25) implies:
% 5.18/1.47 | | | (26) ~ (all_12_1 = 0)
% 5.18/1.47 | | | (27) ~ (all_12_0 = 0)
% 5.18/1.47 | | |
% 5.18/1.47 | | | BETA: splitting (13) gives:
% 5.18/1.47 | | |
% 5.18/1.47 | | | Case 1:
% 5.18/1.47 | | | |
% 5.18/1.47 | | | | (28) xsd_integer(all_12_2) = 0
% 5.18/1.47 | | | |
% 5.18/1.47 | | | | GROUND_INST: instantiating (5) with all_12_0, 0, all_12_2, simplifying
% 5.18/1.47 | | | | with (10), (28) gives:
% 5.18/1.47 | | | | (29) all_12_0 = 0
% 5.18/1.47 | | | |
% 5.18/1.47 | | | | REDUCE: (27), (29) imply:
% 5.18/1.47 | | | | (30) $false
% 5.18/1.47 | | | |
% 5.18/1.47 | | | | CLOSE: (30) is inconsistent.
% 5.18/1.47 | | | |
% 5.18/1.47 | | | Case 2:
% 5.18/1.47 | | | |
% 5.18/1.47 | | | | (31) all_12_1 = 0
% 5.18/1.47 | | | |
% 5.18/1.47 | | | | REDUCE: (26), (31) imply:
% 5.18/1.47 | | | | (32) $false
% 5.18/1.47 | | | |
% 5.18/1.47 | | | | CLOSE: (32) is inconsistent.
% 5.18/1.47 | | | |
% 5.18/1.47 | | | End of split
% 5.18/1.47 | | |
% 5.18/1.47 | | End of split
% 5.18/1.47 | |
% 5.18/1.47 | Case 2:
% 5.18/1.47 | |
% 5.18/1.47 | | (33) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlNothing(v0) = v2 &
% 5.18/1.47 | | cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) | ? [v0:
% 5.18/1.48 | | $i] : (cowlThing(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: int] : (
% 5.18/1.48 | | ~ (v2 = 0) & rprop(v0, v1) = 0 & cA(v1) = v2 & $i(v1)))
% 5.18/1.48 | |
% 5.18/1.48 | | BETA: splitting (33) gives:
% 5.18/1.48 | |
% 5.18/1.48 | | Case 1:
% 5.18/1.48 | | |
% 5.18/1.48 | | | (34) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlNothing(v0) = v2
% 5.18/1.48 | | | & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 5.18/1.48 | | |
% 5.18/1.48 | | | DELTA: instantiating (34) with fresh symbols all_12_0, all_12_1, all_12_2
% 5.18/1.48 | | | gives:
% 5.18/1.48 | | | (35) cowlNothing(all_12_2) = all_12_0 & cowlThing(all_12_2) = all_12_1
% 5.18/1.48 | | | & $i(all_12_2) & ( ~ (all_12_1 = 0) | all_12_0 = 0)
% 5.18/1.48 | | |
% 5.18/1.48 | | | ALPHA: (35) implies:
% 5.18/1.48 | | | (36) $i(all_12_2)
% 5.18/1.48 | | | (37) cowlThing(all_12_2) = all_12_1
% 5.18/1.48 | | | (38) cowlNothing(all_12_2) = all_12_0
% 5.18/1.48 | | | (39) ~ (all_12_1 = 0) | all_12_0 = 0
% 5.18/1.48 | | |
% 5.18/1.48 | | | GROUND_INST: instantiating (2) with all_12_2, all_12_1, simplifying with
% 5.18/1.48 | | | (36), (37) gives:
% 5.18/1.48 | | | (40) all_12_1 = 0
% 5.18/1.48 | | |
% 5.18/1.48 | | | BETA: splitting (39) gives:
% 5.18/1.48 | | |
% 5.18/1.48 | | | Case 1:
% 5.18/1.48 | | | |
% 5.18/1.48 | | | | (41) ~ (all_12_1 = 0)
% 5.18/1.48 | | | |
% 5.18/1.48 | | | | REDUCE: (40), (41) imply:
% 5.18/1.48 | | | | (42) $false
% 5.18/1.48 | | | |
% 5.18/1.48 | | | | CLOSE: (42) is inconsistent.
% 5.18/1.48 | | | |
% 5.18/1.48 | | | Case 2:
% 5.18/1.48 | | | |
% 5.18/1.48 | | | | (43) all_12_0 = 0
% 5.18/1.48 | | | |
% 5.18/1.48 | | | | REDUCE: (38), (43) imply:
% 5.18/1.48 | | | | (44) cowlNothing(all_12_2) = 0
% 5.18/1.48 | | | |
% 5.18/1.48 | | | | GROUND_INST: instantiating (1) with all_12_2, simplifying with (36),
% 5.18/1.48 | | | | (44) gives:
% 5.18/1.48 | | | | (45) $false
% 5.18/1.48 | | | |
% 5.18/1.48 | | | | CLOSE: (45) is inconsistent.
% 5.18/1.48 | | | |
% 5.18/1.48 | | | End of split
% 5.18/1.48 | | |
% 5.18/1.48 | | Case 2:
% 5.18/1.48 | | |
% 5.18/1.48 | | | (46) ? [v0: $i] : (cowlThing(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2:
% 5.18/1.48 | | | int] : ( ~ (v2 = 0) & rprop(v0, v1) = 0 & cA(v1) = v2 &
% 5.18/1.48 | | | $i(v1)))
% 5.18/1.48 | | |
% 5.18/1.48 | | | DELTA: instantiating (46) with fresh symbol all_12_0 gives:
% 5.18/1.48 | | | (47) cowlThing(all_12_0) = 0 & $i(all_12_0) & ? [v0: $i] : ? [v1:
% 5.18/1.48 | | | int] : ( ~ (v1 = 0) & rprop(all_12_0, v0) = 0 & cA(v0) = v1 &
% 5.18/1.48 | | | $i(v0))
% 5.18/1.48 | | |
% 5.18/1.48 | | | ALPHA: (47) implies:
% 5.18/1.48 | | | (48) $i(all_12_0)
% 5.18/1.48 | | | (49) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & rprop(all_12_0, v0) =
% 5.18/1.48 | | | 0 & cA(v0) = v1 & $i(v0))
% 5.18/1.48 | | |
% 5.18/1.48 | | | DELTA: instantiating (49) with fresh symbols all_14_0, all_14_1 gives:
% 5.18/1.48 | | | (50) ~ (all_14_0 = 0) & rprop(all_12_0, all_14_1) = 0 & cA(all_14_1) =
% 5.18/1.48 | | | all_14_0 & $i(all_14_1)
% 5.18/1.48 | | |
% 5.18/1.48 | | | ALPHA: (50) implies:
% 5.18/1.49 | | | (51) ~ (all_14_0 = 0)
% 5.18/1.49 | | | (52) $i(all_14_1)
% 5.18/1.49 | | | (53) cA(all_14_1) = all_14_0
% 5.18/1.49 | | | (54) rprop(all_12_0, all_14_1) = 0
% 5.18/1.49 | | |
% 5.18/1.49 | | | GROUND_INST: instantiating (axiom_2) with all_12_0, all_14_1, simplifying
% 5.18/1.49 | | | with (48), (52), (54) gives:
% 5.18/1.49 | | | (55) cA(all_14_1) = 0
% 5.18/1.49 | | |
% 5.18/1.49 | | | GROUND_INST: instantiating (6) with all_14_0, 0, all_14_1, simplifying
% 5.18/1.49 | | | with (53), (55) gives:
% 5.18/1.49 | | | (56) all_14_0 = 0
% 5.18/1.49 | | |
% 5.18/1.49 | | | REDUCE: (51), (56) imply:
% 5.18/1.49 | | | (57) $false
% 5.18/1.49 | | |
% 5.18/1.49 | | | CLOSE: (57) is inconsistent.
% 5.18/1.49 | | |
% 5.18/1.49 | | End of split
% 5.18/1.49 | |
% 5.18/1.49 | End of split
% 5.18/1.49 |
% 5.18/1.49 End of proof
% 5.18/1.49 % SZS output end Proof for theBenchmark
% 5.18/1.49
% 5.18/1.49 891ms
%------------------------------------------------------------------------------