TSTP Solution File: KRS078+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS078+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 : n025.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 05:51:10 EDT 2023
% Result : Unsatisfiable 5.11s 1.54s
% Output : Proof 7.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : KRS078+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.36 % Computer : n025.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon Aug 28 02:03:09 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.23/0.64 ________ _____
% 0.23/0.64 ___ __ \_________(_)________________________________
% 0.23/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.23/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.23/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.23/0.64
% 0.23/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.23/0.64 (2023-06-19)
% 0.23/0.64
% 0.23/0.64 (c) Philipp Rümmer, 2009-2023
% 0.23/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.23/0.64 Amanda Stjerna.
% 0.23/0.64 Free software under BSD-3-Clause.
% 0.23/0.64
% 0.23/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.23/0.64
% 0.23/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.23/0.66 Running up to 7 provers in parallel.
% 0.23/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.23/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.23/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.23/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.23/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.23/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.23/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.31/1.07 Prover 4: Preprocessing ...
% 2.31/1.07 Prover 1: Preprocessing ...
% 2.31/1.11 Prover 3: Preprocessing ...
% 2.31/1.11 Prover 5: Preprocessing ...
% 2.31/1.11 Prover 0: Preprocessing ...
% 2.31/1.11 Prover 2: Preprocessing ...
% 2.31/1.11 Prover 6: Preprocessing ...
% 3.88/1.37 Prover 5: Proving ...
% 3.88/1.37 Prover 2: Proving ...
% 3.88/1.42 Prover 1: Constructing countermodel ...
% 4.91/1.45 Prover 3: Constructing countermodel ...
% 5.11/1.46 Prover 6: Proving ...
% 5.11/1.47 Prover 4: Constructing countermodel ...
% 5.11/1.52 Prover 0: Proving ...
% 5.11/1.54 Prover 5: proved (862ms)
% 5.11/1.54
% 5.11/1.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.11/1.54
% 5.11/1.54 Prover 2: proved (862ms)
% 5.11/1.54
% 5.11/1.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.11/1.54
% 5.11/1.54 Prover 3: stopped
% 5.11/1.54 Prover 6: stopped
% 5.11/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.11/1.54 Prover 0: stopped
% 5.11/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.11/1.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.78/1.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.78/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.78/1.58 Prover 11: Preprocessing ...
% 5.78/1.58 Prover 7: Preprocessing ...
% 6.08/1.59 Prover 13: Preprocessing ...
% 6.08/1.59 Prover 10: Preprocessing ...
% 6.08/1.60 Prover 8: Preprocessing ...
% 6.08/1.63 Prover 4: Found proof (size 22)
% 6.08/1.63 Prover 4: proved (957ms)
% 6.08/1.63 Prover 1: Found proof (size 24)
% 6.08/1.63 Prover 1: proved (967ms)
% 6.49/1.65 Prover 7: Warning: ignoring some quantifiers
% 6.60/1.65 Prover 10: Warning: ignoring some quantifiers
% 6.60/1.66 Prover 11: stopped
% 6.60/1.66 Prover 13: Warning: ignoring some quantifiers
% 6.60/1.66 Prover 10: Constructing countermodel ...
% 6.60/1.66 Prover 7: Constructing countermodel ...
% 6.60/1.66 Prover 13: Constructing countermodel ...
% 6.60/1.66 Prover 10: stopped
% 6.60/1.66 Prover 7: stopped
% 6.60/1.67 Prover 13: stopped
% 6.92/1.71 Prover 8: Warning: ignoring some quantifiers
% 6.92/1.72 Prover 8: Constructing countermodel ...
% 6.92/1.73 Prover 8: stopped
% 6.92/1.73
% 6.92/1.73 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.92/1.73
% 6.92/1.73 % SZS output start Proof for theBenchmark
% 6.92/1.73 Assumptions after simplification:
% 6.92/1.73 ---------------------------------
% 6.92/1.73
% 6.92/1.73 (axiom_2)
% 7.14/1.77 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : !
% 7.14/1.77 [v5: $i] : (v3 = 0 | v1 = 0 | ~ (rr(v0, v4) = 0) | ~ (rinvR(v4, v5) = 0) |
% 7.14/1.78 ~ (cq(v2) = v3) | ~ (cUnsatisfiable(v0) = v1) | ~ $i(v5) | ~ $i(v4) | ~
% 7.14/1.78 $i(v2) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i]
% 7.14/1.78 : ? [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : ? [v14:
% 7.14/1.78 int] : ($i(v12) & $i(v9) & $i(v8) & ((v13 = 0 & ~ (v14 = 0) & rs(v5, v12)
% 7.14/1.78 = 0 & cp(v12) = v14) | (v11 = 0 & v10 = 0 & ~ (v9 = v8) & rinvR(v4,
% 7.14/1.78 v9) = 0 & rinvR(v4, v8) = 0) | (rs(v0, v2) = v6 & cp(v2) = v7 & ( ~
% 7.14/1.78 (v6 = 0) | v7 = 0))))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] :
% 7.14/1.78 ! [v3: int] : ! [v4: $i] : ! [v5: $i] : (v3 = 0 | v1 = 0 | ~ (rr(v0, v4) =
% 7.14/1.78 0) | ~ (rinvR(v4, v5) = 0) | ~ (cp(v2) = v3) | ~ (cUnsatisfiable(v0) =
% 7.14/1.78 v1) | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ? [v6: any] : ?
% 7.14/1.78 [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : ?
% 7.14/1.78 [v12: $i] : ? [v13: int] : ? [v14: int] : ($i(v12) & $i(v9) & $i(v8) &
% 7.14/1.78 ((v13 = 0 & ~ (v14 = 0) & rs(v5, v12) = 0 & cp(v12) = v14) | (v11 = 0 &
% 7.14/1.78 v10 = 0 & ~ (v9 = v8) & rinvR(v4, v9) = 0 & rinvR(v4, v8) = 0) |
% 7.14/1.78 (rs(v0, v2) = v6 & cq(v2) = v7 & ( ~ (v6 = 0) | v7 = 0))))) & ! [v0:
% 7.14/1.78 $i] : ! [v1: int] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = 0 | ~
% 7.14/1.78 (rs(v0, v2) = 0) | ~ (rr(v0, v3) = 0) | ~ (rinvR(v3, v4) = 0) | ~
% 7.14/1.78 (cUnsatisfiable(v0) = v1) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) |
% 7.14/1.78 ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ?
% 7.14/1.78 [v10: int] : ? [v11: $i] : ? [v12: int] : ? [v13: int] : ($i(v11) &
% 7.14/1.78 $i(v8) & $i(v7) & ((v12 = 0 & ~ (v13 = 0) & rs(v4, v11) = 0 & cp(v11) =
% 7.14/1.78 v13) | (v10 = 0 & v9 = 0 & ~ (v8 = v7) & rinvR(v3, v8) = 0 &
% 7.14/1.78 rinvR(v3, v7) = 0) | (cq(v2) = v5 & cp(v2) = v6 & (v6 = 0 | v5 =
% 7.14/1.78 0))))) & ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ?
% 7.14/1.78 [v1: $i] : ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v2 = 0) & rs(v0,
% 7.14/1.78 v1) = 0 & cq(v1) = v2 & cp(v1) = v3 & $i(v1))) & ! [v0: $i] : ( ~
% 7.14/1.78 (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (rr(v0,
% 7.14/1.78 v1) = 0 & rinvR(v1, v2) = 0 & $i(v2) & $i(v1) & ! [v3: $i] : ! [v4:
% 7.14/1.78 $i] : (v4 = v3 | ~ (rinvR(v1, v4) = 0) | ~ (rinvR(v1, v3) = 0) | ~
% 7.14/1.78 $i(v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (cp(v3)
% 7.14/1.78 = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & rs(v2, v3) = v5)) &
% 7.14/1.78 ! [v3: $i] : ( ~ (rs(v2, v3) = 0) | ~ $i(v3) | cp(v3) = 0)))
% 7.14/1.78
% 7.14/1.78 (axiom_3)
% 7.14/1.78 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rr(v1, v0) = v2) | ~
% 7.14/1.78 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rinvR(v0, v1) = v3)) & !
% 7.14/1.78 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rinvR(v0, v1) = v2) | ~
% 7.14/1.78 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rr(v1, v0) = v3)) & !
% 7.14/1.78 [v0: $i] : ! [v1: $i] : ( ~ (rr(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 7.14/1.78 rinvR(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rinvR(v0, v1) = 0) |
% 7.14/1.78 ~ $i(v1) | ~ $i(v0) | rr(v1, v0) = 0)
% 7.14/1.78
% 7.14/1.78 (axiom_4)
% 7.14/1.78 cUnsatisfiable(i2003_11_14_17_19_13721) = 0 & $i(i2003_11_14_17_19_13721)
% 7.14/1.78
% 7.14/1.78 (function-axioms)
% 7.14/1.79 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.14/1.79 [v3: $i] : (v1 = v0 | ~ (rs(v3, v2) = v1) | ~ (rs(v3, v2) = v0)) & ! [v0:
% 7.14/1.79 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.14/1.79 : (v1 = v0 | ~ (rr(v3, v2) = v1) | ~ (rr(v3, v2) = v0)) & ! [v0:
% 7.14/1.79 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.14/1.79 : (v1 = v0 | ~ (rinvR(v3, v2) = v1) | ~ (rinvR(v3, v2) = v0)) & ! [v0:
% 7.14/1.79 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.14/1.79 ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0:
% 7.14/1.79 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.14/1.79 ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0:
% 7.14/1.79 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.14/1.79 ~ (cq(v2) = v1) | ~ (cq(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.14/1.79 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cp(v2) = v1) | ~ (cp(v2)
% 7.14/1.79 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.14/1.79 $i] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & !
% 7.14/1.79 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 7.14/1.79 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0:
% 7.14/1.79 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.14/1.79 ~ (cUnsatisfiable(v2) = v1) | ~ (cUnsatisfiable(v2) = v0))
% 7.14/1.79
% 7.14/1.79 Further assumptions not needed in the proof:
% 7.14/1.79 --------------------------------------------
% 7.14/1.79 axiom_0, axiom_1, cUnsatisfiable_substitution_1, cowlNothing_substitution_1,
% 7.14/1.79 cowlThing_substitution_1, cp_substitution_1, cq_substitution_1,
% 7.14/1.79 rinvR_substitution_1, rinvR_substitution_2, rr_substitution_1,
% 7.14/1.79 rr_substitution_2, rs_substitution_1, rs_substitution_2,
% 7.14/1.79 xsd_integer_substitution_1, xsd_string_substitution_1
% 7.14/1.79
% 7.14/1.79 Those formulas are unsatisfiable:
% 7.14/1.79 ---------------------------------
% 7.14/1.79
% 7.14/1.79 Begin of proof
% 7.14/1.79 |
% 7.14/1.79 | ALPHA: (axiom_2) implies:
% 7.14/1.79 | (1) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 7.14/1.79 | ? [v2: $i] : (rr(v0, v1) = 0 & rinvR(v1, v2) = 0 & $i(v2) & $i(v1) &
% 7.14/1.79 | ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (rinvR(v1, v4) = 0) | ~
% 7.14/1.79 | (rinvR(v1, v3) = 0) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : !
% 7.14/1.79 | [v4: int] : (v4 = 0 | ~ (cp(v3) = v4) | ~ $i(v3) | ? [v5: int] :
% 7.14/1.79 | ( ~ (v5 = 0) & rs(v2, v3) = v5)) & ! [v3: $i] : ( ~ (rs(v2, v3)
% 7.14/1.79 | = 0) | ~ $i(v3) | cp(v3) = 0)))
% 7.14/1.79 | (2) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 7.14/1.79 | ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v2 = 0) & rs(v0, v1)
% 7.14/1.79 | = 0 & cq(v1) = v2 & cp(v1) = v3 & $i(v1)))
% 7.14/1.79 |
% 7.14/1.79 | ALPHA: (axiom_3) implies:
% 7.14/1.79 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (rr(v1, v0) = 0) | ~ $i(v1) | ~
% 7.14/1.79 | $i(v0) | rinvR(v0, v1) = 0)
% 7.14/1.79 |
% 7.14/1.79 | ALPHA: (axiom_4) implies:
% 7.14/1.79 | (4) $i(i2003_11_14_17_19_13721)
% 7.14/1.79 | (5) cUnsatisfiable(i2003_11_14_17_19_13721) = 0
% 7.14/1.79 |
% 7.14/1.79 | ALPHA: (function-axioms) implies:
% 7.14/1.80 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.14/1.80 | ! [v3: $i] : (v1 = v0 | ~ (rs(v3, v2) = v1) | ~ (rs(v3, v2) = v0))
% 7.14/1.80 |
% 7.14/1.80 | GROUND_INST: instantiating (2) with i2003_11_14_17_19_13721, simplifying with
% 7.14/1.80 | (4), (5) gives:
% 7.14/1.80 | (7) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = 0) & ~ (v1 = 0)
% 7.14/1.80 | & rs(i2003_11_14_17_19_13721, v0) = 0 & cq(v0) = v1 & cp(v0) = v2 &
% 7.14/1.80 | $i(v0))
% 7.14/1.80 |
% 7.14/1.80 | GROUND_INST: instantiating (1) with i2003_11_14_17_19_13721, simplifying with
% 7.14/1.80 | (4), (5) gives:
% 7.14/1.80 | (8) ? [v0: $i] : ? [v1: $i] : (rr(i2003_11_14_17_19_13721, v0) = 0 &
% 7.14/1.80 | rinvR(v0, v1) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3
% 7.14/1.80 | = v2 | ~ (rinvR(v0, v3) = 0) | ~ (rinvR(v0, v2) = 0) | ~ $i(v3)
% 7.14/1.80 | | ~ $i(v2)) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (cp(v2) =
% 7.14/1.80 | v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & rs(v1, v2) = v4))
% 7.14/1.80 | & ! [v2: $i] : ( ~ (rs(v1, v2) = 0) | ~ $i(v2) | cp(v2) = 0))
% 7.14/1.80 |
% 7.14/1.80 | DELTA: instantiating (7) with fresh symbols all_13_0, all_13_1, all_13_2
% 7.14/1.80 | gives:
% 7.14/1.80 | (9) ~ (all_13_0 = 0) & ~ (all_13_1 = 0) & rs(i2003_11_14_17_19_13721,
% 7.14/1.80 | all_13_2) = 0 & cq(all_13_2) = all_13_1 & cp(all_13_2) = all_13_0 &
% 7.14/1.80 | $i(all_13_2)
% 7.14/1.80 |
% 7.14/1.80 | ALPHA: (9) implies:
% 7.14/1.80 | (10) ~ (all_13_0 = 0)
% 7.14/1.80 | (11) $i(all_13_2)
% 7.14/1.80 | (12) cp(all_13_2) = all_13_0
% 7.14/1.80 | (13) rs(i2003_11_14_17_19_13721, all_13_2) = 0
% 7.14/1.80 |
% 7.14/1.80 | DELTA: instantiating (8) with fresh symbols all_15_0, all_15_1 gives:
% 7.14/1.80 | (14) rr(i2003_11_14_17_19_13721, all_15_1) = 0 & rinvR(all_15_1, all_15_0)
% 7.14/1.80 | = 0 & $i(all_15_0) & $i(all_15_1) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 7.14/1.80 | v0 | ~ (rinvR(all_15_1, v1) = 0) | ~ (rinvR(all_15_1, v0) = 0) |
% 7.14/1.80 | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 7.14/1.80 | (cp(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 7.14/1.80 | rs(all_15_0, v0) = v2)) & ! [v0: $i] : ( ~ (rs(all_15_0, v0) = 0)
% 7.14/1.80 | | ~ $i(v0) | cp(v0) = 0)
% 7.14/1.80 |
% 7.14/1.80 | ALPHA: (14) implies:
% 7.14/1.80 | (15) $i(all_15_1)
% 7.14/1.80 | (16) $i(all_15_0)
% 7.14/1.80 | (17) rinvR(all_15_1, all_15_0) = 0
% 7.14/1.80 | (18) rr(i2003_11_14_17_19_13721, all_15_1) = 0
% 7.14/1.80 | (19) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cp(v0) = v1) | ~ $i(v0) |
% 7.14/1.80 | ? [v2: int] : ( ~ (v2 = 0) & rs(all_15_0, v0) = v2))
% 7.14/1.81 | (20) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rinvR(all_15_1, v1) = 0) |
% 7.14/1.81 | ~ (rinvR(all_15_1, v0) = 0) | ~ $i(v1) | ~ $i(v0))
% 7.14/1.81 |
% 7.14/1.81 | GROUND_INST: instantiating (19) with all_13_2, all_13_0, simplifying with
% 7.14/1.81 | (11), (12) gives:
% 7.14/1.81 | (21) all_13_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & rs(all_15_0, all_13_2) =
% 7.14/1.81 | v0)
% 7.14/1.81 |
% 7.14/1.81 | GROUND_INST: instantiating (3) with all_15_1, i2003_11_14_17_19_13721,
% 7.14/1.81 | simplifying with (4), (15), (18) gives:
% 7.14/1.81 | (22) rinvR(all_15_1, i2003_11_14_17_19_13721) = 0
% 7.14/1.81 |
% 7.14/1.81 | BETA: splitting (21) gives:
% 7.14/1.81 |
% 7.14/1.81 | Case 1:
% 7.14/1.81 | |
% 7.14/1.81 | | (23) all_13_0 = 0
% 7.14/1.81 | |
% 7.14/1.81 | | REDUCE: (10), (23) imply:
% 7.14/1.81 | | (24) $false
% 7.14/1.81 | |
% 7.14/1.81 | | CLOSE: (24) is inconsistent.
% 7.14/1.81 | |
% 7.14/1.81 | Case 2:
% 7.14/1.81 | |
% 7.14/1.81 | | (25) ? [v0: int] : ( ~ (v0 = 0) & rs(all_15_0, all_13_2) = v0)
% 7.14/1.81 | |
% 7.14/1.81 | | DELTA: instantiating (25) with fresh symbol all_28_0 gives:
% 7.14/1.81 | | (26) ~ (all_28_0 = 0) & rs(all_15_0, all_13_2) = all_28_0
% 7.14/1.81 | |
% 7.14/1.81 | | ALPHA: (26) implies:
% 7.14/1.81 | | (27) ~ (all_28_0 = 0)
% 7.14/1.81 | | (28) rs(all_15_0, all_13_2) = all_28_0
% 7.14/1.81 | |
% 7.14/1.81 | | GROUND_INST: instantiating (20) with all_15_0, i2003_11_14_17_19_13721,
% 7.14/1.81 | | simplifying with (4), (16), (17), (22) gives:
% 7.14/1.81 | | (29) all_15_0 = i2003_11_14_17_19_13721
% 7.14/1.81 | |
% 7.14/1.81 | | REDUCE: (28), (29) imply:
% 7.14/1.81 | | (30) rs(i2003_11_14_17_19_13721, all_13_2) = all_28_0
% 7.14/1.81 | |
% 7.14/1.81 | | GROUND_INST: instantiating (6) with 0, all_28_0, all_13_2,
% 7.14/1.81 | | i2003_11_14_17_19_13721, simplifying with (13), (30) gives:
% 7.14/1.81 | | (31) all_28_0 = 0
% 7.14/1.81 | |
% 7.14/1.81 | | REDUCE: (27), (31) imply:
% 7.14/1.81 | | (32) $false
% 7.14/1.81 | |
% 7.14/1.81 | | CLOSE: (32) is inconsistent.
% 7.14/1.81 | |
% 7.14/1.81 | End of split
% 7.14/1.81 |
% 7.14/1.81 End of proof
% 7.14/1.81 % SZS output end Proof for theBenchmark
% 7.14/1.81
% 7.14/1.81 1167ms
%------------------------------------------------------------------------------