TSTP Solution File: SET794+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET794+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n013.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 15:26:28 EDT 2023
% Result : Theorem 6.95s 1.69s
% Output : Proof 9.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET794+4 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n013.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 : Sat Aug 26 16:33:47 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.58 ________ _____
% 0.19/0.58 ___ __ \_________(_)________________________________
% 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58 (2023-06-19)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2023
% 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58 Amanda Stjerna.
% 0.19/0.58 Free software under BSD-3-Clause.
% 0.19/0.58
% 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58
% 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 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
% 2.73/1.08 Prover 1: Preprocessing ...
% 2.73/1.08 Prover 4: Preprocessing ...
% 2.73/1.12 Prover 5: Preprocessing ...
% 2.73/1.12 Prover 6: Preprocessing ...
% 2.73/1.12 Prover 3: Preprocessing ...
% 2.73/1.12 Prover 2: Preprocessing ...
% 2.73/1.12 Prover 0: Preprocessing ...
% 4.84/1.41 Prover 5: Proving ...
% 4.84/1.42 Prover 2: Proving ...
% 5.72/1.54 Prover 6: Proving ...
% 6.34/1.60 Prover 3: Constructing countermodel ...
% 6.34/1.61 Prover 1: Constructing countermodel ...
% 6.95/1.68 Prover 3: proved (1079ms)
% 6.95/1.69
% 6.95/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.95/1.69
% 6.95/1.69 Prover 4: Constructing countermodel ...
% 6.95/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.95/1.69 Prover 2: stopped
% 6.95/1.69 Prover 6: stopped
% 6.95/1.71 Prover 5: stopped
% 6.95/1.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.95/1.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.95/1.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.42/1.74 Prover 0: Proving ...
% 7.42/1.75 Prover 10: Preprocessing ...
% 7.42/1.75 Prover 11: Preprocessing ...
% 7.42/1.75 Prover 0: stopped
% 7.42/1.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.74/1.76 Prover 8: Preprocessing ...
% 7.74/1.79 Prover 7: Preprocessing ...
% 7.74/1.81 Prover 13: Preprocessing ...
% 7.74/1.83 Prover 10: Warning: ignoring some quantifiers
% 7.74/1.84 Prover 10: Constructing countermodel ...
% 8.35/1.85 Prover 7: Warning: ignoring some quantifiers
% 8.35/1.86 Prover 7: Constructing countermodel ...
% 8.35/1.87 Prover 1: Found proof (size 50)
% 8.35/1.87 Prover 1: proved (1271ms)
% 8.35/1.87 Prover 7: stopped
% 8.35/1.88 Prover 11: stopped
% 8.35/1.88 Prover 10: stopped
% 8.35/1.88 Prover 4: stopped
% 8.35/1.88 Prover 13: Warning: ignoring some quantifiers
% 8.35/1.89 Prover 13: Constructing countermodel ...
% 8.60/1.89 Prover 13: stopped
% 8.60/1.92 Prover 8: Warning: ignoring some quantifiers
% 8.60/1.92 Prover 8: Constructing countermodel ...
% 8.60/1.93 Prover 8: stopped
% 8.60/1.93
% 8.60/1.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.60/1.93
% 8.83/1.94 % SZS output start Proof for theBenchmark
% 8.88/1.94 Assumptions after simplification:
% 8.88/1.94 ---------------------------------
% 8.88/1.94
% 8.88/1.94 (least)
% 8.88/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.88/1.97 (least(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 8.88/1.97 ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4, v1) = 0 &
% 8.88/1.97 $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0:
% 8.88/1.97 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (least(v2, v0, v1) = 0) | ~ $i(v2) |
% 8.88/1.97 ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & ! [v3: $i] : ! [v4: int] :
% 8.88/1.97 (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5
% 8.88/1.97 = 0) & member(v3, v1) = v5))))
% 8.88/1.97
% 8.88/1.97 (min)
% 8.88/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (min(v2,
% 8.88/1.97 v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ( ~
% 8.88/1.97 (v4 = v2) & apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & $i(v4)) | ? [v4:
% 8.88/1.97 int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0: $i] : ! [v1: $i] :
% 8.88/1.97 ! [v2: $i] : ( ~ (min(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 8.88/1.97 (member(v2, v1) = 0 & ! [v3: $i] : (v3 = v2 | ~ (apply(v0, v3, v2) = 0) |
% 8.88/1.97 ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))))
% 8.88/1.97
% 8.88/1.97 (thIV6)
% 8.88/1.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 8.88/1.98 min(v2, v0, v1) = 0 & least(v2, v0, v1) = v3 & total_order(v0, v1) = 0 &
% 8.88/1.98 $i(v2) & $i(v1) & $i(v0))
% 8.88/1.98
% 8.88/1.98 (total_order)
% 8.88/1.98 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (total_order(v0, v1) =
% 8.88/1.98 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] :
% 8.88/1.98 ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & apply(v0, v4, v3) = v6 &
% 8.88/1.98 apply(v0, v3, v4) = v5 & member(v4, v1) = 0 & member(v3, v1) = 0 & $i(v4)
% 8.88/1.98 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & order(v0, v1) = v3)) & ! [v0:
% 8.88/1.98 $i] : ! [v1: $i] : ( ~ (total_order(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.88/1.98 (order(v0, v1) = 0 & ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 8.88/1.98 (apply(v0, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ?
% 8.88/1.98 [v6: any] : ? [v7: any] : (apply(v0, v3, v2) = v7 & member(v3, v1) = v6
% 8.88/1.98 & member(v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0)))))
% 8.88/1.98
% 8.88/1.98 (function-axioms)
% 8.88/1.99 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.88/1.99 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5,
% 8.88/1.99 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & !
% 8.88/1.99 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.88/1.99 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4,
% 8.88/1.99 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0:
% 8.88/1.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.88/1.99 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) =
% 8.88/1.99 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.88/1.99 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~
% 8.88/1.99 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.88/1.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 8.88/1.99 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0:
% 8.88/1.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.88/1.99 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4,
% 8.88/1.99 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 8.88/1.99 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3,
% 8.88/1.99 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0:
% 8.88/1.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.88/1.99 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~
% 8.88/1.99 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.88/1.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 8.88/1.99 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0:
% 8.88/1.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.88/1.99 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) &
% 8.88/1.99 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.88/1.99 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & !
% 8.88/1.99 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.88/1.99 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 8.88/1.99
% 8.88/1.99 Further assumptions not needed in the proof:
% 8.88/1.99 --------------------------------------------
% 8.88/1.99 greatest, greatest_lower_bound, least_upper_bound, lower_bound, max, order,
% 8.88/1.99 upper_bound
% 8.88/1.99
% 8.88/1.99 Those formulas are unsatisfiable:
% 8.88/1.99 ---------------------------------
% 8.88/1.99
% 8.88/1.99 Begin of proof
% 8.88/1.99 |
% 8.88/1.99 | ALPHA: (total_order) implies:
% 8.88/1.99 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (total_order(v0, v1) = 0) | ~ $i(v1) |
% 8.88/1.99 | ~ $i(v0) | (order(v0, v1) = 0 & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 8.88/1.99 | int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) | ~
% 8.88/1.99 | $i(v2) | ? [v5: any] : ? [v6: any] : ? [v7: any] : (apply(v0,
% 8.88/1.99 | v3, v2) = v7 & member(v3, v1) = v6 & member(v2, v1) = v5 & (
% 8.88/1.99 | ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0)))))
% 8.88/1.99 |
% 8.88/1.99 | ALPHA: (least) implies:
% 8.88/1.99 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.88/1.99 | (least(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 8.88/1.99 | [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 &
% 8.88/1.99 | member(v4, v1) = 0 & $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) &
% 8.88/1.99 | member(v2, v1) = v4))
% 8.88/1.99 |
% 8.88/1.99 | ALPHA: (min) implies:
% 8.88/2.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (min(v2, v0, v1) = 0) |
% 8.88/2.00 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & ! [v3: $i]
% 8.88/2.00 | : (v3 = v2 | ~ (apply(v0, v3, v2) = 0) | ~ $i(v3) | ? [v4: int]
% 8.88/2.00 | : ( ~ (v4 = 0) & member(v3, v1) = v4))))
% 8.88/2.00 |
% 8.88/2.00 | ALPHA: (function-axioms) implies:
% 8.88/2.00 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.88/2.00 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 8.88/2.00 | = v0))
% 8.88/2.00 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.88/2.00 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 8.88/2.00 | (apply(v4, v3, v2) = v0))
% 8.88/2.00 |
% 8.88/2.00 | DELTA: instantiating (thIV6) with fresh symbols all_13_0, all_13_1, all_13_2,
% 8.88/2.00 | all_13_3 gives:
% 8.88/2.00 | (6) ~ (all_13_0 = 0) & min(all_13_1, all_13_3, all_13_2) = 0 &
% 8.88/2.00 | least(all_13_1, all_13_3, all_13_2) = all_13_0 & total_order(all_13_3,
% 8.88/2.00 | all_13_2) = 0 & $i(all_13_1) & $i(all_13_2) & $i(all_13_3)
% 8.88/2.00 |
% 8.88/2.00 | ALPHA: (6) implies:
% 8.88/2.00 | (7) ~ (all_13_0 = 0)
% 8.88/2.00 | (8) $i(all_13_3)
% 8.88/2.00 | (9) $i(all_13_2)
% 8.88/2.00 | (10) $i(all_13_1)
% 8.88/2.00 | (11) total_order(all_13_3, all_13_2) = 0
% 8.88/2.00 | (12) least(all_13_1, all_13_3, all_13_2) = all_13_0
% 8.88/2.00 | (13) min(all_13_1, all_13_3, all_13_2) = 0
% 8.88/2.00 |
% 8.88/2.00 | GROUND_INST: instantiating (1) with all_13_3, all_13_2, simplifying with (8),
% 8.88/2.00 | (9), (11) gives:
% 8.88/2.00 | (14) order(all_13_3, all_13_2) = 0 & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 8.88/2.00 | int] : (v2 = 0 | ~ (apply(all_13_3, v0, v1) = v2) | ~ $i(v1) | ~
% 8.88/2.00 | $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 8.88/2.00 | (apply(all_13_3, v1, v0) = v5 & member(v1, all_13_2) = v4 &
% 8.88/2.00 | member(v0, all_13_2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 8.88/2.00 |
% 8.88/2.00 | ALPHA: (14) implies:
% 8.88/2.00 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 8.88/2.00 | (apply(all_13_3, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 8.88/2.00 | any] : ? [v4: any] : ? [v5: any] : (apply(all_13_3, v1, v0) = v5
% 8.88/2.00 | & member(v1, all_13_2) = v4 & member(v0, all_13_2) = v3 & ( ~ (v4
% 8.88/2.00 | = 0) | ~ (v3 = 0) | v5 = 0)))
% 8.88/2.00 |
% 8.88/2.00 | GROUND_INST: instantiating (2) with all_13_3, all_13_2, all_13_1, all_13_0,
% 8.88/2.00 | simplifying with (8), (9), (10), (12) gives:
% 8.88/2.00 | (16) all_13_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.88/2.00 | apply(all_13_3, all_13_1, v0) = v1 & member(v0, all_13_2) = 0 &
% 8.88/2.00 | $i(v0)) | ? [v0: int] : ( ~ (v0 = 0) & member(all_13_1, all_13_2) =
% 8.88/2.00 | v0)
% 8.88/2.00 |
% 8.88/2.00 | GROUND_INST: instantiating (3) with all_13_3, all_13_2, all_13_1, simplifying
% 8.88/2.00 | with (8), (9), (10), (13) gives:
% 8.88/2.01 | (17) member(all_13_1, all_13_2) = 0 & ! [v0: any] : (v0 = all_13_1 | ~
% 8.88/2.01 | (apply(all_13_3, v0, all_13_1) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 8.88/2.01 | (v1 = 0) & member(v0, all_13_2) = v1))
% 8.88/2.01 |
% 8.88/2.01 | ALPHA: (17) implies:
% 8.88/2.01 | (18) member(all_13_1, all_13_2) = 0
% 8.88/2.01 | (19) ! [v0: any] : (v0 = all_13_1 | ~ (apply(all_13_3, v0, all_13_1) = 0)
% 9.20/2.01 | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_13_2) =
% 9.20/2.01 | v1))
% 9.20/2.01 |
% 9.20/2.01 | BETA: splitting (16) gives:
% 9.20/2.01 |
% 9.20/2.01 | Case 1:
% 9.20/2.01 | |
% 9.20/2.01 | | (20) all_13_0 = 0
% 9.20/2.01 | |
% 9.20/2.01 | | REDUCE: (7), (20) imply:
% 9.20/2.01 | | (21) $false
% 9.20/2.01 | |
% 9.20/2.01 | | CLOSE: (21) is inconsistent.
% 9.20/2.01 | |
% 9.20/2.01 | Case 2:
% 9.20/2.01 | |
% 9.20/2.01 | | (22) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_13_3,
% 9.20/2.01 | | all_13_1, v0) = v1 & member(v0, all_13_2) = 0 & $i(v0)) | ?
% 9.20/2.01 | | [v0: int] : ( ~ (v0 = 0) & member(all_13_1, all_13_2) = v0)
% 9.20/2.01 | |
% 9.20/2.01 | | BETA: splitting (22) gives:
% 9.20/2.01 | |
% 9.20/2.01 | | Case 1:
% 9.20/2.01 | | |
% 9.20/2.01 | | | (23) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_13_3,
% 9.20/2.01 | | | all_13_1, v0) = v1 & member(v0, all_13_2) = 0 & $i(v0))
% 9.20/2.01 | | |
% 9.20/2.01 | | | DELTA: instantiating (23) with fresh symbols all_30_0, all_30_1 gives:
% 9.20/2.01 | | | (24) ~ (all_30_0 = 0) & apply(all_13_3, all_13_1, all_30_1) = all_30_0
% 9.20/2.01 | | | & member(all_30_1, all_13_2) = 0 & $i(all_30_1)
% 9.20/2.01 | | |
% 9.20/2.01 | | | ALPHA: (24) implies:
% 9.20/2.01 | | | (25) ~ (all_30_0 = 0)
% 9.20/2.01 | | | (26) $i(all_30_1)
% 9.20/2.01 | | | (27) member(all_30_1, all_13_2) = 0
% 9.20/2.01 | | | (28) apply(all_13_3, all_13_1, all_30_1) = all_30_0
% 9.20/2.01 | | |
% 9.20/2.01 | | | GROUND_INST: instantiating (15) with all_13_1, all_30_1, all_30_0,
% 9.20/2.01 | | | simplifying with (10), (26), (28) gives:
% 9.20/2.01 | | | (29) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 9.20/2.01 | | | (apply(all_13_3, all_30_1, all_13_1) = v2 & member(all_30_1,
% 9.20/2.01 | | | all_13_2) = v1 & member(all_13_1, all_13_2) = v0 & ( ~ (v1 =
% 9.20/2.01 | | | 0) | ~ (v0 = 0) | v2 = 0))
% 9.20/2.01 | | |
% 9.20/2.01 | | | BETA: splitting (29) gives:
% 9.20/2.01 | | |
% 9.20/2.01 | | | Case 1:
% 9.20/2.01 | | | |
% 9.20/2.01 | | | | (30) all_30_0 = 0
% 9.20/2.01 | | | |
% 9.20/2.01 | | | | REDUCE: (25), (30) imply:
% 9.20/2.01 | | | | (31) $false
% 9.20/2.01 | | | |
% 9.20/2.01 | | | | CLOSE: (31) is inconsistent.
% 9.20/2.01 | | | |
% 9.20/2.01 | | | Case 2:
% 9.20/2.01 | | | |
% 9.20/2.01 | | | | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_13_3,
% 9.20/2.01 | | | | all_30_1, all_13_1) = v2 & member(all_30_1, all_13_2) = v1 &
% 9.20/2.01 | | | | member(all_13_1, all_13_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 9.20/2.01 | | | | v2 = 0))
% 9.20/2.01 | | | |
% 9.20/2.01 | | | | DELTA: instantiating (32) with fresh symbols all_42_0, all_42_1,
% 9.20/2.01 | | | | all_42_2 gives:
% 9.20/2.01 | | | | (33) apply(all_13_3, all_30_1, all_13_1) = all_42_0 &
% 9.20/2.01 | | | | member(all_30_1, all_13_2) = all_42_1 & member(all_13_1,
% 9.20/2.01 | | | | all_13_2) = all_42_2 & ( ~ (all_42_1 = 0) | ~ (all_42_2 = 0)
% 9.20/2.02 | | | | | all_42_0 = 0)
% 9.20/2.02 | | | |
% 9.20/2.02 | | | | ALPHA: (33) implies:
% 9.20/2.02 | | | | (34) member(all_13_1, all_13_2) = all_42_2
% 9.20/2.02 | | | | (35) member(all_30_1, all_13_2) = all_42_1
% 9.20/2.02 | | | | (36) apply(all_13_3, all_30_1, all_13_1) = all_42_0
% 9.20/2.02 | | | | (37) ~ (all_42_1 = 0) | ~ (all_42_2 = 0) | all_42_0 = 0
% 9.20/2.02 | | | |
% 9.20/2.02 | | | | GROUND_INST: instantiating (4) with 0, all_42_2, all_13_2, all_13_1,
% 9.20/2.02 | | | | simplifying with (18), (34) gives:
% 9.20/2.02 | | | | (38) all_42_2 = 0
% 9.20/2.02 | | | |
% 9.20/2.02 | | | | GROUND_INST: instantiating (4) with 0, all_42_1, all_13_2, all_30_1,
% 9.20/2.02 | | | | simplifying with (27), (35) gives:
% 9.20/2.02 | | | | (39) all_42_1 = 0
% 9.20/2.02 | | | |
% 9.20/2.02 | | | | BETA: splitting (37) gives:
% 9.20/2.02 | | | |
% 9.20/2.02 | | | | Case 1:
% 9.20/2.02 | | | | |
% 9.20/2.02 | | | | | (40) ~ (all_42_1 = 0)
% 9.20/2.02 | | | | |
% 9.20/2.02 | | | | | REDUCE: (39), (40) imply:
% 9.20/2.02 | | | | | (41) $false
% 9.20/2.02 | | | | |
% 9.20/2.02 | | | | | CLOSE: (41) is inconsistent.
% 9.20/2.02 | | | | |
% 9.20/2.02 | | | | Case 2:
% 9.20/2.02 | | | | |
% 9.20/2.02 | | | | | (42) ~ (all_42_2 = 0) | all_42_0 = 0
% 9.20/2.02 | | | | |
% 9.20/2.02 | | | | | BETA: splitting (42) gives:
% 9.20/2.02 | | | | |
% 9.20/2.02 | | | | | Case 1:
% 9.20/2.02 | | | | | |
% 9.20/2.02 | | | | | | (43) ~ (all_42_2 = 0)
% 9.20/2.02 | | | | | |
% 9.20/2.02 | | | | | | REDUCE: (38), (43) imply:
% 9.20/2.02 | | | | | | (44) $false
% 9.20/2.02 | | | | | |
% 9.20/2.02 | | | | | | CLOSE: (44) is inconsistent.
% 9.20/2.02 | | | | | |
% 9.20/2.02 | | | | | Case 2:
% 9.20/2.02 | | | | | |
% 9.20/2.02 | | | | | | (45) all_42_0 = 0
% 9.20/2.02 | | | | | |
% 9.20/2.02 | | | | | | REDUCE: (36), (45) imply:
% 9.20/2.02 | | | | | | (46) apply(all_13_3, all_30_1, all_13_1) = 0
% 9.20/2.02 | | | | | |
% 9.20/2.02 | | | | | | GROUND_INST: instantiating (19) with all_30_1, simplifying with
% 9.20/2.02 | | | | | | (26), (46) gives:
% 9.20/2.02 | | | | | | (47) all_30_1 = all_13_1 | ? [v0: int] : ( ~ (v0 = 0) &
% 9.20/2.02 | | | | | | member(all_30_1, all_13_2) = v0)
% 9.20/2.02 | | | | | |
% 9.20/2.02 | | | | | | BETA: splitting (47) gives:
% 9.20/2.02 | | | | | |
% 9.20/2.02 | | | | | | Case 1:
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | (48) all_30_1 = all_13_1
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | REDUCE: (46), (48) imply:
% 9.20/2.02 | | | | | | | (49) apply(all_13_3, all_13_1, all_13_1) = 0
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | REDUCE: (28), (48) imply:
% 9.20/2.02 | | | | | | | (50) apply(all_13_3, all_13_1, all_13_1) = all_30_0
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | GROUND_INST: instantiating (5) with 0, all_30_0, all_13_1,
% 9.20/2.02 | | | | | | | all_13_1, all_13_3, simplifying with (49), (50)
% 9.20/2.02 | | | | | | | gives:
% 9.20/2.02 | | | | | | | (51) all_30_0 = 0
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | REDUCE: (25), (51) imply:
% 9.20/2.02 | | | | | | | (52) $false
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | CLOSE: (52) is inconsistent.
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | Case 2:
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | (53) ? [v0: int] : ( ~ (v0 = 0) & member(all_30_1, all_13_2) =
% 9.20/2.02 | | | | | | | v0)
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | DELTA: instantiating (53) with fresh symbol all_63_0 gives:
% 9.20/2.02 | | | | | | | (54) ~ (all_63_0 = 0) & member(all_30_1, all_13_2) = all_63_0
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | ALPHA: (54) implies:
% 9.20/2.02 | | | | | | | (55) ~ (all_63_0 = 0)
% 9.20/2.02 | | | | | | | (56) member(all_30_1, all_13_2) = all_63_0
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | GROUND_INST: instantiating (4) with 0, all_63_0, all_13_2,
% 9.20/2.02 | | | | | | | all_30_1, simplifying with (27), (56) gives:
% 9.20/2.02 | | | | | | | (57) all_63_0 = 0
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | REDUCE: (55), (57) imply:
% 9.20/2.02 | | | | | | | (58) $false
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | | CLOSE: (58) is inconsistent.
% 9.20/2.02 | | | | | | |
% 9.20/2.02 | | | | | | End of split
% 9.20/2.02 | | | | | |
% 9.20/2.02 | | | | | End of split
% 9.20/2.02 | | | | |
% 9.20/2.02 | | | | End of split
% 9.20/2.02 | | | |
% 9.20/2.02 | | | End of split
% 9.20/2.02 | | |
% 9.20/2.02 | | Case 2:
% 9.20/2.02 | | |
% 9.20/2.02 | | | (59) ? [v0: int] : ( ~ (v0 = 0) & member(all_13_1, all_13_2) = v0)
% 9.20/2.02 | | |
% 9.20/2.02 | | | DELTA: instantiating (59) with fresh symbol all_30_0 gives:
% 9.20/2.02 | | | (60) ~ (all_30_0 = 0) & member(all_13_1, all_13_2) = all_30_0
% 9.20/2.02 | | |
% 9.20/2.02 | | | ALPHA: (60) implies:
% 9.20/2.02 | | | (61) ~ (all_30_0 = 0)
% 9.20/2.02 | | | (62) member(all_13_1, all_13_2) = all_30_0
% 9.20/2.02 | | |
% 9.20/2.03 | | | GROUND_INST: instantiating (4) with 0, all_30_0, all_13_2, all_13_1,
% 9.20/2.03 | | | simplifying with (18), (62) gives:
% 9.20/2.03 | | | (63) all_30_0 = 0
% 9.20/2.03 | | |
% 9.20/2.03 | | | REDUCE: (61), (63) imply:
% 9.20/2.03 | | | (64) $false
% 9.20/2.03 | | |
% 9.20/2.03 | | | CLOSE: (64) is inconsistent.
% 9.20/2.03 | | |
% 9.20/2.03 | | End of split
% 9.20/2.03 | |
% 9.20/2.03 | End of split
% 9.20/2.03 |
% 9.20/2.03 End of proof
% 9.20/2.03 % SZS output end Proof for theBenchmark
% 9.20/2.03
% 9.20/2.03 1440ms
%------------------------------------------------------------------------------