TSTP Solution File: KRS172+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS172+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 : n028.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 05:51:32 EDT 2023
% Result : Theorem 6.15s 1.57s
% Output : Proof 7.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS172+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 01:37:09 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.64 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.05/1.02 Prover 4: Preprocessing ...
% 2.05/1.02 Prover 1: Preprocessing ...
% 2.62/1.05 Prover 3: Preprocessing ...
% 2.62/1.05 Prover 2: Preprocessing ...
% 2.62/1.05 Prover 0: Preprocessing ...
% 2.62/1.05 Prover 6: Preprocessing ...
% 2.62/1.05 Prover 5: Preprocessing ...
% 4.09/1.29 Prover 2: Proving ...
% 4.09/1.29 Prover 5: Proving ...
% 4.09/1.29 Prover 6: Constructing countermodel ...
% 4.09/1.30 Prover 3: Constructing countermodel ...
% 4.09/1.31 Prover 1: Constructing countermodel ...
% 4.09/1.34 Prover 0: Proving ...
% 4.09/1.34 Prover 4: Constructing countermodel ...
% 5.57/1.52 Prover 3: gave up
% 5.57/1.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.57/1.52 Prover 6: gave up
% 5.57/1.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.57/1.54 Prover 8: Preprocessing ...
% 6.04/1.55 Prover 7: Preprocessing ...
% 6.15/1.57 Prover 2: proved (928ms)
% 6.15/1.57
% 6.15/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.15/1.57
% 6.15/1.57 Prover 5: proved (929ms)
% 6.15/1.57
% 6.15/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.15/1.57
% 6.15/1.57 Prover 0: proved (930ms)
% 6.15/1.57
% 6.15/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.15/1.57
% 6.15/1.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.15/1.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.15/1.58 Prover 1: gave up
% 6.15/1.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.15/1.59 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.15/1.60 Prover 10: Preprocessing ...
% 6.15/1.60 Prover 7: Warning: ignoring some quantifiers
% 6.15/1.61 Prover 7: Constructing countermodel ...
% 6.15/1.61 Prover 13: Preprocessing ...
% 6.52/1.61 Prover 11: Preprocessing ...
% 6.52/1.62 Prover 16: Preprocessing ...
% 6.77/1.65 Prover 10: Warning: ignoring some quantifiers
% 6.77/1.65 Prover 10: Constructing countermodel ...
% 6.77/1.65 Prover 16: Warning: ignoring some quantifiers
% 6.77/1.66 Prover 16: Constructing countermodel ...
% 6.77/1.67 Prover 7: gave up
% 6.77/1.69 Prover 4: Found proof (size 60)
% 6.77/1.69 Prover 4: proved (1023ms)
% 6.77/1.69 Prover 13: Warning: ignoring some quantifiers
% 6.77/1.69 Prover 13: Constructing countermodel ...
% 6.77/1.69 Prover 10: gave up
% 6.77/1.69 Prover 8: Warning: ignoring some quantifiers
% 6.77/1.69 Prover 8: Constructing countermodel ...
% 6.77/1.69 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 6.77/1.69 Prover 13: stopped
% 6.77/1.69 Prover 16: stopped
% 6.77/1.70 Prover 8: stopped
% 6.77/1.71 Prover 19: Preprocessing ...
% 6.77/1.72 Prover 11: Constructing countermodel ...
% 6.77/1.72 Prover 11: stopped
% 7.30/1.77 Prover 19: Warning: ignoring some quantifiers
% 7.30/1.77 Prover 19: Constructing countermodel ...
% 7.30/1.78 Prover 19: stopped
% 7.30/1.78
% 7.30/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.30/1.78
% 7.55/1.79 % SZS output start Proof for theBenchmark
% 7.55/1.79 Assumptions after simplification:
% 7.55/1.79 ---------------------------------
% 7.55/1.79
% 7.55/1.79 (axiom_0)
% 7.55/1.81 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) &
% 7.55/1.81 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0))
% 7.55/1.81
% 7.55/1.81 (axiom_1)
% 7.55/1.82 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ $i(v0) |
% 7.55/1.82 xsd_integer(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 7.55/1.82 (xsd_integer(v0) = v1) | ~ $i(v0) | xsd_string(v0) = 0) & ! [v0: $i] : ( ~
% 7.55/1.82 (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 7.55/1.82 xsd_integer(v0) = v1)) & ! [v0: $i] : ( ~ (xsd_integer(v0) = 0) | ~
% 7.55/1.82 $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & xsd_string(v0) = v1))
% 7.55/1.82
% 7.55/1.82 (axiom_2)
% 7.55/1.82 $i(iv) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (rq(v0, iv) = v1) | ~
% 7.55/1.82 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & cd(v0) = v2)) & ! [v0: $i] : ! [v1:
% 7.55/1.82 int] : (v1 = 0 | ~ (cd(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 7.55/1.82 & rq(v0, iv) = v2)) & ! [v0: $i] : ( ~ (rq(v0, iv) = 0) | ~ $i(v0) |
% 7.55/1.82 cd(v0) = 0) & ! [v0: $i] : ( ~ (cd(v0) = 0) | ~ $i(v0) | rq(v0, iv) = 0)
% 7.55/1.82
% 7.55/1.82 (axiom_3)
% 7.55/1.82 $i(iv) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (rp(v0, iv) = v1) | ~
% 7.55/1.82 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & cd(v0) = v2)) & ! [v0: $i] : ! [v1:
% 7.55/1.82 int] : (v1 = 0 | ~ (cd(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 7.55/1.82 & rp(v0, iv) = v2)) & ! [v0: $i] : ( ~ (rp(v0, iv) = 0) | ~ $i(v0) |
% 7.55/1.82 cd(v0) = 0) & ! [v0: $i] : ( ~ (cd(v0) = 0) | ~ $i(v0) | rp(v0, iv) = 0)
% 7.55/1.82
% 7.55/1.82 (axiom_4)
% 7.55/1.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~
% 7.55/1.82 (rp(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 7.55/1.82
% 7.55/1.82 (axiom_5)
% 7.55/1.82 ! [v0: $i] : ! [v1: $i] : ( ~ (rp(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 7.55/1.82 cd(v0) = 0)
% 7.55/1.82
% 7.55/1.82 (axiom_6)
% 7.55/1.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (rq(v0, v2) = 0) | ~
% 7.55/1.82 (rq(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 7.55/1.82
% 7.55/1.82 (axiom_7)
% 7.55/1.83 ! [v0: $i] : ! [v1: $i] : ( ~ (rq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 7.55/1.83 cd(v0) = 0)
% 7.55/1.83
% 7.55/1.83 (axiom_8)
% 7.55/1.83 cowlThing(iv) = 0 & $i(iv)
% 7.55/1.83
% 7.55/1.83 (the_axiom)
% 7.55/1.83 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 7.55/1.83 [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ($i(v7)
% 7.55/1.83 & $i(v4) & $i(v1) & $i(v0) & ((xsd_string(v4) = v5 & xsd_integer(v4) = v6 &
% 7.55/1.83 ((v6 = 0 & v5 = 0) | ( ~ (v6 = 0) & ~ (v5 = 0)))) | (rq(v0, v1) = v2 &
% 7.55/1.83 rp(v0, v1) = v3 & ((v3 = 0 & ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = 0)))) |
% 7.55/1.83 (cowlThing(v7) = v8 & cowlNothing(v7) = v9 & ( ~ (v8 = 0) | v9 = 0))))
% 7.55/1.83
% 7.55/1.83 (function-axioms)
% 7.55/1.83 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.55/1.83 [v3: $i] : (v1 = v0 | ~ (rq(v3, v2) = v1) | ~ (rq(v3, v2) = v0)) & ! [v0:
% 7.55/1.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.55/1.83 : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0:
% 7.55/1.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.55/1.83 ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0:
% 7.55/1.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.55/1.83 ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0:
% 7.55/1.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.55/1.83 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0:
% 7.55/1.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.55/1.83 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0:
% 7.55/1.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.55/1.83 ~ (cd(v2) = v1) | ~ (cd(v2) = v0))
% 7.55/1.83
% 7.55/1.83 Further assumptions not needed in the proof:
% 7.55/1.83 --------------------------------------------
% 7.55/1.83 cd_substitution_1, cowlNothing_substitution_1, cowlThing_substitution_1,
% 7.55/1.83 rp_substitution_1, rp_substitution_2, rq_substitution_1, rq_substitution_2,
% 7.55/1.83 xsd_integer_substitution_1, xsd_string_substitution_1
% 7.55/1.83
% 7.55/1.83 Those formulas are unsatisfiable:
% 7.55/1.83 ---------------------------------
% 7.55/1.83
% 7.55/1.83 Begin of proof
% 7.55/1.83 |
% 7.55/1.83 | ALPHA: (axiom_0) implies:
% 7.55/1.83 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0))
% 7.55/1.83 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~
% 7.55/1.83 | $i(v0))
% 7.55/1.83 |
% 7.55/1.83 | ALPHA: (axiom_1) implies:
% 7.55/1.83 | (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 7.55/1.83 | (v1 = 0) & xsd_integer(v0) = v1))
% 7.55/1.84 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~
% 7.55/1.84 | $i(v0) | xsd_string(v0) = 0)
% 7.55/1.84 |
% 7.55/1.84 | ALPHA: (axiom_2) implies:
% 7.55/1.84 | (5) ! [v0: $i] : ( ~ (cd(v0) = 0) | ~ $i(v0) | rq(v0, iv) = 0)
% 7.55/1.84 |
% 7.55/1.84 | ALPHA: (axiom_3) implies:
% 7.55/1.84 | (6) ! [v0: $i] : ( ~ (cd(v0) = 0) | ~ $i(v0) | rp(v0, iv) = 0)
% 7.55/1.84 |
% 7.55/1.84 | ALPHA: (axiom_8) implies:
% 7.55/1.84 | (7) $i(iv)
% 7.55/1.84 |
% 7.55/1.84 | ALPHA: (function-axioms) implies:
% 7.55/1.84 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.55/1.84 | (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 7.55/1.84 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.55/1.84 | (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 7.55/1.84 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 7.55/1.84 | : ! [v3: $i] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) =
% 7.55/1.84 | v0))
% 7.55/1.84 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 7.55/1.84 | : ! [v3: $i] : (v1 = v0 | ~ (rq(v3, v2) = v1) | ~ (rq(v3, v2) =
% 7.55/1.84 | v0))
% 7.55/1.84 |
% 7.55/1.84 | DELTA: instantiating (the_axiom) with fresh symbols all_12_0, all_12_1,
% 7.55/1.84 | all_12_2, all_12_3, all_12_4, all_12_5, all_12_6, all_12_7, all_12_8,
% 7.55/1.84 | all_12_9 gives:
% 7.55/1.84 | (12) $i(all_12_2) & $i(all_12_5) & $i(all_12_8) & $i(all_12_9) &
% 7.55/1.84 | ((xsd_string(all_12_5) = all_12_4 & xsd_integer(all_12_5) = all_12_3 &
% 7.55/1.84 | ((all_12_3 = 0 & all_12_4 = 0) | ( ~ (all_12_3 = 0) & ~ (all_12_4
% 7.55/1.84 | = 0)))) | (rq(all_12_9, all_12_8) = all_12_7 & rp(all_12_9,
% 7.55/1.84 | all_12_8) = all_12_6 & ((all_12_6 = 0 & ~ (all_12_7 = 0)) |
% 7.55/1.84 | (all_12_7 = 0 & ~ (all_12_6 = 0)))) | (cowlThing(all_12_2) =
% 7.55/1.84 | all_12_1 & cowlNothing(all_12_2) = all_12_0 & ( ~ (all_12_1 = 0) |
% 7.55/1.84 | all_12_0 = 0)))
% 7.55/1.84 |
% 7.55/1.84 | ALPHA: (12) implies:
% 7.55/1.84 | (13) $i(all_12_9)
% 7.55/1.84 | (14) $i(all_12_8)
% 7.55/1.84 | (15) $i(all_12_5)
% 7.55/1.84 | (16) $i(all_12_2)
% 7.55/1.84 | (17) (xsd_string(all_12_5) = all_12_4 & xsd_integer(all_12_5) = all_12_3 &
% 7.55/1.84 | ((all_12_3 = 0 & all_12_4 = 0) | ( ~ (all_12_3 = 0) & ~ (all_12_4 =
% 7.55/1.84 | 0)))) | (rq(all_12_9, all_12_8) = all_12_7 & rp(all_12_9,
% 7.55/1.84 | all_12_8) = all_12_6 & ((all_12_6 = 0 & ~ (all_12_7 = 0)) |
% 7.55/1.84 | (all_12_7 = 0 & ~ (all_12_6 = 0)))) | (cowlThing(all_12_2) =
% 7.55/1.84 | all_12_1 & cowlNothing(all_12_2) = all_12_0 & ( ~ (all_12_1 = 0) |
% 7.55/1.84 | all_12_0 = 0))
% 7.55/1.84 |
% 7.55/1.84 | BETA: splitting (17) gives:
% 7.55/1.84 |
% 7.55/1.84 | Case 1:
% 7.55/1.84 | |
% 7.55/1.85 | | (18) xsd_string(all_12_5) = all_12_4 & xsd_integer(all_12_5) = all_12_3 &
% 7.55/1.85 | | ((all_12_3 = 0 & all_12_4 = 0) | ( ~ (all_12_3 = 0) & ~ (all_12_4 =
% 7.55/1.85 | | 0)))
% 7.55/1.85 | |
% 7.55/1.85 | | ALPHA: (18) implies:
% 7.55/1.85 | | (19) xsd_integer(all_12_5) = all_12_3
% 7.85/1.85 | | (20) xsd_string(all_12_5) = all_12_4
% 7.85/1.85 | | (21) (all_12_3 = 0 & all_12_4 = 0) | ( ~ (all_12_3 = 0) & ~ (all_12_4 =
% 7.85/1.85 | | 0))
% 7.85/1.85 | |
% 7.85/1.85 | | GROUND_INST: instantiating (4) with all_12_5, all_12_3, simplifying with
% 7.85/1.85 | | (15), (19) gives:
% 7.85/1.85 | | (22) all_12_3 = 0 | xsd_string(all_12_5) = 0
% 7.85/1.85 | |
% 7.85/1.85 | | BETA: splitting (21) gives:
% 7.85/1.85 | |
% 7.85/1.85 | | Case 1:
% 7.85/1.85 | | |
% 7.85/1.85 | | | (23) all_12_3 = 0 & all_12_4 = 0
% 7.85/1.85 | | |
% 7.85/1.85 | | | ALPHA: (23) implies:
% 7.85/1.85 | | | (24) all_12_4 = 0
% 7.85/1.85 | | | (25) all_12_3 = 0
% 7.85/1.85 | | |
% 7.85/1.85 | | | REDUCE: (20), (24) imply:
% 7.85/1.85 | | | (26) xsd_string(all_12_5) = 0
% 7.85/1.85 | | |
% 7.85/1.85 | | | REDUCE: (19), (25) imply:
% 7.85/1.85 | | | (27) xsd_integer(all_12_5) = 0
% 7.85/1.85 | | |
% 7.85/1.85 | | | GROUND_INST: instantiating (3) with all_12_5, simplifying with (15), (26)
% 7.85/1.85 | | | gives:
% 7.85/1.85 | | | (28) ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_12_5) = v0)
% 7.85/1.85 | | |
% 7.85/1.85 | | | DELTA: instantiating (28) with fresh symbol all_33_0 gives:
% 7.85/1.85 | | | (29) ~ (all_33_0 = 0) & xsd_integer(all_12_5) = all_33_0
% 7.85/1.85 | | |
% 7.85/1.85 | | | ALPHA: (29) implies:
% 7.85/1.85 | | | (30) ~ (all_33_0 = 0)
% 7.85/1.85 | | | (31) xsd_integer(all_12_5) = all_33_0
% 7.85/1.85 | | |
% 7.85/1.85 | | | GROUND_INST: instantiating (8) with 0, all_33_0, all_12_5, simplifying
% 7.85/1.85 | | | with (27), (31) gives:
% 7.85/1.85 | | | (32) all_33_0 = 0
% 7.85/1.85 | | |
% 7.85/1.85 | | | REDUCE: (30), (32) imply:
% 7.85/1.85 | | | (33) $false
% 7.85/1.85 | | |
% 7.85/1.85 | | | CLOSE: (33) is inconsistent.
% 7.85/1.85 | | |
% 7.85/1.85 | | Case 2:
% 7.85/1.85 | | |
% 7.85/1.85 | | | (34) ~ (all_12_3 = 0) & ~ (all_12_4 = 0)
% 7.85/1.85 | | |
% 7.85/1.85 | | | ALPHA: (34) implies:
% 7.85/1.85 | | | (35) ~ (all_12_4 = 0)
% 7.85/1.85 | | | (36) ~ (all_12_3 = 0)
% 7.85/1.85 | | |
% 7.85/1.85 | | | BETA: splitting (22) gives:
% 7.85/1.85 | | |
% 7.85/1.85 | | | Case 1:
% 7.85/1.85 | | | |
% 7.85/1.85 | | | | (37) xsd_string(all_12_5) = 0
% 7.85/1.85 | | | |
% 7.85/1.85 | | | | GROUND_INST: instantiating (9) with all_12_4, 0, all_12_5, simplifying
% 7.85/1.85 | | | | with (20), (37) gives:
% 7.85/1.85 | | | | (38) all_12_4 = 0
% 7.85/1.85 | | | |
% 7.85/1.85 | | | | REDUCE: (35), (38) imply:
% 7.85/1.85 | | | | (39) $false
% 7.85/1.85 | | | |
% 7.85/1.85 | | | | CLOSE: (39) is inconsistent.
% 7.85/1.85 | | | |
% 7.85/1.85 | | | Case 2:
% 7.85/1.85 | | | |
% 7.85/1.85 | | | | (40) all_12_3 = 0
% 7.85/1.85 | | | |
% 7.85/1.85 | | | | REDUCE: (36), (40) imply:
% 7.85/1.85 | | | | (41) $false
% 7.85/1.85 | | | |
% 7.85/1.85 | | | | CLOSE: (41) is inconsistent.
% 7.85/1.85 | | | |
% 7.85/1.85 | | | End of split
% 7.85/1.85 | | |
% 7.85/1.85 | | End of split
% 7.85/1.85 | |
% 7.85/1.85 | Case 2:
% 7.85/1.85 | |
% 7.85/1.86 | | (42) (rq(all_12_9, all_12_8) = all_12_7 & rp(all_12_9, all_12_8) =
% 7.85/1.86 | | all_12_6 & ((all_12_6 = 0 & ~ (all_12_7 = 0)) | (all_12_7 = 0 &
% 7.85/1.86 | | ~ (all_12_6 = 0)))) | (cowlThing(all_12_2) = all_12_1 &
% 7.85/1.86 | | cowlNothing(all_12_2) = all_12_0 & ( ~ (all_12_1 = 0) | all_12_0 =
% 7.85/1.86 | | 0))
% 7.85/1.86 | |
% 7.85/1.86 | | BETA: splitting (42) gives:
% 7.85/1.86 | |
% 7.85/1.86 | | Case 1:
% 7.85/1.86 | | |
% 7.85/1.86 | | | (43) rq(all_12_9, all_12_8) = all_12_7 & rp(all_12_9, all_12_8) =
% 7.85/1.86 | | | all_12_6 & ((all_12_6 = 0 & ~ (all_12_7 = 0)) | (all_12_7 = 0 &
% 7.85/1.86 | | | ~ (all_12_6 = 0)))
% 7.85/1.86 | | |
% 7.85/1.86 | | | ALPHA: (43) implies:
% 7.85/1.86 | | | (44) rp(all_12_9, all_12_8) = all_12_6
% 7.85/1.86 | | | (45) rq(all_12_9, all_12_8) = all_12_7
% 7.85/1.86 | | | (46) (all_12_6 = 0 & ~ (all_12_7 = 0)) | (all_12_7 = 0 & ~ (all_12_6
% 7.85/1.86 | | | = 0))
% 7.85/1.86 | | |
% 7.85/1.86 | | | BETA: splitting (46) gives:
% 7.85/1.86 | | |
% 7.85/1.86 | | | Case 1:
% 7.85/1.86 | | | |
% 7.85/1.86 | | | | (47) all_12_6 = 0 & ~ (all_12_7 = 0)
% 7.85/1.86 | | | |
% 7.85/1.86 | | | | ALPHA: (47) implies:
% 7.85/1.86 | | | | (48) all_12_6 = 0
% 7.85/1.86 | | | | (49) ~ (all_12_7 = 0)
% 7.85/1.86 | | | |
% 7.85/1.86 | | | | REDUCE: (44), (48) imply:
% 7.85/1.86 | | | | (50) rp(all_12_9, all_12_8) = 0
% 7.85/1.86 | | | |
% 7.85/1.86 | | | | GROUND_INST: instantiating (axiom_5) with all_12_9, all_12_8,
% 7.85/1.86 | | | | simplifying with (13), (14), (50) gives:
% 7.85/1.86 | | | | (51) cd(all_12_9) = 0
% 7.85/1.86 | | | |
% 7.85/1.86 | | | | GROUND_INST: instantiating (5) with all_12_9, simplifying with (13),
% 7.85/1.86 | | | | (51) gives:
% 7.85/1.86 | | | | (52) rq(all_12_9, iv) = 0
% 7.85/1.86 | | | |
% 7.85/1.86 | | | | GROUND_INST: instantiating (6) with all_12_9, simplifying with (13),
% 7.85/1.86 | | | | (51) gives:
% 7.85/1.86 | | | | (53) rp(all_12_9, iv) = 0
% 7.85/1.86 | | | |
% 7.85/1.86 | | | | GROUND_INST: instantiating (axiom_4) with all_12_9, all_12_8, iv,
% 7.85/1.86 | | | | simplifying with (7), (13), (14), (50), (53) gives:
% 7.85/1.86 | | | | (54) all_12_8 = iv
% 7.85/1.86 | | | |
% 7.85/1.86 | | | | REDUCE: (45), (54) imply:
% 7.85/1.86 | | | | (55) rq(all_12_9, iv) = all_12_7
% 7.85/1.86 | | | |
% 7.85/1.86 | | | | GROUND_INST: instantiating (11) with 0, all_12_7, iv, all_12_9,
% 7.85/1.86 | | | | simplifying with (52), (55) gives:
% 7.85/1.86 | | | | (56) all_12_7 = 0
% 7.85/1.86 | | | |
% 7.85/1.86 | | | | REDUCE: (49), (56) imply:
% 7.85/1.86 | | | | (57) $false
% 7.85/1.86 | | | |
% 7.85/1.86 | | | | CLOSE: (57) is inconsistent.
% 7.85/1.86 | | | |
% 7.94/1.86 | | | Case 2:
% 7.94/1.86 | | | |
% 7.94/1.86 | | | | (58) all_12_7 = 0 & ~ (all_12_6 = 0)
% 7.94/1.86 | | | |
% 7.94/1.86 | | | | ALPHA: (58) implies:
% 7.94/1.86 | | | | (59) all_12_7 = 0
% 7.94/1.86 | | | | (60) ~ (all_12_6 = 0)
% 7.94/1.86 | | | |
% 7.94/1.86 | | | | REDUCE: (45), (59) imply:
% 7.94/1.86 | | | | (61) rq(all_12_9, all_12_8) = 0
% 7.94/1.86 | | | |
% 7.94/1.86 | | | | GROUND_INST: instantiating (axiom_7) with all_12_9, all_12_8,
% 7.94/1.86 | | | | simplifying with (13), (14), (61) gives:
% 7.94/1.86 | | | | (62) cd(all_12_9) = 0
% 7.94/1.86 | | | |
% 7.94/1.86 | | | | GROUND_INST: instantiating (5) with all_12_9, simplifying with (13),
% 7.94/1.86 | | | | (62) gives:
% 7.94/1.86 | | | | (63) rq(all_12_9, iv) = 0
% 7.94/1.86 | | | |
% 7.94/1.86 | | | | GROUND_INST: instantiating (6) with all_12_9, simplifying with (13),
% 7.94/1.86 | | | | (62) gives:
% 7.94/1.86 | | | | (64) rp(all_12_9, iv) = 0
% 7.94/1.86 | | | |
% 7.94/1.87 | | | | GROUND_INST: instantiating (axiom_6) with all_12_9, all_12_8, iv,
% 7.94/1.87 | | | | simplifying with (7), (13), (14), (61), (63) gives:
% 7.94/1.87 | | | | (65) all_12_8 = iv
% 7.94/1.87 | | | |
% 7.94/1.87 | | | | REDUCE: (44), (65) imply:
% 7.94/1.87 | | | | (66) rp(all_12_9, iv) = all_12_6
% 7.94/1.87 | | | |
% 7.94/1.87 | | | | GROUND_INST: instantiating (10) with 0, all_12_6, iv, all_12_9,
% 7.94/1.87 | | | | simplifying with (64), (66) gives:
% 7.94/1.87 | | | | (67) all_12_6 = 0
% 7.94/1.87 | | | |
% 7.94/1.87 | | | | REDUCE: (60), (67) imply:
% 7.94/1.87 | | | | (68) $false
% 7.94/1.87 | | | |
% 7.94/1.87 | | | | CLOSE: (68) is inconsistent.
% 7.94/1.87 | | | |
% 7.94/1.87 | | | End of split
% 7.94/1.87 | | |
% 7.94/1.87 | | Case 2:
% 7.94/1.87 | | |
% 7.94/1.87 | | | (69) cowlThing(all_12_2) = all_12_1 & cowlNothing(all_12_2) = all_12_0
% 7.94/1.87 | | | & ( ~ (all_12_1 = 0) | all_12_0 = 0)
% 7.94/1.87 | | |
% 7.94/1.87 | | | ALPHA: (69) implies:
% 7.94/1.87 | | | (70) cowlNothing(all_12_2) = all_12_0
% 7.94/1.87 | | | (71) cowlThing(all_12_2) = all_12_1
% 7.94/1.87 | | | (72) ~ (all_12_1 = 0) | all_12_0 = 0
% 7.94/1.87 | | |
% 7.94/1.87 | | | GROUND_INST: instantiating (2) with all_12_2, all_12_1, simplifying with
% 7.94/1.87 | | | (16), (71) gives:
% 7.94/1.87 | | | (73) all_12_1 = 0
% 7.94/1.87 | | |
% 7.94/1.87 | | | BETA: splitting (72) gives:
% 7.94/1.87 | | |
% 7.94/1.87 | | | Case 1:
% 7.94/1.87 | | | |
% 7.94/1.87 | | | | (74) ~ (all_12_1 = 0)
% 7.94/1.87 | | | |
% 7.94/1.87 | | | | REDUCE: (73), (74) imply:
% 7.94/1.87 | | | | (75) $false
% 7.94/1.87 | | | |
% 7.94/1.87 | | | | CLOSE: (75) is inconsistent.
% 7.94/1.87 | | | |
% 7.94/1.87 | | | Case 2:
% 7.94/1.87 | | | |
% 7.94/1.87 | | | | (76) all_12_0 = 0
% 7.94/1.87 | | | |
% 7.94/1.87 | | | | REDUCE: (70), (76) imply:
% 7.94/1.87 | | | | (77) cowlNothing(all_12_2) = 0
% 7.94/1.87 | | | |
% 7.94/1.87 | | | | GROUND_INST: instantiating (1) with all_12_2, simplifying with (16),
% 7.94/1.87 | | | | (77) gives:
% 7.94/1.87 | | | | (78) $false
% 7.94/1.87 | | | |
% 7.94/1.87 | | | | CLOSE: (78) is inconsistent.
% 7.94/1.87 | | | |
% 7.94/1.87 | | | End of split
% 7.94/1.87 | | |
% 7.94/1.87 | | End of split
% 7.94/1.87 | |
% 7.94/1.87 | End of split
% 7.94/1.87 |
% 7.94/1.87 End of proof
% 7.94/1.87 % SZS output end Proof for theBenchmark
% 7.94/1.87
% 7.94/1.87 1246ms
%------------------------------------------------------------------------------