TSTP Solution File: SEU062+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU062+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n023.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 17:42:26 EDT 2023
% Result : Theorem 9.07s 2.04s
% Output : Proof 15.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU062+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n023.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 : Wed Aug 23 20:12:27 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.65/0.66 ________ _____
% 0.65/0.66 ___ __ \_________(_)________________________________
% 0.65/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.65/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.65/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.65/0.66
% 0.65/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.65/0.66 (2023-06-19)
% 0.65/0.66
% 0.65/0.66 (c) Philipp Rümmer, 2009-2023
% 0.65/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.65/0.66 Amanda Stjerna.
% 0.65/0.66 Free software under BSD-3-Clause.
% 0.65/0.66
% 0.65/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.65/0.66
% 0.65/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.67 Running up to 7 provers in parallel.
% 0.74/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.74/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.74/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.74/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.74/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.74/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.74/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.95/1.14 Prover 4: Preprocessing ...
% 2.95/1.14 Prover 1: Preprocessing ...
% 3.13/1.18 Prover 5: Preprocessing ...
% 3.13/1.18 Prover 6: Preprocessing ...
% 3.13/1.18 Prover 0: Preprocessing ...
% 3.13/1.18 Prover 2: Preprocessing ...
% 3.13/1.18 Prover 3: Preprocessing ...
% 5.27/1.51 Prover 2: Proving ...
% 5.73/1.54 Prover 1: Warning: ignoring some quantifiers
% 5.73/1.54 Prover 5: Proving ...
% 5.73/1.56 Prover 1: Constructing countermodel ...
% 5.99/1.58 Prover 3: Warning: ignoring some quantifiers
% 5.99/1.59 Prover 3: Constructing countermodel ...
% 5.99/1.60 Prover 4: Warning: ignoring some quantifiers
% 5.99/1.63 Prover 4: Constructing countermodel ...
% 5.99/1.64 Prover 6: Proving ...
% 6.84/1.73 Prover 0: Proving ...
% 8.09/1.88 Prover 3: gave up
% 8.09/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.09/1.93 Prover 7: Preprocessing ...
% 8.71/1.95 Prover 1: gave up
% 8.71/1.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.07/1.98 Prover 8: Preprocessing ...
% 9.07/1.99 Prover 7: Warning: ignoring some quantifiers
% 9.07/2.00 Prover 7: Constructing countermodel ...
% 9.07/2.04 Prover 0: proved (1358ms)
% 9.07/2.04
% 9.07/2.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.07/2.04
% 9.53/2.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.53/2.06 Prover 2: stopped
% 9.62/2.07 Prover 6: stopped
% 9.62/2.07 Prover 5: stopped
% 9.62/2.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.62/2.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.62/2.08 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.62/2.09 Prover 10: Preprocessing ...
% 9.62/2.11 Prover 16: Preprocessing ...
% 10.02/2.12 Prover 11: Preprocessing ...
% 10.02/2.13 Prover 13: Preprocessing ...
% 10.02/2.13 Prover 8: Warning: ignoring some quantifiers
% 10.02/2.14 Prover 8: Constructing countermodel ...
% 10.37/2.16 Prover 16: Warning: ignoring some quantifiers
% 10.37/2.17 Prover 10: Warning: ignoring some quantifiers
% 10.37/2.18 Prover 16: Constructing countermodel ...
% 10.37/2.18 Prover 10: Constructing countermodel ...
% 10.37/2.21 Prover 13: Warning: ignoring some quantifiers
% 10.37/2.23 Prover 13: Constructing countermodel ...
% 11.02/2.24 Prover 10: gave up
% 11.02/2.26 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.02/2.26 Prover 7: gave up
% 11.02/2.28 Prover 11: Warning: ignoring some quantifiers
% 11.02/2.28 Prover 11: Constructing countermodel ...
% 11.02/2.29 Prover 19: Preprocessing ...
% 11.83/2.39 Prover 19: Warning: ignoring some quantifiers
% 12.23/2.41 Prover 19: Constructing countermodel ...
% 12.23/2.45 Prover 8: gave up
% 14.95/2.77 Prover 19: gave up
% 14.95/2.77 Prover 13: gave up
% 14.95/2.78 Prover 4: Found proof (size 66)
% 14.95/2.78 Prover 4: proved (2102ms)
% 14.95/2.78 Prover 16: stopped
% 14.95/2.78 Prover 11: stopped
% 14.95/2.78
% 14.95/2.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.95/2.78
% 14.95/2.79 % SZS output start Proof for theBenchmark
% 14.95/2.80 Assumptions after simplification:
% 14.95/2.80 ---------------------------------
% 14.95/2.80
% 14.95/2.80 (d3_tarski)
% 14.95/2.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.95/2.82 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 14.95/2.82 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 14.95/2.82 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 14.95/2.82 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 14.95/2.82 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.95/2.82 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 14.95/2.82 $i(v0) | in(v2, v1) = 0)
% 14.95/2.82
% 14.95/2.82 (fc6_relat_1)
% 14.95/2.83 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 14.95/2.83 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_rng(v0) = v3 &
% 14.95/2.83 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 14.95/2.83 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 14.95/2.83 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 14.95/2.83 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) &
% 14.95/2.83 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 14.95/2.83 : ? [v3: any] : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 &
% 14.95/2.83 $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 14.95/2.83
% 14.95/2.83 (rc1_subset_1)
% 14.95/2.83 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 14.95/2.83 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v0) = v2 &
% 14.95/2.83 element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) & $i(v2))) & ! [v0: $i] :
% 14.95/2.83 ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i]
% 14.95/2.83 : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) &
% 14.95/2.83 element(v3, v1) = 0 & empty(v3) = v5) | (v2 = 0 & empty(v0) = 0))))
% 14.95/2.83
% 14.95/2.83 (rc2_relat_1)
% 14.95/2.83 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1
% 14.95/2.83 & $i(v0))
% 14.95/2.83
% 14.95/2.83 (rc2_xboole_0)
% 14.95/2.83 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0))
% 14.95/2.83
% 14.95/2.83 (t142_funct_1)
% 14.95/2.83 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 14.95/2.83 (relation_inverse_image(v1, v2) = v3) | ~ (singleton(v0) = v2) | ~ $i(v1)
% 14.95/2.83 | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (relation_rng(v1)
% 14.95/2.83 = v5 & relation(v1) = v4 & in(v0, v5) = v6 & $i(v5) & ( ~ (v4 = 0) | (( ~
% 14.95/2.83 (v6 = 0) | ~ (v3 = empty_set)) & (v6 = 0 | v3 = empty_set))))) & !
% 14.95/2.83 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (relation_rng(v1) =
% 14.95/2.83 v2) | ~ (in(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 14.95/2.83 [v5: $i] : ? [v6: $i] : (relation_inverse_image(v1, v5) = v6 &
% 14.95/2.83 singleton(v0) = v5 & relation(v1) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) |
% 14.95/2.83 (( ~ (v6 = empty_set) | ~ (v3 = 0)) & (v6 = empty_set | v3 = 0)))))
% 14.95/2.83
% 14.95/2.83 (t143_funct_1)
% 14.95/2.83 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~
% 14.95/2.83 (v3 = 0) & relation_rng(v1) = v2 & subset(v0, v2) = v3 & relation(v1) = 0 &
% 14.95/2.83 $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~ (singleton(v4) =
% 14.95/2.83 v5) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] :
% 14.95/2.83 (relation_inverse_image(v1, v5) = v7 & in(v4, v0) = v6 & $i(v7) & ( ~ (v7
% 14.95/2.83 = empty_set) | ~ (v6 = 0)))) & ! [v4: $i] : ( ~ (in(v4, v0) = 0) |
% 14.95/2.83 ~ $i(v4) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = empty_set) &
% 14.95/2.83 relation_inverse_image(v1, v5) = v6 & singleton(v4) = v5 & $i(v6) &
% 14.95/2.83 $i(v5))))
% 14.95/2.83
% 14.95/2.84 (function-axioms)
% 14.95/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.95/2.84 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) =
% 14.95/2.84 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.95/2.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 14.95/2.84 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 14.95/2.84 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~
% 14.95/2.84 (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.95/2.84 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) =
% 14.95/2.84 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.95/2.84 (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0:
% 14.95/2.84 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 14.95/2.84 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 14.95/2.84 ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0:
% 14.95/2.84 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 14.95/2.84 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) =
% 14.95/2.84 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.95/2.84 $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & !
% 14.95/2.84 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 14.95/2.84 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0:
% 14.95/2.84 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 14.95/2.84 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 14.95/2.84 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 14.95/2.84 ~ (empty(v2) = v0))
% 14.95/2.84
% 14.95/2.84 Further assumptions not needed in the proof:
% 14.95/2.84 --------------------------------------------
% 14.95/2.84 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1,
% 14.95/2.84 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc2_subset_1,
% 14.95/2.84 fc4_relat_1, fc8_relat_1, rc1_funct_1, rc1_relat_1, rc1_xboole_0, rc2_funct_1,
% 14.95/2.84 rc2_subset_1, rc3_funct_1, rc3_relat_1, reflexivity_r1_tarski, t1_subset,
% 14.95/2.84 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 14.95/2.84
% 14.95/2.84 Those formulas are unsatisfiable:
% 14.95/2.84 ---------------------------------
% 14.95/2.84
% 14.95/2.84 Begin of proof
% 14.95/2.84 |
% 14.95/2.84 | ALPHA: (d3_tarski) implies:
% 14.95/2.84 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 14.95/2.84 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 14.95/2.84 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 14.95/2.84 |
% 14.95/2.84 | ALPHA: (fc6_relat_1) implies:
% 14.95/2.84 | (2) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 14.95/2.84 | [v2: $i] : ? [v3: any] : (relation_rng(v0) = v2 & empty(v2) = v3 &
% 14.95/2.84 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 14.95/2.84 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 14.95/2.84 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 14.95/2.84 | empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 =
% 14.95/2.84 | 0)))
% 14.95/2.85 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0)
% 14.95/2.85 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_rng(v0) = v3
% 14.95/2.85 | & relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~
% 14.95/2.85 | (v2 = 0))))
% 14.95/2.85 |
% 14.95/2.85 | ALPHA: (rc1_subset_1) implies:
% 14.95/2.85 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0)
% 14.95/2.85 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 14.95/2.85 | powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) &
% 14.95/2.85 | $i(v2)))
% 14.95/2.85 |
% 14.95/2.85 | ALPHA: (t142_funct_1) implies:
% 14.95/2.85 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 14.95/2.85 | (relation_rng(v1) = v2) | ~ (in(v0, v2) = v3) | ~ $i(v1) | ~
% 14.95/2.85 | $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] :
% 14.95/2.85 | (relation_inverse_image(v1, v5) = v6 & singleton(v0) = v5 &
% 14.95/2.85 | relation(v1) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | (( ~ (v6 =
% 14.95/2.85 | empty_set) | ~ (v3 = 0)) & (v6 = empty_set | v3 = 0)))))
% 14.95/2.85 |
% 14.95/2.85 | ALPHA: (t143_funct_1) implies:
% 14.95/2.85 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 14.95/2.85 | relation_rng(v1) = v2 & subset(v0, v2) = v3 & relation(v1) = 0 &
% 14.95/2.85 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~
% 14.95/2.85 | (singleton(v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] :
% 14.95/2.85 | (relation_inverse_image(v1, v5) = v7 & in(v4, v0) = v6 & $i(v7) & (
% 14.95/2.85 | ~ (v7 = empty_set) | ~ (v6 = 0)))) & ! [v4: $i] : ( ~ (in(v4,
% 14.95/2.85 | v0) = 0) | ~ $i(v4) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 =
% 14.95/2.85 | empty_set) & relation_inverse_image(v1, v5) = v6 &
% 14.95/2.85 | singleton(v4) = v5 & $i(v6) & $i(v5))))
% 14.95/2.85 |
% 14.95/2.85 | ALPHA: (function-axioms) implies:
% 14.95/2.85 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.95/2.85 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 14.95/2.85 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 14.95/2.85 | = v1) | ~ (singleton(v2) = v0))
% 14.95/2.85 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.95/2.85 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 14.95/2.85 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.95/2.85 | (relation_inverse_image(v3, v2) = v1) | ~
% 14.95/2.85 | (relation_inverse_image(v3, v2) = v0))
% 14.95/2.85 |
% 14.95/2.85 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_27_0, all_27_1
% 14.95/2.85 | gives:
% 14.95/2.85 | (12) ~ (all_27_0 = 0) & empty(all_27_1) = all_27_0 & $i(all_27_1)
% 14.95/2.85 |
% 14.95/2.85 | ALPHA: (12) implies:
% 14.95/2.85 | (13) ~ (all_27_0 = 0)
% 14.95/2.85 | (14) $i(all_27_1)
% 14.95/2.85 | (15) empty(all_27_1) = all_27_0
% 14.95/2.85 |
% 14.95/2.85 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_40_0, all_40_1
% 14.95/2.85 | gives:
% 15.47/2.85 | (16) ~ (all_40_0 = 0) & relation(all_40_1) = 0 & empty(all_40_1) =
% 15.47/2.85 | all_40_0 & $i(all_40_1)
% 15.47/2.85 |
% 15.47/2.85 | ALPHA: (16) implies:
% 15.47/2.85 | (17) ~ (all_40_0 = 0)
% 15.47/2.85 | (18) $i(all_40_1)
% 15.47/2.85 | (19) empty(all_40_1) = all_40_0
% 15.47/2.85 | (20) relation(all_40_1) = 0
% 15.47/2.85 |
% 15.47/2.85 | DELTA: instantiating (7) with fresh symbols all_42_0, all_42_1, all_42_2,
% 15.47/2.85 | all_42_3 gives:
% 15.47/2.86 | (21) ~ (all_42_0 = 0) & relation_rng(all_42_2) = all_42_1 &
% 15.47/2.86 | subset(all_42_3, all_42_1) = all_42_0 & relation(all_42_2) = 0 &
% 15.47/2.86 | $i(all_42_1) & $i(all_42_2) & $i(all_42_3) & ! [v0: $i] : ! [v1: $i]
% 15.47/2.86 | : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] :
% 15.47/2.86 | (relation_inverse_image(all_42_2, v1) = v3 & in(v0, all_42_3) = v2 &
% 15.47/2.86 | $i(v3) & ( ~ (v3 = empty_set) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~
% 15.47/2.86 | (in(v0, all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ( ~
% 15.47/2.86 | (v2 = empty_set) & relation_inverse_image(all_42_2, v1) = v2 &
% 15.47/2.86 | singleton(v0) = v1 & $i(v2) & $i(v1)))
% 15.47/2.86 |
% 15.47/2.86 | ALPHA: (21) implies:
% 15.47/2.86 | (22) ~ (all_42_0 = 0)
% 15.47/2.86 | (23) $i(all_42_3)
% 15.47/2.86 | (24) $i(all_42_2)
% 15.47/2.86 | (25) $i(all_42_1)
% 15.47/2.86 | (26) relation(all_42_2) = 0
% 15.47/2.86 | (27) subset(all_42_3, all_42_1) = all_42_0
% 15.47/2.86 | (28) relation_rng(all_42_2) = all_42_1
% 15.47/2.86 | (29) ! [v0: $i] : ( ~ (in(v0, all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] :
% 15.47/2.86 | ? [v2: $i] : ( ~ (v2 = empty_set) & relation_inverse_image(all_42_2,
% 15.47/2.86 | v1) = v2 & singleton(v0) = v1 & $i(v2) & $i(v1)))
% 15.47/2.86 |
% 15.47/2.86 | GROUND_INST: instantiating (5) with all_27_1, all_27_0, simplifying with (14),
% 15.47/2.86 | (15) gives:
% 15.47/2.86 | (30) all_27_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 15.47/2.86 | & powerset(all_27_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2 &
% 15.47/2.86 | $i(v1) & $i(v0))
% 15.47/2.86 |
% 15.47/2.86 | GROUND_INST: instantiating (4) with all_40_1, all_40_0, simplifying with (18),
% 15.47/2.86 | (19) gives:
% 15.47/2.86 | (31) all_40_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 15.47/2.86 | (relation_rng(all_40_1) = v1 & relation(all_40_1) = v0 & empty(v1) =
% 15.47/2.86 | v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 15.47/2.86 |
% 15.47/2.86 | GROUND_INST: instantiating (2) with all_42_2, simplifying with (24), (26)
% 15.47/2.86 | gives:
% 15.47/2.86 | (32) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_rng(all_42_2) =
% 15.47/2.86 | v1 & empty(v1) = v2 & empty(all_42_2) = v0 & $i(v1) & ( ~ (v2 = 0) |
% 15.47/2.86 | v0 = 0))
% 15.47/2.86 |
% 15.47/2.86 | GROUND_INST: instantiating (1) with all_42_3, all_42_1, all_42_0, simplifying
% 15.47/2.86 | with (23), (25), (27) gives:
% 15.47/2.86 | (33) all_42_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 15.47/2.86 | all_42_1) = v1 & in(v0, all_42_3) = 0 & $i(v0))
% 15.47/2.86 |
% 15.47/2.86 | GROUND_INST: instantiating (3) with all_42_2, all_42_1, simplifying with (24),
% 15.47/2.86 | (28) gives:
% 15.47/2.86 | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_42_2) = v1
% 15.47/2.86 | & empty(all_42_1) = v2 & empty(all_42_2) = v0 & ( ~ (v2 = 0) | ~
% 15.47/2.86 | (v1 = 0) | v0 = 0))
% 15.47/2.86 |
% 15.47/2.86 | DELTA: instantiating (34) with fresh symbols all_63_0, all_63_1, all_63_2
% 15.47/2.86 | gives:
% 15.47/2.86 | (35) relation(all_42_2) = all_63_1 & empty(all_42_1) = all_63_0 &
% 15.47/2.86 | empty(all_42_2) = all_63_2 & ( ~ (all_63_0 = 0) | ~ (all_63_1 = 0) |
% 15.47/2.86 | all_63_2 = 0)
% 15.47/2.86 |
% 15.47/2.86 | ALPHA: (35) implies:
% 15.47/2.86 | (36) relation(all_42_2) = all_63_1
% 15.47/2.86 |
% 15.47/2.86 | DELTA: instantiating (32) with fresh symbols all_85_0, all_85_1, all_85_2
% 15.47/2.86 | gives:
% 15.47/2.86 | (37) relation_rng(all_42_2) = all_85_1 & empty(all_85_1) = all_85_0 &
% 15.47/2.86 | empty(all_42_2) = all_85_2 & $i(all_85_1) & ( ~ (all_85_0 = 0) |
% 15.47/2.86 | all_85_2 = 0)
% 15.47/2.86 |
% 15.47/2.86 | ALPHA: (37) implies:
% 15.47/2.86 | (38) relation_rng(all_42_2) = all_85_1
% 15.47/2.86 |
% 15.47/2.86 | BETA: splitting (31) gives:
% 15.47/2.86 |
% 15.47/2.86 | Case 1:
% 15.47/2.86 | |
% 15.47/2.86 | | (39) all_40_0 = 0
% 15.47/2.86 | |
% 15.47/2.87 | | REDUCE: (17), (39) imply:
% 15.47/2.87 | | (40) $false
% 15.47/2.87 | |
% 15.47/2.87 | | CLOSE: (40) is inconsistent.
% 15.47/2.87 | |
% 15.47/2.87 | Case 2:
% 15.47/2.87 | |
% 15.47/2.87 | | (41) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_rng(all_40_1)
% 15.47/2.87 | | = v1 & relation(all_40_1) = v0 & empty(v1) = v2 & $i(v1) & ( ~ (v2
% 15.47/2.87 | | = 0) | ~ (v0 = 0)))
% 15.47/2.87 | |
% 15.47/2.87 | | DELTA: instantiating (41) with fresh symbols all_115_0, all_115_1, all_115_2
% 15.47/2.87 | | gives:
% 15.47/2.87 | | (42) relation_rng(all_40_1) = all_115_1 & relation(all_40_1) = all_115_2
% 15.47/2.87 | | & empty(all_115_1) = all_115_0 & $i(all_115_1) & ( ~ (all_115_0 = 0)
% 15.47/2.87 | | | ~ (all_115_2 = 0))
% 15.47/2.87 | |
% 15.47/2.87 | | ALPHA: (42) implies:
% 15.47/2.87 | | (43) relation(all_40_1) = all_115_2
% 15.47/2.87 | | (44) ~ (all_115_0 = 0) | ~ (all_115_2 = 0)
% 15.47/2.87 | |
% 15.47/2.87 | | BETA: splitting (33) gives:
% 15.47/2.87 | |
% 15.47/2.87 | | Case 1:
% 15.47/2.87 | | |
% 15.47/2.87 | | | (45) all_42_0 = 0
% 15.47/2.87 | | |
% 15.47/2.87 | | | REDUCE: (22), (45) imply:
% 15.47/2.87 | | | (46) $false
% 15.47/2.87 | | |
% 15.47/2.87 | | | CLOSE: (46) is inconsistent.
% 15.47/2.87 | | |
% 15.47/2.87 | | Case 2:
% 15.47/2.87 | | |
% 15.47/2.87 | | | (47) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_42_1) = v1
% 15.47/2.87 | | | & in(v0, all_42_3) = 0 & $i(v0))
% 15.47/2.87 | | |
% 15.47/2.87 | | | DELTA: instantiating (47) with fresh symbols all_120_0, all_120_1 gives:
% 15.47/2.87 | | | (48) ~ (all_120_0 = 0) & in(all_120_1, all_42_1) = all_120_0 &
% 15.47/2.87 | | | in(all_120_1, all_42_3) = 0 & $i(all_120_1)
% 15.47/2.87 | | |
% 15.47/2.87 | | | ALPHA: (48) implies:
% 15.47/2.87 | | | (49) ~ (all_120_0 = 0)
% 15.47/2.87 | | | (50) $i(all_120_1)
% 15.47/2.87 | | | (51) in(all_120_1, all_42_3) = 0
% 15.47/2.87 | | | (52) in(all_120_1, all_42_1) = all_120_0
% 15.47/2.87 | | |
% 15.47/2.87 | | | BETA: splitting (30) gives:
% 15.47/2.87 | | |
% 15.47/2.87 | | | Case 1:
% 15.47/2.87 | | | |
% 15.47/2.87 | | | | (53) all_27_0 = 0
% 15.47/2.87 | | | |
% 15.47/2.87 | | | | REDUCE: (13), (53) imply:
% 15.47/2.87 | | | | (54) $false
% 15.47/2.87 | | | |
% 15.47/2.87 | | | | CLOSE: (54) is inconsistent.
% 15.47/2.87 | | | |
% 15.47/2.87 | | | Case 2:
% 15.47/2.87 | | | |
% 15.47/2.87 | | | |
% 15.47/2.87 | | | | GROUND_INST: instantiating (8) with 0, all_115_2, all_40_1, simplifying
% 15.47/2.87 | | | | with (20), (43) gives:
% 15.47/2.87 | | | | (55) all_115_2 = 0
% 15.47/2.87 | | | |
% 15.47/2.87 | | | | GROUND_INST: instantiating (8) with 0, all_63_1, all_42_2, simplifying
% 15.47/2.87 | | | | with (26), (36) gives:
% 15.47/2.87 | | | | (56) all_63_1 = 0
% 15.47/2.87 | | | |
% 15.47/2.87 | | | | GROUND_INST: instantiating (10) with all_42_1, all_85_1, all_42_2,
% 15.47/2.87 | | | | simplifying with (28), (38) gives:
% 15.47/2.87 | | | | (57) all_85_1 = all_42_1
% 15.47/2.87 | | | |
% 15.47/2.87 | | | | BETA: splitting (44) gives:
% 15.47/2.87 | | | |
% 15.47/2.87 | | | | Case 1:
% 15.47/2.87 | | | | |
% 15.47/2.87 | | | | |
% 15.47/2.87 | | | | | GROUND_INST: instantiating (29) with all_120_1, simplifying with (50),
% 15.47/2.87 | | | | | (51) gives:
% 15.47/2.87 | | | | | (58) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) &
% 15.47/2.87 | | | | | relation_inverse_image(all_42_2, v0) = v1 &
% 15.47/2.87 | | | | | singleton(all_120_1) = v0 & $i(v1) & $i(v0))
% 15.47/2.87 | | | | |
% 15.47/2.87 | | | | | GROUND_INST: instantiating (6) with all_120_1, all_42_2, all_42_1,
% 15.47/2.87 | | | | | all_120_0, simplifying with (24), (28), (50), (52) gives:
% 15.47/2.87 | | | | | (59) ? [v0: any] : ? [v1: $i] : ? [v2: $i] :
% 15.47/2.87 | | | | | (relation_inverse_image(all_42_2, v1) = v2 &
% 15.47/2.87 | | | | | singleton(all_120_1) = v1 & relation(all_42_2) = v0 & $i(v2)
% 15.47/2.87 | | | | | & $i(v1) & ( ~ (v0 = 0) | (( ~ (v2 = empty_set) | ~
% 15.47/2.87 | | | | | (all_120_0 = 0)) & (v2 = empty_set | all_120_0 = 0))))
% 15.47/2.87 | | | | |
% 15.47/2.87 | | | | | DELTA: instantiating (58) with fresh symbols all_207_0, all_207_1
% 15.47/2.87 | | | | | gives:
% 15.47/2.87 | | | | | (60) ~ (all_207_0 = empty_set) & relation_inverse_image(all_42_2,
% 15.47/2.87 | | | | | all_207_1) = all_207_0 & singleton(all_120_1) = all_207_1 &
% 15.47/2.87 | | | | | $i(all_207_0) & $i(all_207_1)
% 15.47/2.87 | | | | |
% 15.47/2.88 | | | | | ALPHA: (60) implies:
% 15.47/2.88 | | | | | (61) ~ (all_207_0 = empty_set)
% 15.47/2.88 | | | | | (62) singleton(all_120_1) = all_207_1
% 15.47/2.88 | | | | | (63) relation_inverse_image(all_42_2, all_207_1) = all_207_0
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | | DELTA: instantiating (59) with fresh symbols all_245_0, all_245_1,
% 15.47/2.88 | | | | | all_245_2 gives:
% 15.47/2.88 | | | | | (64) relation_inverse_image(all_42_2, all_245_1) = all_245_0 &
% 15.47/2.88 | | | | | singleton(all_120_1) = all_245_1 & relation(all_42_2) =
% 15.47/2.88 | | | | | all_245_2 & $i(all_245_0) & $i(all_245_1) & ( ~ (all_245_2 =
% 15.47/2.88 | | | | | 0) | (( ~ (all_245_0 = empty_set) | ~ (all_120_0 = 0)) &
% 15.47/2.88 | | | | | (all_245_0 = empty_set | all_120_0 = 0)))
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | | ALPHA: (64) implies:
% 15.47/2.88 | | | | | (65) relation(all_42_2) = all_245_2
% 15.47/2.88 | | | | | (66) singleton(all_120_1) = all_245_1
% 15.47/2.88 | | | | | (67) relation_inverse_image(all_42_2, all_245_1) = all_245_0
% 15.47/2.88 | | | | | (68) ~ (all_245_2 = 0) | (( ~ (all_245_0 = empty_set) | ~
% 15.47/2.88 | | | | | (all_120_0 = 0)) & (all_245_0 = empty_set | all_120_0 =
% 15.47/2.88 | | | | | 0))
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | | GROUND_INST: instantiating (8) with 0, all_245_2, all_42_2,
% 15.47/2.88 | | | | | simplifying with (26), (65) gives:
% 15.47/2.88 | | | | | (69) all_245_2 = 0
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | | GROUND_INST: instantiating (9) with all_207_1, all_245_1, all_120_1,
% 15.47/2.88 | | | | | simplifying with (62), (66) gives:
% 15.47/2.88 | | | | | (70) all_245_1 = all_207_1
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | | REDUCE: (67), (70) imply:
% 15.47/2.88 | | | | | (71) relation_inverse_image(all_42_2, all_207_1) = all_245_0
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | | BETA: splitting (68) gives:
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | | Case 1:
% 15.47/2.88 | | | | | |
% 15.47/2.88 | | | | | | (72) ~ (all_245_2 = 0)
% 15.47/2.88 | | | | | |
% 15.47/2.88 | | | | | | REDUCE: (69), (72) imply:
% 15.47/2.88 | | | | | | (73) $false
% 15.47/2.88 | | | | | |
% 15.47/2.88 | | | | | | CLOSE: (73) is inconsistent.
% 15.47/2.88 | | | | | |
% 15.47/2.88 | | | | | Case 2:
% 15.47/2.88 | | | | | |
% 15.47/2.88 | | | | | | (74) ( ~ (all_245_0 = empty_set) | ~ (all_120_0 = 0)) &
% 15.47/2.88 | | | | | | (all_245_0 = empty_set | all_120_0 = 0)
% 15.47/2.88 | | | | | |
% 15.47/2.88 | | | | | | ALPHA: (74) implies:
% 15.47/2.88 | | | | | | (75) all_245_0 = empty_set | all_120_0 = 0
% 15.47/2.88 | | | | | |
% 15.47/2.88 | | | | | | BETA: splitting (75) gives:
% 15.47/2.88 | | | | | |
% 15.47/2.88 | | | | | | Case 1:
% 15.47/2.88 | | | | | | |
% 15.47/2.88 | | | | | | | (76) all_245_0 = empty_set
% 15.47/2.88 | | | | | | |
% 15.47/2.88 | | | | | | | REDUCE: (71), (76) imply:
% 15.47/2.88 | | | | | | | (77) relation_inverse_image(all_42_2, all_207_1) = empty_set
% 15.47/2.88 | | | | | | |
% 15.47/2.88 | | | | | | | GROUND_INST: instantiating (11) with all_207_0, empty_set,
% 15.47/2.88 | | | | | | | all_207_1, all_42_2, simplifying with (63), (77)
% 15.47/2.88 | | | | | | | gives:
% 15.47/2.88 | | | | | | | (78) all_207_0 = empty_set
% 15.47/2.88 | | | | | | |
% 15.47/2.88 | | | | | | | REDUCE: (61), (78) imply:
% 15.47/2.88 | | | | | | | (79) $false
% 15.47/2.88 | | | | | | |
% 15.47/2.88 | | | | | | | CLOSE: (79) is inconsistent.
% 15.47/2.88 | | | | | | |
% 15.47/2.88 | | | | | | Case 2:
% 15.47/2.88 | | | | | | |
% 15.47/2.88 | | | | | | | (80) all_120_0 = 0
% 15.47/2.88 | | | | | | |
% 15.47/2.88 | | | | | | | REDUCE: (49), (80) imply:
% 15.47/2.88 | | | | | | | (81) $false
% 15.47/2.88 | | | | | | |
% 15.47/2.88 | | | | | | | CLOSE: (81) is inconsistent.
% 15.47/2.88 | | | | | | |
% 15.47/2.88 | | | | | | End of split
% 15.47/2.88 | | | | | |
% 15.47/2.88 | | | | | End of split
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | Case 2:
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | | (82) ~ (all_115_2 = 0)
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | | REDUCE: (55), (82) imply:
% 15.47/2.88 | | | | | (83) $false
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | | CLOSE: (83) is inconsistent.
% 15.47/2.88 | | | | |
% 15.47/2.88 | | | | End of split
% 15.47/2.88 | | | |
% 15.47/2.88 | | | End of split
% 15.47/2.88 | | |
% 15.47/2.88 | | End of split
% 15.47/2.88 | |
% 15.47/2.88 | End of split
% 15.47/2.88 |
% 15.47/2.88 End of proof
% 15.47/2.88 % SZS output end Proof for theBenchmark
% 15.47/2.88
% 15.47/2.88 2223ms
%------------------------------------------------------------------------------