TSTP Solution File: KRS170+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS170+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 : n026.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 05:51:31 EDT 2023
% Result : Theorem 4.39s 1.31s
% Output : Proof 6.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS170+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 02:15:19 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.73/0.97 Prover 1: Preprocessing ...
% 1.73/0.97 Prover 4: Preprocessing ...
% 2.30/1.02 Prover 6: Preprocessing ...
% 2.30/1.02 Prover 3: Preprocessing ...
% 2.30/1.02 Prover 2: Preprocessing ...
% 2.30/1.02 Prover 5: Preprocessing ...
% 2.30/1.02 Prover 0: Preprocessing ...
% 2.80/1.13 Prover 2: Proving ...
% 2.80/1.13 Prover 5: Proving ...
% 2.80/1.15 Prover 1: Constructing countermodel ...
% 2.80/1.16 Prover 6: Constructing countermodel ...
% 2.80/1.17 Prover 3: Constructing countermodel ...
% 3.47/1.18 Prover 4: Constructing countermodel ...
% 3.55/1.20 Prover 0: Proving ...
% 4.39/1.31 Prover 3: proved (674ms)
% 4.39/1.31
% 4.39/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.39/1.31
% 4.39/1.31 Prover 6: stopped
% 4.39/1.31 Prover 0: stopped
% 4.39/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.39/1.32 Prover 2: stopped
% 4.39/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.39/1.32 Prover 5: stopped
% 4.39/1.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.39/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.39/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.39/1.34 Prover 13: Preprocessing ...
% 4.39/1.34 Prover 10: Preprocessing ...
% 4.39/1.34 Prover 11: Preprocessing ...
% 4.39/1.35 Prover 7: Preprocessing ...
% 4.39/1.35 Prover 8: Preprocessing ...
% 4.39/1.36 Prover 10: Warning: ignoring some quantifiers
% 4.39/1.37 Prover 10: Constructing countermodel ...
% 4.39/1.37 Prover 7: Warning: ignoring some quantifiers
% 4.39/1.37 Prover 7: Constructing countermodel ...
% 4.39/1.37 Prover 13: Warning: ignoring some quantifiers
% 4.39/1.38 Prover 13: Constructing countermodel ...
% 4.97/1.41 Prover 10: gave up
% 4.97/1.41 Prover 8: Warning: ignoring some quantifiers
% 4.97/1.41 Prover 13: gave up
% 4.97/1.42 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.97/1.42 Prover 8: Constructing countermodel ...
% 4.97/1.42 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.97/1.42 Prover 7: gave up
% 4.97/1.44 Prover 16: Preprocessing ...
% 4.97/1.44 Prover 1: Found proof (size 53)
% 4.97/1.44 Prover 1: proved (814ms)
% 4.97/1.44 Prover 4: stopped
% 4.97/1.44 Prover 8: stopped
% 4.97/1.44 Prover 19: Preprocessing ...
% 4.97/1.45 Prover 11: Constructing countermodel ...
% 4.97/1.46 Prover 11: stopped
% 4.97/1.46 Prover 16: Warning: ignoring some quantifiers
% 4.97/1.46 Prover 16: Constructing countermodel ...
% 4.97/1.47 Prover 16: stopped
% 4.97/1.49 Prover 19: Warning: ignoring some quantifiers
% 4.97/1.50 Prover 19: Constructing countermodel ...
% 4.97/1.50 Prover 19: stopped
% 4.97/1.50
% 4.97/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.97/1.50
% 4.97/1.51 % SZS output start Proof for theBenchmark
% 4.97/1.51 Assumptions after simplification:
% 4.97/1.51 ---------------------------------
% 4.97/1.51
% 4.97/1.51 (axiom_0)
% 4.97/1.55 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) &
% 4.97/1.55 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0))
% 4.97/1.55
% 4.97/1.55 (axiom_1)
% 4.97/1.55 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ $i(v0) |
% 4.97/1.55 xsd_integer(v0) = 0) & ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) |
% 4.97/1.55 ? [v1: int] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 4.97/1.55
% 4.97/1.55 (axiom_2)
% 4.97/1.55 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rhasLeader(v0, v1) =
% 4.97/1.55 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rhasHead(v0,
% 4.97/1.55 v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (rhasLeader(v0, v1) = 0) |
% 4.97/1.55 ~ $i(v1) | ~ $i(v0) | rhasHead(v0, v1) = 0)
% 4.97/1.55
% 4.97/1.55 (the_axiom)
% 4.97/1.56 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & rhasLeader(v0, v1) =
% 4.97/1.56 v2 & rhasHead(v0, v1) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] :
% 4.97/1.56 ? [v2: int] : ( ~ (v2 = 0) & rhasLeader(v0, v1) = 0 & rhasHead(v0, v1) = v2 &
% 4.97/1.56 $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 4.97/1.56 (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | (
% 4.97/1.56 ~ (v2 = 0) & ~ (v1 = 0)))) | ? [v0: $i] : ? [v1: any] : ? [v2: any]
% 4.97/1.56 : (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 =
% 4.97/1.56 0))
% 4.97/1.56
% 4.97/1.56 (function-axioms)
% 4.97/1.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.97/1.56 [v3: $i] : (v1 = v0 | ~ (rhasLeader(v3, v2) = v1) | ~ (rhasLeader(v3, v2) =
% 4.97/1.56 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 4.97/1.56 $i] : ! [v3: $i] : (v1 = v0 | ~ (rhasHead(v3, v2) = v1) | ~ (rhasHead(v3,
% 4.97/1.56 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 4.97/1.56 ! [v2: $i] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) &
% 4.97/1.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 4.97/1.56 v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0:
% 4.97/1.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 4.97/1.56 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0:
% 4.97/1.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 4.97/1.56 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 4.97/1.56
% 4.97/1.56 Those formulas are unsatisfiable:
% 4.97/1.56 ---------------------------------
% 4.97/1.56
% 4.97/1.56 Begin of proof
% 4.97/1.56 |
% 4.97/1.56 | ALPHA: (axiom_0) implies:
% 4.97/1.57 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0))
% 4.97/1.57 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~
% 4.97/1.57 | $i(v0))
% 4.97/1.57 |
% 4.97/1.57 | ALPHA: (axiom_1) implies:
% 4.97/1.57 | (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 4.97/1.57 | (v1 = 0) & xsd_integer(v0) = v1))
% 4.97/1.57 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~
% 4.97/1.57 | $i(v0) | xsd_integer(v0) = 0)
% 4.97/1.57 |
% 4.97/1.57 | ALPHA: (axiom_2) implies:
% 4.97/1.57 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (rhasLeader(v0, v1) = 0) | ~ $i(v1) |
% 4.97/1.57 | ~ $i(v0) | rhasHead(v0, v1) = 0)
% 4.97/1.57 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rhasLeader(v0,
% 4.97/1.57 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 4.97/1.57 | rhasHead(v0, v1) = v3))
% 4.97/1.57 |
% 4.97/1.57 | ALPHA: (function-axioms) implies:
% 4.97/1.57 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.97/1.57 | (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 4.97/1.57 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.97/1.57 | ! [v3: $i] : (v1 = v0 | ~ (rhasHead(v3, v2) = v1) | ~ (rhasHead(v3,
% 4.97/1.57 | v2) = v0))
% 4.97/1.57 |
% 4.97/1.57 | BETA: splitting (the_axiom) gives:
% 4.97/1.57 |
% 4.97/1.57 | Case 1:
% 4.97/1.57 | |
% 4.97/1.58 | | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 4.97/1.58 | | rhasLeader(v0, v1) = v2 & rhasHead(v0, v1) = 0 & $i(v1) & $i(v0)) |
% 4.97/1.58 | | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 4.97/1.58 | | rhasLeader(v0, v1) = 0 & rhasHead(v0, v1) = v2 & $i(v1) & $i(v0))
% 4.97/1.58 | |
% 4.97/1.58 | | BETA: splitting (9) gives:
% 4.97/1.58 | |
% 4.97/1.58 | | Case 1:
% 4.97/1.58 | | |
% 4.97/1.58 | | | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 4.97/1.58 | | | rhasLeader(v0, v1) = v2 & rhasHead(v0, v1) = 0 & $i(v1) &
% 4.97/1.58 | | | $i(v0))
% 4.97/1.58 | | |
% 4.97/1.58 | | | DELTA: instantiating (10) with fresh symbols all_12_0, all_12_1, all_12_2
% 4.97/1.58 | | | gives:
% 4.97/1.58 | | | (11) ~ (all_12_0 = 0) & rhasLeader(all_12_2, all_12_1) = all_12_0 &
% 4.97/1.58 | | | rhasHead(all_12_2, all_12_1) = 0 & $i(all_12_1) & $i(all_12_2)
% 4.97/1.58 | | |
% 4.97/1.58 | | | ALPHA: (11) implies:
% 4.97/1.58 | | | (12) ~ (all_12_0 = 0)
% 4.97/1.58 | | | (13) $i(all_12_2)
% 4.97/1.58 | | | (14) $i(all_12_1)
% 4.97/1.58 | | | (15) rhasHead(all_12_2, all_12_1) = 0
% 4.97/1.58 | | | (16) rhasLeader(all_12_2, all_12_1) = all_12_0
% 4.97/1.58 | | |
% 4.97/1.58 | | | GROUND_INST: instantiating (6) with all_12_2, all_12_1, all_12_0,
% 4.97/1.58 | | | simplifying with (13), (14), (16) gives:
% 4.97/1.58 | | | (17) all_12_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & rhasHead(all_12_2,
% 4.97/1.58 | | | all_12_1) = v0)
% 4.97/1.58 | | |
% 4.97/1.58 | | | BETA: splitting (17) gives:
% 4.97/1.58 | | |
% 4.97/1.58 | | | Case 1:
% 4.97/1.58 | | | |
% 4.97/1.58 | | | | (18) all_12_0 = 0
% 4.97/1.58 | | | |
% 4.97/1.58 | | | | REDUCE: (12), (18) imply:
% 4.97/1.58 | | | | (19) $false
% 5.66/1.58 | | | |
% 5.66/1.58 | | | | CLOSE: (19) is inconsistent.
% 5.66/1.58 | | | |
% 5.66/1.58 | | | Case 2:
% 5.66/1.58 | | | |
% 5.66/1.58 | | | | (20) ? [v0: int] : ( ~ (v0 = 0) & rhasHead(all_12_2, all_12_1) = v0)
% 5.66/1.58 | | | |
% 5.66/1.59 | | | | DELTA: instantiating (20) with fresh symbol all_21_0 gives:
% 5.66/1.59 | | | | (21) ~ (all_21_0 = 0) & rhasHead(all_12_2, all_12_1) = all_21_0
% 5.66/1.59 | | | |
% 5.66/1.59 | | | | ALPHA: (21) implies:
% 5.66/1.59 | | | | (22) ~ (all_21_0 = 0)
% 5.66/1.59 | | | | (23) rhasHead(all_12_2, all_12_1) = all_21_0
% 5.66/1.59 | | | |
% 5.66/1.59 | | | | GROUND_INST: instantiating (8) with 0, all_21_0, all_12_1, all_12_2,
% 5.66/1.59 | | | | simplifying with (15), (23) gives:
% 5.66/1.59 | | | | (24) all_21_0 = 0
% 5.66/1.59 | | | |
% 5.66/1.59 | | | | REDUCE: (22), (24) imply:
% 5.66/1.59 | | | | (25) $false
% 5.66/1.59 | | | |
% 5.66/1.59 | | | | CLOSE: (25) is inconsistent.
% 5.66/1.59 | | | |
% 5.66/1.59 | | | End of split
% 5.66/1.59 | | |
% 5.66/1.59 | | Case 2:
% 5.66/1.59 | | |
% 5.66/1.59 | | | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 5.66/1.59 | | | rhasLeader(v0, v1) = 0 & rhasHead(v0, v1) = v2 & $i(v1) &
% 5.66/1.59 | | | $i(v0))
% 5.66/1.59 | | |
% 5.66/1.59 | | | DELTA: instantiating (26) with fresh symbols all_12_0, all_12_1, all_12_2
% 5.66/1.59 | | | gives:
% 5.66/1.59 | | | (27) ~ (all_12_0 = 0) & rhasLeader(all_12_2, all_12_1) = 0 &
% 5.66/1.59 | | | rhasHead(all_12_2, all_12_1) = all_12_0 & $i(all_12_1) &
% 5.66/1.59 | | | $i(all_12_2)
% 5.66/1.59 | | |
% 5.66/1.59 | | | ALPHA: (27) implies:
% 5.66/1.59 | | | (28) ~ (all_12_0 = 0)
% 5.66/1.59 | | | (29) $i(all_12_2)
% 5.66/1.59 | | | (30) $i(all_12_1)
% 5.66/1.59 | | | (31) rhasHead(all_12_2, all_12_1) = all_12_0
% 5.66/1.59 | | | (32) rhasLeader(all_12_2, all_12_1) = 0
% 5.66/1.59 | | |
% 5.66/1.59 | | | GROUND_INST: instantiating (5) with all_12_2, all_12_1, simplifying with
% 5.66/1.59 | | | (29), (30), (32) gives:
% 5.66/1.59 | | | (33) rhasHead(all_12_2, all_12_1) = 0
% 5.66/1.59 | | |
% 5.66/1.59 | | | GROUND_INST: instantiating (8) with all_12_0, 0, all_12_1, all_12_2,
% 5.66/1.59 | | | simplifying with (31), (33) gives:
% 5.66/1.59 | | | (34) all_12_0 = 0
% 5.66/1.59 | | |
% 5.66/1.59 | | | REDUCE: (28), (34) imply:
% 5.66/1.59 | | | (35) $false
% 5.66/1.59 | | |
% 5.66/1.59 | | | CLOSE: (35) is inconsistent.
% 5.66/1.59 | | |
% 5.66/1.59 | | End of split
% 5.66/1.59 | |
% 5.66/1.59 | Case 2:
% 5.66/1.59 | |
% 6.10/1.59 | | (36) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 &
% 6.10/1.59 | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0)
% 6.10/1.59 | | & ~ (v1 = 0)))) | ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 6.10/1.59 | | (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) |
% 6.10/1.59 | | v2 = 0))
% 6.10/1.59 | |
% 6.10/1.59 | | BETA: splitting (36) gives:
% 6.10/1.59 | |
% 6.10/1.59 | | Case 1:
% 6.10/1.59 | | |
% 6.10/1.59 | | | (37) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (xsd_string(v0) = v1 &
% 6.10/1.60 | | | xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 =
% 6.10/1.60 | | | 0) & ~ (v1 = 0))))
% 6.10/1.60 | | |
% 6.10/1.60 | | | DELTA: instantiating (37) with fresh symbols all_12_0, all_12_1, all_12_2
% 6.10/1.60 | | | gives:
% 6.10/1.60 | | | (38) xsd_string(all_12_2) = all_12_1 & xsd_integer(all_12_2) = all_12_0
% 6.10/1.60 | | | & $i(all_12_2) & ((all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 =
% 6.10/1.60 | | | 0) & ~ (all_12_1 = 0)))
% 6.10/1.60 | | |
% 6.10/1.60 | | | ALPHA: (38) implies:
% 6.10/1.60 | | | (39) $i(all_12_2)
% 6.10/1.60 | | | (40) xsd_integer(all_12_2) = all_12_0
% 6.10/1.60 | | | (41) xsd_string(all_12_2) = all_12_1
% 6.10/1.60 | | | (42) (all_12_0 = 0 & all_12_1 = 0) | ( ~ (all_12_0 = 0) & ~ (all_12_1
% 6.10/1.60 | | | = 0))
% 6.10/1.60 | | |
% 6.10/1.60 | | | GROUND_INST: instantiating (4) with all_12_2, all_12_1, simplifying with
% 6.10/1.60 | | | (39), (41) gives:
% 6.10/1.60 | | | (43) all_12_1 = 0 | xsd_integer(all_12_2) = 0
% 6.10/1.60 | | |
% 6.10/1.60 | | | BETA: splitting (42) gives:
% 6.10/1.60 | | |
% 6.10/1.60 | | | Case 1:
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | (44) all_12_0 = 0 & all_12_1 = 0
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | ALPHA: (44) implies:
% 6.10/1.60 | | | | (45) all_12_1 = 0
% 6.10/1.60 | | | | (46) all_12_0 = 0
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | REDUCE: (41), (45) imply:
% 6.10/1.60 | | | | (47) xsd_string(all_12_2) = 0
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | REDUCE: (40), (46) imply:
% 6.10/1.60 | | | | (48) xsd_integer(all_12_2) = 0
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | GROUND_INST: instantiating (3) with all_12_2, simplifying with (39),
% 6.10/1.60 | | | | (47) gives:
% 6.10/1.60 | | | | (49) ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_12_2) = v0)
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | DELTA: instantiating (49) with fresh symbol all_26_0 gives:
% 6.10/1.60 | | | | (50) ~ (all_26_0 = 0) & xsd_integer(all_12_2) = all_26_0
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | ALPHA: (50) implies:
% 6.10/1.60 | | | | (51) ~ (all_26_0 = 0)
% 6.10/1.60 | | | | (52) xsd_integer(all_12_2) = all_26_0
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | GROUND_INST: instantiating (7) with 0, all_26_0, all_12_2, simplifying
% 6.10/1.60 | | | | with (48), (52) gives:
% 6.10/1.60 | | | | (53) all_26_0 = 0
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | REDUCE: (51), (53) imply:
% 6.10/1.60 | | | | (54) $false
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | CLOSE: (54) is inconsistent.
% 6.10/1.60 | | | |
% 6.10/1.60 | | | Case 2:
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | (55) ~ (all_12_0 = 0) & ~ (all_12_1 = 0)
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | ALPHA: (55) implies:
% 6.10/1.60 | | | | (56) ~ (all_12_1 = 0)
% 6.10/1.60 | | | | (57) ~ (all_12_0 = 0)
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | BETA: splitting (43) gives:
% 6.10/1.60 | | | |
% 6.10/1.60 | | | | Case 1:
% 6.10/1.60 | | | | |
% 6.10/1.60 | | | | | (58) xsd_integer(all_12_2) = 0
% 6.10/1.60 | | | | |
% 6.10/1.60 | | | | | GROUND_INST: instantiating (7) with all_12_0, 0, all_12_2, simplifying
% 6.10/1.60 | | | | | with (40), (58) gives:
% 6.10/1.60 | | | | | (59) all_12_0 = 0
% 6.10/1.60 | | | | |
% 6.10/1.60 | | | | | REDUCE: (57), (59) imply:
% 6.10/1.60 | | | | | (60) $false
% 6.10/1.60 | | | | |
% 6.10/1.60 | | | | | CLOSE: (60) is inconsistent.
% 6.10/1.60 | | | | |
% 6.10/1.60 | | | | Case 2:
% 6.10/1.60 | | | | |
% 6.10/1.60 | | | | | (61) all_12_1 = 0
% 6.10/1.60 | | | | |
% 6.10/1.60 | | | | | REDUCE: (56), (61) imply:
% 6.10/1.60 | | | | | (62) $false
% 6.10/1.60 | | | | |
% 6.10/1.60 | | | | | CLOSE: (62) is inconsistent.
% 6.10/1.60 | | | | |
% 6.10/1.60 | | | | End of split
% 6.10/1.60 | | | |
% 6.10/1.60 | | | End of split
% 6.10/1.60 | | |
% 6.10/1.60 | | Case 2:
% 6.10/1.60 | | |
% 6.10/1.61 | | | (63) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (cowlNothing(v0) = v2
% 6.10/1.61 | | | & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 6.10/1.61 | | |
% 6.10/1.61 | | | DELTA: instantiating (63) with fresh symbols all_12_0, all_12_1, all_12_2
% 6.10/1.61 | | | gives:
% 6.10/1.61 | | | (64) cowlNothing(all_12_2) = all_12_0 & cowlThing(all_12_2) = all_12_1
% 6.10/1.61 | | | & $i(all_12_2) & ( ~ (all_12_1 = 0) | all_12_0 = 0)
% 6.10/1.61 | | |
% 6.10/1.61 | | | ALPHA: (64) implies:
% 6.10/1.61 | | | (65) $i(all_12_2)
% 6.10/1.61 | | | (66) cowlThing(all_12_2) = all_12_1
% 6.10/1.61 | | | (67) cowlNothing(all_12_2) = all_12_0
% 6.10/1.61 | | | (68) ~ (all_12_1 = 0) | all_12_0 = 0
% 6.10/1.61 | | |
% 6.10/1.61 | | | GROUND_INST: instantiating (2) with all_12_2, all_12_1, simplifying with
% 6.10/1.61 | | | (65), (66) gives:
% 6.10/1.61 | | | (69) all_12_1 = 0
% 6.10/1.61 | | |
% 6.10/1.61 | | | BETA: splitting (68) gives:
% 6.10/1.61 | | |
% 6.10/1.61 | | | Case 1:
% 6.10/1.61 | | | |
% 6.10/1.61 | | | | (70) ~ (all_12_1 = 0)
% 6.10/1.61 | | | |
% 6.10/1.61 | | | | REDUCE: (69), (70) imply:
% 6.10/1.61 | | | | (71) $false
% 6.10/1.61 | | | |
% 6.10/1.61 | | | | CLOSE: (71) is inconsistent.
% 6.10/1.61 | | | |
% 6.10/1.61 | | | Case 2:
% 6.10/1.61 | | | |
% 6.10/1.61 | | | | (72) all_12_0 = 0
% 6.10/1.61 | | | |
% 6.10/1.61 | | | | REDUCE: (67), (72) imply:
% 6.10/1.61 | | | | (73) cowlNothing(all_12_2) = 0
% 6.10/1.61 | | | |
% 6.10/1.61 | | | | GROUND_INST: instantiating (1) with all_12_2, simplifying with (65),
% 6.10/1.61 | | | | (73) gives:
% 6.10/1.61 | | | | (74) $false
% 6.10/1.61 | | | |
% 6.10/1.61 | | | | CLOSE: (74) is inconsistent.
% 6.10/1.61 | | | |
% 6.10/1.61 | | | End of split
% 6.10/1.61 | | |
% 6.10/1.61 | | End of split
% 6.10/1.61 | |
% 6.10/1.61 | End of split
% 6.10/1.61 |
% 6.10/1.61 End of proof
% 6.10/1.61 % SZS output end Proof for theBenchmark
% 6.10/1.61
% 6.10/1.61 1003ms
%------------------------------------------------------------------------------