TSTP Solution File: SEU173+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU173+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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:43:02 EDT 2023
% Result : Theorem 8.95s 1.98s
% Output : Proof 14.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU173+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 17:43:31 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.44/1.02 Prover 4: Preprocessing ...
% 2.44/1.02 Prover 1: Preprocessing ...
% 2.50/1.06 Prover 5: Preprocessing ...
% 2.50/1.06 Prover 6: Preprocessing ...
% 2.50/1.06 Prover 3: Preprocessing ...
% 2.50/1.06 Prover 2: Preprocessing ...
% 2.50/1.06 Prover 0: Preprocessing ...
% 4.42/1.37 Prover 5: Proving ...
% 4.42/1.38 Prover 4: Warning: ignoring some quantifiers
% 4.42/1.38 Prover 1: Warning: ignoring some quantifiers
% 4.42/1.38 Prover 2: Proving ...
% 4.42/1.39 Prover 3: Warning: ignoring some quantifiers
% 4.42/1.39 Prover 1: Constructing countermodel ...
% 4.42/1.40 Prover 4: Constructing countermodel ...
% 4.42/1.40 Prover 3: Constructing countermodel ...
% 4.98/1.42 Prover 6: Proving ...
% 4.98/1.43 Prover 0: Proving ...
% 7.13/1.79 Prover 3: gave up
% 7.13/1.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.80/1.83 Prover 7: Preprocessing ...
% 7.80/1.83 Prover 1: gave up
% 7.80/1.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.80/1.86 Prover 8: Preprocessing ...
% 7.80/1.88 Prover 7: Warning: ignoring some quantifiers
% 8.33/1.89 Prover 7: Constructing countermodel ...
% 8.33/1.94 Prover 8: Warning: ignoring some quantifiers
% 8.33/1.94 Prover 8: Constructing countermodel ...
% 8.95/1.97 Prover 0: proved (1341ms)
% 8.95/1.98
% 8.95/1.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.95/1.98
% 8.95/1.98 Prover 5: stopped
% 9.01/1.98 Prover 6: stopped
% 9.01/1.98 Prover 2: stopped
% 9.01/1.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.01/1.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.01/1.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.01/1.99 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.21/2.01 Prover 13: Preprocessing ...
% 9.21/2.01 Prover 16: Preprocessing ...
% 9.21/2.02 Prover 10: Preprocessing ...
% 9.21/2.02 Prover 11: Preprocessing ...
% 9.30/2.05 Prover 13: Warning: ignoring some quantifiers
% 9.30/2.06 Prover 10: Warning: ignoring some quantifiers
% 9.30/2.06 Prover 13: Constructing countermodel ...
% 9.30/2.06 Prover 16: Warning: ignoring some quantifiers
% 9.30/2.07 Prover 10: Constructing countermodel ...
% 9.30/2.08 Prover 16: Constructing countermodel ...
% 9.92/2.11 Prover 11: Warning: ignoring some quantifiers
% 9.92/2.12 Prover 11: Constructing countermodel ...
% 10.42/2.21 Prover 8: gave up
% 10.42/2.21 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 10.42/2.22 Prover 19: Preprocessing ...
% 10.42/2.27 Prover 10: gave up
% 10.42/2.28 Prover 13: gave up
% 10.42/2.33 Prover 19: Warning: ignoring some quantifiers
% 10.42/2.36 Prover 19: Constructing countermodel ...
% 10.42/2.36 Prover 7: gave up
% 12.36/2.49 Prover 16: gave up
% 13.40/2.63 Prover 4: Found proof (size 107)
% 13.40/2.63 Prover 4: proved (2001ms)
% 13.40/2.63 Prover 19: stopped
% 13.40/2.63 Prover 11: stopped
% 13.40/2.63
% 13.40/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.40/2.63
% 13.40/2.65 % SZS output start Proof for theBenchmark
% 13.40/2.65 Assumptions after simplification:
% 13.40/2.65 ---------------------------------
% 13.40/2.65
% 13.40/2.65 (d1_zfmisc_1)
% 13.64/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.64/2.69 (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.64/2.69 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0: $i] : !
% 13.64/2.69 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (powerset(v0) = v1) | ~
% 13.64/2.69 (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~
% 13.64/2.69 (v4 = 0) & subset(v2, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.64/2.69 : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 13.64/2.69 ~ $i(v0) | in(v2, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 13.64/2.69 (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 13.64/2.69 $i(v0) | subset(v2, v0) = 0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2
% 13.64/2.69 = v0 | ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 13.64/2.69 [v4: any] : ? [v5: any] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & $i(v3) &
% 13.64/2.69 ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 13.64/2.69
% 13.64/2.69 (d2_subset_1)
% 13.64/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | ~
% 13.64/2.70 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v1) = v4 &
% 13.64/2.70 empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) |
% 13.64/2.70 v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 13.64/2.70 (element(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any]
% 13.64/2.70 : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & (
% 13.64/2.70 ~ (v2 = 0) | v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any]
% 13.64/2.70 : ( ~ (in(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any]
% 13.64/2.70 : (empty(v0) = v3 & element(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0)
% 13.64/2.70 & ( ~ (v2 = 0) | v4 = 0)))))
% 13.64/2.70
% 13.64/2.70 (d3_tarski)
% 13.64/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.64/2.70 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.64/2.70 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 13.64/2.70 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 13.64/2.70 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 13.64/2.70 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 13.64/2.70 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 13.64/2.70 $i(v0) | in(v2, v1) = 0)
% 13.64/2.70
% 13.64/2.70 (fc1_subset_1)
% 13.64/2.70 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int]
% 13.64/2.70 : ( ~ (v2 = 0) & empty(v1) = v2))
% 13.64/2.70
% 13.64/2.70 (l71_subset_1)
% 13.64/2.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 13.64/2.70 element(v0, v2) = v3 & powerset(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & !
% 13.64/2.70 [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v1) = v5) | ~ $i(v4) | ?
% 13.64/2.70 [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6)) & ! [v4: $i] : ( ~ (in(v4,
% 13.64/2.70 v0) = 0) | ~ $i(v4) | in(v4, v1) = 0))
% 13.64/2.70
% 13.64/2.70 (rc1_subset_1)
% 13.64/2.70 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 13.64/2.70 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & empty(v3) = v4 &
% 13.64/2.70 element(v3, v2) = 0 & powerset(v0) = v2 & $i(v3) & $i(v2))) & ! [v0: $i]
% 13.64/2.70 : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 13.64/2.70 $i] : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) &
% 13.64/2.70 empty(v3) = v5 & element(v3, v1) = 0) | (v2 = 0 & empty(v0) = 0))))
% 13.64/2.70
% 13.64/2.70 (rc2_xboole_0)
% 13.64/2.71 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0))
% 13.64/2.71
% 13.64/2.71 (function-axioms)
% 13.64/2.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.64/2.71 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 13.64/2.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.64/2.71 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 13.64/2.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.64/2.71 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 13.64/2.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 13.64/2.71 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 13.64/2.71 [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 13.64/2.71
% 13.64/2.71 Further assumptions not needed in the proof:
% 13.64/2.71 --------------------------------------------
% 13.64/2.71 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_m1_subset_1,
% 13.64/2.71 existence_m1_subset_1, fc1_xboole_0, rc1_xboole_0, rc2_subset_1,
% 13.64/2.71 reflexivity_r1_tarski, t6_boole, t7_boole, t8_boole
% 13.64/2.71
% 13.64/2.71 Those formulas are unsatisfiable:
% 13.64/2.71 ---------------------------------
% 13.64/2.71
% 13.64/2.71 Begin of proof
% 13.64/2.71 |
% 13.64/2.71 | ALPHA: (d1_zfmisc_1) implies:
% 13.64/2.71 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.64/2.71 | (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 13.64/2.71 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v2, v0) = v4))
% 13.64/2.71 |
% 13.64/2.71 | ALPHA: (d2_subset_1) implies:
% 13.64/2.71 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) |
% 13.64/2.71 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v0) = v3
% 13.64/2.71 | & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 =
% 13.64/2.71 | 0) | v4 = 0)))))
% 13.64/2.71 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) |
% 13.64/2.71 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v1) = v4
% 13.64/2.71 | & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2
% 13.64/2.71 | = 0) | v4 = 0)))))
% 13.64/2.71 |
% 13.64/2.71 | ALPHA: (d3_tarski) implies:
% 13.64/2.71 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 13.64/2.71 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 13.64/2.71 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 13.64/2.71 |
% 13.64/2.71 | ALPHA: (rc1_subset_1) implies:
% 13.64/2.71 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0)
% 13.64/2.71 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & empty(v3)
% 13.64/2.71 | = v4 & element(v3, v2) = 0 & powerset(v0) = v2 & $i(v3) & $i(v2)))
% 13.64/2.71 |
% 13.64/2.71 | ALPHA: (function-axioms) implies:
% 13.64/2.71 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.64/2.71 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 13.64/2.71 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.64/2.71 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 13.64/2.71 |
% 13.64/2.72 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_17_0, all_17_1
% 13.64/2.72 | gives:
% 13.64/2.72 | (8) ~ (all_17_0 = 0) & empty(all_17_1) = all_17_0 & $i(all_17_1)
% 13.64/2.72 |
% 13.64/2.72 | ALPHA: (8) implies:
% 13.64/2.72 | (9) ~ (all_17_0 = 0)
% 13.64/2.72 | (10) $i(all_17_1)
% 13.64/2.72 | (11) empty(all_17_1) = all_17_0
% 13.64/2.72 |
% 13.64/2.72 | DELTA: instantiating (l71_subset_1) with fresh symbols all_22_0, all_22_1,
% 13.64/2.72 | all_22_2, all_22_3 gives:
% 13.64/2.72 | (12) ~ (all_22_0 = 0) & element(all_22_3, all_22_1) = all_22_0 &
% 13.64/2.72 | powerset(all_22_2) = all_22_1 & $i(all_22_1) & $i(all_22_2) &
% 13.64/2.72 | $i(all_22_3) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 13.64/2.72 | all_22_2) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 13.64/2.72 | in(v0, all_22_3) = v2)) & ! [v0: $i] : ( ~ (in(v0, all_22_3) = 0)
% 13.64/2.72 | | ~ $i(v0) | in(v0, all_22_2) = 0)
% 13.64/2.72 |
% 13.64/2.72 | ALPHA: (12) implies:
% 13.64/2.72 | (13) ~ (all_22_0 = 0)
% 13.64/2.72 | (14) $i(all_22_3)
% 13.64/2.72 | (15) $i(all_22_2)
% 13.64/2.72 | (16) $i(all_22_1)
% 13.64/2.72 | (17) powerset(all_22_2) = all_22_1
% 13.64/2.72 | (18) element(all_22_3, all_22_1) = all_22_0
% 13.64/2.72 | (19) ! [v0: $i] : ( ~ (in(v0, all_22_3) = 0) | ~ $i(v0) | in(v0,
% 13.64/2.72 | all_22_2) = 0)
% 13.64/2.72 |
% 13.64/2.72 | GROUND_INST: instantiating (fc1_subset_1) with all_22_2, all_22_1, simplifying
% 13.64/2.72 | with (15), (17) gives:
% 13.64/2.72 | (20) ? [v0: int] : ( ~ (v0 = 0) & empty(all_22_1) = v0)
% 13.64/2.72 |
% 13.64/2.72 | GROUND_INST: instantiating (3) with all_22_1, all_22_3, all_22_0, simplifying
% 13.64/2.72 | with (14), (16), (18) gives:
% 13.64/2.72 | (21) ? [v0: any] : ? [v1: any] : (empty(all_22_1) = v0 & empty(all_22_3)
% 13.64/2.72 | = v1 & ( ~ (v0 = 0) | (( ~ (v1 = 0) | all_22_0 = 0) & ( ~ (all_22_0
% 13.64/2.72 | = 0) | v1 = 0))))
% 13.64/2.72 |
% 13.64/2.72 | GROUND_INST: instantiating (2) with all_22_1, all_22_3, all_22_0, simplifying
% 13.64/2.72 | with (14), (16), (18) gives:
% 13.64/2.72 | (22) ? [v0: any] : ? [v1: any] : (empty(all_22_1) = v0 & in(all_22_3,
% 13.64/2.72 | all_22_1) = v1 & (v0 = 0 | (( ~ (v1 = 0) | all_22_0 = 0) & ( ~
% 13.64/2.72 | (all_22_0 = 0) | v1 = 0))))
% 13.64/2.72 |
% 13.64/2.72 | GROUND_INST: instantiating (5) with all_17_1, all_17_0, simplifying with (10),
% 13.64/2.72 | (11) gives:
% 13.64/2.72 | (23) all_17_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 13.64/2.72 | & empty(v1) = v2 & element(v1, v0) = 0 & powerset(all_17_1) = v0 &
% 13.64/2.72 | $i(v1) & $i(v0))
% 13.64/2.72 |
% 13.64/2.72 | DELTA: instantiating (20) with fresh symbol all_31_0 gives:
% 13.64/2.72 | (24) ~ (all_31_0 = 0) & empty(all_22_1) = all_31_0
% 13.64/2.72 |
% 13.64/2.72 | ALPHA: (24) implies:
% 13.64/2.72 | (25) ~ (all_31_0 = 0)
% 13.64/2.72 | (26) empty(all_22_1) = all_31_0
% 13.64/2.72 |
% 13.64/2.72 | DELTA: instantiating (22) with fresh symbols all_35_0, all_35_1 gives:
% 13.64/2.72 | (27) empty(all_22_1) = all_35_1 & in(all_22_3, all_22_1) = all_35_0 &
% 13.64/2.72 | (all_35_1 = 0 | (( ~ (all_35_0 = 0) | all_22_0 = 0) & ( ~ (all_22_0 =
% 13.64/2.72 | 0) | all_35_0 = 0)))
% 13.64/2.72 |
% 13.64/2.72 | ALPHA: (27) implies:
% 13.64/2.72 | (28) in(all_22_3, all_22_1) = all_35_0
% 13.64/2.72 | (29) empty(all_22_1) = all_35_1
% 13.64/2.72 | (30) all_35_1 = 0 | (( ~ (all_35_0 = 0) | all_22_0 = 0) & ( ~ (all_22_0 =
% 13.64/2.72 | 0) | all_35_0 = 0))
% 13.64/2.72 |
% 13.64/2.72 | DELTA: instantiating (21) with fresh symbols all_37_0, all_37_1 gives:
% 13.64/2.72 | (31) empty(all_22_1) = all_37_1 & empty(all_22_3) = all_37_0 & ( ~
% 13.64/2.73 | (all_37_1 = 0) | (( ~ (all_37_0 = 0) | all_22_0 = 0) & ( ~ (all_22_0
% 13.64/2.73 | = 0) | all_37_0 = 0)))
% 13.64/2.73 |
% 13.64/2.73 | ALPHA: (31) implies:
% 13.64/2.73 | (32) empty(all_22_1) = all_37_1
% 13.64/2.73 |
% 13.64/2.73 | BETA: splitting (23) gives:
% 13.64/2.73 |
% 13.64/2.73 | Case 1:
% 13.64/2.73 | |
% 13.64/2.73 | | (33) all_17_0 = 0
% 13.64/2.73 | |
% 13.64/2.73 | | REDUCE: (9), (33) imply:
% 13.64/2.73 | | (34) $false
% 13.64/2.73 | |
% 13.64/2.73 | | CLOSE: (34) is inconsistent.
% 13.64/2.73 | |
% 13.64/2.73 | Case 2:
% 13.64/2.73 | |
% 13.64/2.73 | | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & empty(v1)
% 13.64/2.73 | | = v2 & element(v1, v0) = 0 & powerset(all_17_1) = v0 & $i(v1) &
% 13.64/2.73 | | $i(v0))
% 13.64/2.73 | |
% 13.64/2.73 | | DELTA: instantiating (35) with fresh symbols all_45_0, all_45_1, all_45_2
% 13.64/2.73 | | gives:
% 13.64/2.73 | | (36) ~ (all_45_0 = 0) & empty(all_45_1) = all_45_0 & element(all_45_1,
% 13.64/2.73 | | all_45_2) = 0 & powerset(all_17_1) = all_45_2 & $i(all_45_1) &
% 13.64/2.73 | | $i(all_45_2)
% 13.64/2.73 | |
% 13.64/2.73 | | ALPHA: (36) implies:
% 13.64/2.73 | | (37) $i(all_45_2)
% 13.64/2.73 | | (38) $i(all_45_1)
% 13.64/2.73 | | (39) powerset(all_17_1) = all_45_2
% 13.64/2.73 | | (40) element(all_45_1, all_45_2) = 0
% 13.64/2.73 | |
% 13.64/2.73 | | GROUND_INST: instantiating (6) with all_35_1, all_37_1, all_22_1,
% 13.64/2.73 | | simplifying with (29), (32) gives:
% 13.64/2.73 | | (41) all_37_1 = all_35_1
% 13.64/2.73 | |
% 13.64/2.73 | | GROUND_INST: instantiating (6) with all_31_0, all_37_1, all_22_1,
% 13.64/2.73 | | simplifying with (26), (32) gives:
% 13.64/2.73 | | (42) all_37_1 = all_31_0
% 13.64/2.73 | |
% 13.64/2.73 | | COMBINE_EQS: (41), (42) imply:
% 13.64/2.73 | | (43) all_35_1 = all_31_0
% 13.64/2.73 | |
% 13.64/2.73 | | SIMP: (43) implies:
% 13.64/2.73 | | (44) all_35_1 = all_31_0
% 13.64/2.73 | |
% 13.64/2.73 | | BETA: splitting (30) gives:
% 13.64/2.73 | |
% 13.64/2.73 | | Case 1:
% 13.64/2.73 | | |
% 13.64/2.73 | | | (45) all_35_1 = 0
% 13.64/2.73 | | |
% 13.64/2.73 | | | COMBINE_EQS: (44), (45) imply:
% 13.64/2.73 | | | (46) all_31_0 = 0
% 13.64/2.73 | | |
% 13.64/2.73 | | | SIMP: (46) implies:
% 13.64/2.73 | | | (47) all_31_0 = 0
% 13.64/2.73 | | |
% 13.64/2.73 | | | REDUCE: (25), (47) imply:
% 13.64/2.73 | | | (48) $false
% 13.64/2.73 | | |
% 13.64/2.73 | | | CLOSE: (48) is inconsistent.
% 13.64/2.73 | | |
% 13.64/2.73 | | Case 2:
% 13.64/2.73 | | |
% 13.64/2.73 | | | (49) ~ (all_35_1 = 0)
% 13.64/2.73 | | | (50) ( ~ (all_35_0 = 0) | all_22_0 = 0) & ( ~ (all_22_0 = 0) | all_35_0
% 13.64/2.73 | | | = 0)
% 13.64/2.73 | | |
% 13.64/2.73 | | | ALPHA: (50) implies:
% 13.64/2.73 | | | (51) ~ (all_35_0 = 0) | all_22_0 = 0
% 13.64/2.73 | | |
% 13.64/2.73 | | | BETA: splitting (51) gives:
% 13.64/2.73 | | |
% 13.64/2.73 | | | Case 1:
% 13.64/2.73 | | | |
% 13.64/2.73 | | | | (52) ~ (all_35_0 = 0)
% 13.64/2.73 | | | |
% 13.64/2.73 | | | | GROUND_INST: instantiating (1) with all_22_2, all_22_1, all_22_3,
% 13.64/2.73 | | | | all_35_0, simplifying with (14), (15), (16), (17), (28)
% 13.64/2.73 | | | | gives:
% 13.64/2.73 | | | | (53) all_35_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_22_3,
% 13.64/2.73 | | | | all_22_2) = v0)
% 13.64/2.73 | | | |
% 13.64/2.73 | | | | GROUND_INST: instantiating (fc1_subset_1) with all_17_1, all_45_2,
% 13.64/2.73 | | | | simplifying with (10), (39) gives:
% 13.64/2.73 | | | | (54) ? [v0: int] : ( ~ (v0 = 0) & empty(all_45_2) = v0)
% 13.64/2.73 | | | |
% 13.64/2.73 | | | | GROUND_INST: instantiating (3) with all_45_2, all_45_1, 0, simplifying
% 13.64/2.73 | | | | with (37), (38), (40) gives:
% 13.64/2.73 | | | | (55) ? [v0: any] : ? [v1: any] : (empty(all_45_1) = v1 &
% 13.64/2.73 | | | | empty(all_45_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 13.64/2.73 | | | |
% 13.64/2.73 | | | | GROUND_INST: instantiating (2) with all_45_2, all_45_1, 0, simplifying
% 13.64/2.73 | | | | with (37), (38), (40) gives:
% 13.64/2.73 | | | | (56) ? [v0: any] : ? [v1: any] : (empty(all_45_2) = v0 &
% 13.64/2.73 | | | | in(all_45_1, all_45_2) = v1 & (v1 = 0 | v0 = 0))
% 13.64/2.73 | | | |
% 13.64/2.74 | | | | GROUND_INST: instantiating (5) with all_22_1, all_31_0, simplifying with
% 13.64/2.74 | | | | (16), (26) gives:
% 13.64/2.74 | | | | (57) all_31_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~
% 13.64/2.74 | | | | (v2 = 0) & empty(v1) = v2 & element(v1, v0) = 0 &
% 13.64/2.74 | | | | powerset(all_22_1) = v0 & $i(v1) & $i(v0))
% 13.64/2.74 | | | |
% 13.64/2.74 | | | | DELTA: instantiating (54) with fresh symbol all_65_0 gives:
% 13.64/2.74 | | | | (58) ~ (all_65_0 = 0) & empty(all_45_2) = all_65_0
% 13.64/2.74 | | | |
% 13.64/2.74 | | | | ALPHA: (58) implies:
% 13.64/2.74 | | | | (59) ~ (all_65_0 = 0)
% 13.64/2.74 | | | | (60) empty(all_45_2) = all_65_0
% 13.64/2.74 | | | |
% 13.64/2.74 | | | | DELTA: instantiating (56) with fresh symbols all_71_0, all_71_1 gives:
% 13.64/2.74 | | | | (61) empty(all_45_2) = all_71_1 & in(all_45_1, all_45_2) = all_71_0 &
% 13.64/2.74 | | | | (all_71_0 = 0 | all_71_1 = 0)
% 13.64/2.74 | | | |
% 13.64/2.74 | | | | ALPHA: (61) implies:
% 13.64/2.74 | | | | (62) empty(all_45_2) = all_71_1
% 13.64/2.74 | | | | (63) all_71_0 = 0 | all_71_1 = 0
% 13.64/2.74 | | | |
% 13.64/2.74 | | | | DELTA: instantiating (55) with fresh symbols all_73_0, all_73_1 gives:
% 13.64/2.74 | | | | (64) empty(all_45_1) = all_73_0 & empty(all_45_2) = all_73_1 & ( ~
% 13.64/2.74 | | | | (all_73_1 = 0) | all_73_0 = 0)
% 13.64/2.74 | | | |
% 13.64/2.74 | | | | ALPHA: (64) implies:
% 13.64/2.74 | | | | (65) empty(all_45_2) = all_73_1
% 13.64/2.74 | | | |
% 13.64/2.74 | | | | BETA: splitting (57) gives:
% 13.64/2.74 | | | |
% 13.64/2.74 | | | | Case 1:
% 13.64/2.74 | | | | |
% 13.64/2.74 | | | | | (66) all_31_0 = 0
% 13.64/2.74 | | | | |
% 13.64/2.74 | | | | | REDUCE: (25), (66) imply:
% 13.64/2.74 | | | | | (67) $false
% 13.64/2.74 | | | | |
% 13.64/2.74 | | | | | CLOSE: (67) is inconsistent.
% 13.64/2.74 | | | | |
% 13.64/2.74 | | | | Case 2:
% 13.64/2.74 | | | | |
% 13.64/2.74 | | | | | (68) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 13.64/2.74 | | | | | empty(v1) = v2 & element(v1, v0) = 0 & powerset(all_22_1) =
% 13.64/2.74 | | | | | v0 & $i(v1) & $i(v0))
% 13.64/2.74 | | | | |
% 13.64/2.74 | | | | | DELTA: instantiating (68) with fresh symbols all_85_0, all_85_1,
% 13.64/2.74 | | | | | all_85_2 gives:
% 13.64/2.74 | | | | | (69) ~ (all_85_0 = 0) & empty(all_85_1) = all_85_0 &
% 13.64/2.74 | | | | | element(all_85_1, all_85_2) = 0 & powerset(all_22_1) =
% 13.64/2.74 | | | | | all_85_2 & $i(all_85_1) & $i(all_85_2)
% 13.64/2.74 | | | | |
% 13.64/2.74 | | | | | ALPHA: (69) implies:
% 13.64/2.74 | | | | | (70) ~ (all_85_0 = 0)
% 13.64/2.74 | | | | | (71) $i(all_85_2)
% 13.64/2.74 | | | | | (72) $i(all_85_1)
% 13.64/2.74 | | | | | (73) powerset(all_22_1) = all_85_2
% 13.64/2.74 | | | | | (74) element(all_85_1, all_85_2) = 0
% 13.64/2.74 | | | | | (75) empty(all_85_1) = all_85_0
% 13.64/2.74 | | | | |
% 13.64/2.74 | | | | | BETA: splitting (53) gives:
% 13.64/2.74 | | | | |
% 13.64/2.74 | | | | | Case 1:
% 13.64/2.74 | | | | | |
% 13.64/2.74 | | | | | | (76) all_35_0 = 0
% 13.64/2.74 | | | | | |
% 13.64/2.74 | | | | | | REDUCE: (52), (76) imply:
% 13.64/2.74 | | | | | | (77) $false
% 13.64/2.74 | | | | | |
% 13.64/2.74 | | | | | | CLOSE: (77) is inconsistent.
% 13.64/2.74 | | | | | |
% 13.64/2.74 | | | | | Case 2:
% 13.64/2.74 | | | | | |
% 13.64/2.74 | | | | | | (78) ? [v0: int] : ( ~ (v0 = 0) & subset(all_22_3, all_22_2) =
% 13.64/2.74 | | | | | | v0)
% 13.64/2.74 | | | | | |
% 13.64/2.74 | | | | | | DELTA: instantiating (78) with fresh symbol all_95_0 gives:
% 14.00/2.74 | | | | | | (79) ~ (all_95_0 = 0) & subset(all_22_3, all_22_2) = all_95_0
% 14.00/2.74 | | | | | |
% 14.00/2.74 | | | | | | ALPHA: (79) implies:
% 14.00/2.74 | | | | | | (80) ~ (all_95_0 = 0)
% 14.00/2.74 | | | | | | (81) subset(all_22_3, all_22_2) = all_95_0
% 14.00/2.74 | | | | | |
% 14.00/2.74 | | | | | | GROUND_INST: instantiating (6) with all_71_1, all_73_1, all_45_2,
% 14.00/2.74 | | | | | | simplifying with (62), (65) gives:
% 14.00/2.74 | | | | | | (82) all_73_1 = all_71_1
% 14.00/2.74 | | | | | |
% 14.00/2.74 | | | | | | GROUND_INST: instantiating (6) with all_65_0, all_73_1, all_45_2,
% 14.00/2.74 | | | | | | simplifying with (60), (65) gives:
% 14.00/2.74 | | | | | | (83) all_73_1 = all_65_0
% 14.00/2.74 | | | | | |
% 14.00/2.74 | | | | | | COMBINE_EQS: (82), (83) imply:
% 14.00/2.74 | | | | | | (84) all_71_1 = all_65_0
% 14.00/2.74 | | | | | |
% 14.00/2.74 | | | | | | SIMP: (84) implies:
% 14.00/2.74 | | | | | | (85) all_71_1 = all_65_0
% 14.00/2.74 | | | | | |
% 14.00/2.74 | | | | | | BETA: splitting (63) gives:
% 14.00/2.74 | | | | | |
% 14.00/2.74 | | | | | | Case 1:
% 14.00/2.74 | | | | | | |
% 14.00/2.74 | | | | | | |
% 14.00/2.74 | | | | | | | GROUND_INST: instantiating (4) with all_22_3, all_22_2, all_95_0,
% 14.00/2.74 | | | | | | | simplifying with (14), (15), (81) gives:
% 14.00/2.74 | | | | | | | (86) all_95_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 14.00/2.74 | | | | | | | in(v0, all_22_2) = v1 & in(v0, all_22_3) = 0 & $i(v0))
% 14.00/2.74 | | | | | | |
% 14.00/2.74 | | | | | | | GROUND_INST: instantiating (fc1_subset_1) with all_22_1, all_85_2,
% 14.00/2.74 | | | | | | | simplifying with (16), (73) gives:
% 14.00/2.74 | | | | | | | (87) ? [v0: int] : ( ~ (v0 = 0) & empty(all_85_2) = v0)
% 14.00/2.74 | | | | | | |
% 14.00/2.74 | | | | | | | GROUND_INST: instantiating (3) with all_85_2, all_85_1, 0,
% 14.00/2.74 | | | | | | | simplifying with (71), (72), (74) gives:
% 14.00/2.75 | | | | | | | (88) ? [v0: any] : ? [v1: any] : (empty(all_85_1) = v1 &
% 14.00/2.75 | | | | | | | empty(all_85_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 14.00/2.75 | | | | | | |
% 14.00/2.75 | | | | | | | GROUND_INST: instantiating (2) with all_85_2, all_85_1, 0,
% 14.00/2.75 | | | | | | | simplifying with (71), (72), (74) gives:
% 14.00/2.75 | | | | | | | (89) ? [v0: any] : ? [v1: any] : (empty(all_85_2) = v0 &
% 14.00/2.75 | | | | | | | in(all_85_1, all_85_2) = v1 & (v1 = 0 | v0 = 0))
% 14.00/2.75 | | | | | | |
% 14.00/2.75 | | | | | | | GROUND_INST: instantiating (5) with all_85_1, all_85_0,
% 14.00/2.75 | | | | | | | simplifying with (72), (75) gives:
% 14.00/2.75 | | | | | | | (90) all_85_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] :
% 14.00/2.75 | | | | | | | ( ~ (v2 = 0) & empty(v1) = v2 & element(v1, v0) = 0 &
% 14.00/2.75 | | | | | | | powerset(all_85_1) = v0 & $i(v1) & $i(v0))
% 14.00/2.75 | | | | | | |
% 14.00/2.75 | | | | | | | DELTA: instantiating (87) with fresh symbol all_121_0 gives:
% 14.00/2.75 | | | | | | | (91) ~ (all_121_0 = 0) & empty(all_85_2) = all_121_0
% 14.00/2.75 | | | | | | |
% 14.00/2.75 | | | | | | | ALPHA: (91) implies:
% 14.00/2.75 | | | | | | | (92) ~ (all_121_0 = 0)
% 14.00/2.75 | | | | | | | (93) empty(all_85_2) = all_121_0
% 14.00/2.75 | | | | | | |
% 14.00/2.75 | | | | | | | DELTA: instantiating (89) with fresh symbols all_131_0, all_131_1
% 14.00/2.75 | | | | | | | gives:
% 14.00/2.75 | | | | | | | (94) empty(all_85_2) = all_131_1 & in(all_85_1, all_85_2) =
% 14.00/2.75 | | | | | | | all_131_0 & (all_131_0 = 0 | all_131_1 = 0)
% 14.00/2.75 | | | | | | |
% 14.00/2.75 | | | | | | | ALPHA: (94) implies:
% 14.00/2.75 | | | | | | | (95) empty(all_85_2) = all_131_1
% 14.00/2.75 | | | | | | | (96) all_131_0 = 0 | all_131_1 = 0
% 14.00/2.75 | | | | | | |
% 14.00/2.75 | | | | | | | DELTA: instantiating (88) with fresh symbols all_133_0, all_133_1
% 14.00/2.75 | | | | | | | gives:
% 14.00/2.75 | | | | | | | (97) empty(all_85_1) = all_133_0 & empty(all_85_2) = all_133_1
% 14.00/2.75 | | | | | | | & ( ~ (all_133_1 = 0) | all_133_0 = 0)
% 14.00/2.75 | | | | | | |
% 14.00/2.75 | | | | | | | ALPHA: (97) implies:
% 14.00/2.75 | | | | | | | (98) empty(all_85_2) = all_133_1
% 14.00/2.75 | | | | | | |
% 14.00/2.75 | | | | | | | BETA: splitting (86) gives:
% 14.00/2.75 | | | | | | |
% 14.00/2.75 | | | | | | | Case 1:
% 14.00/2.75 | | | | | | | |
% 14.00/2.75 | | | | | | | | (99) all_95_0 = 0
% 14.00/2.75 | | | | | | | |
% 14.00/2.75 | | | | | | | | REDUCE: (80), (99) imply:
% 14.00/2.75 | | | | | | | | (100) $false
% 14.00/2.75 | | | | | | | |
% 14.00/2.75 | | | | | | | | CLOSE: (100) is inconsistent.
% 14.00/2.75 | | | | | | | |
% 14.00/2.75 | | | | | | | Case 2:
% 14.00/2.75 | | | | | | | |
% 14.00/2.75 | | | | | | | | (101) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 14.00/2.75 | | | | | | | | all_22_2) = v1 & in(v0, all_22_3) = 0 & $i(v0))
% 14.00/2.75 | | | | | | | |
% 14.00/2.75 | | | | | | | | DELTA: instantiating (101) with fresh symbols all_150_0,
% 14.00/2.75 | | | | | | | | all_150_1 gives:
% 14.00/2.75 | | | | | | | | (102) ~ (all_150_0 = 0) & in(all_150_1, all_22_2) =
% 14.00/2.75 | | | | | | | | all_150_0 & in(all_150_1, all_22_3) = 0 & $i(all_150_1)
% 14.00/2.75 | | | | | | | |
% 14.00/2.75 | | | | | | | | ALPHA: (102) implies:
% 14.00/2.75 | | | | | | | | (103) ~ (all_150_0 = 0)
% 14.00/2.75 | | | | | | | | (104) $i(all_150_1)
% 14.00/2.75 | | | | | | | | (105) in(all_150_1, all_22_3) = 0
% 14.00/2.75 | | | | | | | | (106) in(all_150_1, all_22_2) = all_150_0
% 14.00/2.75 | | | | | | | |
% 14.00/2.75 | | | | | | | | BETA: splitting (90) gives:
% 14.00/2.75 | | | | | | | |
% 14.00/2.75 | | | | | | | | Case 1:
% 14.00/2.75 | | | | | | | | |
% 14.00/2.75 | | | | | | | | | (107) all_85_0 = 0
% 14.00/2.75 | | | | | | | | |
% 14.00/2.75 | | | | | | | | | REDUCE: (70), (107) imply:
% 14.00/2.75 | | | | | | | | | (108) $false
% 14.00/2.75 | | | | | | | | |
% 14.00/2.75 | | | | | | | | | CLOSE: (108) is inconsistent.
% 14.00/2.75 | | | | | | | | |
% 14.00/2.75 | | | | | | | | Case 2:
% 14.00/2.75 | | | | | | | | |
% 14.00/2.75 | | | | | | | | |
% 14.00/2.75 | | | | | | | | | GROUND_INST: instantiating (6) with all_131_1, all_133_1,
% 14.00/2.75 | | | | | | | | | all_85_2, simplifying with (95), (98) gives:
% 14.00/2.75 | | | | | | | | | (109) all_133_1 = all_131_1
% 14.00/2.75 | | | | | | | | |
% 14.00/2.75 | | | | | | | | | GROUND_INST: instantiating (6) with all_121_0, all_133_1,
% 14.00/2.75 | | | | | | | | | all_85_2, simplifying with (93), (98) gives:
% 14.00/2.75 | | | | | | | | | (110) all_133_1 = all_121_0
% 14.00/2.75 | | | | | | | | |
% 14.00/2.75 | | | | | | | | | COMBINE_EQS: (109), (110) imply:
% 14.00/2.75 | | | | | | | | | (111) all_131_1 = all_121_0
% 14.00/2.75 | | | | | | | | |
% 14.00/2.75 | | | | | | | | | SIMP: (111) implies:
% 14.00/2.75 | | | | | | | | | (112) all_131_1 = all_121_0
% 14.00/2.75 | | | | | | | | |
% 14.00/2.75 | | | | | | | | | BETA: splitting (96) gives:
% 14.00/2.75 | | | | | | | | |
% 14.00/2.75 | | | | | | | | | Case 1:
% 14.00/2.75 | | | | | | | | | |
% 14.00/2.75 | | | | | | | | | |
% 14.00/2.75 | | | | | | | | | | GROUND_INST: instantiating (19) with all_150_1, simplifying
% 14.00/2.75 | | | | | | | | | | with (104), (105) gives:
% 14.00/2.75 | | | | | | | | | | (113) in(all_150_1, all_22_2) = 0
% 14.00/2.75 | | | | | | | | | |
% 14.00/2.75 | | | | | | | | | | GROUND_INST: instantiating (7) with all_150_0, 0, all_22_2,
% 14.00/2.75 | | | | | | | | | | all_150_1, simplifying with (106), (113) gives:
% 14.00/2.75 | | | | | | | | | | (114) all_150_0 = 0
% 14.00/2.75 | | | | | | | | | |
% 14.00/2.75 | | | | | | | | | | REDUCE: (103), (114) imply:
% 14.00/2.75 | | | | | | | | | | (115) $false
% 14.00/2.75 | | | | | | | | | |
% 14.00/2.75 | | | | | | | | | | CLOSE: (115) is inconsistent.
% 14.00/2.75 | | | | | | | | | |
% 14.00/2.75 | | | | | | | | | Case 2:
% 14.00/2.75 | | | | | | | | | |
% 14.00/2.75 | | | | | | | | | | (116) all_131_1 = 0
% 14.00/2.75 | | | | | | | | | |
% 14.00/2.75 | | | | | | | | | | COMBINE_EQS: (112), (116) imply:
% 14.00/2.75 | | | | | | | | | | (117) all_121_0 = 0
% 14.00/2.75 | | | | | | | | | |
% 14.00/2.76 | | | | | | | | | | REDUCE: (92), (117) imply:
% 14.00/2.76 | | | | | | | | | | (118) $false
% 14.00/2.76 | | | | | | | | | |
% 14.00/2.76 | | | | | | | | | | CLOSE: (118) is inconsistent.
% 14.00/2.76 | | | | | | | | | |
% 14.00/2.76 | | | | | | | | | End of split
% 14.00/2.76 | | | | | | | | |
% 14.00/2.76 | | | | | | | | End of split
% 14.00/2.76 | | | | | | | |
% 14.00/2.76 | | | | | | | End of split
% 14.00/2.76 | | | | | | |
% 14.00/2.76 | | | | | | Case 2:
% 14.00/2.76 | | | | | | |
% 14.00/2.76 | | | | | | | (119) all_71_1 = 0
% 14.00/2.76 | | | | | | |
% 14.00/2.76 | | | | | | | COMBINE_EQS: (85), (119) imply:
% 14.00/2.76 | | | | | | | (120) all_65_0 = 0
% 14.00/2.76 | | | | | | |
% 14.00/2.76 | | | | | | | SIMP: (120) implies:
% 14.00/2.76 | | | | | | | (121) all_65_0 = 0
% 14.00/2.76 | | | | | | |
% 14.00/2.76 | | | | | | | REDUCE: (59), (121) imply:
% 14.00/2.76 | | | | | | | (122) $false
% 14.00/2.76 | | | | | | |
% 14.00/2.76 | | | | | | | CLOSE: (122) is inconsistent.
% 14.00/2.76 | | | | | | |
% 14.00/2.76 | | | | | | End of split
% 14.00/2.76 | | | | | |
% 14.00/2.76 | | | | | End of split
% 14.00/2.76 | | | | |
% 14.00/2.76 | | | | End of split
% 14.00/2.76 | | | |
% 14.00/2.76 | | | Case 2:
% 14.00/2.76 | | | |
% 14.00/2.76 | | | | (123) all_22_0 = 0
% 14.00/2.76 | | | |
% 14.00/2.76 | | | | REDUCE: (13), (123) imply:
% 14.00/2.76 | | | | (124) $false
% 14.00/2.76 | | | |
% 14.00/2.76 | | | | CLOSE: (124) is inconsistent.
% 14.00/2.76 | | | |
% 14.00/2.76 | | | End of split
% 14.00/2.76 | | |
% 14.00/2.76 | | End of split
% 14.00/2.76 | |
% 14.00/2.76 | End of split
% 14.00/2.76 |
% 14.00/2.76 End of proof
% 14.00/2.76 % SZS output end Proof for theBenchmark
% 14.00/2.76
% 14.00/2.76 2145ms
%------------------------------------------------------------------------------