TSTP Solution File: SEU159+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU159+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n019.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 17:42:53 EDT 2023
% Result : Theorem 5.57s 1.53s
% Output : Proof 6.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU159+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 13:06:44 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.21/1.01 Prover 1: Preprocessing ...
% 2.21/1.01 Prover 4: Preprocessing ...
% 2.21/1.06 Prover 3: Preprocessing ...
% 2.21/1.06 Prover 0: Preprocessing ...
% 2.21/1.06 Prover 2: Preprocessing ...
% 2.21/1.06 Prover 6: Preprocessing ...
% 2.21/1.06 Prover 5: Preprocessing ...
% 3.79/1.23 Prover 5: Proving ...
% 3.79/1.23 Prover 6: Proving ...
% 3.80/1.24 Prover 1: Warning: ignoring some quantifiers
% 3.80/1.24 Prover 3: Warning: ignoring some quantifiers
% 3.80/1.24 Prover 4: Warning: ignoring some quantifiers
% 3.80/1.25 Prover 3: Constructing countermodel ...
% 3.80/1.25 Prover 1: Constructing countermodel ...
% 3.80/1.25 Prover 4: Constructing countermodel ...
% 3.80/1.25 Prover 0: Proving ...
% 3.80/1.26 Prover 2: Proving ...
% 4.83/1.45 Prover 1: gave up
% 4.83/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.83/1.47 Prover 3: gave up
% 4.83/1.49 Prover 7: Preprocessing ...
% 4.83/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.57/1.50 Prover 8: Preprocessing ...
% 5.57/1.52 Prover 7: Warning: ignoring some quantifiers
% 5.57/1.53 Prover 0: proved (904ms)
% 5.57/1.53
% 5.57/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.57/1.53
% 5.57/1.54 Prover 2: stopped
% 5.57/1.54 Prover 5: stopped
% 5.57/1.54 Prover 7: Constructing countermodel ...
% 5.57/1.54 Prover 6: stopped
% 5.57/1.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.57/1.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.57/1.54 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.57/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.57/1.56 Prover 13: Preprocessing ...
% 5.57/1.56 Prover 16: Preprocessing ...
% 5.57/1.56 Prover 10: Preprocessing ...
% 5.57/1.58 Prover 8: Warning: ignoring some quantifiers
% 5.57/1.58 Prover 11: Preprocessing ...
% 5.57/1.59 Prover 8: Constructing countermodel ...
% 6.36/1.60 Prover 13: Warning: ignoring some quantifiers
% 6.36/1.61 Prover 16: Warning: ignoring some quantifiers
% 6.36/1.61 Prover 4: Found proof (size 51)
% 6.36/1.61 Prover 4: proved (979ms)
% 6.36/1.61 Prover 10: Warning: ignoring some quantifiers
% 6.36/1.61 Prover 16: Constructing countermodel ...
% 6.36/1.61 Prover 13: Constructing countermodel ...
% 6.36/1.62 Prover 16: stopped
% 6.36/1.62 Prover 13: stopped
% 6.36/1.62 Prover 7: stopped
% 6.36/1.62 Prover 8: stopped
% 6.36/1.62 Prover 10: Constructing countermodel ...
% 6.36/1.62 Prover 10: stopped
% 6.36/1.64 Prover 11: Warning: ignoring some quantifiers
% 6.36/1.64 Prover 11: Constructing countermodel ...
% 6.36/1.65 Prover 11: stopped
% 6.36/1.65
% 6.36/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.36/1.65
% 6.36/1.66 % SZS output start Proof for theBenchmark
% 6.36/1.66 Assumptions after simplification:
% 6.36/1.66 ---------------------------------
% 6.36/1.66
% 6.36/1.66 (commutativity_k2_tarski)
% 6.36/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) |
% 6.36/1.69 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i]
% 6.36/1.69 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) |
% 6.36/1.69 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 6.36/1.69
% 6.36/1.69 (d2_tarski)
% 6.36/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 |
% 6.36/1.69 ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 6.36/1.69 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 6.36/1.69 ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) =
% 6.36/1.69 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 6.36/1.70 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~
% 6.36/1.70 (in(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : !
% 6.36/1.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) =
% 6.36/1.70 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] :
% 6.36/1.70 (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) &
% 6.36/1.70 (v5 = 0 | v4 = v2 | v4 = v1)))
% 6.36/1.70
% 6.36/1.70 (d3_tarski)
% 6.87/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.87/1.70 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 6.87/1.70 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 6.87/1.70 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 6.87/1.70 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 6.87/1.70 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 6.87/1.70 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 6.87/1.70 $i(v0) | in(v2, v1) = 0)
% 6.87/1.70
% 6.87/1.70 (t38_zfmisc_1)
% 6.87/1.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5:
% 6.87/1.70 any] : ? [v6: any] : (subset(v3, v2) = v4 & unordered_pair(v0, v1) = v3 &
% 6.87/1.70 in(v1, v2) = v6 & in(v0, v2) = v5 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6
% 6.87/1.70 = 0 & v5 = 0 & ~ (v4 = 0)) | (v4 = 0 & ( ~ (v6 = 0) | ~ (v5 = 0)))))
% 6.87/1.70
% 6.87/1.70 (function-axioms)
% 6.87/1.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.87/1.71 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 6.87/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.87/1.71 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 6.87/1.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 6.87/1.71 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.87/1.71
% 6.87/1.71 Further assumptions not needed in the proof:
% 6.87/1.71 --------------------------------------------
% 6.87/1.71 antisymmetry_r2_hidden, dt_k2_tarski, reflexivity_r1_tarski
% 6.87/1.71
% 6.87/1.71 Those formulas are unsatisfiable:
% 6.87/1.71 ---------------------------------
% 6.87/1.71
% 6.87/1.71 Begin of proof
% 6.87/1.71 |
% 6.87/1.71 | ALPHA: (commutativity_k2_tarski) implies:
% 6.87/1.71 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 6.87/1.71 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 &
% 6.87/1.71 | $i(v2)))
% 6.87/1.71 |
% 6.87/1.71 | ALPHA: (d2_tarski) implies:
% 6.87/1.71 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.87/1.71 | (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ $i(v2) | ~
% 6.87/1.71 | $i(v1) | ~ $i(v0))
% 6.87/1.71 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.87/1.71 | (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3) | ~ $i(v2) | ~
% 6.87/1.71 | $i(v1) | ~ $i(v0))
% 6.87/1.72 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 =
% 6.87/1.72 | v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~
% 6.87/1.72 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 6.87/1.72 |
% 6.87/1.72 | ALPHA: (d3_tarski) implies:
% 6.87/1.72 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 6.87/1.72 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 6.87/1.72 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 6.87/1.72 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.87/1.72 | (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 6.87/1.72 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 6.87/1.72 |
% 6.87/1.72 | ALPHA: (function-axioms) implies:
% 6.87/1.72 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.87/1.72 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.87/1.72 |
% 6.87/1.72 | DELTA: instantiating (t38_zfmisc_1) with fresh symbols all_10_0, all_10_1,
% 6.87/1.72 | all_10_2, all_10_3, all_10_4, all_10_5, all_10_6 gives:
% 6.87/1.72 | (8) subset(all_10_3, all_10_4) = all_10_2 & unordered_pair(all_10_6,
% 6.87/1.72 | all_10_5) = all_10_3 & in(all_10_5, all_10_4) = all_10_0 &
% 6.87/1.72 | in(all_10_6, all_10_4) = all_10_1 & $i(all_10_3) & $i(all_10_4) &
% 6.87/1.72 | $i(all_10_5) & $i(all_10_6) & ((all_10_0 = 0 & all_10_1 = 0 & ~
% 6.87/1.72 | (all_10_2 = 0)) | (all_10_2 = 0 & ( ~ (all_10_0 = 0) | ~ (all_10_1
% 6.87/1.72 | = 0))))
% 6.87/1.72 |
% 6.87/1.72 | ALPHA: (8) implies:
% 6.87/1.72 | (9) $i(all_10_6)
% 6.87/1.72 | (10) $i(all_10_5)
% 6.87/1.72 | (11) $i(all_10_4)
% 6.87/1.72 | (12) in(all_10_6, all_10_4) = all_10_1
% 6.87/1.72 | (13) in(all_10_5, all_10_4) = all_10_0
% 6.87/1.72 | (14) unordered_pair(all_10_6, all_10_5) = all_10_3
% 6.87/1.72 | (15) subset(all_10_3, all_10_4) = all_10_2
% 6.87/1.72 | (16) (all_10_0 = 0 & all_10_1 = 0 & ~ (all_10_2 = 0)) | (all_10_2 = 0 & (
% 6.87/1.72 | ~ (all_10_0 = 0) | ~ (all_10_1 = 0)))
% 6.87/1.72 |
% 6.87/1.73 | GROUND_INST: instantiating (1) with all_10_5, all_10_6, all_10_3, simplifying
% 6.87/1.73 | with (9), (10), (14) gives:
% 6.87/1.73 | (17) unordered_pair(all_10_5, all_10_6) = all_10_3 & $i(all_10_3)
% 6.87/1.73 |
% 6.87/1.73 | ALPHA: (17) implies:
% 6.87/1.73 | (18) $i(all_10_3)
% 6.87/1.73 |
% 6.87/1.73 | GROUND_INST: instantiating (5) with all_10_3, all_10_4, all_10_2, simplifying
% 6.87/1.73 | with (11), (15), (18) gives:
% 6.87/1.73 | (19) all_10_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 6.87/1.73 | all_10_3) = 0 & in(v0, all_10_4) = v1 & $i(v0))
% 6.87/1.73 |
% 6.87/1.73 | BETA: splitting (16) gives:
% 6.87/1.73 |
% 6.87/1.73 | Case 1:
% 6.87/1.73 | |
% 6.87/1.73 | | (20) all_10_0 = 0 & all_10_1 = 0 & ~ (all_10_2 = 0)
% 6.87/1.73 | |
% 6.87/1.73 | | ALPHA: (20) implies:
% 6.87/1.73 | | (21) all_10_1 = 0
% 6.87/1.73 | | (22) all_10_0 = 0
% 6.87/1.73 | | (23) ~ (all_10_2 = 0)
% 6.87/1.73 | |
% 6.87/1.73 | | REDUCE: (13), (22) imply:
% 6.87/1.73 | | (24) in(all_10_5, all_10_4) = 0
% 6.87/1.73 | |
% 6.87/1.73 | | REDUCE: (12), (21) imply:
% 6.87/1.73 | | (25) in(all_10_6, all_10_4) = 0
% 6.87/1.73 | |
% 6.87/1.73 | | BETA: splitting (19) gives:
% 6.87/1.73 | |
% 6.87/1.73 | | Case 1:
% 6.87/1.73 | | |
% 6.87/1.73 | | | (26) all_10_2 = 0
% 6.87/1.73 | | |
% 6.87/1.73 | | | REDUCE: (23), (26) imply:
% 6.87/1.73 | | | (27) $false
% 6.87/1.73 | | |
% 6.87/1.73 | | | CLOSE: (27) is inconsistent.
% 6.87/1.73 | | |
% 6.87/1.73 | | Case 2:
% 6.87/1.73 | | |
% 6.87/1.73 | | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_10_3) = 0 &
% 6.87/1.73 | | | in(v0, all_10_4) = v1 & $i(v0))
% 6.87/1.73 | | |
% 6.87/1.73 | | | DELTA: instantiating (28) with fresh symbols all_29_0, all_29_1 gives:
% 6.87/1.73 | | | (29) ~ (all_29_0 = 0) & in(all_29_1, all_10_3) = 0 & in(all_29_1,
% 6.87/1.73 | | | all_10_4) = all_29_0 & $i(all_29_1)
% 6.87/1.73 | | |
% 6.87/1.73 | | | ALPHA: (29) implies:
% 6.87/1.73 | | | (30) ~ (all_29_0 = 0)
% 6.87/1.73 | | | (31) $i(all_29_1)
% 6.87/1.73 | | | (32) in(all_29_1, all_10_4) = all_29_0
% 6.87/1.73 | | | (33) in(all_29_1, all_10_3) = 0
% 6.87/1.73 | | |
% 6.87/1.74 | | | GROUND_INST: instantiating (4) with all_10_6, all_10_5, all_10_3,
% 6.87/1.74 | | | all_29_1, simplifying with (9), (10), (14), (18), (31), (33)
% 6.87/1.74 | | | gives:
% 6.87/1.74 | | | (34) all_29_1 = all_10_5 | all_29_1 = all_10_6
% 6.87/1.74 | | |
% 6.87/1.74 | | | BETA: splitting (34) gives:
% 6.87/1.74 | | |
% 6.87/1.74 | | | Case 1:
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | (35) all_29_1 = all_10_5
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | REDUCE: (32), (35) imply:
% 6.87/1.74 | | | | (36) in(all_10_5, all_10_4) = all_29_0
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | GROUND_INST: instantiating (7) with 0, all_29_0, all_10_4, all_10_5,
% 6.87/1.74 | | | | simplifying with (24), (36) gives:
% 6.87/1.74 | | | | (37) all_29_0 = 0
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | REDUCE: (30), (37) imply:
% 6.87/1.74 | | | | (38) $false
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | CLOSE: (38) is inconsistent.
% 6.87/1.74 | | | |
% 6.87/1.74 | | | Case 2:
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | (39) all_29_1 = all_10_6
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | REDUCE: (32), (39) imply:
% 6.87/1.74 | | | | (40) in(all_10_6, all_10_4) = all_29_0
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | GROUND_INST: instantiating (7) with 0, all_29_0, all_10_4, all_10_6,
% 6.87/1.74 | | | | simplifying with (25), (40) gives:
% 6.87/1.74 | | | | (41) all_29_0 = 0
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | REDUCE: (30), (41) imply:
% 6.87/1.74 | | | | (42) $false
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | CLOSE: (42) is inconsistent.
% 6.87/1.74 | | | |
% 6.87/1.74 | | | End of split
% 6.87/1.74 | | |
% 6.87/1.74 | | End of split
% 6.87/1.74 | |
% 6.87/1.74 | Case 2:
% 6.87/1.74 | |
% 6.87/1.74 | | (43) all_10_2 = 0 & ( ~ (all_10_0 = 0) | ~ (all_10_1 = 0))
% 6.87/1.74 | |
% 6.87/1.74 | | ALPHA: (43) implies:
% 6.87/1.74 | | (44) all_10_2 = 0
% 6.87/1.74 | | (45) ~ (all_10_0 = 0) | ~ (all_10_1 = 0)
% 6.87/1.74 | |
% 6.87/1.74 | | REDUCE: (15), (44) imply:
% 6.87/1.74 | | (46) subset(all_10_3, all_10_4) = 0
% 6.87/1.74 | |
% 6.87/1.74 | | GROUND_INST: instantiating (6) with all_10_3, all_10_4, all_10_5, all_10_0,
% 6.87/1.74 | | simplifying with (10), (11), (13), (18), (46) gives:
% 6.87/1.74 | | (47) all_10_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_10_5, all_10_3)
% 6.87/1.74 | | = v0)
% 6.87/1.74 | |
% 6.87/1.74 | | GROUND_INST: instantiating (6) with all_10_3, all_10_4, all_10_6, all_10_1,
% 6.87/1.74 | | simplifying with (9), (11), (12), (18), (46) gives:
% 6.87/1.74 | | (48) all_10_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_10_6, all_10_3)
% 6.87/1.74 | | = v0)
% 6.87/1.74 | |
% 6.87/1.74 | | BETA: splitting (45) gives:
% 6.87/1.74 | |
% 6.87/1.74 | | Case 1:
% 6.87/1.74 | | |
% 6.87/1.74 | | | (49) ~ (all_10_0 = 0)
% 6.87/1.74 | | |
% 6.87/1.74 | | | BETA: splitting (47) gives:
% 6.87/1.74 | | |
% 6.87/1.74 | | | Case 1:
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | (50) all_10_0 = 0
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | REDUCE: (49), (50) imply:
% 6.87/1.74 | | | | (51) $false
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | CLOSE: (51) is inconsistent.
% 6.87/1.74 | | | |
% 6.87/1.74 | | | Case 2:
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & in(all_10_5, all_10_3) = v0)
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | DELTA: instantiating (52) with fresh symbol all_50_0 gives:
% 6.87/1.74 | | | | (53) ~ (all_50_0 = 0) & in(all_10_5, all_10_3) = all_50_0
% 6.87/1.74 | | | |
% 6.87/1.74 | | | | ALPHA: (53) implies:
% 6.87/1.74 | | | | (54) ~ (all_50_0 = 0)
% 6.87/1.75 | | | | (55) in(all_10_5, all_10_3) = all_50_0
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | GROUND_INST: instantiating (3) with all_10_6, all_10_5, all_10_3,
% 6.87/1.75 | | | | all_50_0, simplifying with (9), (10), (14), (18), (55)
% 6.87/1.75 | | | | gives:
% 6.87/1.75 | | | | (56) all_50_0 = 0
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | REDUCE: (54), (56) imply:
% 6.87/1.75 | | | | (57) $false
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | CLOSE: (57) is inconsistent.
% 6.87/1.75 | | | |
% 6.87/1.75 | | | End of split
% 6.87/1.75 | | |
% 6.87/1.75 | | Case 2:
% 6.87/1.75 | | |
% 6.87/1.75 | | | (58) ~ (all_10_1 = 0)
% 6.87/1.75 | | |
% 6.87/1.75 | | | BETA: splitting (48) gives:
% 6.87/1.75 | | |
% 6.87/1.75 | | | Case 1:
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | (59) all_10_1 = 0
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | REDUCE: (58), (59) imply:
% 6.87/1.75 | | | | (60) $false
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | CLOSE: (60) is inconsistent.
% 6.87/1.75 | | | |
% 6.87/1.75 | | | Case 2:
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | (61) ? [v0: int] : ( ~ (v0 = 0) & in(all_10_6, all_10_3) = v0)
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | DELTA: instantiating (61) with fresh symbol all_50_0 gives:
% 6.87/1.75 | | | | (62) ~ (all_50_0 = 0) & in(all_10_6, all_10_3) = all_50_0
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | ALPHA: (62) implies:
% 6.87/1.75 | | | | (63) ~ (all_50_0 = 0)
% 6.87/1.75 | | | | (64) in(all_10_6, all_10_3) = all_50_0
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | GROUND_INST: instantiating (2) with all_10_6, all_10_5, all_10_3,
% 6.87/1.75 | | | | all_50_0, simplifying with (9), (10), (14), (18), (64)
% 6.87/1.75 | | | | gives:
% 6.87/1.75 | | | | (65) all_50_0 = 0
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | REDUCE: (63), (65) imply:
% 6.87/1.75 | | | | (66) $false
% 6.87/1.75 | | | |
% 6.87/1.75 | | | | CLOSE: (66) is inconsistent.
% 6.87/1.75 | | | |
% 6.87/1.75 | | | End of split
% 6.87/1.75 | | |
% 6.87/1.75 | | End of split
% 6.87/1.75 | |
% 6.87/1.75 | End of split
% 6.87/1.75 |
% 6.87/1.75 End of proof
% 6.87/1.75 % SZS output end Proof for theBenchmark
% 6.87/1.75
% 6.87/1.75 1140ms
%------------------------------------------------------------------------------