TSTP Solution File: KRS098+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS098+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 : n031.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 05:51:14 EDT 2023
% Result : Unsatisfiable 6.80s 1.76s
% Output : Proof 9.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS098+1 : TPTP v8.1.2. Released v3.1.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n031.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 02:51:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.03/1.12 Prover 4: Preprocessing ...
% 3.03/1.12 Prover 1: Preprocessing ...
% 3.15/1.15 Prover 6: Preprocessing ...
% 3.15/1.15 Prover 0: Preprocessing ...
% 3.15/1.15 Prover 3: Preprocessing ...
% 3.15/1.15 Prover 2: Preprocessing ...
% 3.15/1.16 Prover 5: Preprocessing ...
% 5.61/1.53 Prover 5: Proving ...
% 5.61/1.53 Prover 2: Proving ...
% 6.36/1.61 Prover 1: Constructing countermodel ...
% 6.36/1.61 Prover 3: Constructing countermodel ...
% 6.36/1.65 Prover 6: Proving ...
% 6.80/1.75 Prover 2: proved (1145ms)
% 6.80/1.76
% 6.80/1.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.80/1.76
% 6.80/1.76 Prover 6: stopped
% 6.80/1.76 Prover 5: stopped
% 7.55/1.77 Prover 3: stopped
% 7.55/1.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.55/1.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.55/1.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.55/1.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.04/1.84 Prover 4: Constructing countermodel ...
% 8.04/1.85 Prover 0: Proving ...
% 8.04/1.85 Prover 0: stopped
% 8.04/1.86 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.04/1.86 Prover 7: Preprocessing ...
% 8.04/1.87 Prover 8: Preprocessing ...
% 8.04/1.90 Prover 1: Found proof (size 47)
% 8.04/1.90 Prover 1: proved (1293ms)
% 8.04/1.90 Prover 7: stopped
% 8.04/1.90 Prover 11: Preprocessing ...
% 8.04/1.90 Prover 4: stopped
% 8.04/1.91 Prover 10: Preprocessing ...
% 8.04/1.93 Prover 10: stopped
% 8.04/1.95 Prover 13: Preprocessing ...
% 8.04/1.96 Prover 11: stopped
% 8.04/1.97 Prover 13: stopped
% 8.68/2.00 Prover 8: Warning: ignoring some quantifiers
% 8.68/2.01 Prover 8: Constructing countermodel ...
% 8.68/2.02 Prover 8: stopped
% 8.68/2.02
% 8.68/2.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.68/2.02
% 8.68/2.04 % SZS output start Proof for theBenchmark
% 8.68/2.04 Assumptions after simplification:
% 8.68/2.04 ---------------------------------
% 8.68/2.04
% 8.68/2.04 (axiom_10)
% 9.38/2.07 ! [v0: $i] : ! [v1: $i] : ( ~ (rt1(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 9.38/2.07 rtt(v0, v1) = 0)
% 9.38/2.07
% 9.38/2.07 (axiom_11)
% 9.38/2.07 ! [v0: $i] : ! [v1: $i] : ( ~ (rt2(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 9.38/2.08 rtt(v0, v1) = 0)
% 9.38/2.08
% 9.38/2.08 (axiom_12)
% 9.38/2.08 ! [v0: $i] : ! [v1: $i] : ( ~ (rr3(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 9.38/2.08 rr(v0, v1) = 0)
% 9.38/2.08
% 9.38/2.08 (axiom_13)
% 9.38/2.08 ! [v0: $i] : ! [v1: $i] : ( ~ (rt3(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 9.38/2.08 rtt(v0, v1) = 0)
% 9.38/2.08
% 9.38/2.08 (axiom_2)
% 9.38/2.09 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cUnsatisfiable(v0) = v1) | ~
% 9.38/2.09 $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & rr(v0, v3) = 0 & rr(v0,
% 9.38/2.09 v2) = 0 & $i(v3) & $i(v2)) | ! [v2: $i] : ( ~ (rr3(v0, v2) = 0) | ~
% 9.38/2.09 $i(v2) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & rtt(v2, v4) = 0 &
% 9.38/2.09 rtt(v2, v3) = 0 & $i(v4) & $i(v3)) | ! [v3: $i] : ( ~ (ce(v3) = 0) | ~
% 9.38/2.09 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & rt3(v2, v3) = v4))) | ! [v2: $i]
% 9.38/2.09 : ( ~ (rr2(v0, v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 =
% 9.38/2.09 v3) & rtt(v2, v4) = 0 & rtt(v2, v3) = 0 & $i(v4) & $i(v3)) | ! [v3:
% 9.38/2.09 $i] : ( ~ (rt2(v2, v3) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) &
% 9.38/2.09 cd(v3) = v4))) | ! [v2: $i] : ( ~ (rr1(v0, v2) = 0) | ~ $i(v2) | ?
% 9.38/2.09 [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & rtt(v2, v4) = 0 & rtt(v2, v3) = 0
% 9.38/2.09 & $i(v4) & $i(v3)) | ! [v3: $i] : ( ~ (rt1(v2, v3) = 0) | ~ $i(v3) |
% 9.38/2.09 ? [v4: int] : ( ~ (v4 = 0) & cc(v3) = v4)))) & ! [v0: $i] : ( ~
% 9.38/2.09 (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: $i] : (v2 = v1
% 9.38/2.09 | ~ (rr(v0, v2) = 0) | ~ (rr(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1)) &
% 9.38/2.09 ? [v1: $i] : (rr3(v0, v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: $i] : (v3 =
% 9.38/2.09 v2 | ~ (rtt(v1, v3) = 0) | ~ (rtt(v1, v2) = 0) | ~ $i(v3) | ~
% 9.38/2.09 $i(v2)) & ? [v2: $i] : (rt3(v1, v2) = 0 & ce(v2) = 0 & $i(v2))) & ?
% 9.38/2.09 [v1: $i] : (rr2(v0, v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: $i] : (v3 =
% 9.38/2.09 v2 | ~ (rtt(v1, v3) = 0) | ~ (rtt(v1, v2) = 0) | ~ $i(v3) | ~
% 9.38/2.09 $i(v2)) & ? [v2: $i] : (rt2(v1, v2) = 0 & cd(v2) = 0 & $i(v2))) & ?
% 9.38/2.09 [v1: $i] : (rr1(v0, v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: $i] : (v3 =
% 9.38/2.09 v2 | ~ (rtt(v1, v3) = 0) | ~ (rtt(v1, v2) = 0) | ~ $i(v3) | ~
% 9.38/2.09 $i(v2)) & ? [v2: $i] : (rt1(v1, v2) = 0 & cc(v2) = 0 & $i(v2)))))
% 9.38/2.09
% 9.38/2.09 (axiom_4)
% 9.38/2.09 cUnsatisfiable(i2003_11_14_17_20_25524) = 0 & $i(i2003_11_14_17_20_25524)
% 9.38/2.09
% 9.38/2.09 (axiom_5)
% 9.38/2.09 ! [v0: $i] : ( ~ (cd(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 9.38/2.09 cc(v0) = v1))
% 9.38/2.09
% 9.38/2.09 (axiom_6)
% 9.38/2.09 ! [v0: $i] : ( ~ (ce(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 9.38/2.09 cc(v0) = v1))
% 9.38/2.09
% 9.38/2.09 (axiom_8)
% 9.38/2.10 ! [v0: $i] : ! [v1: $i] : ( ~ (rr1(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 9.38/2.10 rr(v0, v1) = 0)
% 9.38/2.10
% 9.38/2.10 (axiom_9)
% 9.38/2.10 ! [v0: $i] : ! [v1: $i] : ( ~ (rr2(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 9.38/2.10 rr(v0, v1) = 0)
% 9.38/2.10
% 9.38/2.10 (function-axioms)
% 9.38/2.10 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.38/2.10 [v3: $i] : (v1 = v0 | ~ (rtt(v3, v2) = v1) | ~ (rtt(v3, v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.38/2.10 : (v1 = v0 | ~ (rt3(v3, v2) = v1) | ~ (rt3(v3, v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.38/2.10 : (v1 = v0 | ~ (rt2(v3, v2) = v1) | ~ (rt2(v3, v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.38/2.10 : (v1 = v0 | ~ (rt1(v3, v2) = v1) | ~ (rt1(v3, v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.38/2.10 : (v1 = v0 | ~ (rr3(v3, v2) = v1) | ~ (rr3(v3, v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.38/2.10 : (v1 = v0 | ~ (rr2(v3, v2) = v1) | ~ (rr2(v3, v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.38/2.10 : (v1 = v0 | ~ (rr1(v3, v2) = v1) | ~ (rr1(v3, v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.38/2.10 : (v1 = v0 | ~ (rr(v3, v2) = v1) | ~ (rr(v3, v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.38/2.10 ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.38/2.10 ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.38/2.10 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.38/2.10 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.38/2.10 ~ (ce(v2) = v1) | ~ (ce(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.38/2.10 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cd(v2) = v1) | ~ (cd(v2)
% 9.38/2.10 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.38/2.10 $i] : (v1 = v0 | ~ (cc(v2) = v1) | ~ (cc(v2) = v0)) & ! [v0:
% 9.38/2.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.38/2.10 ~ (ca(v2) = v1) | ~ (ca(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.38/2.10 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cUnsatisfiable(v2) = v1) |
% 9.38/2.10 ~ (cUnsatisfiable(v2) = v0))
% 9.38/2.10
% 9.38/2.10 Further assumptions not needed in the proof:
% 9.38/2.10 --------------------------------------------
% 9.38/2.10 axiom_0, axiom_1, axiom_3, axiom_7, cUnsatisfiable_substitution_1,
% 9.38/2.10 ca_substitution_1, cc_substitution_1, cd_substitution_1, ce_substitution_1,
% 9.38/2.10 cowlNothing_substitution_1, cowlThing_substitution_1, rr1_substitution_1,
% 9.38/2.10 rr1_substitution_2, rr2_substitution_1, rr2_substitution_2, rr3_substitution_1,
% 9.38/2.10 rr3_substitution_2, rr_substitution_1, rr_substitution_2, rt1_substitution_1,
% 9.38/2.10 rt1_substitution_2, rt2_substitution_1, rt2_substitution_2, rt3_substitution_1,
% 9.38/2.10 rt3_substitution_2, rtt_substitution_1, rtt_substitution_2,
% 9.38/2.10 xsd_integer_substitution_1, xsd_string_substitution_1
% 9.38/2.10
% 9.38/2.10 Those formulas are unsatisfiable:
% 9.38/2.10 ---------------------------------
% 9.38/2.10
% 9.38/2.10 Begin of proof
% 9.38/2.10 |
% 9.38/2.10 | ALPHA: (axiom_2) implies:
% 9.38/2.11 | (1) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] :
% 9.38/2.11 | ! [v2: $i] : (v2 = v1 | ~ (rr(v0, v2) = 0) | ~ (rr(v0, v1) = 0)
% 9.38/2.11 | | ~ $i(v2) | ~ $i(v1)) & ? [v1: $i] : (rr3(v0, v1) = 0 &
% 9.38/2.11 | $i(v1) & ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (rtt(v1, v3) =
% 9.38/2.11 | 0) | ~ (rtt(v1, v2) = 0) | ~ $i(v3) | ~ $i(v2)) & ? [v2:
% 9.38/2.11 | $i] : (rt3(v1, v2) = 0 & ce(v2) = 0 & $i(v2))) & ? [v1: $i] :
% 9.38/2.11 | (rr2(v0, v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: $i] : (v3 = v2 |
% 9.38/2.11 | ~ (rtt(v1, v3) = 0) | ~ (rtt(v1, v2) = 0) | ~ $i(v3) | ~
% 9.38/2.11 | $i(v2)) & ? [v2: $i] : (rt2(v1, v2) = 0 & cd(v2) = 0 &
% 9.38/2.11 | $i(v2))) & ? [v1: $i] : (rr1(v0, v1) = 0 & $i(v1) & ! [v2:
% 9.38/2.11 | $i] : ! [v3: $i] : (v3 = v2 | ~ (rtt(v1, v3) = 0) | ~
% 9.38/2.11 | (rtt(v1, v2) = 0) | ~ $i(v3) | ~ $i(v2)) & ? [v2: $i] :
% 9.38/2.11 | (rt1(v1, v2) = 0 & cc(v2) = 0 & $i(v2)))))
% 9.38/2.11 |
% 9.38/2.11 | ALPHA: (axiom_4) implies:
% 9.38/2.11 | (2) $i(i2003_11_14_17_20_25524)
% 9.38/2.11 | (3) cUnsatisfiable(i2003_11_14_17_20_25524) = 0
% 9.38/2.11 |
% 9.38/2.11 | ALPHA: (function-axioms) implies:
% 9.38/2.11 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.38/2.11 | (v1 = v0 | ~ (cc(v2) = v1) | ~ (cc(v2) = v0))
% 9.38/2.11 |
% 9.38/2.11 | GROUND_INST: instantiating (1) with i2003_11_14_17_20_25524, simplifying with
% 9.38/2.11 | (2), (3) gives:
% 9.38/2.12 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rr(i2003_11_14_17_20_25524,
% 9.38/2.12 | v1) = 0) | ~ (rr(i2003_11_14_17_20_25524, v0) = 0) | ~ $i(v1) |
% 9.38/2.12 | ~ $i(v0)) & ? [v0: $i] : (rr3(i2003_11_14_17_20_25524, v0) = 0 &
% 9.38/2.12 | $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (rtt(v0, v2) = 0)
% 9.38/2.12 | | ~ (rtt(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1)) & ? [v1: $i] :
% 9.38/2.12 | (rt3(v0, v1) = 0 & ce(v1) = 0 & $i(v1))) & ? [v0: $i] :
% 9.38/2.12 | (rr2(i2003_11_14_17_20_25524, v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2:
% 9.38/2.12 | $i] : (v2 = v1 | ~ (rtt(v0, v2) = 0) | ~ (rtt(v0, v1) = 0) | ~
% 9.38/2.12 | $i(v2) | ~ $i(v1)) & ? [v1: $i] : (rt2(v0, v1) = 0 & cd(v1) = 0 &
% 9.38/2.12 | $i(v1))) & ? [v0: $i] : (rr1(i2003_11_14_17_20_25524, v0) = 0 &
% 9.38/2.12 | $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (rtt(v0, v2) = 0)
% 9.38/2.12 | | ~ (rtt(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1)) & ? [v1: $i] :
% 9.38/2.12 | (rt1(v0, v1) = 0 & cc(v1) = 0 & $i(v1)))
% 9.38/2.12 |
% 9.38/2.12 | ALPHA: (5) implies:
% 9.38/2.12 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rr(i2003_11_14_17_20_25524,
% 9.38/2.12 | v1) = 0) | ~ (rr(i2003_11_14_17_20_25524, v0) = 0) | ~ $i(v1) |
% 9.38/2.12 | ~ $i(v0))
% 9.38/2.12 | (7) ? [v0: $i] : (rr1(i2003_11_14_17_20_25524, v0) = 0 & $i(v0) & ! [v1:
% 9.38/2.12 | $i] : ! [v2: $i] : (v2 = v1 | ~ (rtt(v0, v2) = 0) | ~ (rtt(v0,
% 9.38/2.12 | v1) = 0) | ~ $i(v2) | ~ $i(v1)) & ? [v1: $i] : (rt1(v0, v1)
% 9.38/2.12 | = 0 & cc(v1) = 0 & $i(v1)))
% 9.38/2.12 | (8) ? [v0: $i] : (rr2(i2003_11_14_17_20_25524, v0) = 0 & $i(v0) & ! [v1:
% 9.38/2.12 | $i] : ! [v2: $i] : (v2 = v1 | ~ (rtt(v0, v2) = 0) | ~ (rtt(v0,
% 9.38/2.12 | v1) = 0) | ~ $i(v2) | ~ $i(v1)) & ? [v1: $i] : (rt2(v0, v1)
% 9.38/2.12 | = 0 & cd(v1) = 0 & $i(v1)))
% 9.38/2.12 | (9) ? [v0: $i] : (rr3(i2003_11_14_17_20_25524, v0) = 0 & $i(v0) & ! [v1:
% 9.38/2.12 | $i] : ! [v2: $i] : (v2 = v1 | ~ (rtt(v0, v2) = 0) | ~ (rtt(v0,
% 9.38/2.12 | v1) = 0) | ~ $i(v2) | ~ $i(v1)) & ? [v1: $i] : (rt3(v0, v1)
% 9.38/2.12 | = 0 & ce(v1) = 0 & $i(v1)))
% 9.38/2.12 |
% 9.38/2.12 | DELTA: instantiating (8) with fresh symbol all_23_0 gives:
% 9.38/2.12 | (10) rr2(i2003_11_14_17_20_25524, all_23_0) = 0 & $i(all_23_0) & ! [v0:
% 9.38/2.12 | $i] : ! [v1: $i] : (v1 = v0 | ~ (rtt(all_23_0, v1) = 0) | ~
% 9.38/2.12 | (rtt(all_23_0, v0) = 0) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] :
% 9.38/2.12 | (rt2(all_23_0, v0) = 0 & cd(v0) = 0 & $i(v0))
% 9.38/2.12 |
% 9.38/2.12 | ALPHA: (10) implies:
% 9.38/2.12 | (11) $i(all_23_0)
% 9.38/2.12 | (12) rr2(i2003_11_14_17_20_25524, all_23_0) = 0
% 9.38/2.12 | (13) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rtt(all_23_0, v1) = 0) | ~
% 9.38/2.12 | (rtt(all_23_0, v0) = 0) | ~ $i(v1) | ~ $i(v0))
% 9.38/2.12 | (14) ? [v0: $i] : (rt2(all_23_0, v0) = 0 & cd(v0) = 0 & $i(v0))
% 9.38/2.12 |
% 9.38/2.12 | DELTA: instantiating (14) with fresh symbol all_26_0 gives:
% 9.38/2.12 | (15) rt2(all_23_0, all_26_0) = 0 & cd(all_26_0) = 0 & $i(all_26_0)
% 9.38/2.12 |
% 9.38/2.12 | ALPHA: (15) implies:
% 9.38/2.12 | (16) $i(all_26_0)
% 9.38/2.12 | (17) cd(all_26_0) = 0
% 9.38/2.12 | (18) rt2(all_23_0, all_26_0) = 0
% 9.38/2.12 |
% 9.38/2.12 | DELTA: instantiating (7) with fresh symbol all_28_0 gives:
% 9.38/2.13 | (19) rr1(i2003_11_14_17_20_25524, all_28_0) = 0 & $i(all_28_0) & ! [v0:
% 9.38/2.13 | $i] : ! [v1: $i] : (v1 = v0 | ~ (rtt(all_28_0, v1) = 0) | ~
% 9.38/2.13 | (rtt(all_28_0, v0) = 0) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] :
% 9.38/2.13 | (rt1(all_28_0, v0) = 0 & cc(v0) = 0 & $i(v0))
% 9.38/2.13 |
% 9.38/2.13 | ALPHA: (19) implies:
% 9.38/2.13 | (20) $i(all_28_0)
% 9.38/2.13 | (21) rr1(i2003_11_14_17_20_25524, all_28_0) = 0
% 9.38/2.13 | (22) ? [v0: $i] : (rt1(all_28_0, v0) = 0 & cc(v0) = 0 & $i(v0))
% 9.38/2.13 |
% 9.38/2.13 | DELTA: instantiating (9) with fresh symbol all_31_0 gives:
% 9.38/2.13 | (23) rr3(i2003_11_14_17_20_25524, all_31_0) = 0 & $i(all_31_0) & ! [v0:
% 9.38/2.13 | $i] : ! [v1: $i] : (v1 = v0 | ~ (rtt(all_31_0, v1) = 0) | ~
% 9.38/2.13 | (rtt(all_31_0, v0) = 0) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] :
% 9.38/2.13 | (rt3(all_31_0, v0) = 0 & ce(v0) = 0 & $i(v0))
% 9.38/2.13 |
% 9.38/2.13 | ALPHA: (23) implies:
% 9.38/2.13 | (24) $i(all_31_0)
% 9.38/2.13 | (25) rr3(i2003_11_14_17_20_25524, all_31_0) = 0
% 9.38/2.13 | (26) ? [v0: $i] : (rt3(all_31_0, v0) = 0 & ce(v0) = 0 & $i(v0))
% 9.38/2.13 |
% 9.38/2.13 | DELTA: instantiating (22) with fresh symbol all_34_0 gives:
% 9.38/2.13 | (27) rt1(all_28_0, all_34_0) = 0 & cc(all_34_0) = 0 & $i(all_34_0)
% 9.38/2.13 |
% 9.38/2.13 | ALPHA: (27) implies:
% 9.38/2.13 | (28) $i(all_34_0)
% 9.38/2.13 | (29) cc(all_34_0) = 0
% 9.38/2.13 | (30) rt1(all_28_0, all_34_0) = 0
% 9.38/2.13 |
% 9.38/2.13 | DELTA: instantiating (26) with fresh symbol all_36_0 gives:
% 9.38/2.13 | (31) rt3(all_31_0, all_36_0) = 0 & ce(all_36_0) = 0 & $i(all_36_0)
% 9.38/2.13 |
% 9.38/2.13 | ALPHA: (31) implies:
% 9.38/2.13 | (32) $i(all_36_0)
% 9.38/2.13 | (33) ce(all_36_0) = 0
% 9.38/2.13 | (34) rt3(all_31_0, all_36_0) = 0
% 9.38/2.13 |
% 9.38/2.13 | GROUND_INST: instantiating (axiom_5) with all_26_0, simplifying with (16),
% 9.38/2.13 | (17) gives:
% 9.38/2.13 | (35) ? [v0: int] : ( ~ (v0 = 0) & cc(all_26_0) = v0)
% 9.38/2.13 |
% 9.38/2.13 | GROUND_INST: instantiating (axiom_6) with all_36_0, simplifying with (32),
% 9.38/2.13 | (33) gives:
% 9.38/2.13 | (36) ? [v0: int] : ( ~ (v0 = 0) & cc(all_36_0) = v0)
% 9.38/2.13 |
% 9.38/2.13 | GROUND_INST: instantiating (axiom_8) with i2003_11_14_17_20_25524, all_28_0,
% 9.38/2.13 | simplifying with (2), (20), (21) gives:
% 9.38/2.13 | (37) rr(i2003_11_14_17_20_25524, all_28_0) = 0
% 9.38/2.13 |
% 9.38/2.13 | GROUND_INST: instantiating (axiom_9) with i2003_11_14_17_20_25524, all_23_0,
% 9.38/2.13 | simplifying with (2), (11), (12) gives:
% 9.38/2.13 | (38) rr(i2003_11_14_17_20_25524, all_23_0) = 0
% 9.38/2.13 |
% 9.38/2.13 | GROUND_INST: instantiating (axiom_12) with i2003_11_14_17_20_25524, all_31_0,
% 9.38/2.13 | simplifying with (2), (24), (25) gives:
% 9.38/2.13 | (39) rr(i2003_11_14_17_20_25524, all_31_0) = 0
% 9.38/2.13 |
% 9.38/2.13 | GROUND_INST: instantiating (axiom_10) with all_28_0, all_34_0, simplifying
% 9.38/2.13 | with (20), (28), (30) gives:
% 9.38/2.13 | (40) rtt(all_28_0, all_34_0) = 0
% 9.38/2.13 |
% 9.38/2.13 | GROUND_INST: instantiating (axiom_11) with all_23_0, all_26_0, simplifying
% 9.38/2.13 | with (11), (16), (18) gives:
% 9.38/2.13 | (41) rtt(all_23_0, all_26_0) = 0
% 9.38/2.13 |
% 9.38/2.13 | GROUND_INST: instantiating (axiom_13) with all_31_0, all_36_0, simplifying
% 9.38/2.13 | with (24), (32), (34) gives:
% 9.38/2.13 | (42) rtt(all_31_0, all_36_0) = 0
% 9.38/2.13 |
% 9.38/2.13 | DELTA: instantiating (36) with fresh symbol all_44_0 gives:
% 9.38/2.13 | (43) ~ (all_44_0 = 0) & cc(all_36_0) = all_44_0
% 9.38/2.13 |
% 9.38/2.13 | ALPHA: (43) implies:
% 9.38/2.14 | (44) ~ (all_44_0 = 0)
% 9.38/2.14 | (45) cc(all_36_0) = all_44_0
% 9.38/2.14 |
% 9.38/2.14 | DELTA: instantiating (35) with fresh symbol all_48_0 gives:
% 9.38/2.14 | (46) ~ (all_48_0 = 0) & cc(all_26_0) = all_48_0
% 9.38/2.14 |
% 9.38/2.14 | ALPHA: (46) implies:
% 9.38/2.14 | (47) cc(all_26_0) = all_48_0
% 9.38/2.14 |
% 9.38/2.14 | GROUND_INST: instantiating (6) with all_28_0, all_31_0, simplifying with (20),
% 9.38/2.14 | (24), (37), (39) gives:
% 9.38/2.14 | (48) all_31_0 = all_28_0
% 9.38/2.14 |
% 9.38/2.14 | GROUND_INST: instantiating (6) with all_23_0, all_31_0, simplifying with (11),
% 9.38/2.14 | (24), (38), (39) gives:
% 9.38/2.14 | (49) all_31_0 = all_23_0
% 9.38/2.14 |
% 9.38/2.14 | COMBINE_EQS: (48), (49) imply:
% 9.38/2.14 | (50) all_28_0 = all_23_0
% 9.38/2.14 |
% 9.38/2.14 | SIMP: (50) implies:
% 9.38/2.14 | (51) all_28_0 = all_23_0
% 9.38/2.14 |
% 9.38/2.14 | REDUCE: (42), (49) imply:
% 9.38/2.14 | (52) rtt(all_23_0, all_36_0) = 0
% 9.38/2.14 |
% 9.38/2.14 | REDUCE: (40), (51) imply:
% 9.38/2.14 | (53) rtt(all_23_0, all_34_0) = 0
% 9.38/2.14 |
% 9.38/2.14 | GROUND_INST: instantiating (13) with all_26_0, all_36_0, simplifying with
% 9.38/2.14 | (16), (32), (41), (52) gives:
% 9.38/2.14 | (54) all_36_0 = all_26_0
% 9.38/2.14 |
% 9.38/2.14 | GROUND_INST: instantiating (13) with all_34_0, all_36_0, simplifying with
% 9.38/2.14 | (28), (32), (52), (53) gives:
% 9.38/2.14 | (55) all_36_0 = all_34_0
% 9.38/2.14 |
% 9.38/2.14 | COMBINE_EQS: (54), (55) imply:
% 9.38/2.14 | (56) all_34_0 = all_26_0
% 9.38/2.14 |
% 9.38/2.14 | REDUCE: (45), (54) imply:
% 9.38/2.14 | (57) cc(all_26_0) = all_44_0
% 9.38/2.14 |
% 9.38/2.14 | REDUCE: (29), (56) imply:
% 9.38/2.14 | (58) cc(all_26_0) = 0
% 9.38/2.14 |
% 9.38/2.14 | GROUND_INST: instantiating (4) with all_48_0, 0, all_26_0, simplifying with
% 9.38/2.14 | (47), (58) gives:
% 9.38/2.14 | (59) all_48_0 = 0
% 9.38/2.14 |
% 9.38/2.14 | GROUND_INST: instantiating (4) with all_48_0, all_44_0, all_26_0, simplifying
% 9.38/2.14 | with (47), (57) gives:
% 9.38/2.14 | (60) all_48_0 = all_44_0
% 9.38/2.14 |
% 9.38/2.14 | COMBINE_EQS: (59), (60) imply:
% 9.38/2.14 | (61) all_44_0 = 0
% 9.38/2.14 |
% 9.38/2.14 | SIMP: (61) implies:
% 9.38/2.14 | (62) all_44_0 = 0
% 9.38/2.14 |
% 9.38/2.14 | REDUCE: (44), (62) imply:
% 9.38/2.14 | (63) $false
% 9.38/2.14 |
% 9.38/2.14 | CLOSE: (63) is inconsistent.
% 9.38/2.14 |
% 9.38/2.14 End of proof
% 9.38/2.14 % SZS output end Proof for theBenchmark
% 9.38/2.14
% 9.38/2.14 1555ms
%------------------------------------------------------------------------------