TSTP Solution File: SEU240+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU240+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 : n032.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 17:43:35 EDT 2023
% Result : Theorem 12.02s 2.31s
% Output : Proof 17.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU240+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Wed Aug 23 19:52:56 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.51 ________ _____
% 0.14/0.51 ___ __ \_________(_)________________________________
% 0.14/0.51 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.51 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.51 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.51
% 0.14/0.51 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.51 (2023-06-19)
% 0.14/0.51
% 0.14/0.51 (c) Philipp Rümmer, 2009-2023
% 0.14/0.51 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.51 Amanda Stjerna.
% 0.14/0.51 Free software under BSD-3-Clause.
% 0.14/0.51
% 0.14/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.51
% 0.14/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.14/0.53 Running up to 7 provers in parallel.
% 0.14/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.14/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.21/0.94 Prover 4: Preprocessing ...
% 2.21/0.94 Prover 1: Preprocessing ...
% 2.44/0.98 Prover 5: Preprocessing ...
% 2.44/0.98 Prover 2: Preprocessing ...
% 2.44/0.98 Prover 6: Preprocessing ...
% 2.44/0.98 Prover 0: Preprocessing ...
% 2.44/0.98 Prover 3: Preprocessing ...
% 4.69/1.36 Prover 1: Warning: ignoring some quantifiers
% 4.69/1.37 Prover 5: Proving ...
% 4.69/1.40 Prover 3: Warning: ignoring some quantifiers
% 4.69/1.40 Prover 1: Constructing countermodel ...
% 4.69/1.42 Prover 3: Constructing countermodel ...
% 5.66/1.47 Prover 2: Proving ...
% 6.13/1.49 Prover 6: Proving ...
% 6.73/1.57 Prover 4: Warning: ignoring some quantifiers
% 6.73/1.59 Prover 4: Constructing countermodel ...
% 6.73/1.60 Prover 0: Proving ...
% 7.93/1.76 Prover 3: gave up
% 7.93/1.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.35/1.81 Prover 7: Preprocessing ...
% 8.94/1.90 Prover 1: gave up
% 9.25/1.91 Prover 7: Warning: ignoring some quantifiers
% 9.25/1.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.25/1.94 Prover 8: Preprocessing ...
% 9.25/1.94 Prover 7: Constructing countermodel ...
% 9.25/2.03 Prover 8: Warning: ignoring some quantifiers
% 9.25/2.05 Prover 8: Constructing countermodel ...
% 12.02/2.31 Prover 0: proved (1774ms)
% 12.02/2.31
% 12.02/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.02/2.31
% 12.02/2.31 Prover 2: stopped
% 12.02/2.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.02/2.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.02/2.31 Prover 6: stopped
% 12.02/2.32 Prover 5: stopped
% 12.02/2.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.02/2.34 Prover 11: Preprocessing ...
% 12.02/2.34 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.34/2.36 Prover 10: Preprocessing ...
% 12.34/2.36 Prover 16: Preprocessing ...
% 12.34/2.37 Prover 13: Preprocessing ...
% 12.34/2.40 Prover 10: Warning: ignoring some quantifiers
% 12.34/2.41 Prover 10: Constructing countermodel ...
% 12.34/2.42 Prover 8: gave up
% 12.34/2.44 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.34/2.44 Prover 16: Warning: ignoring some quantifiers
% 12.98/2.44 Prover 16: Constructing countermodel ...
% 12.98/2.46 Prover 13: Warning: ignoring some quantifiers
% 12.98/2.46 Prover 19: Preprocessing ...
% 12.98/2.47 Prover 11: Warning: ignoring some quantifiers
% 12.98/2.48 Prover 13: Constructing countermodel ...
% 13.36/2.50 Prover 10: gave up
% 13.36/2.50 Prover 11: Constructing countermodel ...
% 14.22/2.61 Prover 19: Warning: ignoring some quantifiers
% 14.22/2.62 Prover 19: Constructing countermodel ...
% 16.04/2.89 Prover 13: gave up
% 16.70/2.98 Prover 4: Found proof (size 153)
% 16.70/2.98 Prover 4: proved (2445ms)
% 16.70/2.98 Prover 19: stopped
% 16.70/2.98 Prover 7: stopped
% 16.70/2.98 Prover 11: stopped
% 16.70/2.98 Prover 16: stopped
% 16.70/2.98
% 16.70/2.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.70/2.98
% 16.70/3.00 % SZS output start Proof for theBenchmark
% 16.70/3.00 Assumptions after simplification:
% 16.70/3.00 ---------------------------------
% 16.70/3.00
% 16.70/3.01 (cc2_funct_1)
% 16.70/3.03 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 16.70/3.03 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 16.70/3.03 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 16.70/3.03 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 16.70/3.03 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 16.70/3.03 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 16.70/3.03 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 16.70/3.03 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 16.70/3.03 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 16.70/3.03 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 16.70/3.03 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 16.70/3.03 0)))
% 16.70/3.03
% 16.70/3.03 (commutativity_k2_xboole_0)
% 16.70/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 16.70/3.04 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 16.70/3.04 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 16.70/3.04 | (set_union2(v1, v0) = v2 & $i(v2)))
% 16.70/3.04
% 16.70/3.04 (d16_relat_2)
% 17.25/3.04 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ?
% 17.25/3.04 [v2: any] : ? [v3: any] : ? [v4: any] : (transitive(v0) = v3 &
% 17.25/3.04 is_transitive_in(v0, v1) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~
% 17.25/3.04 (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0))))) & ! [v0: $i] : !
% 17.25/3.04 [v1: any] : ( ~ (transitive(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i]
% 17.25/3.04 : ? [v4: any] : (relation_field(v0) = v3 & is_transitive_in(v0, v3) = v4 &
% 17.25/3.04 relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v4 = 0) | v1 = 0) & ( ~
% 17.25/3.04 (v1 = 0) | v4 = 0))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~
% 17.25/3.04 $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any] : (relation_field(v0) =
% 17.25/3.04 v2 & transitive(v0) = v1 & is_transitive_in(v0, v2) = v3 & $i(v2) & ( ~
% 17.25/3.04 (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 17.25/3.04
% 17.25/3.04 (d6_relat_1)
% 17.25/3.04 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 17.25/3.04 any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v4 &
% 17.25/3.04 relation_field(v0) = v3 & set_union2(v1, v4) = v5 & relation(v0) = v2 &
% 17.25/3.04 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : !
% 17.25/3.04 [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 17.25/3.04 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 &
% 17.25/3.04 relation_field(v0) = v3 & set_union2(v4, v1) = v5 & relation(v0) = v2 &
% 17.25/3.04 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : !
% 17.25/3.04 [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 17.25/3.04 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v3 &
% 17.25/3.04 relation_rng(v0) = v4 & set_union2(v3, v4) = v5 & relation(v0) = v2 &
% 17.25/3.04 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v1))) & ! [v0: $i] : ( ~
% 17.25/3.04 (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 17.25/3.04 (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 &
% 17.25/3.04 set_union2(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 17.25/3.04
% 17.25/3.04 (d8_relat_2)
% 17.25/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.25/3.05 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (ordered_pair(v3, v4) = v5)
% 17.25/3.05 | ~ (ordered_pair(v2, v4) = v6) | ~ (is_transitive_in(v0, v1) = 0) | ~
% 17.25/3.05 (relation(v0) = 0) | ~ (in(v6, v0) = v7) | ~ (in(v5, v0) = 0) | ~ $i(v4)
% 17.25/3.05 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9:
% 17.25/3.05 any] : ? [v10: any] : ? [v11: $i] : ? [v12: any] : (ordered_pair(v2,
% 17.25/3.05 v3) = v11 & in(v11, v0) = v12 & in(v4, v1) = v10 & in(v3, v1) = v9 &
% 17.25/3.05 in(v2, v1) = v8 & $i(v11) & ( ~ (v12 = 0) | ~ (v10 = 0) | ~ (v9 = 0) |
% 17.25/3.05 ~ (v8 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 17.25/3.05 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~
% 17.25/3.05 (ordered_pair(v2, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~
% 17.25/3.05 (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v6, v0) =
% 17.25/3.05 v7) | ~ (in(v5, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 17.25/3.05 | ~ $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: any] : ? [v11: $i] :
% 17.25/3.05 ? [v12: any] : (ordered_pair(v3, v4) = v11 & in(v11, v0) = v12 & in(v4, v1)
% 17.25/3.05 = v10 & in(v3, v1) = v9 & in(v2, v1) = v8 & $i(v11) & ( ~ (v12 = 0) | ~
% 17.25/3.05 (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v0: $i] : ! [v1: $i] :
% 17.25/3.05 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0
% 17.25/3.05 | ~ (ordered_pair(v2, v4) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~
% 17.25/3.05 (relation(v0) = 0) | ~ (in(v5, v0) = v6) | ~ (in(v3, v1) = 0) | ~ $i(v4)
% 17.25/3.05 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8:
% 17.25/3.05 any] : ? [v9: $i] : ? [v10: any] : ? [v11: $i] : ? [v12: any] :
% 17.25/3.05 (ordered_pair(v3, v4) = v11 & ordered_pair(v2, v3) = v9 & in(v11, v0) = v12
% 17.25/3.05 & in(v9, v0) = v10 & in(v4, v1) = v8 & in(v2, v1) = v7 & $i(v11) & $i(v9)
% 17.25/3.05 & ( ~ (v12 = 0) | ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0:
% 17.25/3.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 17.25/3.05 ! [v6: $i] : ( ~ (ordered_pair(v3, v4) = v6) | ~ (ordered_pair(v2, v3) = v5)
% 17.25/3.05 | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v6, v0)
% 17.25/3.05 = 0) | ~ (in(v5, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 17.25/3.05 | ~ $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: $i] : ?
% 17.25/3.05 [v11: any] : (ordered_pair(v2, v4) = v10 & in(v10, v0) = v11 & in(v4, v1) =
% 17.25/3.05 v9 & in(v3, v1) = v8 & in(v2, v1) = v7 & $i(v10) & ( ~ (v9 = 0) | ~ (v8 =
% 17.25/3.05 0) | ~ (v7 = 0) | v11 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.25/3.05 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v3, v4) =
% 17.25/3.05 v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~
% 17.25/3.05 (in(v5, v0) = 0) | ~ (in(v2, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 17.25/3.05 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 17.25/3.05 any] : ? [v10: $i] : ? [v11: any] : (ordered_pair(v2, v4) = v10 &
% 17.25/3.05 ordered_pair(v2, v3) = v8 & in(v10, v0) = v11 & in(v8, v0) = v9 & in(v4,
% 17.25/3.05 v1) = v7 & in(v3, v1) = v6 & $i(v10) & $i(v8) & ( ~ (v9 = 0) | ~ (v7 =
% 17.25/3.05 0) | ~ (v6 = 0) | v11 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.25/3.05 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v2, v3) =
% 17.25/3.05 v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~
% 17.25/3.05 (in(v5, v0) = 0) | ~ (in(v4, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 17.25/3.05 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 17.25/3.05 any] : ? [v10: $i] : ? [v11: any] : (ordered_pair(v3, v4) = v8 &
% 17.25/3.05 ordered_pair(v2, v4) = v10 & in(v10, v0) = v11 & in(v8, v0) = v9 & in(v3,
% 17.25/3.05 v1) = v7 & in(v2, v1) = v6 & $i(v10) & $i(v8) & ( ~ (v9 = 0) | ~ (v7 =
% 17.25/3.05 0) | ~ (v6 = 0) | v11 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.25/3.05 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (is_transitive_in(v0, v1) = 0) | ~
% 17.25/3.05 (relation(v0) = 0) | ~ (in(v4, v1) = 0) | ~ (in(v3, v1) = 0) | ~ (in(v2,
% 17.25/3.05 v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.25/3.05 ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ?
% 17.25/3.05 [v10: any] : (ordered_pair(v3, v4) = v7 & ordered_pair(v2, v4) = v9 &
% 17.25/3.05 ordered_pair(v2, v3) = v5 & in(v9, v0) = v10 & in(v7, v0) = v8 & in(v5,
% 17.25/3.05 v0) = v6 & $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 =
% 17.25/3.05 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 17.25/3.05 (is_transitive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~
% 17.25/3.05 $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 17.25/3.05 : ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) & ordered_pair(v4, v5) = v7 &
% 17.25/3.05 ordered_pair(v3, v5) = v8 & ordered_pair(v3, v4) = v6 & in(v8, v0) = v9 &
% 17.25/3.05 in(v7, v0) = 0 & in(v6, v0) = 0 & in(v5, v1) = 0 & in(v4, v1) = 0 & in(v3,
% 17.25/3.05 v1) = 0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)))
% 17.25/3.05
% 17.25/3.05 (l2_wellord1)
% 17.25/3.06 ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 17.25/3.06 $i] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10:
% 17.25/3.06 int] : (transitive(v0) = v1 & relation(v0) = 0 & $i(v4) & $i(v3) & $i(v2) &
% 17.25/3.06 $i(v0) & ((v8 = 0 & v6 = 0 & v1 = 0 & ~ (v10 = 0) & ordered_pair(v3, v4) =
% 17.25/3.06 v7 & ordered_pair(v2, v4) = v9 & ordered_pair(v2, v3) = v5 & in(v9, v0)
% 17.25/3.06 = v10 & in(v7, v0) = 0 & in(v5, v0) = 0 & $i(v9) & $i(v7) & $i(v5)) | (
% 17.25/3.06 ~ (v1 = 0) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] :
% 17.25/3.06 ! [v15: $i] : ! [v16: int] : (v16 = 0 | ~ (ordered_pair(v12, v13) =
% 17.25/3.06 v14) | ~ (ordered_pair(v11, v13) = v15) | ~ (in(v15, v0) = v16) |
% 17.25/3.06 ~ (in(v14, v0) = 0) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ? [v17:
% 17.25/3.06 $i] : ? [v18: int] : ( ~ (v18 = 0) & ordered_pair(v11, v12) = v17 &
% 17.25/3.06 in(v17, v0) = v18 & $i(v17))) & ! [v11: $i] : ! [v12: $i] : !
% 17.25/3.06 [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: int] : (v16 = 0 | ~
% 17.25/3.06 (ordered_pair(v11, v13) = v15) | ~ (ordered_pair(v11, v12) = v14) |
% 17.25/3.06 ~ (in(v15, v0) = v16) | ~ (in(v14, v0) = 0) | ~ $i(v13) | ~ $i(v12)
% 17.25/3.06 | ~ $i(v11) | ? [v17: $i] : ? [v18: int] : ( ~ (v18 = 0) &
% 17.25/3.06 ordered_pair(v12, v13) = v17 & in(v17, v0) = v18 & $i(v17))) & !
% 17.25/3.06 [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] :
% 17.25/3.06 ( ~ (ordered_pair(v12, v13) = v15) | ~ (ordered_pair(v11, v12) = v14) |
% 17.25/3.06 ~ (in(v15, v0) = 0) | ~ (in(v14, v0) = 0) | ~ $i(v13) | ~ $i(v12)
% 17.25/3.06 | ~ $i(v11) | ? [v16: $i] : (ordered_pair(v11, v13) = v16 & in(v16,
% 17.25/3.06 v0) = 0 & $i(v16))))))
% 17.25/3.06
% 17.25/3.06 (t2_subset)
% 17.25/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 17.25/3.06 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 &
% 17.25/3.06 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : (
% 17.25/3.06 ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 17.25/3.06 any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 17.25/3.06
% 17.25/3.06 (t30_relat_1)
% 17.25/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0,
% 17.25/3.06 v1) = v3) | ~ (in(v3, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 17.25/3.06 [v4: any] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : (relation_field(v2)
% 17.25/3.06 = v5 & relation(v2) = v4 & in(v1, v5) = v7 & in(v0, v5) = v6 & $i(v5) & (
% 17.25/3.06 ~ (v4 = 0) | (v7 = 0 & v6 = 0))))
% 17.25/3.06
% 17.25/3.06 (function-axioms)
% 17.25/3.06 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 17.25/3.06 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 17.25/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.25/3.06 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0:
% 17.25/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.25/3.06 : (v1 = v0 | ~ (is_transitive_in(v3, v2) = v1) | ~ (is_transitive_in(v3, v2)
% 17.25/3.06 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 17.25/3.06 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i]
% 17.25/3.06 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3,
% 17.25/3.06 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 17.25/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.25/3.06 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 17.25/3.06 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 17.25/3.06 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 17.25/3.06 v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i]
% 17.25/3.06 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 17.25/3.06 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 17.25/3.06 ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0:
% 17.25/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 17.25/3.06 ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0)) & ! [v0:
% 17.25/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 17.25/3.06 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0:
% 17.25/3.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 17.25/3.06 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 17.25/3.06 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1)
% 17.25/3.06 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.25/3.06 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 17.25/3.06 (empty(v2) = v0))
% 17.25/3.06
% 17.25/3.06 Further assumptions not needed in the proof:
% 17.25/3.06 --------------------------------------------
% 17.25/3.06 antisymmetry_r2_hidden, cc1_funct_1, commutativity_k2_tarski, d5_tarski,
% 17.25/3.06 dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0, dt_k2_relat_1, dt_k2_tarski,
% 17.25/3.06 dt_k2_xboole_0, dt_k3_relat_1, dt_k4_tarski, dt_m1_subset_1,
% 17.25/3.06 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0,
% 17.25/3.06 idempotence_k2_xboole_0, rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0,
% 17.25/3.06 rc3_funct_1, t1_boole, t1_subset, t6_boole, t7_boole, t8_boole
% 17.25/3.06
% 17.25/3.06 Those formulas are unsatisfiable:
% 17.25/3.06 ---------------------------------
% 17.25/3.06
% 17.25/3.06 Begin of proof
% 17.25/3.07 |
% 17.25/3.07 | ALPHA: (cc2_funct_1) implies:
% 17.25/3.07 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 17.25/3.07 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 17.25/3.07 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 17.25/3.07 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ?
% 17.25/3.07 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 &
% 17.25/3.07 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 17.25/3.07 | ~ (v2 = 0) | v1 = 0)))
% 17.25/3.07 |
% 17.25/3.07 | ALPHA: (commutativity_k2_xboole_0) implies:
% 17.25/3.07 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 17.25/3.07 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 17.25/3.07 |
% 17.25/3.07 | ALPHA: (d16_relat_2) implies:
% 17.25/3.07 | (4) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 17.25/3.07 | [v2: $i] : ? [v3: any] : (relation_field(v0) = v2 & transitive(v0) =
% 17.25/3.07 | v1 & is_transitive_in(v0, v2) = v3 & $i(v2) & ( ~ (v3 = 0) | v1 =
% 17.25/3.07 | 0) & ( ~ (v1 = 0) | v3 = 0)))
% 17.25/3.07 | (5) ! [v0: $i] : ! [v1: any] : ( ~ (transitive(v0) = v1) | ~ $i(v0) | ?
% 17.25/3.07 | [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_field(v0) = v3 &
% 17.25/3.07 | is_transitive_in(v0, v3) = v4 & relation(v0) = v2 & $i(v3) & ( ~
% 17.25/3.07 | (v2 = 0) | (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) | v4 = 0)))))
% 17.25/3.07 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 17.25/3.07 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (transitive(v0) = v3 &
% 17.25/3.07 | is_transitive_in(v0, v1) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) |
% 17.25/3.07 | (( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0)))))
% 17.25/3.07 |
% 17.25/3.07 | ALPHA: (d6_relat_1) implies:
% 17.25/3.07 | (7) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 17.25/3.07 | [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & relation_rng(v0) =
% 17.25/3.07 | v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1 & $i(v3) &
% 17.25/3.07 | $i(v2) & $i(v1)))
% 17.25/3.07 |
% 17.25/3.07 | ALPHA: (d8_relat_2) implies:
% 17.25/3.07 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 17.25/3.07 | (is_transitive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) |
% 17.25/3.07 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 17.25/3.07 | ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) &
% 17.25/3.07 | ordered_pair(v4, v5) = v7 & ordered_pair(v3, v5) = v8 &
% 17.25/3.07 | ordered_pair(v3, v4) = v6 & in(v8, v0) = v9 & in(v7, v0) = 0 &
% 17.25/3.07 | in(v6, v0) = 0 & in(v5, v1) = 0 & in(v4, v1) = 0 & in(v3, v1) = 0 &
% 17.25/3.07 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)))
% 17.25/3.07 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.25/3.07 | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v4) = v6) | ~
% 17.25/3.07 | (ordered_pair(v2, v3) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~
% 17.25/3.07 | (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v5, v0) = 0) | ~
% 17.25/3.07 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any]
% 17.25/3.07 | : ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: any] :
% 17.25/3.07 | (ordered_pair(v2, v4) = v10 & in(v10, v0) = v11 & in(v4, v1) = v9 &
% 17.25/3.07 | in(v3, v1) = v8 & in(v2, v1) = v7 & $i(v10) & ( ~ (v9 = 0) | ~ (v8
% 17.25/3.07 | = 0) | ~ (v7 = 0) | v11 = 0)))
% 17.25/3.07 |
% 17.25/3.07 | ALPHA: (t2_subset) implies:
% 17.25/3.08 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 17.25/3.08 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 17.25/3.08 | (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 17.25/3.08 |
% 17.25/3.08 | ALPHA: (function-axioms) implies:
% 17.25/3.08 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.25/3.08 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 17.25/3.08 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.25/3.08 | : (v1 = v0 | ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0))
% 17.25/3.08 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.25/3.08 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 17.25/3.08 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.25/3.08 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 17.25/3.08 | v0))
% 17.25/3.08 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.25/3.08 | : ! [v3: $i] : (v1 = v0 | ~ (is_transitive_in(v3, v2) = v1) | ~
% 17.25/3.08 | (is_transitive_in(v3, v2) = v0))
% 17.25/3.08 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.25/3.08 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 17.25/3.08 |
% 17.25/3.08 | DELTA: instantiating (l2_wellord1) with fresh symbols all_35_0, all_35_1,
% 17.25/3.08 | all_35_2, all_35_3, all_35_4, all_35_5, all_35_6, all_35_7, all_35_8,
% 17.25/3.08 | all_35_9, all_35_10 gives:
% 17.25/3.08 | (17) transitive(all_35_10) = all_35_9 & relation(all_35_10) = 0 &
% 17.25/3.08 | $i(all_35_6) & $i(all_35_7) & $i(all_35_8) & $i(all_35_10) &
% 17.25/3.08 | ((all_35_2 = 0 & all_35_4 = 0 & all_35_9 = 0 & ~ (all_35_0 = 0) &
% 17.25/3.08 | ordered_pair(all_35_7, all_35_6) = all_35_3 &
% 17.25/3.08 | ordered_pair(all_35_8, all_35_6) = all_35_1 &
% 17.25/3.08 | ordered_pair(all_35_8, all_35_7) = all_35_5 & in(all_35_1,
% 17.25/3.08 | all_35_10) = all_35_0 & in(all_35_3, all_35_10) = 0 &
% 17.25/3.08 | in(all_35_5, all_35_10) = 0 & $i(all_35_1) & $i(all_35_3) &
% 17.25/3.08 | $i(all_35_5)) | ( ~ (all_35_9 = 0) & ! [v0: $i] : ! [v1: $i] :
% 17.25/3.08 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 |
% 17.25/3.08 | ~ (ordered_pair(v1, v2) = v3) | ~ (ordered_pair(v0, v2) = v4) |
% 17.25/3.08 | ~ (in(v4, all_35_10) = v5) | ~ (in(v3, all_35_10) = 0) | ~
% 17.25/3.08 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: int] : (
% 17.25/3.08 | ~ (v7 = 0) & ordered_pair(v0, v1) = v6 & in(v6, all_35_10) =
% 17.25/3.08 | v7 & $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.25/3.08 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~
% 17.25/3.08 | (ordered_pair(v0, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) |
% 17.25/3.08 | ~ (in(v4, all_35_10) = v5) | ~ (in(v3, all_35_10) = 0) | ~
% 17.25/3.08 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: int] : (
% 17.25/3.08 | ~ (v7 = 0) & ordered_pair(v1, v2) = v6 & in(v6, all_35_10) =
% 17.25/3.08 | v7 & $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.25/3.08 | [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v1, v2) = v4) | ~
% 17.25/3.08 | (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_35_10) = 0) | ~
% 17.25/3.08 | (in(v3, all_35_10) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 17.25/3.08 | [v5: $i] : (ordered_pair(v0, v2) = v5 & in(v5, all_35_10) = 0 &
% 17.25/3.08 | $i(v5)))))
% 17.25/3.08 |
% 17.25/3.08 | ALPHA: (17) implies:
% 17.25/3.08 | (18) $i(all_35_10)
% 17.25/3.08 | (19) $i(all_35_8)
% 17.25/3.08 | (20) $i(all_35_7)
% 17.25/3.08 | (21) $i(all_35_6)
% 17.25/3.08 | (22) relation(all_35_10) = 0
% 17.25/3.08 | (23) transitive(all_35_10) = all_35_9
% 17.25/3.09 | (24) (all_35_2 = 0 & all_35_4 = 0 & all_35_9 = 0 & ~ (all_35_0 = 0) &
% 17.25/3.09 | ordered_pair(all_35_7, all_35_6) = all_35_3 & ordered_pair(all_35_8,
% 17.25/3.09 | all_35_6) = all_35_1 & ordered_pair(all_35_8, all_35_7) = all_35_5
% 17.25/3.09 | & in(all_35_1, all_35_10) = all_35_0 & in(all_35_3, all_35_10) = 0 &
% 17.25/3.09 | in(all_35_5, all_35_10) = 0 & $i(all_35_1) & $i(all_35_3) &
% 17.25/3.09 | $i(all_35_5)) | ( ~ (all_35_9 = 0) & ! [v0: $i] : ! [v1: $i] : !
% 17.25/3.09 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~
% 17.25/3.09 | (ordered_pair(v1, v2) = v3) | ~ (ordered_pair(v0, v2) = v4) | ~
% 17.25/3.09 | (in(v4, all_35_10) = v5) | ~ (in(v3, all_35_10) = 0) | ~ $i(v2)
% 17.25/3.09 | | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: int] : ( ~ (v7 =
% 17.25/3.09 | 0) & ordered_pair(v0, v1) = v6 & in(v6, all_35_10) = v7 &
% 17.25/3.09 | $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 17.25/3.09 | : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (ordered_pair(v0, v2) =
% 17.25/3.09 | v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_35_10) =
% 17.25/3.09 | v5) | ~ (in(v3, all_35_10) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 17.25/3.09 | $i(v0) | ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) &
% 17.25/3.09 | ordered_pair(v1, v2) = v6 & in(v6, all_35_10) = v7 & $i(v6))) &
% 17.25/3.09 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.25/3.09 | ( ~ (ordered_pair(v1, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) |
% 17.25/3.09 | ~ (in(v4, all_35_10) = 0) | ~ (in(v3, all_35_10) = 0) | ~ $i(v2)
% 17.25/3.09 | | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (ordered_pair(v0, v2) = v5
% 17.25/3.09 | & in(v5, all_35_10) = 0 & $i(v5))))
% 17.25/3.09 |
% 17.25/3.09 | GROUND_INST: instantiating (7) with all_35_10, simplifying with (18), (22)
% 17.25/3.09 | gives:
% 17.50/3.09 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_35_10) =
% 17.50/3.09 | v1 & relation_rng(all_35_10) = v2 & relation_field(all_35_10) = v0 &
% 17.50/3.09 | set_union2(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 17.50/3.09 |
% 17.50/3.09 | GROUND_INST: instantiating (4) with all_35_10, simplifying with (18), (22)
% 17.50/3.09 | gives:
% 17.50/3.09 | (26) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_field(all_35_10)
% 17.50/3.09 | = v1 & transitive(all_35_10) = v0 & is_transitive_in(all_35_10, v1)
% 17.50/3.09 | = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 17.50/3.09 |
% 17.50/3.09 | GROUND_INST: instantiating (1) with all_35_10, simplifying with (18), (22)
% 17.50/3.09 | gives:
% 17.50/3.09 | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_35_10) =
% 17.50/3.09 | v2 & function(all_35_10) = v1 & empty(all_35_10) = v0 & ( ~ (v1 = 0)
% 17.50/3.09 | | ~ (v0 = 0) | v2 = 0))
% 17.50/3.09 |
% 17.50/3.09 | GROUND_INST: instantiating (5) with all_35_10, all_35_9, simplifying with
% 17.50/3.09 | (18), (23) gives:
% 17.50/3.09 | (28) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_field(all_35_10)
% 17.50/3.09 | = v1 & is_transitive_in(all_35_10, v1) = v2 & relation(all_35_10) =
% 17.50/3.09 | v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (v2 = 0) | all_35_9 = 0) & ( ~
% 17.50/3.09 | (all_35_9 = 0) | v2 = 0))))
% 17.50/3.09 |
% 17.50/3.09 | DELTA: instantiating (27) with fresh symbols all_49_0, all_49_1, all_49_2
% 17.50/3.09 | gives:
% 17.50/3.09 | (29) one_to_one(all_35_10) = all_49_0 & function(all_35_10) = all_49_1 &
% 17.50/3.09 | empty(all_35_10) = all_49_2 & ( ~ (all_49_1 = 0) | ~ (all_49_2 = 0) |
% 17.50/3.09 | all_49_0 = 0)
% 17.50/3.09 |
% 17.50/3.09 | ALPHA: (29) implies:
% 17.50/3.09 | (30) one_to_one(all_35_10) = all_49_0
% 17.50/3.09 |
% 17.50/3.09 | DELTA: instantiating (25) with fresh symbols all_65_0, all_65_1, all_65_2
% 17.50/3.09 | gives:
% 17.50/3.09 | (31) relation_dom(all_35_10) = all_65_1 & relation_rng(all_35_10) =
% 17.50/3.09 | all_65_0 & relation_field(all_35_10) = all_65_2 & set_union2(all_65_1,
% 17.50/3.09 | all_65_0) = all_65_2 & $i(all_65_0) & $i(all_65_1) & $i(all_65_2)
% 17.50/3.09 |
% 17.50/3.09 | ALPHA: (31) implies:
% 17.50/3.09 | (32) $i(all_65_1)
% 17.50/3.09 | (33) $i(all_65_0)
% 17.50/3.09 | (34) set_union2(all_65_1, all_65_0) = all_65_2
% 17.50/3.09 | (35) relation_field(all_35_10) = all_65_2
% 17.50/3.09 |
% 17.50/3.09 | DELTA: instantiating (26) with fresh symbols all_73_0, all_73_1, all_73_2
% 17.50/3.09 | gives:
% 17.50/3.09 | (36) relation_field(all_35_10) = all_73_1 & transitive(all_35_10) =
% 17.50/3.09 | all_73_2 & is_transitive_in(all_35_10, all_73_1) = all_73_0 &
% 17.50/3.09 | $i(all_73_1) & ( ~ (all_73_0 = 0) | all_73_2 = 0) & ( ~ (all_73_2 = 0)
% 17.50/3.09 | | all_73_0 = 0)
% 17.50/3.09 |
% 17.50/3.09 | ALPHA: (36) implies:
% 17.50/3.09 | (37) is_transitive_in(all_35_10, all_73_1) = all_73_0
% 17.50/3.09 | (38) transitive(all_35_10) = all_73_2
% 17.50/3.09 | (39) relation_field(all_35_10) = all_73_1
% 17.50/3.09 |
% 17.50/3.09 | DELTA: instantiating (28) with fresh symbols all_81_0, all_81_1, all_81_2
% 17.50/3.09 | gives:
% 17.50/3.09 | (40) relation_field(all_35_10) = all_81_1 & is_transitive_in(all_35_10,
% 17.50/3.09 | all_81_1) = all_81_0 & relation(all_35_10) = all_81_2 & $i(all_81_1)
% 17.50/3.09 | & ( ~ (all_81_2 = 0) | (( ~ (all_81_0 = 0) | all_35_9 = 0) & ( ~
% 17.50/3.09 | (all_35_9 = 0) | all_81_0 = 0)))
% 17.50/3.09 |
% 17.50/3.09 | ALPHA: (40) implies:
% 17.50/3.09 | (41) relation(all_35_10) = all_81_2
% 17.50/3.09 | (42) is_transitive_in(all_35_10, all_81_1) = all_81_0
% 17.50/3.09 | (43) relation_field(all_35_10) = all_81_1
% 17.50/3.09 |
% 17.50/3.09 | GROUND_INST: instantiating (11) with 0, all_81_2, all_35_10, simplifying with
% 17.50/3.09 | (22), (41) gives:
% 17.50/3.09 | (44) all_81_2 = 0
% 17.50/3.09 |
% 17.50/3.09 | GROUND_INST: instantiating (12) with all_35_9, all_73_2, all_35_10,
% 17.50/3.09 | simplifying with (23), (38) gives:
% 17.50/3.09 | (45) all_73_2 = all_35_9
% 17.50/3.09 |
% 17.50/3.09 | GROUND_INST: instantiating (13) with all_73_1, all_81_1, all_35_10,
% 17.50/3.10 | simplifying with (39), (43) gives:
% 17.50/3.10 | (46) all_81_1 = all_73_1
% 17.50/3.10 |
% 17.50/3.10 | GROUND_INST: instantiating (13) with all_65_2, all_81_1, all_35_10,
% 17.50/3.10 | simplifying with (35), (43) gives:
% 17.50/3.10 | (47) all_81_1 = all_65_2
% 17.50/3.10 |
% 17.50/3.10 | COMBINE_EQS: (46), (47) imply:
% 17.50/3.10 | (48) all_73_1 = all_65_2
% 17.50/3.10 |
% 17.50/3.10 | SIMP: (48) implies:
% 17.50/3.10 | (49) all_73_1 = all_65_2
% 17.50/3.10 |
% 17.50/3.10 | REDUCE: (42), (47) imply:
% 17.50/3.10 | (50) is_transitive_in(all_35_10, all_65_2) = all_81_0
% 17.50/3.10 |
% 17.50/3.10 | REDUCE: (37), (49) imply:
% 17.50/3.10 | (51) is_transitive_in(all_35_10, all_65_2) = all_73_0
% 17.50/3.10 |
% 17.50/3.10 | GROUND_INST: instantiating (15) with all_73_0, all_81_0, all_65_2, all_35_10,
% 17.50/3.10 | simplifying with (50), (51) gives:
% 17.50/3.10 | (52) all_81_0 = all_73_0
% 17.50/3.10 |
% 17.50/3.10 | GROUND_INST: instantiating (2) with all_35_10, all_49_0, simplifying with
% 17.50/3.10 | (18), (30) gives:
% 17.50/3.10 | (53) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_35_10) = v0
% 17.50/3.10 | & function(all_35_10) = v2 & empty(all_35_10) = v1 & ( ~ (v2 = 0) |
% 17.50/3.10 | ~ (v1 = 0) | ~ (v0 = 0) | all_49_0 = 0))
% 17.50/3.10 |
% 17.50/3.10 | GROUND_INST: instantiating (3) with all_65_0, all_65_1, all_65_2, simplifying
% 17.50/3.10 | with (32), (33), (34) gives:
% 17.50/3.10 | (54) set_union2(all_65_0, all_65_1) = all_65_2 & $i(all_65_2)
% 17.50/3.10 |
% 17.50/3.10 | ALPHA: (54) implies:
% 17.50/3.10 | (55) $i(all_65_2)
% 17.50/3.10 |
% 17.50/3.10 | GROUND_INST: instantiating (8) with all_35_10, all_65_2, all_73_0, simplifying
% 17.50/3.10 | with (18), (22), (51), (55) gives:
% 17.50/3.10 | (56) all_73_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 17.50/3.10 | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 17.50/3.10 | ordered_pair(v1, v2) = v4 & ordered_pair(v0, v2) = v5 &
% 17.50/3.10 | ordered_pair(v0, v1) = v3 & in(v5, all_35_10) = v6 & in(v4,
% 17.50/3.10 | all_35_10) = 0 & in(v3, all_35_10) = 0 & in(v2, all_65_2) = 0 &
% 17.50/3.10 | in(v1, all_65_2) = 0 & in(v0, all_65_2) = 0 & $i(v5) & $i(v4) &
% 17.50/3.10 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.50/3.10 |
% 17.50/3.10 | GROUND_INST: instantiating (6) with all_35_10, all_65_2, simplifying with
% 17.50/3.10 | (18), (35) gives:
% 17.50/3.10 | (57) ? [v0: any] : ? [v1: any] : ? [v2: any] : (transitive(all_35_10) =
% 17.50/3.10 | v1 & is_transitive_in(all_35_10, all_65_2) = v2 &
% 17.50/3.10 | relation(all_35_10) = v0 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 = 0) &
% 17.50/3.10 | ( ~ (v1 = 0) | v2 = 0))))
% 17.50/3.10 |
% 17.50/3.10 | DELTA: instantiating (53) with fresh symbols all_133_0, all_133_1, all_133_2
% 17.50/3.10 | gives:
% 17.50/3.10 | (58) relation(all_35_10) = all_133_2 & function(all_35_10) = all_133_0 &
% 17.50/3.10 | empty(all_35_10) = all_133_1 & ( ~ (all_133_0 = 0) | ~ (all_133_1 =
% 17.50/3.10 | 0) | ~ (all_133_2 = 0) | all_49_0 = 0)
% 17.50/3.10 |
% 17.50/3.10 | ALPHA: (58) implies:
% 17.50/3.10 | (59) relation(all_35_10) = all_133_2
% 17.50/3.10 |
% 17.50/3.10 | DELTA: instantiating (57) with fresh symbols all_137_0, all_137_1, all_137_2
% 17.50/3.10 | gives:
% 17.50/3.10 | (60) transitive(all_35_10) = all_137_1 & is_transitive_in(all_35_10,
% 17.50/3.10 | all_65_2) = all_137_0 & relation(all_35_10) = all_137_2 & ( ~
% 17.50/3.10 | (all_137_2 = 0) | (( ~ (all_137_0 = 0) | all_137_1 = 0) & ( ~
% 17.50/3.10 | (all_137_1 = 0) | all_137_0 = 0)))
% 17.50/3.10 |
% 17.50/3.10 | ALPHA: (60) implies:
% 17.50/3.10 | (61) relation(all_35_10) = all_137_2
% 17.50/3.10 | (62) is_transitive_in(all_35_10, all_65_2) = all_137_0
% 17.50/3.10 | (63) transitive(all_35_10) = all_137_1
% 17.50/3.10 | (64) ~ (all_137_2 = 0) | (( ~ (all_137_0 = 0) | all_137_1 = 0) & ( ~
% 17.50/3.10 | (all_137_1 = 0) | all_137_0 = 0))
% 17.50/3.10 |
% 17.50/3.10 | GROUND_INST: instantiating (11) with 0, all_137_2, all_35_10, simplifying with
% 17.50/3.10 | (22), (61) gives:
% 17.50/3.10 | (65) all_137_2 = 0
% 17.50/3.10 |
% 17.50/3.10 | GROUND_INST: instantiating (11) with all_133_2, all_137_2, all_35_10,
% 17.50/3.10 | simplifying with (59), (61) gives:
% 17.50/3.10 | (66) all_137_2 = all_133_2
% 17.50/3.10 |
% 17.50/3.10 | GROUND_INST: instantiating (15) with all_73_0, all_137_0, all_65_2, all_35_10,
% 17.50/3.10 | simplifying with (51), (62) gives:
% 17.50/3.10 | (67) all_137_0 = all_73_0
% 17.50/3.10 |
% 17.50/3.10 | GROUND_INST: instantiating (12) with all_35_9, all_137_1, all_35_10,
% 17.50/3.10 | simplifying with (23), (63) gives:
% 17.50/3.10 | (68) all_137_1 = all_35_9
% 17.50/3.10 |
% 17.50/3.10 | COMBINE_EQS: (65), (66) imply:
% 17.50/3.10 | (69) all_133_2 = 0
% 17.50/3.10 |
% 17.50/3.10 | BETA: splitting (24) gives:
% 17.50/3.10 |
% 17.50/3.10 | Case 1:
% 17.50/3.10 | |
% 17.50/3.10 | | (70) all_35_2 = 0 & all_35_4 = 0 & all_35_9 = 0 & ~ (all_35_0 = 0) &
% 17.50/3.10 | | ordered_pair(all_35_7, all_35_6) = all_35_3 & ordered_pair(all_35_8,
% 17.50/3.10 | | all_35_6) = all_35_1 & ordered_pair(all_35_8, all_35_7) = all_35_5
% 17.50/3.10 | | & in(all_35_1, all_35_10) = all_35_0 & in(all_35_3, all_35_10) = 0 &
% 17.50/3.10 | | in(all_35_5, all_35_10) = 0 & $i(all_35_1) & $i(all_35_3) &
% 17.50/3.10 | | $i(all_35_5)
% 17.50/3.10 | |
% 17.50/3.10 | | ALPHA: (70) implies:
% 17.50/3.10 | | (71) all_35_9 = 0
% 17.50/3.10 | | (72) ~ (all_35_0 = 0)
% 17.50/3.10 | | (73) $i(all_35_1)
% 17.50/3.10 | | (74) in(all_35_5, all_35_10) = 0
% 17.50/3.10 | | (75) in(all_35_3, all_35_10) = 0
% 17.50/3.10 | | (76) in(all_35_1, all_35_10) = all_35_0
% 17.50/3.10 | | (77) ordered_pair(all_35_8, all_35_7) = all_35_5
% 17.50/3.10 | | (78) ordered_pair(all_35_8, all_35_6) = all_35_1
% 17.50/3.10 | | (79) ordered_pair(all_35_7, all_35_6) = all_35_3
% 17.50/3.10 | |
% 17.50/3.11 | | COMBINE_EQS: (68), (71) imply:
% 17.50/3.11 | | (80) all_137_1 = 0
% 17.50/3.11 | |
% 17.50/3.11 | | BETA: splitting (64) gives:
% 17.50/3.11 | |
% 17.50/3.11 | | Case 1:
% 17.50/3.11 | | |
% 17.50/3.11 | | | (81) ~ (all_137_2 = 0)
% 17.50/3.11 | | |
% 17.50/3.11 | | | REDUCE: (65), (81) imply:
% 17.50/3.11 | | | (82) $false
% 17.50/3.11 | | |
% 17.50/3.11 | | | CLOSE: (82) is inconsistent.
% 17.50/3.11 | | |
% 17.50/3.11 | | Case 2:
% 17.50/3.11 | | |
% 17.50/3.11 | | | (83) ( ~ (all_137_0 = 0) | all_137_1 = 0) & ( ~ (all_137_1 = 0) |
% 17.50/3.11 | | | all_137_0 = 0)
% 17.50/3.11 | | |
% 17.50/3.11 | | | ALPHA: (83) implies:
% 17.50/3.11 | | | (84) ~ (all_137_1 = 0) | all_137_0 = 0
% 17.50/3.11 | | |
% 17.50/3.11 | | | BETA: splitting (84) gives:
% 17.50/3.11 | | |
% 17.50/3.11 | | | Case 1:
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | (85) ~ (all_137_1 = 0)
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | REDUCE: (80), (85) imply:
% 17.50/3.11 | | | | (86) $false
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | CLOSE: (86) is inconsistent.
% 17.50/3.11 | | | |
% 17.50/3.11 | | | Case 2:
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | (87) all_137_0 = 0
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | COMBINE_EQS: (67), (87) imply:
% 17.50/3.11 | | | | (88) all_73_0 = 0
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | SIMP: (88) implies:
% 17.50/3.11 | | | | (89) all_73_0 = 0
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | REDUCE: (51), (89) imply:
% 17.50/3.11 | | | | (90) is_transitive_in(all_35_10, all_65_2) = 0
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | GROUND_INST: instantiating (10) with all_35_1, all_35_10, all_35_0,
% 17.50/3.11 | | | | simplifying with (18), (73), (76) gives:
% 17.50/3.11 | | | | (91) all_35_0 = 0 | ? [v0: any] : ? [v1: any] : (element(all_35_1,
% 17.50/3.11 | | | | all_35_10) = v0 & empty(all_35_10) = v1 & ( ~ (v0 = 0) | v1
% 17.50/3.11 | | | | = 0))
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | GROUND_INST: instantiating (t30_relat_1) with all_35_8, all_35_7,
% 17.50/3.11 | | | | all_35_10, all_35_5, simplifying with (18), (19), (20),
% 17.50/3.11 | | | | (74), (77) gives:
% 17.50/3.11 | | | | (92) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 17.50/3.11 | | | | (relation_field(all_35_10) = v1 & relation(all_35_10) = v0 &
% 17.50/3.11 | | | | in(all_35_7, v1) = v3 & in(all_35_8, v1) = v2 & $i(v1) & ( ~
% 17.50/3.11 | | | | (v0 = 0) | (v3 = 0 & v2 = 0)))
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | GROUND_INST: instantiating (9) with all_35_10, all_65_2, all_35_8,
% 17.50/3.11 | | | | all_35_7, all_35_6, all_35_5, all_35_3, simplifying with
% 17.50/3.11 | | | | (18), (19), (20), (21), (22), (55), (74), (75), (77), (79),
% 17.50/3.11 | | | | (90) gives:
% 17.50/3.11 | | | | (93) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ?
% 17.50/3.11 | | | | [v4: any] : (ordered_pair(all_35_8, all_35_6) = v3 & in(v3,
% 17.50/3.11 | | | | all_35_10) = v4 & in(all_35_6, all_65_2) = v2 & in(all_35_7,
% 17.50/3.11 | | | | all_65_2) = v1 & in(all_35_8, all_65_2) = v0 & $i(v3) & ( ~
% 17.50/3.11 | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | GROUND_INST: instantiating (t30_relat_1) with all_35_7, all_35_6,
% 17.50/3.11 | | | | all_35_10, all_35_3, simplifying with (18), (20), (21),
% 17.50/3.11 | | | | (75), (79) gives:
% 17.50/3.11 | | | | (94) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 17.50/3.11 | | | | (relation_field(all_35_10) = v1 & relation(all_35_10) = v0 &
% 17.50/3.11 | | | | in(all_35_6, v1) = v3 & in(all_35_7, v1) = v2 & $i(v1) & ( ~
% 17.50/3.11 | | | | (v0 = 0) | (v3 = 0 & v2 = 0)))
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | DELTA: instantiating (92) with fresh symbols all_254_0, all_254_1,
% 17.50/3.11 | | | | all_254_2, all_254_3 gives:
% 17.50/3.11 | | | | (95) relation_field(all_35_10) = all_254_2 & relation(all_35_10) =
% 17.50/3.11 | | | | all_254_3 & in(all_35_7, all_254_2) = all_254_0 & in(all_35_8,
% 17.50/3.11 | | | | all_254_2) = all_254_1 & $i(all_254_2) & ( ~ (all_254_3 = 0) |
% 17.50/3.11 | | | | (all_254_0 = 0 & all_254_1 = 0))
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | ALPHA: (95) implies:
% 17.50/3.11 | | | | (96) in(all_35_8, all_254_2) = all_254_1
% 17.50/3.11 | | | | (97) in(all_35_7, all_254_2) = all_254_0
% 17.50/3.11 | | | | (98) relation(all_35_10) = all_254_3
% 17.50/3.11 | | | | (99) relation_field(all_35_10) = all_254_2
% 17.50/3.11 | | | | (100) ~ (all_254_3 = 0) | (all_254_0 = 0 & all_254_1 = 0)
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | DELTA: instantiating (94) with fresh symbols all_256_0, all_256_1,
% 17.50/3.11 | | | | all_256_2, all_256_3 gives:
% 17.50/3.11 | | | | (101) relation_field(all_35_10) = all_256_2 & relation(all_35_10) =
% 17.50/3.11 | | | | all_256_3 & in(all_35_6, all_256_2) = all_256_0 & in(all_35_7,
% 17.50/3.11 | | | | all_256_2) = all_256_1 & $i(all_256_2) & ( ~ (all_256_3 = 0)
% 17.50/3.11 | | | | | (all_256_0 = 0 & all_256_1 = 0))
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | ALPHA: (101) implies:
% 17.50/3.11 | | | | (102) in(all_35_6, all_256_2) = all_256_0
% 17.50/3.11 | | | | (103) relation(all_35_10) = all_256_3
% 17.50/3.11 | | | | (104) relation_field(all_35_10) = all_256_2
% 17.50/3.11 | | | | (105) ~ (all_256_3 = 0) | (all_256_0 = 0 & all_256_1 = 0)
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | DELTA: instantiating (93) with fresh symbols all_258_0, all_258_1,
% 17.50/3.11 | | | | all_258_2, all_258_3, all_258_4 gives:
% 17.50/3.11 | | | | (106) ordered_pair(all_35_8, all_35_6) = all_258_1 & in(all_258_1,
% 17.50/3.11 | | | | all_35_10) = all_258_0 & in(all_35_6, all_65_2) = all_258_2 &
% 17.50/3.11 | | | | in(all_35_7, all_65_2) = all_258_3 & in(all_35_8, all_65_2) =
% 17.50/3.11 | | | | all_258_4 & $i(all_258_1) & ( ~ (all_258_2 = 0) | ~ (all_258_3
% 17.50/3.11 | | | | = 0) | ~ (all_258_4 = 0) | all_258_0 = 0)
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | ALPHA: (106) implies:
% 17.50/3.11 | | | | (107) in(all_35_8, all_65_2) = all_258_4
% 17.50/3.11 | | | | (108) in(all_35_7, all_65_2) = all_258_3
% 17.50/3.11 | | | | (109) in(all_35_6, all_65_2) = all_258_2
% 17.50/3.11 | | | | (110) in(all_258_1, all_35_10) = all_258_0
% 17.50/3.11 | | | | (111) ordered_pair(all_35_8, all_35_6) = all_258_1
% 17.50/3.11 | | | | (112) ~ (all_258_2 = 0) | ~ (all_258_3 = 0) | ~ (all_258_4 = 0) |
% 17.50/3.11 | | | | all_258_0 = 0
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | BETA: splitting (91) gives:
% 17.50/3.11 | | | |
% 17.50/3.11 | | | | Case 1:
% 17.50/3.11 | | | | |
% 17.50/3.11 | | | | | (113) all_35_0 = 0
% 17.50/3.11 | | | | |
% 17.50/3.11 | | | | | REDUCE: (72), (113) imply:
% 17.50/3.11 | | | | | (114) $false
% 17.50/3.11 | | | | |
% 17.50/3.11 | | | | | CLOSE: (114) is inconsistent.
% 17.50/3.11 | | | | |
% 17.50/3.11 | | | | Case 2:
% 17.50/3.11 | | | | |
% 17.50/3.11 | | | | |
% 17.50/3.11 | | | | | GROUND_INST: instantiating (11) with 0, all_256_3, all_35_10,
% 17.50/3.11 | | | | | simplifying with (22), (103) gives:
% 17.50/3.11 | | | | | (115) all_256_3 = 0
% 17.50/3.11 | | | | |
% 17.50/3.11 | | | | | GROUND_INST: instantiating (11) with all_254_3, all_256_3, all_35_10,
% 17.50/3.11 | | | | | simplifying with (98), (103) gives:
% 17.50/3.11 | | | | | (116) all_256_3 = all_254_3
% 17.50/3.11 | | | | |
% 17.50/3.11 | | | | | GROUND_INST: instantiating (13) with all_65_2, all_256_2, all_35_10,
% 17.50/3.11 | | | | | simplifying with (35), (104) gives:
% 17.50/3.11 | | | | | (117) all_256_2 = all_65_2
% 17.50/3.11 | | | | |
% 17.50/3.12 | | | | | GROUND_INST: instantiating (13) with all_254_2, all_256_2, all_35_10,
% 17.50/3.12 | | | | | simplifying with (99), (104) gives:
% 17.50/3.12 | | | | | (118) all_256_2 = all_254_2
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | GROUND_INST: instantiating (16) with all_35_1, all_258_1, all_35_6,
% 17.50/3.12 | | | | | all_35_8, simplifying with (78), (111) gives:
% 17.50/3.12 | | | | | (119) all_258_1 = all_35_1
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | COMBINE_EQS: (117), (118) imply:
% 17.50/3.12 | | | | | (120) all_254_2 = all_65_2
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | SIMP: (120) implies:
% 17.50/3.12 | | | | | (121) all_254_2 = all_65_2
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | COMBINE_EQS: (115), (116) imply:
% 17.50/3.12 | | | | | (122) all_254_3 = 0
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | SIMP: (122) implies:
% 17.50/3.12 | | | | | (123) all_254_3 = 0
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | REDUCE: (110), (119) imply:
% 17.50/3.12 | | | | | (124) in(all_35_1, all_35_10) = all_258_0
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | REDUCE: (102), (117) imply:
% 17.50/3.12 | | | | | (125) in(all_35_6, all_65_2) = all_256_0
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | REDUCE: (97), (121) imply:
% 17.50/3.12 | | | | | (126) in(all_35_7, all_65_2) = all_254_0
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | REDUCE: (96), (121) imply:
% 17.50/3.12 | | | | | (127) in(all_35_8, all_65_2) = all_254_1
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | BETA: splitting (105) gives:
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | Case 1:
% 17.50/3.12 | | | | | |
% 17.50/3.12 | | | | | | (128) ~ (all_256_3 = 0)
% 17.50/3.12 | | | | | |
% 17.50/3.12 | | | | | | REDUCE: (115), (128) imply:
% 17.50/3.12 | | | | | | (129) $false
% 17.50/3.12 | | | | | |
% 17.50/3.12 | | | | | | CLOSE: (129) is inconsistent.
% 17.50/3.12 | | | | | |
% 17.50/3.12 | | | | | Case 2:
% 17.50/3.12 | | | | | |
% 17.50/3.12 | | | | | | (130) all_256_0 = 0 & all_256_1 = 0
% 17.50/3.12 | | | | | |
% 17.50/3.12 | | | | | | ALPHA: (130) implies:
% 17.50/3.12 | | | | | | (131) all_256_0 = 0
% 17.50/3.12 | | | | | |
% 17.50/3.12 | | | | | | REDUCE: (125), (131) imply:
% 17.50/3.12 | | | | | | (132) in(all_35_6, all_65_2) = 0
% 17.50/3.12 | | | | | |
% 17.50/3.12 | | | | | | BETA: splitting (100) gives:
% 17.50/3.12 | | | | | |
% 17.50/3.12 | | | | | | Case 1:
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | (133) ~ (all_254_3 = 0)
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | REDUCE: (123), (133) imply:
% 17.50/3.12 | | | | | | | (134) $false
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | CLOSE: (134) is inconsistent.
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | Case 2:
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | (135) all_254_0 = 0 & all_254_1 = 0
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | ALPHA: (135) implies:
% 17.50/3.12 | | | | | | | (136) all_254_1 = 0
% 17.50/3.12 | | | | | | | (137) all_254_0 = 0
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | REDUCE: (126), (137) imply:
% 17.50/3.12 | | | | | | | (138) in(all_35_7, all_65_2) = 0
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | REDUCE: (127), (136) imply:
% 17.50/3.12 | | | | | | | (139) in(all_35_8, all_65_2) = 0
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | GROUND_INST: instantiating (14) with all_258_4, 0, all_65_2,
% 17.50/3.12 | | | | | | | all_35_8, simplifying with (107), (139) gives:
% 17.50/3.12 | | | | | | | (140) all_258_4 = 0
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | GROUND_INST: instantiating (14) with all_258_3, 0, all_65_2,
% 17.50/3.12 | | | | | | | all_35_7, simplifying with (108), (138) gives:
% 17.50/3.12 | | | | | | | (141) all_258_3 = 0
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | GROUND_INST: instantiating (14) with all_258_2, 0, all_65_2,
% 17.50/3.12 | | | | | | | all_35_6, simplifying with (109), (132) gives:
% 17.50/3.12 | | | | | | | (142) all_258_2 = 0
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | GROUND_INST: instantiating (14) with all_35_0, all_258_0,
% 17.50/3.12 | | | | | | | all_35_10, all_35_1, simplifying with (76), (124)
% 17.50/3.12 | | | | | | | gives:
% 17.50/3.12 | | | | | | | (143) all_258_0 = all_35_0
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | BETA: splitting (112) gives:
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | | Case 1:
% 17.50/3.12 | | | | | | | |
% 17.50/3.12 | | | | | | | | (144) ~ (all_258_2 = 0)
% 17.50/3.12 | | | | | | | |
% 17.50/3.12 | | | | | | | | REDUCE: (142), (144) imply:
% 17.50/3.12 | | | | | | | | (145) $false
% 17.50/3.12 | | | | | | | |
% 17.50/3.12 | | | | | | | | CLOSE: (145) is inconsistent.
% 17.50/3.12 | | | | | | | |
% 17.50/3.12 | | | | | | | Case 2:
% 17.50/3.12 | | | | | | | |
% 17.50/3.12 | | | | | | | | (146) ~ (all_258_3 = 0) | ~ (all_258_4 = 0) | all_258_0 = 0
% 17.50/3.12 | | | | | | | |
% 17.50/3.12 | | | | | | | | BETA: splitting (146) gives:
% 17.50/3.12 | | | | | | | |
% 17.50/3.12 | | | | | | | | Case 1:
% 17.50/3.12 | | | | | | | | |
% 17.50/3.12 | | | | | | | | | (147) ~ (all_258_3 = 0)
% 17.50/3.12 | | | | | | | | |
% 17.50/3.12 | | | | | | | | | REDUCE: (141), (147) imply:
% 17.50/3.12 | | | | | | | | | (148) $false
% 17.50/3.12 | | | | | | | | |
% 17.50/3.12 | | | | | | | | | CLOSE: (148) is inconsistent.
% 17.50/3.12 | | | | | | | | |
% 17.50/3.12 | | | | | | | | Case 2:
% 17.50/3.12 | | | | | | | | |
% 17.50/3.12 | | | | | | | | | (149) ~ (all_258_4 = 0) | all_258_0 = 0
% 17.50/3.12 | | | | | | | | |
% 17.50/3.12 | | | | | | | | | BETA: splitting (149) gives:
% 17.50/3.12 | | | | | | | | |
% 17.50/3.12 | | | | | | | | | Case 1:
% 17.50/3.12 | | | | | | | | | |
% 17.50/3.12 | | | | | | | | | | (150) ~ (all_258_4 = 0)
% 17.50/3.12 | | | | | | | | | |
% 17.50/3.12 | | | | | | | | | | REDUCE: (140), (150) imply:
% 17.50/3.12 | | | | | | | | | | (151) $false
% 17.50/3.12 | | | | | | | | | |
% 17.50/3.12 | | | | | | | | | | CLOSE: (151) is inconsistent.
% 17.50/3.12 | | | | | | | | | |
% 17.50/3.12 | | | | | | | | | Case 2:
% 17.50/3.12 | | | | | | | | | |
% 17.50/3.12 | | | | | | | | | | (152) all_258_0 = 0
% 17.50/3.12 | | | | | | | | | |
% 17.50/3.12 | | | | | | | | | | COMBINE_EQS: (143), (152) imply:
% 17.50/3.12 | | | | | | | | | | (153) all_35_0 = 0
% 17.50/3.12 | | | | | | | | | |
% 17.50/3.12 | | | | | | | | | | REDUCE: (72), (153) imply:
% 17.50/3.12 | | | | | | | | | | (154) $false
% 17.50/3.12 | | | | | | | | | |
% 17.50/3.12 | | | | | | | | | | CLOSE: (154) is inconsistent.
% 17.50/3.12 | | | | | | | | | |
% 17.50/3.12 | | | | | | | | | End of split
% 17.50/3.12 | | | | | | | | |
% 17.50/3.12 | | | | | | | | End of split
% 17.50/3.12 | | | | | | | |
% 17.50/3.12 | | | | | | | End of split
% 17.50/3.12 | | | | | | |
% 17.50/3.12 | | | | | | End of split
% 17.50/3.12 | | | | | |
% 17.50/3.12 | | | | | End of split
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | End of split
% 17.50/3.12 | | | |
% 17.50/3.12 | | | End of split
% 17.50/3.12 | | |
% 17.50/3.12 | | End of split
% 17.50/3.12 | |
% 17.50/3.12 | Case 2:
% 17.50/3.12 | |
% 17.50/3.12 | | (155) ~ (all_35_9 = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.50/3.12 | | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~
% 17.50/3.12 | | (ordered_pair(v1, v2) = v3) | ~ (ordered_pair(v0, v2) = v4) | ~
% 17.50/3.12 | | (in(v4, all_35_10) = v5) | ~ (in(v3, all_35_10) = 0) | ~ $i(v2)
% 17.50/3.12 | | | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: int] : ( ~ (v7 =
% 17.50/3.12 | | 0) & ordered_pair(v0, v1) = v6 & in(v6, all_35_10) = v7 &
% 17.50/3.12 | | $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 17.50/3.12 | | $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (ordered_pair(v0,
% 17.50/3.12 | | v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4,
% 17.50/3.12 | | all_35_10) = v5) | ~ (in(v3, all_35_10) = 0) | ~ $i(v2) |
% 17.50/3.12 | | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0)
% 17.50/3.12 | | & ordered_pair(v1, v2) = v6 & in(v6, all_35_10) = v7 & $i(v6)))
% 17.50/3.12 | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 17.50/3.12 | | $i] : ( ~ (ordered_pair(v1, v2) = v4) | ~ (ordered_pair(v0, v1)
% 17.50/3.12 | | = v3) | ~ (in(v4, all_35_10) = 0) | ~ (in(v3, all_35_10) = 0)
% 17.50/3.12 | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] :
% 17.50/3.12 | | (ordered_pair(v0, v2) = v5 & in(v5, all_35_10) = 0 & $i(v5)))
% 17.50/3.12 | |
% 17.50/3.12 | | ALPHA: (155) implies:
% 17.50/3.12 | | (156) ~ (all_35_9 = 0)
% 17.50/3.12 | | (157) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 17.50/3.12 | | : ( ~ (ordered_pair(v1, v2) = v4) | ~ (ordered_pair(v0, v1) = v3)
% 17.50/3.12 | | | ~ (in(v4, all_35_10) = 0) | ~ (in(v3, all_35_10) = 0) | ~
% 17.50/3.12 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (ordered_pair(v0,
% 17.50/3.12 | | v2) = v5 & in(v5, all_35_10) = 0 & $i(v5)))
% 17.50/3.12 | |
% 17.50/3.12 | | BETA: splitting (64) gives:
% 17.50/3.12 | |
% 17.50/3.12 | | Case 1:
% 17.50/3.12 | | |
% 17.50/3.12 | | | (158) ~ (all_137_2 = 0)
% 17.50/3.12 | | |
% 17.50/3.12 | | | REDUCE: (65), (158) imply:
% 17.50/3.12 | | | (159) $false
% 17.50/3.12 | | |
% 17.50/3.12 | | | CLOSE: (159) is inconsistent.
% 17.50/3.12 | | |
% 17.50/3.12 | | Case 2:
% 17.50/3.12 | | |
% 17.50/3.12 | | | (160) ( ~ (all_137_0 = 0) | all_137_1 = 0) & ( ~ (all_137_1 = 0) |
% 17.50/3.12 | | | all_137_0 = 0)
% 17.50/3.12 | | |
% 17.50/3.12 | | | ALPHA: (160) implies:
% 17.50/3.12 | | | (161) ~ (all_137_0 = 0) | all_137_1 = 0
% 17.50/3.12 | | |
% 17.50/3.12 | | | BETA: splitting (161) gives:
% 17.50/3.12 | | |
% 17.50/3.12 | | | Case 1:
% 17.50/3.12 | | | |
% 17.50/3.12 | | | | (162) ~ (all_137_0 = 0)
% 17.50/3.12 | | | |
% 17.50/3.12 | | | | REDUCE: (67), (162) imply:
% 17.50/3.12 | | | | (163) ~ (all_73_0 = 0)
% 17.50/3.12 | | | |
% 17.50/3.12 | | | | BETA: splitting (56) gives:
% 17.50/3.12 | | | |
% 17.50/3.12 | | | | Case 1:
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | (164) all_73_0 = 0
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | REDUCE: (163), (164) imply:
% 17.50/3.12 | | | | | (165) $false
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | | CLOSE: (165) is inconsistent.
% 17.50/3.12 | | | | |
% 17.50/3.12 | | | | Case 2:
% 17.50/3.12 | | | | |
% 17.50/3.13 | | | | | (166) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 17.50/3.13 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 17.50/3.13 | | | | | ordered_pair(v1, v2) = v4 & ordered_pair(v0, v2) = v5 &
% 17.50/3.13 | | | | | ordered_pair(v0, v1) = v3 & in(v5, all_35_10) = v6 & in(v4,
% 17.50/3.13 | | | | | all_35_10) = 0 & in(v3, all_35_10) = 0 & in(v2, all_65_2)
% 17.50/3.13 | | | | | = 0 & in(v1, all_65_2) = 0 & in(v0, all_65_2) = 0 & $i(v5)
% 17.50/3.13 | | | | | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.50/3.13 | | | | |
% 17.50/3.13 | | | | | DELTA: instantiating (166) with fresh symbols all_215_0, all_215_1,
% 17.50/3.13 | | | | | all_215_2, all_215_3, all_215_4, all_215_5, all_215_6 gives:
% 17.50/3.13 | | | | | (167) ~ (all_215_0 = 0) & ordered_pair(all_215_5, all_215_4) =
% 17.50/3.13 | | | | | all_215_2 & ordered_pair(all_215_6, all_215_4) = all_215_1 &
% 17.50/3.13 | | | | | ordered_pair(all_215_6, all_215_5) = all_215_3 &
% 17.50/3.13 | | | | | in(all_215_1, all_35_10) = all_215_0 & in(all_215_2,
% 17.50/3.13 | | | | | all_35_10) = 0 & in(all_215_3, all_35_10) = 0 &
% 17.50/3.13 | | | | | in(all_215_4, all_65_2) = 0 & in(all_215_5, all_65_2) = 0 &
% 17.50/3.13 | | | | | in(all_215_6, all_65_2) = 0 & $i(all_215_1) & $i(all_215_2) &
% 17.50/3.13 | | | | | $i(all_215_3) & $i(all_215_4) & $i(all_215_5) & $i(all_215_6)
% 17.50/3.13 | | | | |
% 17.50/3.13 | | | | | ALPHA: (167) implies:
% 17.50/3.13 | | | | | (168) ~ (all_215_0 = 0)
% 17.50/3.13 | | | | | (169) $i(all_215_6)
% 17.50/3.13 | | | | | (170) $i(all_215_5)
% 17.50/3.13 | | | | | (171) $i(all_215_4)
% 17.50/3.13 | | | | | (172) $i(all_215_1)
% 17.50/3.13 | | | | | (173) in(all_215_3, all_35_10) = 0
% 17.50/3.13 | | | | | (174) in(all_215_2, all_35_10) = 0
% 17.50/3.13 | | | | | (175) in(all_215_1, all_35_10) = all_215_0
% 17.50/3.13 | | | | | (176) ordered_pair(all_215_6, all_215_5) = all_215_3
% 17.50/3.13 | | | | | (177) ordered_pair(all_215_6, all_215_4) = all_215_1
% 17.50/3.13 | | | | | (178) ordered_pair(all_215_5, all_215_4) = all_215_2
% 17.50/3.13 | | | | |
% 17.50/3.13 | | | | | GROUND_INST: instantiating (10) with all_215_1, all_35_10, all_215_0,
% 17.50/3.13 | | | | | simplifying with (18), (172), (175) gives:
% 17.50/3.13 | | | | | (179) all_215_0 = 0 | ? [v0: any] : ? [v1: any] :
% 17.50/3.13 | | | | | (element(all_215_1, all_35_10) = v0 & empty(all_35_10) = v1 &
% 17.50/3.13 | | | | | ( ~ (v0 = 0) | v1 = 0))
% 17.50/3.13 | | | | |
% 17.50/3.13 | | | | | GROUND_INST: instantiating (157) with all_215_6, all_215_5, all_215_4,
% 17.50/3.13 | | | | | all_215_3, all_215_2, simplifying with (169), (170),
% 17.50/3.13 | | | | | (171), (173), (174), (176), (178) gives:
% 17.50/3.13 | | | | | (180) ? [v0: $i] : (ordered_pair(all_215_6, all_215_4) = v0 &
% 17.50/3.13 | | | | | in(v0, all_35_10) = 0 & $i(v0))
% 17.50/3.13 | | | | |
% 17.50/3.13 | | | | | DELTA: instantiating (180) with fresh symbol all_263_0 gives:
% 17.50/3.13 | | | | | (181) ordered_pair(all_215_6, all_215_4) = all_263_0 &
% 17.50/3.13 | | | | | in(all_263_0, all_35_10) = 0 & $i(all_263_0)
% 17.50/3.13 | | | | |
% 17.50/3.13 | | | | | ALPHA: (181) implies:
% 17.50/3.13 | | | | | (182) in(all_263_0, all_35_10) = 0
% 17.50/3.13 | | | | | (183) ordered_pair(all_215_6, all_215_4) = all_263_0
% 17.50/3.13 | | | | |
% 17.50/3.13 | | | | | BETA: splitting (179) gives:
% 17.50/3.13 | | | | |
% 17.50/3.13 | | | | | Case 1:
% 17.50/3.13 | | | | | |
% 17.50/3.13 | | | | | | (184) all_215_0 = 0
% 17.50/3.13 | | | | | |
% 17.50/3.13 | | | | | | REDUCE: (168), (184) imply:
% 17.50/3.13 | | | | | | (185) $false
% 17.50/3.13 | | | | | |
% 17.50/3.13 | | | | | | CLOSE: (185) is inconsistent.
% 17.50/3.13 | | | | | |
% 17.50/3.13 | | | | | Case 2:
% 17.50/3.13 | | | | | |
% 17.50/3.13 | | | | | |
% 17.50/3.13 | | | | | | GROUND_INST: instantiating (16) with all_215_1, all_263_0,
% 17.50/3.13 | | | | | | all_215_4, all_215_6, simplifying with (177), (183)
% 17.50/3.13 | | | | | | gives:
% 17.50/3.13 | | | | | | (186) all_263_0 = all_215_1
% 17.50/3.13 | | | | | |
% 17.50/3.13 | | | | | | REDUCE: (182), (186) imply:
% 17.50/3.13 | | | | | | (187) in(all_215_1, all_35_10) = 0
% 17.50/3.13 | | | | | |
% 17.50/3.13 | | | | | | GROUND_INST: instantiating (14) with all_215_0, 0, all_35_10,
% 17.50/3.13 | | | | | | all_215_1, simplifying with (175), (187) gives:
% 17.50/3.13 | | | | | | (188) all_215_0 = 0
% 17.50/3.13 | | | | | |
% 17.50/3.13 | | | | | | REDUCE: (168), (188) imply:
% 17.50/3.13 | | | | | | (189) $false
% 17.50/3.13 | | | | | |
% 17.50/3.13 | | | | | | CLOSE: (189) is inconsistent.
% 17.50/3.13 | | | | | |
% 17.50/3.13 | | | | | End of split
% 17.50/3.13 | | | | |
% 17.50/3.13 | | | | End of split
% 17.50/3.13 | | | |
% 17.50/3.13 | | | Case 2:
% 17.50/3.13 | | | |
% 17.50/3.13 | | | | (190) all_137_1 = 0
% 17.50/3.13 | | | |
% 17.50/3.13 | | | | COMBINE_EQS: (68), (190) imply:
% 17.50/3.13 | | | | (191) all_35_9 = 0
% 17.50/3.13 | | | |
% 17.50/3.13 | | | | SIMP: (191) implies:
% 17.50/3.13 | | | | (192) all_35_9 = 0
% 17.50/3.13 | | | |
% 17.50/3.13 | | | | REDUCE: (156), (192) imply:
% 17.50/3.13 | | | | (193) $false
% 17.50/3.13 | | | |
% 17.50/3.13 | | | | CLOSE: (193) is inconsistent.
% 17.50/3.13 | | | |
% 17.50/3.13 | | | End of split
% 17.50/3.13 | | |
% 17.50/3.13 | | End of split
% 17.50/3.13 | |
% 17.50/3.13 | End of split
% 17.50/3.13 |
% 17.50/3.13 End of proof
% 17.50/3.13 % SZS output end Proof for theBenchmark
% 17.50/3.13
% 17.50/3.13 2614ms
%------------------------------------------------------------------------------