TSTP Solution File: SEU242+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU242+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 : n003.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 17:43:36 EDT 2023
% Result : Theorem 10.46s 2.16s
% Output : Proof 15.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU242+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 18:57:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.45/1.05 Prover 1: Preprocessing ...
% 2.45/1.05 Prover 4: Preprocessing ...
% 2.73/1.09 Prover 3: Preprocessing ...
% 2.73/1.09 Prover 2: Preprocessing ...
% 2.73/1.09 Prover 5: Preprocessing ...
% 2.73/1.09 Prover 6: Preprocessing ...
% 2.73/1.09 Prover 0: Preprocessing ...
% 5.52/1.50 Prover 1: Warning: ignoring some quantifiers
% 5.52/1.50 Prover 2: Proving ...
% 5.52/1.51 Prover 3: Warning: ignoring some quantifiers
% 5.52/1.51 Prover 5: Proving ...
% 5.52/1.52 Prover 3: Constructing countermodel ...
% 6.04/1.52 Prover 1: Constructing countermodel ...
% 6.04/1.55 Prover 4: Warning: ignoring some quantifiers
% 6.04/1.55 Prover 6: Proving ...
% 6.37/1.57 Prover 4: Constructing countermodel ...
% 6.37/1.62 Prover 0: Proving ...
% 7.73/1.80 Prover 3: gave up
% 7.73/1.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.28/1.86 Prover 7: Preprocessing ...
% 9.17/1.96 Prover 1: gave up
% 9.17/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.17/1.98 Prover 7: Warning: ignoring some quantifiers
% 9.17/1.99 Prover 7: Constructing countermodel ...
% 9.17/1.99 Prover 8: Preprocessing ...
% 10.46/2.14 Prover 8: Warning: ignoring some quantifiers
% 10.46/2.15 Prover 8: Constructing countermodel ...
% 10.46/2.16 Prover 0: proved (1513ms)
% 10.46/2.16
% 10.46/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.46/2.16
% 10.46/2.16 Prover 5: stopped
% 10.46/2.16 Prover 2: stopped
% 10.46/2.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.46/2.17 Prover 6: stopped
% 10.46/2.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.46/2.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.46/2.18 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.46/2.19 Prover 10: Preprocessing ...
% 10.46/2.21 Prover 11: Preprocessing ...
% 10.46/2.21 Prover 16: Preprocessing ...
% 10.46/2.22 Prover 13: Preprocessing ...
% 11.08/2.26 Prover 16: Warning: ignoring some quantifiers
% 11.08/2.28 Prover 16: Constructing countermodel ...
% 11.08/2.28 Prover 10: Warning: ignoring some quantifiers
% 11.54/2.29 Prover 10: Constructing countermodel ...
% 11.54/2.29 Prover 13: Warning: ignoring some quantifiers
% 11.54/2.30 Prover 13: Constructing countermodel ...
% 12.24/2.37 Prover 11: Warning: ignoring some quantifiers
% 12.24/2.38 Prover 11: Constructing countermodel ...
% 12.24/2.38 Prover 10: gave up
% 12.24/2.38 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.24/2.39 Prover 8: gave up
% 12.24/2.40 Prover 19: Preprocessing ...
% 12.74/2.50 Prover 19: Warning: ignoring some quantifiers
% 12.74/2.51 Prover 19: Constructing countermodel ...
% 13.40/2.54 Prover 13: gave up
% 13.85/2.70 Prover 7: gave up
% 13.85/2.72 Prover 4: Found proof (size 194)
% 13.85/2.72 Prover 4: proved (2067ms)
% 13.85/2.72 Prover 16: stopped
% 13.85/2.72 Prover 19: stopped
% 13.85/2.72 Prover 11: stopped
% 13.85/2.72
% 13.85/2.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.85/2.72
% 13.85/2.74 % SZS output start Proof for theBenchmark
% 13.85/2.74 Assumptions after simplification:
% 13.85/2.74 ---------------------------------
% 13.85/2.74
% 13.85/2.74 (cc2_funct_1)
% 14.71/2.77 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.71/2.77 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 14.71/2.77 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 14.71/2.77 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 14.71/2.77 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 14.71/2.77 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 14.71/2.77 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 14.71/2.77 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 14.71/2.77 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 14.71/2.77 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 14.71/2.77 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 14.71/2.77 0)))
% 14.71/2.77
% 14.71/2.77 (commutativity_k2_xboole_0)
% 15.10/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 15.10/2.78 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 15.10/2.78 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 15.10/2.78 | (set_union2(v1, v0) = v2 & $i(v2)))
% 15.10/2.78
% 15.10/2.78 (d14_relat_2)
% 15.10/2.78 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ?
% 15.10/2.78 [v2: any] : ? [v3: any] : ? [v4: any] : (connected(v0) = v3 &
% 15.10/2.78 is_connected_in(v0, v1) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v4
% 15.10/2.78 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0))))) & ! [v0: $i] : !
% 15.10/2.78 [v1: any] : ( ~ (connected(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i]
% 15.10/2.78 : ? [v4: any] : (relation_field(v0) = v3 & is_connected_in(v0, v3) = v4 &
% 15.10/2.78 relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v4 = 0) | v1 = 0) & ( ~
% 15.10/2.78 (v1 = 0) | v4 = 0))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~
% 15.10/2.78 $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any] : (relation_field(v0) =
% 15.10/2.78 v2 & connected(v0) = v1 & is_connected_in(v0, v2) = v3 & $i(v2) & ( ~ (v3
% 15.10/2.78 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 15.10/2.78
% 15.10/2.78 (d6_relat_1)
% 15.10/2.79 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 15.10/2.79 any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v4 &
% 15.10/2.79 relation_field(v0) = v3 & set_union2(v1, v4) = v5 & relation(v0) = v2 &
% 15.10/2.79 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : !
% 15.10/2.79 [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 15.10/2.79 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 &
% 15.10/2.79 relation_field(v0) = v3 & set_union2(v4, v1) = v5 & relation(v0) = v2 &
% 15.10/2.79 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : !
% 15.10/2.79 [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 15.10/2.79 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v3 &
% 15.10/2.79 relation_rng(v0) = v4 & set_union2(v3, v4) = v5 & relation(v0) = v2 &
% 15.10/2.79 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v1))) & ! [v0: $i] : ( ~
% 15.10/2.79 (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 15.10/2.79 (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 &
% 15.10/2.79 set_union2(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 15.10/2.79
% 15.10/2.79 (d6_relat_2)
% 15.10/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2
% 15.10/2.79 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_connected_in(v0, v1) = 0) | ~
% 15.10/2.79 (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 15.10/2.79 any] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] :
% 15.10/2.79 (ordered_pair(v2, v3) = v7 & in(v7, v0) = v8 & in(v4, v0) = v9 & in(v3, v1)
% 15.10/2.79 = v6 & in(v2, v1) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v8
% 15.10/2.79 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 15.10/2.79 $i] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ (is_connected_in(v0,
% 15.10/2.79 v1) = 0) | ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 15.10/2.79 ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 15.10/2.79 [v9: any] : (ordered_pair(v3, v2) = v8 & in(v8, v0) = v9 & in(v4, v0) = v7 &
% 15.10/2.79 in(v3, v1) = v6 & in(v2, v1) = v5 & $i(v8) & ( ~ (v6 = 0) | ~ (v5 = 0) |
% 15.10/2.79 v9 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0
% 15.10/2.79 | ~ (is_connected_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~
% 15.10/2.79 $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7:
% 15.10/2.79 $i] : ? [v8: int] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = v3) &
% 15.10/2.79 ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 &
% 15.10/2.79 in(v5, v0) = v6 & in(v4, v1) = 0 & in(v3, v1) = 0 & $i(v7) & $i(v5) &
% 15.10/2.79 $i(v4) & $i(v3)))
% 15.10/2.79
% 15.10/2.79 (l4_wellord1)
% 15.10/2.79 ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 15.10/2.79 int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10:
% 15.10/2.79 int] : (relation_field(v0) = v2 & connected(v0) = v1 & relation(v0) = 0 &
% 15.10/2.79 $i(v4) & $i(v3) & $i(v2) & $i(v0) & ((v6 = 0 & v5 = 0 & v1 = 0 & ~ (v10 =
% 15.10/2.79 0) & ~ (v8 = 0) & ~ (v4 = v3) & ordered_pair(v4, v3) = v9 &
% 15.10/2.79 ordered_pair(v3, v4) = v7 & in(v9, v0) = v10 & in(v7, v0) = v8 & in(v4,
% 15.10/2.79 v2) = 0 & in(v3, v2) = 0 & $i(v9) & $i(v7)) | ( ~ (v1 = 0) & ! [v11:
% 15.10/2.79 $i] : ! [v12: $i] : ! [v13: $i] : (v12 = v11 | ~ (ordered_pair(v12,
% 15.10/2.79 v11) = v13) | ~ $i(v12) | ~ $i(v11) | ? [v14: any] : ? [v15:
% 15.10/2.79 any] : ? [v16: $i] : ? [v17: any] : ? [v18: any] :
% 15.10/2.79 (ordered_pair(v11, v12) = v16 & in(v16, v0) = v17 & in(v13, v0) = v18
% 15.10/2.79 & in(v12, v2) = v15 & in(v11, v2) = v14 & $i(v16) & ( ~ (v15 = 0) |
% 15.10/2.79 ~ (v14 = 0) | v18 = 0 | v17 = 0))) & ! [v11: $i] : ! [v12: $i] :
% 15.10/2.79 ! [v13: $i] : (v12 = v11 | ~ (ordered_pair(v11, v12) = v13) | ~
% 15.10/2.79 $i(v12) | ~ $i(v11) | ? [v14: any] : ? [v15: any] : ? [v16: any] :
% 15.10/2.79 ? [v17: $i] : ? [v18: any] : (ordered_pair(v12, v11) = v17 & in(v17,
% 15.10/2.79 v0) = v18 & in(v13, v0) = v16 & in(v12, v2) = v15 & in(v11, v2) =
% 15.10/2.79 v14 & $i(v17) & ( ~ (v15 = 0) | ~ (v14 = 0) | v18 = 0 | v16 =
% 15.10/2.79 0))))))
% 15.10/2.79
% 15.10/2.79 (t2_subset)
% 15.10/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 15.10/2.80 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 &
% 15.10/2.80 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : (
% 15.10/2.80 ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 15.10/2.80 any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 15.10/2.80
% 15.10/2.80 (function-axioms)
% 15.10/2.80 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 15.10/2.80 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 15.10/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.10/2.80 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0:
% 15.10/2.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.10/2.80 : (v1 = v0 | ~ (is_connected_in(v3, v2) = v1) | ~ (is_connected_in(v3, v2) =
% 15.10/2.80 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 15.10/2.80 ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] :
% 15.10/2.80 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2)
% 15.10/2.80 = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 15.10/2.80 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3,
% 15.10/2.80 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 15.10/2.80 $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) &
% 15.10/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1)
% 15.10/2.80 | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.10/2.80 (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] :
% 15.10/2.80 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~
% 15.10/2.80 (relation_field(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.10/2.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (connected(v2) = v1) | ~
% 15.10/2.80 (connected(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.10/2.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~
% 15.10/2.80 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.10/2.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 15.10/2.80 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.10/2.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 15.10/2.80 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.10/2.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 15.10/2.80 (empty(v2) = v0))
% 15.10/2.80
% 15.10/2.80 Further assumptions not needed in the proof:
% 15.10/2.80 --------------------------------------------
% 15.10/2.80 antisymmetry_r2_hidden, cc1_funct_1, commutativity_k2_tarski, d5_tarski,
% 15.10/2.80 dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0, dt_k2_relat_1, dt_k2_tarski,
% 15.10/2.80 dt_k2_xboole_0, dt_k3_relat_1, dt_k4_tarski, dt_m1_subset_1,
% 15.10/2.80 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0,
% 15.10/2.80 idempotence_k2_xboole_0, rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0,
% 15.10/2.80 rc3_funct_1, t1_boole, t1_subset, t6_boole, t7_boole, t8_boole
% 15.10/2.80
% 15.10/2.80 Those formulas are unsatisfiable:
% 15.10/2.80 ---------------------------------
% 15.10/2.80
% 15.10/2.80 Begin of proof
% 15.10/2.80 |
% 15.10/2.80 | ALPHA: (cc2_funct_1) implies:
% 15.10/2.80 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 15.10/2.80 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 15.10/2.80 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 15.10/2.80 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ?
% 15.10/2.80 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 &
% 15.10/2.80 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 15.10/2.80 | ~ (v2 = 0) | v1 = 0)))
% 15.10/2.80 |
% 15.10/2.80 | ALPHA: (commutativity_k2_xboole_0) implies:
% 15.10/2.80 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 15.10/2.80 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 15.10/2.81 |
% 15.10/2.81 | ALPHA: (d14_relat_2) implies:
% 15.10/2.81 | (4) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 15.10/2.81 | [v2: $i] : ? [v3: any] : (relation_field(v0) = v2 & connected(v0) =
% 15.10/2.81 | v1 & is_connected_in(v0, v2) = v3 & $i(v2) & ( ~ (v3 = 0) | v1 = 0)
% 15.10/2.81 | & ( ~ (v1 = 0) | v3 = 0)))
% 15.10/2.81 | (5) ! [v0: $i] : ! [v1: any] : ( ~ (connected(v0) = v1) | ~ $i(v0) | ?
% 15.10/2.81 | [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_field(v0) = v3 &
% 15.10/2.81 | is_connected_in(v0, v3) = v4 & relation(v0) = v2 & $i(v3) & ( ~ (v2
% 15.10/2.81 | = 0) | (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) | v4 = 0)))))
% 15.10/2.81 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 15.10/2.81 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (connected(v0) = v3 &
% 15.10/2.81 | is_connected_in(v0, v1) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) |
% 15.10/2.81 | (( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0)))))
% 15.10/2.81 |
% 15.10/2.81 | ALPHA: (d6_relat_1) implies:
% 15.10/2.81 | (7) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 15.10/2.81 | [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & relation_rng(v0) =
% 15.10/2.81 | v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1 & $i(v3) &
% 15.10/2.81 | $i(v2) & $i(v1)))
% 15.10/2.81 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 15.10/2.81 | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 15.10/2.81 | (relation_dom(v0) = v3 & relation_rng(v0) = v4 & set_union2(v3, v4) =
% 15.10/2.81 | v5 & relation(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) |
% 15.10/2.81 | v5 = v1)))
% 15.10/2.81 |
% 15.10/2.81 | ALPHA: (d6_relat_2) implies:
% 15.10/2.81 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 15.10/2.81 | (is_connected_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) |
% 15.10/2.81 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] :
% 15.10/2.81 | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = v3)
% 15.10/2.81 | & ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7,
% 15.10/2.81 | v0) = v8 & in(v5, v0) = v6 & in(v4, v1) = 0 & in(v3, v1) = 0 &
% 15.10/2.81 | $i(v7) & $i(v5) & $i(v4) & $i(v3)))
% 15.10/2.81 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 15.10/2.81 | (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ (is_connected_in(v0,
% 15.10/2.81 | v1) = 0) | ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 15.10/2.81 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ?
% 15.10/2.81 | [v8: $i] : ? [v9: any] : (ordered_pair(v3, v2) = v8 & in(v8, v0) =
% 15.10/2.81 | v9 & in(v4, v0) = v7 & in(v3, v1) = v6 & in(v2, v1) = v5 & $i(v8)
% 15.10/2.81 | & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v7 = 0)))
% 15.10/2.81 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 15.10/2.81 | (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_connected_in(v0,
% 15.10/2.81 | v1) = 0) | ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 15.10/2.81 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ?
% 15.10/2.81 | [v8: any] : ? [v9: any] : (ordered_pair(v2, v3) = v7 & in(v7, v0) =
% 15.10/2.81 | v8 & in(v4, v0) = v9 & in(v3, v1) = v6 & in(v2, v1) = v5 & $i(v7)
% 15.10/2.81 | & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v8 = 0)))
% 15.10/2.81 |
% 15.10/2.81 | ALPHA: (t2_subset) implies:
% 15.10/2.81 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 15.10/2.81 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 15.10/2.81 | (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 15.10/2.81 |
% 15.10/2.81 | ALPHA: (function-axioms) implies:
% 15.10/2.82 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.10/2.82 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 15.10/2.82 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.10/2.82 | : (v1 = v0 | ~ (connected(v2) = v1) | ~ (connected(v2) = v0))
% 15.30/2.82 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.30/2.82 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 15.30/2.82 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.30/2.82 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 15.30/2.82 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.30/2.82 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 15.30/2.82 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.30/2.82 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 15.30/2.82 | v0))
% 15.30/2.82 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.30/2.82 | : ! [v3: $i] : (v1 = v0 | ~ (is_connected_in(v3, v2) = v1) | ~
% 15.30/2.82 | (is_connected_in(v3, v2) = v0))
% 15.30/2.82 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.30/2.82 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 15.30/2.82 |
% 15.30/2.82 | DELTA: instantiating (l4_wellord1) with fresh symbols all_34_0, all_34_1,
% 15.30/2.82 | all_34_2, all_34_3, all_34_4, all_34_5, all_34_6, all_34_7, all_34_8,
% 15.30/2.82 | all_34_9, all_34_10 gives:
% 15.30/2.82 | (21) relation_field(all_34_10) = all_34_8 & connected(all_34_10) = all_34_9
% 15.30/2.82 | & relation(all_34_10) = 0 & $i(all_34_6) & $i(all_34_7) & $i(all_34_8)
% 15.30/2.82 | & $i(all_34_10) & ((all_34_4 = 0 & all_34_5 = 0 & all_34_9 = 0 & ~
% 15.30/2.82 | (all_34_0 = 0) & ~ (all_34_2 = 0) & ~ (all_34_6 = all_34_7) &
% 15.30/2.82 | ordered_pair(all_34_6, all_34_7) = all_34_1 &
% 15.30/2.82 | ordered_pair(all_34_7, all_34_6) = all_34_3 & in(all_34_1,
% 15.30/2.82 | all_34_10) = all_34_0 & in(all_34_3, all_34_10) = all_34_2 &
% 15.30/2.82 | in(all_34_6, all_34_8) = 0 & in(all_34_7, all_34_8) = 0 &
% 15.30/2.82 | $i(all_34_1) & $i(all_34_3)) | ( ~ (all_34_9 = 0) & ! [v0: $i] :
% 15.30/2.82 | ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (ordered_pair(v1, v0) =
% 15.30/2.82 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 15.30/2.82 | [v5: $i] : ? [v6: any] : ? [v7: any] : (ordered_pair(v0, v1) =
% 15.30/2.82 | v5 & in(v5, all_34_10) = v6 & in(v2, all_34_10) = v7 & in(v1,
% 15.30/2.82 | all_34_8) = v4 & in(v0, all_34_8) = v3 & $i(v5) & ( ~ (v4 =
% 15.30/2.82 | 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0: $i] : !
% 15.30/2.82 | [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2)
% 15.30/2.82 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 15.30/2.82 | any] : ? [v6: $i] : ? [v7: any] : (ordered_pair(v1, v0) = v6
% 15.30/2.82 | & in(v6, all_34_10) = v7 & in(v2, all_34_10) = v5 & in(v1,
% 15.30/2.82 | all_34_8) = v4 & in(v0, all_34_8) = v3 & $i(v6) & ( ~ (v4 =
% 15.30/2.82 | 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0)))))
% 15.30/2.82 |
% 15.30/2.82 | ALPHA: (21) implies:
% 15.30/2.82 | (22) $i(all_34_10)
% 15.30/2.82 | (23) $i(all_34_7)
% 15.30/2.82 | (24) $i(all_34_6)
% 15.30/2.82 | (25) relation(all_34_10) = 0
% 15.30/2.82 | (26) connected(all_34_10) = all_34_9
% 15.30/2.82 | (27) relation_field(all_34_10) = all_34_8
% 15.30/2.83 | (28) (all_34_4 = 0 & all_34_5 = 0 & all_34_9 = 0 & ~ (all_34_0 = 0) & ~
% 15.30/2.83 | (all_34_2 = 0) & ~ (all_34_6 = all_34_7) & ordered_pair(all_34_6,
% 15.30/2.83 | all_34_7) = all_34_1 & ordered_pair(all_34_7, all_34_6) = all_34_3
% 15.30/2.83 | & in(all_34_1, all_34_10) = all_34_0 & in(all_34_3, all_34_10) =
% 15.30/2.83 | all_34_2 & in(all_34_6, all_34_8) = 0 & in(all_34_7, all_34_8) = 0 &
% 15.30/2.83 | $i(all_34_1) & $i(all_34_3)) | ( ~ (all_34_9 = 0) & ! [v0: $i] : !
% 15.30/2.83 | [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) |
% 15.30/2.83 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i]
% 15.30/2.83 | : ? [v6: any] : ? [v7: any] : (ordered_pair(v0, v1) = v5 &
% 15.30/2.83 | in(v5, all_34_10) = v6 & in(v2, all_34_10) = v7 & in(v1,
% 15.30/2.83 | all_34_8) = v4 & in(v0, all_34_8) = v3 & $i(v5) & ( ~ (v4 = 0)
% 15.30/2.83 | | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0: $i] : ! [v1: $i]
% 15.30/2.83 | : ! [v2: $i] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ~
% 15.30/2.83 | $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 15.30/2.83 | ? [v6: $i] : ? [v7: any] : (ordered_pair(v1, v0) = v6 & in(v6,
% 15.30/2.83 | all_34_10) = v7 & in(v2, all_34_10) = v5 & in(v1, all_34_8) =
% 15.30/2.83 | v4 & in(v0, all_34_8) = v3 & $i(v6) & ( ~ (v4 = 0) | ~ (v3 = 0)
% 15.30/2.83 | | v7 = 0 | v5 = 0))))
% 15.30/2.83 |
% 15.30/2.83 | GROUND_INST: instantiating (7) with all_34_10, simplifying with (22), (25)
% 15.30/2.83 | gives:
% 15.30/2.83 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_34_10) =
% 15.30/2.83 | v1 & relation_rng(all_34_10) = v2 & relation_field(all_34_10) = v0 &
% 15.30/2.83 | set_union2(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 15.30/2.83 |
% 15.30/2.83 | GROUND_INST: instantiating (4) with all_34_10, simplifying with (22), (25)
% 15.30/2.83 | gives:
% 15.30/2.83 | (30) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_field(all_34_10)
% 15.30/2.83 | = v1 & connected(all_34_10) = v0 & is_connected_in(all_34_10, v1) =
% 15.30/2.83 | v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 15.30/2.83 |
% 15.30/2.83 | GROUND_INST: instantiating (1) with all_34_10, simplifying with (22), (25)
% 15.30/2.83 | gives:
% 15.30/2.83 | (31) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_34_10) =
% 15.30/2.83 | v2 & function(all_34_10) = v1 & empty(all_34_10) = v0 & ( ~ (v1 = 0)
% 15.30/2.83 | | ~ (v0 = 0) | v2 = 0))
% 15.30/2.83 |
% 15.30/2.83 | GROUND_INST: instantiating (5) with all_34_10, all_34_9, simplifying with
% 15.30/2.83 | (22), (26) gives:
% 15.30/2.83 | (32) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_field(all_34_10)
% 15.30/2.83 | = v1 & is_connected_in(all_34_10, v1) = v2 & relation(all_34_10) =
% 15.30/2.83 | v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (v2 = 0) | all_34_9 = 0) & ( ~
% 15.30/2.83 | (all_34_9 = 0) | v2 = 0))))
% 15.30/2.83 |
% 15.30/2.83 | GROUND_INST: instantiating (8) with all_34_10, all_34_8, simplifying with
% 15.30/2.83 | (22), (27) gives:
% 15.30/2.83 | (33) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 15.30/2.83 | (relation_dom(all_34_10) = v1 & relation_rng(all_34_10) = v2 &
% 15.30/2.83 | set_union2(v1, v2) = v3 & relation(all_34_10) = v0 & $i(v3) & $i(v2)
% 15.30/2.83 | & $i(v1) & ( ~ (v0 = 0) | v3 = all_34_8))
% 15.30/2.83 |
% 15.30/2.83 | GROUND_INST: instantiating (6) with all_34_10, all_34_8, simplifying with
% 15.30/2.83 | (22), (27) gives:
% 15.30/2.83 | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : (connected(all_34_10) =
% 15.30/2.83 | v1 & is_connected_in(all_34_10, all_34_8) = v2 & relation(all_34_10)
% 15.30/2.83 | = v0 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 =
% 15.30/2.83 | 0))))
% 15.30/2.83 |
% 15.30/2.83 | DELTA: instantiating (31) with fresh symbols all_44_0, all_44_1, all_44_2
% 15.30/2.83 | gives:
% 15.30/2.83 | (35) one_to_one(all_34_10) = all_44_0 & function(all_34_10) = all_44_1 &
% 15.30/2.83 | empty(all_34_10) = all_44_2 & ( ~ (all_44_1 = 0) | ~ (all_44_2 = 0) |
% 15.30/2.83 | all_44_0 = 0)
% 15.30/2.83 |
% 15.30/2.83 | ALPHA: (35) implies:
% 15.30/2.83 | (36) one_to_one(all_34_10) = all_44_0
% 15.30/2.83 |
% 15.30/2.83 | DELTA: instantiating (29) with fresh symbols all_64_0, all_64_1, all_64_2
% 15.30/2.83 | gives:
% 15.30/2.83 | (37) relation_dom(all_34_10) = all_64_1 & relation_rng(all_34_10) =
% 15.30/2.83 | all_64_0 & relation_field(all_34_10) = all_64_2 & set_union2(all_64_1,
% 15.30/2.83 | all_64_0) = all_64_2 & $i(all_64_0) & $i(all_64_1) & $i(all_64_2)
% 15.30/2.83 |
% 15.30/2.83 | ALPHA: (37) implies:
% 15.30/2.84 | (38) relation_field(all_34_10) = all_64_2
% 15.30/2.84 | (39) relation_rng(all_34_10) = all_64_0
% 15.30/2.84 | (40) relation_dom(all_34_10) = all_64_1
% 15.30/2.84 |
% 15.30/2.84 | DELTA: instantiating (34) with fresh symbols all_72_0, all_72_1, all_72_2
% 15.30/2.84 | gives:
% 15.30/2.84 | (41) connected(all_34_10) = all_72_1 & is_connected_in(all_34_10, all_34_8)
% 15.30/2.84 | = all_72_0 & relation(all_34_10) = all_72_2 & ( ~ (all_72_2 = 0) | ((
% 15.30/2.84 | ~ (all_72_0 = 0) | all_72_1 = 0) & ( ~ (all_72_1 = 0) | all_72_0
% 15.30/2.84 | = 0)))
% 15.30/2.84 |
% 15.30/2.84 | ALPHA: (41) implies:
% 15.39/2.84 | (42) relation(all_34_10) = all_72_2
% 15.39/2.84 | (43) is_connected_in(all_34_10, all_34_8) = all_72_0
% 15.39/2.84 | (44) connected(all_34_10) = all_72_1
% 15.39/2.84 | (45) ~ (all_72_2 = 0) | (( ~ (all_72_0 = 0) | all_72_1 = 0) & ( ~
% 15.39/2.84 | (all_72_1 = 0) | all_72_0 = 0))
% 15.39/2.84 |
% 15.39/2.84 | DELTA: instantiating (30) with fresh symbols all_80_0, all_80_1, all_80_2
% 15.39/2.84 | gives:
% 15.39/2.84 | (46) relation_field(all_34_10) = all_80_1 & connected(all_34_10) = all_80_2
% 15.39/2.84 | & is_connected_in(all_34_10, all_80_1) = all_80_0 & $i(all_80_1) & ( ~
% 15.39/2.84 | (all_80_0 = 0) | all_80_2 = 0) & ( ~ (all_80_2 = 0) | all_80_0 = 0)
% 15.39/2.84 |
% 15.39/2.84 | ALPHA: (46) implies:
% 15.39/2.84 | (47) is_connected_in(all_34_10, all_80_1) = all_80_0
% 15.39/2.84 | (48) connected(all_34_10) = all_80_2
% 15.39/2.84 | (49) relation_field(all_34_10) = all_80_1
% 15.39/2.84 |
% 15.39/2.84 | DELTA: instantiating (33) with fresh symbols all_82_0, all_82_1, all_82_2,
% 15.39/2.84 | all_82_3 gives:
% 15.39/2.84 | (50) relation_dom(all_34_10) = all_82_2 & relation_rng(all_34_10) =
% 15.39/2.84 | all_82_1 & set_union2(all_82_2, all_82_1) = all_82_0 &
% 15.39/2.84 | relation(all_34_10) = all_82_3 & $i(all_82_0) & $i(all_82_1) &
% 15.39/2.84 | $i(all_82_2) & ( ~ (all_82_3 = 0) | all_82_0 = all_34_8)
% 15.39/2.84 |
% 15.39/2.84 | ALPHA: (50) implies:
% 15.39/2.84 | (51) $i(all_82_2)
% 15.39/2.84 | (52) $i(all_82_1)
% 15.39/2.84 | (53) relation(all_34_10) = all_82_3
% 15.39/2.84 | (54) set_union2(all_82_2, all_82_1) = all_82_0
% 15.39/2.84 | (55) relation_rng(all_34_10) = all_82_1
% 15.39/2.84 | (56) relation_dom(all_34_10) = all_82_2
% 15.39/2.84 | (57) ~ (all_82_3 = 0) | all_82_0 = all_34_8
% 15.39/2.84 |
% 15.39/2.84 | DELTA: instantiating (32) with fresh symbols all_84_0, all_84_1, all_84_2
% 15.39/2.84 | gives:
% 15.39/2.84 | (58) relation_field(all_34_10) = all_84_1 & is_connected_in(all_34_10,
% 15.39/2.84 | all_84_1) = all_84_0 & relation(all_34_10) = all_84_2 & $i(all_84_1)
% 15.39/2.84 | & ( ~ (all_84_2 = 0) | (( ~ (all_84_0 = 0) | all_34_9 = 0) & ( ~
% 15.39/2.84 | (all_34_9 = 0) | all_84_0 = 0)))
% 15.39/2.84 |
% 15.39/2.84 | ALPHA: (58) implies:
% 15.39/2.84 | (59) relation(all_34_10) = all_84_2
% 15.39/2.84 | (60) is_connected_in(all_34_10, all_84_1) = all_84_0
% 15.39/2.84 | (61) relation_field(all_34_10) = all_84_1
% 15.39/2.84 |
% 15.39/2.84 | GROUND_INST: instantiating (13) with 0, all_84_2, all_34_10, simplifying with
% 15.39/2.84 | (25), (59) gives:
% 15.39/2.84 | (62) all_84_2 = 0
% 15.39/2.84 |
% 15.39/2.84 | GROUND_INST: instantiating (13) with all_82_3, all_84_2, all_34_10,
% 15.39/2.84 | simplifying with (53), (59) gives:
% 15.39/2.84 | (63) all_84_2 = all_82_3
% 15.39/2.84 |
% 15.39/2.84 | GROUND_INST: instantiating (13) with all_72_2, all_84_2, all_34_10,
% 15.39/2.84 | simplifying with (42), (59) gives:
% 15.39/2.84 | (64) all_84_2 = all_72_2
% 15.39/2.84 |
% 15.39/2.84 | GROUND_INST: instantiating (14) with all_34_9, all_80_2, all_34_10,
% 15.39/2.84 | simplifying with (26), (48) gives:
% 15.39/2.84 | (65) all_80_2 = all_34_9
% 15.39/2.84 |
% 15.39/2.84 | GROUND_INST: instantiating (14) with all_72_1, all_80_2, all_34_10,
% 15.39/2.84 | simplifying with (44), (48) gives:
% 15.39/2.84 | (66) all_80_2 = all_72_1
% 15.39/2.84 |
% 15.39/2.84 | GROUND_INST: instantiating (15) with all_34_8, all_80_1, all_34_10,
% 15.39/2.84 | simplifying with (27), (49) gives:
% 15.39/2.84 | (67) all_80_1 = all_34_8
% 15.39/2.84 |
% 15.39/2.84 | GROUND_INST: instantiating (15) with all_80_1, all_84_1, all_34_10,
% 15.39/2.84 | simplifying with (49), (61) gives:
% 15.39/2.84 | (68) all_84_1 = all_80_1
% 15.39/2.84 |
% 15.39/2.84 | GROUND_INST: instantiating (15) with all_64_2, all_84_1, all_34_10,
% 15.39/2.84 | simplifying with (38), (61) gives:
% 15.39/2.84 | (69) all_84_1 = all_64_2
% 15.39/2.84 |
% 15.39/2.84 | GROUND_INST: instantiating (16) with all_64_0, all_82_1, all_34_10,
% 15.39/2.84 | simplifying with (39), (55) gives:
% 15.39/2.84 | (70) all_82_1 = all_64_0
% 15.39/2.84 |
% 15.39/2.84 | GROUND_INST: instantiating (17) with all_64_1, all_82_2, all_34_10,
% 15.39/2.84 | simplifying with (40), (56) gives:
% 15.39/2.84 | (71) all_82_2 = all_64_1
% 15.39/2.84 |
% 15.39/2.84 | COMBINE_EQS: (68), (69) imply:
% 15.39/2.84 | (72) all_80_1 = all_64_2
% 15.39/2.84 |
% 15.39/2.84 | SIMP: (72) implies:
% 15.39/2.84 | (73) all_80_1 = all_64_2
% 15.39/2.84 |
% 15.39/2.84 | COMBINE_EQS: (62), (63) imply:
% 15.39/2.84 | (74) all_82_3 = 0
% 15.39/2.84 |
% 15.39/2.84 | COMBINE_EQS: (63), (64) imply:
% 15.39/2.84 | (75) all_82_3 = all_72_2
% 15.39/2.84 |
% 15.39/2.84 | COMBINE_EQS: (74), (75) imply:
% 15.39/2.84 | (76) all_72_2 = 0
% 15.39/2.84 |
% 15.39/2.84 | SIMP: (76) implies:
% 15.39/2.84 | (77) all_72_2 = 0
% 15.39/2.84 |
% 15.39/2.84 | COMBINE_EQS: (67), (73) imply:
% 15.39/2.84 | (78) all_64_2 = all_34_8
% 15.39/2.84 |
% 15.39/2.84 | COMBINE_EQS: (65), (66) imply:
% 15.39/2.84 | (79) all_72_1 = all_34_9
% 15.39/2.84 |
% 15.39/2.84 | SIMP: (79) implies:
% 15.39/2.84 | (80) all_72_1 = all_34_9
% 15.39/2.84 |
% 15.39/2.84 | COMBINE_EQS: (69), (78) imply:
% 15.39/2.85 | (81) all_84_1 = all_34_8
% 15.39/2.85 |
% 15.39/2.85 | REDUCE: (60), (81) imply:
% 15.39/2.85 | (82) is_connected_in(all_34_10, all_34_8) = all_84_0
% 15.39/2.85 |
% 15.39/2.85 | REDUCE: (47), (67) imply:
% 15.39/2.85 | (83) is_connected_in(all_34_10, all_34_8) = all_80_0
% 15.39/2.85 |
% 15.39/2.85 | REDUCE: (54), (70), (71) imply:
% 15.39/2.85 | (84) set_union2(all_64_1, all_64_0) = all_82_0
% 15.39/2.85 |
% 15.39/2.85 | REDUCE: (52), (70) imply:
% 15.39/2.85 | (85) $i(all_64_0)
% 15.39/2.85 |
% 15.39/2.85 | REDUCE: (51), (71) imply:
% 15.39/2.85 | (86) $i(all_64_1)
% 15.39/2.85 |
% 15.39/2.85 | BETA: splitting (57) gives:
% 15.39/2.85 |
% 15.39/2.85 | Case 1:
% 15.39/2.85 | |
% 15.39/2.85 | | (87) ~ (all_82_3 = 0)
% 15.39/2.85 | |
% 15.39/2.85 | | REDUCE: (74), (87) imply:
% 15.39/2.85 | | (88) $false
% 15.39/2.85 | |
% 15.39/2.85 | | CLOSE: (88) is inconsistent.
% 15.39/2.85 | |
% 15.39/2.85 | Case 2:
% 15.39/2.85 | |
% 15.39/2.85 | | (89) all_82_0 = all_34_8
% 15.39/2.85 | |
% 15.39/2.85 | | REDUCE: (84), (89) imply:
% 15.39/2.85 | | (90) set_union2(all_64_1, all_64_0) = all_34_8
% 15.39/2.85 | |
% 15.39/2.85 | | GROUND_INST: instantiating (19) with all_72_0, all_84_0, all_34_8,
% 15.39/2.85 | | all_34_10, simplifying with (43), (82) gives:
% 15.39/2.85 | | (91) all_84_0 = all_72_0
% 15.39/2.85 | |
% 15.39/2.85 | | GROUND_INST: instantiating (19) with all_80_0, all_84_0, all_34_8,
% 15.39/2.85 | | all_34_10, simplifying with (82), (83) gives:
% 15.39/2.85 | | (92) all_84_0 = all_80_0
% 15.39/2.85 | |
% 15.39/2.85 | | COMBINE_EQS: (91), (92) imply:
% 15.39/2.85 | | (93) all_80_0 = all_72_0
% 15.39/2.85 | |
% 15.39/2.85 | | GROUND_INST: instantiating (2) with all_34_10, all_44_0, simplifying with
% 15.39/2.85 | | (22), (36) gives:
% 15.39/2.85 | | (94) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_34_10) =
% 15.39/2.85 | | v0 & function(all_34_10) = v2 & empty(all_34_10) = v1 & ( ~ (v2 =
% 15.39/2.85 | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | all_44_0 = 0))
% 15.39/2.85 | |
% 15.39/2.85 | | GROUND_INST: instantiating (3) with all_64_0, all_64_1, all_34_8,
% 15.39/2.85 | | simplifying with (85), (86), (90) gives:
% 15.39/2.85 | | (95) set_union2(all_64_0, all_64_1) = all_34_8 & $i(all_34_8)
% 15.39/2.85 | |
% 15.39/2.85 | | ALPHA: (95) implies:
% 15.39/2.85 | | (96) $i(all_34_8)
% 15.39/2.85 | |
% 15.39/2.85 | | GROUND_INST: instantiating (9) with all_34_10, all_34_8, all_72_0,
% 15.39/2.85 | | simplifying with (22), (25), (43), (96) gives:
% 15.39/2.85 | | (97) all_72_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 15.39/2.85 | | int] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & ~ (v3 = 0) &
% 15.39/2.85 | | ~ (v1 = v0) & ordered_pair(v1, v0) = v4 & ordered_pair(v0, v1) =
% 15.39/2.85 | | v2 & in(v4, all_34_10) = v5 & in(v2, all_34_10) = v3 & in(v1,
% 15.39/2.85 | | all_34_8) = 0 & in(v0, all_34_8) = 0 & $i(v4) & $i(v2) & $i(v1)
% 15.39/2.85 | | & $i(v0))
% 15.39/2.85 | |
% 15.39/2.85 | | DELTA: instantiating (94) with fresh symbols all_128_0, all_128_1, all_128_2
% 15.39/2.85 | | gives:
% 15.39/2.85 | | (98) relation(all_34_10) = all_128_2 & function(all_34_10) = all_128_0 &
% 15.39/2.85 | | empty(all_34_10) = all_128_1 & ( ~ (all_128_0 = 0) | ~ (all_128_1 =
% 15.39/2.85 | | 0) | ~ (all_128_2 = 0) | all_44_0 = 0)
% 15.39/2.85 | |
% 15.39/2.85 | | ALPHA: (98) implies:
% 15.39/2.85 | | (99) relation(all_34_10) = all_128_2
% 15.39/2.85 | |
% 15.39/2.85 | | GROUND_INST: instantiating (13) with 0, all_128_2, all_34_10, simplifying
% 15.39/2.85 | | with (25), (99) gives:
% 15.39/2.85 | | (100) all_128_2 = 0
% 15.39/2.85 | |
% 15.39/2.85 | | BETA: splitting (28) gives:
% 15.39/2.85 | |
% 15.39/2.85 | | Case 1:
% 15.39/2.85 | | |
% 15.39/2.85 | | | (101) all_34_4 = 0 & all_34_5 = 0 & all_34_9 = 0 & ~ (all_34_0 = 0) &
% 15.39/2.85 | | | ~ (all_34_2 = 0) & ~ (all_34_6 = all_34_7) &
% 15.39/2.85 | | | ordered_pair(all_34_6, all_34_7) = all_34_1 &
% 15.39/2.85 | | | ordered_pair(all_34_7, all_34_6) = all_34_3 & in(all_34_1,
% 15.39/2.85 | | | all_34_10) = all_34_0 & in(all_34_3, all_34_10) = all_34_2 &
% 15.39/2.85 | | | in(all_34_6, all_34_8) = 0 & in(all_34_7, all_34_8) = 0 &
% 15.39/2.85 | | | $i(all_34_1) & $i(all_34_3)
% 15.39/2.85 | | |
% 15.39/2.85 | | | ALPHA: (101) implies:
% 15.39/2.85 | | | (102) all_34_9 = 0
% 15.39/2.85 | | | (103) ~ (all_34_6 = all_34_7)
% 15.39/2.85 | | | (104) ~ (all_34_2 = 0)
% 15.39/2.85 | | | (105) ~ (all_34_0 = 0)
% 15.39/2.85 | | | (106) $i(all_34_3)
% 15.39/2.85 | | | (107) in(all_34_7, all_34_8) = 0
% 15.39/2.85 | | | (108) in(all_34_6, all_34_8) = 0
% 15.39/2.85 | | | (109) in(all_34_3, all_34_10) = all_34_2
% 15.39/2.85 | | | (110) in(all_34_1, all_34_10) = all_34_0
% 15.39/2.85 | | | (111) ordered_pair(all_34_7, all_34_6) = all_34_3
% 15.39/2.85 | | | (112) ordered_pair(all_34_6, all_34_7) = all_34_1
% 15.39/2.85 | | |
% 15.39/2.85 | | | COMBINE_EQS: (80), (102) imply:
% 15.39/2.85 | | | (113) all_72_1 = 0
% 15.39/2.85 | | |
% 15.39/2.85 | | | BETA: splitting (45) gives:
% 15.39/2.85 | | |
% 15.39/2.85 | | | Case 1:
% 15.39/2.85 | | | |
% 15.39/2.85 | | | | (114) ~ (all_72_2 = 0)
% 15.39/2.85 | | | |
% 15.39/2.85 | | | | REDUCE: (77), (114) imply:
% 15.39/2.85 | | | | (115) $false
% 15.39/2.85 | | | |
% 15.39/2.85 | | | | CLOSE: (115) is inconsistent.
% 15.39/2.85 | | | |
% 15.39/2.85 | | | Case 2:
% 15.39/2.85 | | | |
% 15.39/2.85 | | | | (116) ( ~ (all_72_0 = 0) | all_72_1 = 0) & ( ~ (all_72_1 = 0) |
% 15.39/2.85 | | | | all_72_0 = 0)
% 15.39/2.85 | | | |
% 15.39/2.85 | | | | ALPHA: (116) implies:
% 15.39/2.85 | | | | (117) ~ (all_72_1 = 0) | all_72_0 = 0
% 15.39/2.85 | | | |
% 15.39/2.85 | | | | BETA: splitting (117) gives:
% 15.39/2.85 | | | |
% 15.39/2.85 | | | | Case 1:
% 15.39/2.85 | | | | |
% 15.39/2.85 | | | | | (118) ~ (all_72_1 = 0)
% 15.39/2.85 | | | | |
% 15.39/2.85 | | | | | REDUCE: (113), (118) imply:
% 15.39/2.85 | | | | | (119) $false
% 15.39/2.85 | | | | |
% 15.39/2.85 | | | | | CLOSE: (119) is inconsistent.
% 15.39/2.85 | | | | |
% 15.39/2.85 | | | | Case 2:
% 15.39/2.85 | | | | |
% 15.39/2.85 | | | | | (120) all_72_0 = 0
% 15.39/2.86 | | | | |
% 15.39/2.86 | | | | | REDUCE: (43), (120) imply:
% 15.39/2.86 | | | | | (121) is_connected_in(all_34_10, all_34_8) = 0
% 15.39/2.86 | | | | |
% 15.39/2.86 | | | | | GROUND_INST: instantiating (12) with all_34_3, all_34_10, all_34_2,
% 15.39/2.86 | | | | | simplifying with (22), (106), (109) gives:
% 15.39/2.86 | | | | | (122) all_34_2 = 0 | ? [v0: any] : ? [v1: any] :
% 15.39/2.86 | | | | | (element(all_34_3, all_34_10) = v0 & empty(all_34_10) = v1 &
% 15.39/2.86 | | | | | ( ~ (v0 = 0) | v1 = 0))
% 15.39/2.86 | | | | |
% 15.39/2.86 | | | | | GROUND_INST: instantiating (11) with all_34_10, all_34_8, all_34_6,
% 15.39/2.86 | | | | | all_34_7, all_34_3, simplifying with (22), (23), (24),
% 15.39/2.86 | | | | | (25), (96), (111), (121) gives:
% 15.39/2.86 | | | | | (123) all_34_6 = all_34_7 | ? [v0: any] : ? [v1: any] : ? [v2:
% 15.39/2.86 | | | | | $i] : ? [v3: any] : ? [v4: any] : (ordered_pair(all_34_6,
% 15.39/2.86 | | | | | all_34_7) = v2 & in(v2, all_34_10) = v3 & in(all_34_3,
% 15.39/2.86 | | | | | all_34_10) = v4 & in(all_34_6, all_34_8) = v0 &
% 15.39/2.86 | | | | | in(all_34_7, all_34_8) = v1 & $i(v2) & ( ~ (v1 = 0) | ~
% 15.39/2.86 | | | | | (v0 = 0) | v4 = 0 | v3 = 0))
% 15.39/2.86 | | | | |
% 15.39/2.86 | | | | | GROUND_INST: instantiating (10) with all_34_10, all_34_8, all_34_7,
% 15.39/2.86 | | | | | all_34_6, all_34_3, simplifying with (22), (23), (24),
% 15.39/2.86 | | | | | (25), (96), (111), (121) gives:
% 15.39/2.86 | | | | | (124) all_34_6 = all_34_7 | ? [v0: any] : ? [v1: any] : ? [v2:
% 15.39/2.86 | | | | | any] : ? [v3: $i] : ? [v4: any] : (ordered_pair(all_34_6,
% 15.39/2.86 | | | | | all_34_7) = v3 & in(v3, all_34_10) = v4 & in(all_34_3,
% 15.39/2.86 | | | | | all_34_10) = v2 & in(all_34_6, all_34_8) = v1 &
% 15.39/2.86 | | | | | in(all_34_7, all_34_8) = v0 & $i(v3) & ( ~ (v1 = 0) | ~
% 15.39/2.86 | | | | | (v0 = 0) | v4 = 0 | v2 = 0))
% 15.39/2.86 | | | | |
% 15.39/2.86 | | | | | GROUND_INST: instantiating (10) with all_34_10, all_34_8, all_34_6,
% 15.39/2.86 | | | | | all_34_7, all_34_1, simplifying with (22), (23), (24),
% 15.39/2.86 | | | | | (25), (96), (112), (121) gives:
% 15.39/2.86 | | | | | (125) all_34_6 = all_34_7 | ? [v0: any] : ? [v1: any] : ? [v2:
% 15.39/2.86 | | | | | any] : ? [v3: $i] : ? [v4: any] : (ordered_pair(all_34_7,
% 15.39/2.86 | | | | | all_34_6) = v3 & in(v3, all_34_10) = v4 & in(all_34_1,
% 15.39/2.86 | | | | | all_34_10) = v2 & in(all_34_6, all_34_8) = v0 &
% 15.39/2.86 | | | | | in(all_34_7, all_34_8) = v1 & $i(v3) & ( ~ (v1 = 0) | ~
% 15.39/2.86 | | | | | (v0 = 0) | v4 = 0 | v2 = 0))
% 15.39/2.86 | | | | |
% 15.39/2.86 | | | | | BETA: splitting (125) gives:
% 15.39/2.86 | | | | |
% 15.39/2.86 | | | | | Case 1:
% 15.39/2.86 | | | | | |
% 15.39/2.86 | | | | | | (126) all_34_6 = all_34_7
% 15.39/2.86 | | | | | |
% 15.39/2.86 | | | | | | REDUCE: (103), (126) imply:
% 15.39/2.86 | | | | | | (127) $false
% 15.39/2.86 | | | | | |
% 15.39/2.86 | | | | | | CLOSE: (127) is inconsistent.
% 15.39/2.86 | | | | | |
% 15.39/2.86 | | | | | Case 2:
% 15.39/2.86 | | | | | |
% 15.39/2.86 | | | | | | (128) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] :
% 15.39/2.86 | | | | | | ? [v4: any] : (ordered_pair(all_34_7, all_34_6) = v3 &
% 15.39/2.86 | | | | | | in(v3, all_34_10) = v4 & in(all_34_1, all_34_10) = v2 &
% 15.39/2.86 | | | | | | in(all_34_6, all_34_8) = v0 & in(all_34_7, all_34_8) = v1
% 15.39/2.86 | | | | | | & $i(v3) & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 = 0))
% 15.39/2.86 | | | | | |
% 15.39/2.86 | | | | | | DELTA: instantiating (128) with fresh symbols all_249_0, all_249_1,
% 15.39/2.86 | | | | | | all_249_2, all_249_3, all_249_4 gives:
% 15.39/2.86 | | | | | | (129) ordered_pair(all_34_7, all_34_6) = all_249_1 &
% 15.39/2.86 | | | | | | in(all_249_1, all_34_10) = all_249_0 & in(all_34_1,
% 15.39/2.86 | | | | | | all_34_10) = all_249_2 & in(all_34_6, all_34_8) =
% 15.39/2.86 | | | | | | all_249_4 & in(all_34_7, all_34_8) = all_249_3 &
% 15.39/2.86 | | | | | | $i(all_249_1) & ( ~ (all_249_3 = 0) | ~ (all_249_4 = 0) |
% 15.39/2.86 | | | | | | all_249_0 = 0 | all_249_2 = 0)
% 15.39/2.86 | | | | | |
% 15.39/2.86 | | | | | | ALPHA: (129) implies:
% 15.39/2.86 | | | | | | (130) in(all_34_7, all_34_8) = all_249_3
% 15.39/2.86 | | | | | | (131) in(all_34_6, all_34_8) = all_249_4
% 15.39/2.86 | | | | | | (132) in(all_34_1, all_34_10) = all_249_2
% 15.39/2.86 | | | | | | (133) in(all_249_1, all_34_10) = all_249_0
% 15.39/2.86 | | | | | | (134) ordered_pair(all_34_7, all_34_6) = all_249_1
% 15.39/2.86 | | | | | | (135) ~ (all_249_3 = 0) | ~ (all_249_4 = 0) | all_249_0 = 0 |
% 15.39/2.86 | | | | | | all_249_2 = 0
% 15.39/2.86 | | | | | |
% 15.39/2.86 | | | | | | BETA: splitting (122) gives:
% 15.39/2.86 | | | | | |
% 15.39/2.86 | | | | | | Case 1:
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | | (136) all_34_2 = 0
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | | REDUCE: (104), (136) imply:
% 15.39/2.86 | | | | | | | (137) $false
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | | CLOSE: (137) is inconsistent.
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | Case 2:
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | | GROUND_INST: instantiating (18) with 0, all_249_3, all_34_8,
% 15.39/2.86 | | | | | | | all_34_7, simplifying with (107), (130) gives:
% 15.39/2.86 | | | | | | | (138) all_249_3 = 0
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | | GROUND_INST: instantiating (18) with 0, all_249_4, all_34_8,
% 15.39/2.86 | | | | | | | all_34_6, simplifying with (108), (131) gives:
% 15.39/2.86 | | | | | | | (139) all_249_4 = 0
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | | GROUND_INST: instantiating (18) with all_34_0, all_249_2,
% 15.39/2.86 | | | | | | | all_34_10, all_34_1, simplifying with (110), (132)
% 15.39/2.86 | | | | | | | gives:
% 15.39/2.86 | | | | | | | (140) all_249_2 = all_34_0
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | | GROUND_INST: instantiating (20) with all_34_3, all_249_1,
% 15.39/2.86 | | | | | | | all_34_6, all_34_7, simplifying with (111), (134)
% 15.39/2.86 | | | | | | | gives:
% 15.39/2.86 | | | | | | | (141) all_249_1 = all_34_3
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | | REDUCE: (133), (141) imply:
% 15.39/2.86 | | | | | | | (142) in(all_34_3, all_34_10) = all_249_0
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | | BETA: splitting (124) gives:
% 15.39/2.86 | | | | | | |
% 15.39/2.86 | | | | | | | Case 1:
% 15.39/2.86 | | | | | | | |
% 15.39/2.86 | | | | | | | | (143) all_34_6 = all_34_7
% 15.39/2.86 | | | | | | | |
% 15.39/2.86 | | | | | | | | REDUCE: (103), (143) imply:
% 15.39/2.86 | | | | | | | | (144) $false
% 15.39/2.86 | | | | | | | |
% 15.39/2.86 | | | | | | | | CLOSE: (144) is inconsistent.
% 15.39/2.86 | | | | | | | |
% 15.39/2.86 | | | | | | | Case 2:
% 15.39/2.86 | | | | | | | |
% 15.39/2.86 | | | | | | | | (145) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 15.39/2.86 | | | | | | | | $i] : ? [v4: any] : (ordered_pair(all_34_6,
% 15.39/2.86 | | | | | | | | all_34_7) = v3 & in(v3, all_34_10) = v4 &
% 15.39/2.86 | | | | | | | | in(all_34_3, all_34_10) = v2 & in(all_34_6, all_34_8)
% 15.39/2.86 | | | | | | | | = v1 & in(all_34_7, all_34_8) = v0 & $i(v3) & ( ~ (v1
% 15.39/2.86 | | | | | | | | = 0) | ~ (v0 = 0) | v4 = 0 | v2 = 0))
% 15.39/2.86 | | | | | | | |
% 15.39/2.86 | | | | | | | | DELTA: instantiating (145) with fresh symbols all_274_0,
% 15.39/2.86 | | | | | | | | all_274_1, all_274_2, all_274_3, all_274_4 gives:
% 15.39/2.86 | | | | | | | | (146) ordered_pair(all_34_6, all_34_7) = all_274_1 &
% 15.39/2.86 | | | | | | | | in(all_274_1, all_34_10) = all_274_0 & in(all_34_3,
% 15.39/2.86 | | | | | | | | all_34_10) = all_274_2 & in(all_34_6, all_34_8) =
% 15.39/2.86 | | | | | | | | all_274_3 & in(all_34_7, all_34_8) = all_274_4 &
% 15.39/2.86 | | | | | | | | $i(all_274_1) & ( ~ (all_274_3 = 0) | ~ (all_274_4 =
% 15.39/2.86 | | | | | | | | 0) | all_274_0 = 0 | all_274_2 = 0)
% 15.39/2.86 | | | | | | | |
% 15.39/2.86 | | | | | | | | ALPHA: (146) implies:
% 15.39/2.86 | | | | | | | | (147) in(all_34_3, all_34_10) = all_274_2
% 15.39/2.86 | | | | | | | |
% 15.39/2.86 | | | | | | | | BETA: splitting (135) gives:
% 15.39/2.86 | | | | | | | |
% 15.39/2.86 | | | | | | | | Case 1:
% 15.39/2.86 | | | | | | | | |
% 15.39/2.86 | | | | | | | | | (148) ~ (all_249_3 = 0)
% 15.39/2.86 | | | | | | | | |
% 15.39/2.86 | | | | | | | | | REDUCE: (138), (148) imply:
% 15.39/2.86 | | | | | | | | | (149) $false
% 15.39/2.86 | | | | | | | | |
% 15.39/2.86 | | | | | | | | | CLOSE: (149) is inconsistent.
% 15.39/2.86 | | | | | | | | |
% 15.39/2.86 | | | | | | | | Case 2:
% 15.39/2.86 | | | | | | | | |
% 15.39/2.86 | | | | | | | | | (150) ~ (all_249_4 = 0) | all_249_0 = 0 | all_249_2 = 0
% 15.39/2.86 | | | | | | | | |
% 15.39/2.86 | | | | | | | | | BETA: splitting (123) gives:
% 15.39/2.86 | | | | | | | | |
% 15.39/2.86 | | | | | | | | | Case 1:
% 15.39/2.86 | | | | | | | | | |
% 15.39/2.86 | | | | | | | | | | (151) all_34_6 = all_34_7
% 15.39/2.86 | | | | | | | | | |
% 15.39/2.86 | | | | | | | | | | REDUCE: (103), (151) imply:
% 15.39/2.86 | | | | | | | | | | (152) $false
% 15.39/2.86 | | | | | | | | | |
% 15.39/2.86 | | | | | | | | | | CLOSE: (152) is inconsistent.
% 15.39/2.86 | | | | | | | | | |
% 15.39/2.86 | | | | | | | | | Case 2:
% 15.39/2.86 | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | (153) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3:
% 15.39/2.87 | | | | | | | | | | any] : ? [v4: any] : (ordered_pair(all_34_6,
% 15.39/2.87 | | | | | | | | | | all_34_7) = v2 & in(v2, all_34_10) = v3 &
% 15.39/2.87 | | | | | | | | | | in(all_34_3, all_34_10) = v4 & in(all_34_6,
% 15.39/2.87 | | | | | | | | | | all_34_8) = v0 & in(all_34_7, all_34_8) = v1 &
% 15.39/2.87 | | | | | | | | | | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v3
% 15.39/2.87 | | | | | | | | | | = 0))
% 15.39/2.87 | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | DELTA: instantiating (153) with fresh symbols all_288_0,
% 15.39/2.87 | | | | | | | | | | all_288_1, all_288_2, all_288_3, all_288_4 gives:
% 15.39/2.87 | | | | | | | | | | (154) ordered_pair(all_34_6, all_34_7) = all_288_2 &
% 15.39/2.87 | | | | | | | | | | in(all_288_2, all_34_10) = all_288_1 & in(all_34_3,
% 15.39/2.87 | | | | | | | | | | all_34_10) = all_288_0 & in(all_34_6, all_34_8) =
% 15.39/2.87 | | | | | | | | | | all_288_4 & in(all_34_7, all_34_8) = all_288_3 &
% 15.39/2.87 | | | | | | | | | | $i(all_288_2) & ( ~ (all_288_3 = 0) | ~ (all_288_4
% 15.39/2.87 | | | | | | | | | | = 0) | all_288_0 = 0 | all_288_1 = 0)
% 15.39/2.87 | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | ALPHA: (154) implies:
% 15.39/2.87 | | | | | | | | | | (155) in(all_34_3, all_34_10) = all_288_0
% 15.39/2.87 | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | BETA: splitting (150) gives:
% 15.39/2.87 | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | Case 1:
% 15.39/2.87 | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | (156) ~ (all_249_4 = 0)
% 15.39/2.87 | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | REDUCE: (139), (156) imply:
% 15.39/2.87 | | | | | | | | | | | (157) $false
% 15.39/2.87 | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | CLOSE: (157) is inconsistent.
% 15.39/2.87 | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | Case 2:
% 15.39/2.87 | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | (158) all_249_0 = 0 | all_249_2 = 0
% 15.39/2.87 | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | BETA: splitting (158) gives:
% 15.39/2.87 | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | Case 1:
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | (159) all_249_0 = 0
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | REDUCE: (142), (159) imply:
% 15.39/2.87 | | | | | | | | | | | | (160) in(all_34_3, all_34_10) = 0
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_34_2, all_288_0,
% 15.39/2.87 | | | | | | | | | | | | all_34_10, all_34_3, simplifying with (109), (155)
% 15.39/2.87 | | | | | | | | | | | | gives:
% 15.39/2.87 | | | | | | | | | | | | (161) all_288_0 = all_34_2
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_274_2, all_288_0,
% 15.39/2.87 | | | | | | | | | | | | all_34_10, all_34_3, simplifying with (147), (155)
% 15.39/2.87 | | | | | | | | | | | | gives:
% 15.39/2.87 | | | | | | | | | | | | (162) all_288_0 = all_274_2
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_288_0, all_34_10,
% 15.39/2.87 | | | | | | | | | | | | all_34_3, simplifying with (155), (160) gives:
% 15.39/2.87 | | | | | | | | | | | | (163) all_288_0 = 0
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | COMBINE_EQS: (161), (162) imply:
% 15.39/2.87 | | | | | | | | | | | | (164) all_274_2 = all_34_2
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | COMBINE_EQS: (162), (163) imply:
% 15.39/2.87 | | | | | | | | | | | | (165) all_274_2 = 0
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | COMBINE_EQS: (164), (165) imply:
% 15.39/2.87 | | | | | | | | | | | | (166) all_34_2 = 0
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | REDUCE: (104), (166) imply:
% 15.39/2.87 | | | | | | | | | | | | (167) $false
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | Case 2:
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | (168) all_249_2 = 0
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | COMBINE_EQS: (140), (168) imply:
% 15.39/2.87 | | | | | | | | | | | | (169) all_34_0 = 0
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | REDUCE: (105), (169) imply:
% 15.39/2.87 | | | | | | | | | | | | (170) $false
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 15.39/2.87 | | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | | End of split
% 15.39/2.87 | | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | | End of split
% 15.39/2.87 | | | | | | | | | |
% 15.39/2.87 | | | | | | | | | End of split
% 15.39/2.87 | | | | | | | | |
% 15.39/2.87 | | | | | | | | End of split
% 15.39/2.87 | | | | | | | |
% 15.39/2.87 | | | | | | | End of split
% 15.39/2.87 | | | | | | |
% 15.39/2.87 | | | | | | End of split
% 15.39/2.87 | | | | | |
% 15.39/2.87 | | | | | End of split
% 15.39/2.87 | | | | |
% 15.39/2.87 | | | | End of split
% 15.39/2.87 | | | |
% 15.39/2.87 | | | End of split
% 15.39/2.87 | | |
% 15.39/2.87 | | Case 2:
% 15.39/2.87 | | |
% 15.39/2.87 | | | (171) ~ (all_34_9 = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 15.39/2.87 | | | = v0 | ~ (ordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) |
% 15.39/2.87 | | | ? [v3: any] : ? [v4: any] : ? [v5: $i] : ? [v6: any] : ?
% 15.39/2.87 | | | [v7: any] : (ordered_pair(v0, v1) = v5 & in(v5, all_34_10) = v6
% 15.39/2.87 | | | & in(v2, all_34_10) = v7 & in(v1, all_34_8) = v4 & in(v0,
% 15.39/2.87 | | | all_34_8) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 =
% 15.39/2.87 | | | 0 | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.39/2.87 | | | (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 15.39/2.87 | | | | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ?
% 15.39/2.87 | | | [v7: any] : (ordered_pair(v1, v0) = v6 & in(v6, all_34_10) = v7
% 15.39/2.87 | | | & in(v2, all_34_10) = v5 & in(v1, all_34_8) = v4 & in(v0,
% 15.39/2.87 | | | all_34_8) = v3 & $i(v6) & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 =
% 15.39/2.87 | | | 0 | v5 = 0)))
% 15.39/2.87 | | |
% 15.39/2.87 | | | ALPHA: (171) implies:
% 15.39/2.87 | | | (172) ~ (all_34_9 = 0)
% 15.39/2.87 | | | (173) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.39/2.87 | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 15.39/2.87 | | | any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7:
% 15.39/2.87 | | | any] : (ordered_pair(v1, v0) = v6 & in(v6, all_34_10) = v7 &
% 15.39/2.87 | | | in(v2, all_34_10) = v5 & in(v1, all_34_8) = v4 & in(v0,
% 15.39/2.87 | | | all_34_8) = v3 & $i(v6) & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 =
% 15.39/2.87 | | | 0 | v5 = 0)))
% 15.39/2.87 | | | (174) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.39/2.87 | | | (ordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 15.39/2.87 | | | any] : ? [v4: any] : ? [v5: $i] : ? [v6: any] : ? [v7:
% 15.39/2.87 | | | any] : (ordered_pair(v0, v1) = v5 & in(v5, all_34_10) = v6 &
% 15.39/2.87 | | | in(v2, all_34_10) = v7 & in(v1, all_34_8) = v4 & in(v0,
% 15.39/2.87 | | | all_34_8) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 =
% 15.39/2.87 | | | 0 | v6 = 0)))
% 15.39/2.87 | | |
% 15.39/2.87 | | | BETA: splitting (45) gives:
% 15.39/2.87 | | |
% 15.39/2.87 | | | Case 1:
% 15.39/2.87 | | | |
% 15.39/2.87 | | | | (175) ~ (all_72_2 = 0)
% 15.39/2.87 | | | |
% 15.39/2.87 | | | | REDUCE: (77), (175) imply:
% 15.39/2.87 | | | | (176) $false
% 15.39/2.87 | | | |
% 15.39/2.87 | | | | CLOSE: (176) is inconsistent.
% 15.39/2.87 | | | |
% 15.39/2.87 | | | Case 2:
% 15.39/2.87 | | | |
% 15.39/2.87 | | | | (177) ( ~ (all_72_0 = 0) | all_72_1 = 0) & ( ~ (all_72_1 = 0) |
% 15.39/2.87 | | | | all_72_0 = 0)
% 15.39/2.87 | | | |
% 15.39/2.87 | | | | ALPHA: (177) implies:
% 15.39/2.87 | | | | (178) ~ (all_72_0 = 0) | all_72_1 = 0
% 15.39/2.87 | | | |
% 15.39/2.87 | | | | BETA: splitting (178) gives:
% 15.39/2.87 | | | |
% 15.39/2.87 | | | | Case 1:
% 15.39/2.87 | | | | |
% 15.39/2.87 | | | | | (179) ~ (all_72_0 = 0)
% 15.39/2.87 | | | | |
% 15.39/2.87 | | | | | BETA: splitting (97) gives:
% 15.39/2.87 | | | | |
% 15.39/2.87 | | | | | Case 1:
% 15.39/2.87 | | | | | |
% 15.39/2.87 | | | | | | (180) all_72_0 = 0
% 15.39/2.87 | | | | | |
% 15.39/2.87 | | | | | | REDUCE: (179), (180) imply:
% 15.39/2.87 | | | | | | (181) $false
% 15.39/2.87 | | | | | |
% 15.39/2.87 | | | | | | CLOSE: (181) is inconsistent.
% 15.39/2.87 | | | | | |
% 15.39/2.87 | | | | | Case 2:
% 15.39/2.87 | | | | | |
% 15.39/2.87 | | | | | | (182) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ?
% 15.39/2.87 | | | | | | [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & ~ (v3 = 0) & ~
% 15.39/2.87 | | | | | | (v1 = v0) & ordered_pair(v1, v0) = v4 & ordered_pair(v0,
% 15.39/2.87 | | | | | | v1) = v2 & in(v4, all_34_10) = v5 & in(v2, all_34_10) =
% 15.39/2.87 | | | | | | v3 & in(v1, all_34_8) = 0 & in(v0, all_34_8) = 0 & $i(v4)
% 15.39/2.87 | | | | | | & $i(v2) & $i(v1) & $i(v0))
% 15.39/2.87 | | | | | |
% 15.39/2.87 | | | | | | DELTA: instantiating (182) with fresh symbols all_206_0, all_206_1,
% 15.39/2.87 | | | | | | all_206_2, all_206_3, all_206_4, all_206_5 gives:
% 15.39/2.87 | | | | | | (183) ~ (all_206_0 = 0) & ~ (all_206_2 = 0) & ~ (all_206_4 =
% 15.39/2.87 | | | | | | all_206_5) & ordered_pair(all_206_4, all_206_5) =
% 15.39/2.87 | | | | | | all_206_1 & ordered_pair(all_206_5, all_206_4) = all_206_3
% 15.39/2.87 | | | | | | & in(all_206_1, all_34_10) = all_206_0 & in(all_206_3,
% 15.39/2.87 | | | | | | all_34_10) = all_206_2 & in(all_206_4, all_34_8) = 0 &
% 15.39/2.87 | | | | | | in(all_206_5, all_34_8) = 0 & $i(all_206_1) & $i(all_206_3)
% 15.39/2.87 | | | | | | & $i(all_206_4) & $i(all_206_5)
% 15.39/2.87 | | | | | |
% 15.39/2.87 | | | | | | ALPHA: (183) implies:
% 15.39/2.87 | | | | | | (184) ~ (all_206_4 = all_206_5)
% 15.39/2.87 | | | | | | (185) ~ (all_206_2 = 0)
% 15.39/2.87 | | | | | | (186) ~ (all_206_0 = 0)
% 15.39/2.87 | | | | | | (187) $i(all_206_5)
% 15.39/2.87 | | | | | | (188) $i(all_206_4)
% 15.39/2.87 | | | | | | (189) in(all_206_5, all_34_8) = 0
% 15.39/2.87 | | | | | | (190) in(all_206_4, all_34_8) = 0
% 15.39/2.87 | | | | | | (191) in(all_206_3, all_34_10) = all_206_2
% 15.39/2.87 | | | | | | (192) in(all_206_1, all_34_10) = all_206_0
% 15.39/2.87 | | | | | | (193) ordered_pair(all_206_5, all_206_4) = all_206_3
% 15.39/2.87 | | | | | | (194) ordered_pair(all_206_4, all_206_5) = all_206_1
% 15.39/2.87 | | | | | |
% 15.39/2.87 | | | | | | GROUND_INST: instantiating (173) with all_206_5, all_206_4,
% 15.39/2.87 | | | | | | all_206_3, simplifying with (187), (188), (193) gives:
% 15.39/2.87 | | | | | | (195) all_206_4 = all_206_5 | ? [v0: any] : ? [v1: any] : ?
% 15.39/2.87 | | | | | | [v2: any] : ? [v3: $i] : ? [v4: any] :
% 15.39/2.87 | | | | | | (ordered_pair(all_206_4, all_206_5) = v3 & in(v3,
% 15.39/2.87 | | | | | | all_34_10) = v4 & in(all_206_3, all_34_10) = v2 &
% 15.39/2.87 | | | | | | in(all_206_4, all_34_8) = v1 & in(all_206_5, all_34_8) =
% 15.39/2.87 | | | | | | v0 & $i(v3) & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 =
% 15.39/2.87 | | | | | | 0))
% 15.39/2.87 | | | | | |
% 15.39/2.87 | | | | | | GROUND_INST: instantiating (174) with all_206_5, all_206_4,
% 15.39/2.87 | | | | | | all_206_1, simplifying with (187), (188), (194) gives:
% 15.39/2.88 | | | | | | (196) all_206_4 = all_206_5 | ? [v0: any] : ? [v1: any] : ?
% 15.39/2.88 | | | | | | [v2: $i] : ? [v3: any] : ? [v4: any] :
% 15.39/2.88 | | | | | | (ordered_pair(all_206_5, all_206_4) = v2 & in(v2,
% 15.39/2.88 | | | | | | all_34_10) = v3 & in(all_206_1, all_34_10) = v4 &
% 15.39/2.88 | | | | | | in(all_206_4, all_34_8) = v1 & in(all_206_5, all_34_8) =
% 15.39/2.88 | | | | | | v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v3 =
% 15.39/2.88 | | | | | | 0))
% 15.39/2.88 | | | | | |
% 15.39/2.88 | | | | | | GROUND_INST: instantiating (173) with all_206_4, all_206_5,
% 15.39/2.88 | | | | | | all_206_1, simplifying with (187), (188), (194) gives:
% 15.39/2.88 | | | | | | (197) all_206_4 = all_206_5 | ? [v0: any] : ? [v1: any] : ?
% 15.39/2.88 | | | | | | [v2: any] : ? [v3: $i] : ? [v4: any] :
% 15.39/2.88 | | | | | | (ordered_pair(all_206_5, all_206_4) = v3 & in(v3,
% 15.39/2.88 | | | | | | all_34_10) = v4 & in(all_206_1, all_34_10) = v2 &
% 15.39/2.88 | | | | | | in(all_206_4, all_34_8) = v0 & in(all_206_5, all_34_8) =
% 15.39/2.88 | | | | | | v1 & $i(v3) & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 =
% 15.39/2.88 | | | | | | 0))
% 15.39/2.88 | | | | | |
% 15.39/2.88 | | | | | | BETA: splitting (195) gives:
% 15.39/2.88 | | | | | |
% 15.39/2.88 | | | | | | Case 1:
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | (198) all_206_4 = all_206_5
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | REDUCE: (184), (198) imply:
% 15.39/2.88 | | | | | | | (199) $false
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | CLOSE: (199) is inconsistent.
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | Case 2:
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | (200) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i]
% 15.39/2.88 | | | | | | | : ? [v4: any] : (ordered_pair(all_206_4, all_206_5) = v3
% 15.39/2.88 | | | | | | | & in(v3, all_34_10) = v4 & in(all_206_3, all_34_10) =
% 15.39/2.88 | | | | | | | v2 & in(all_206_4, all_34_8) = v1 & in(all_206_5,
% 15.39/2.88 | | | | | | | all_34_8) = v0 & $i(v3) & ( ~ (v1 = 0) | ~ (v0 = 0)
% 15.39/2.88 | | | | | | | | v4 = 0 | v2 = 0))
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | DELTA: instantiating (200) with fresh symbols all_248_0,
% 15.39/2.88 | | | | | | | all_248_1, all_248_2, all_248_3, all_248_4 gives:
% 15.39/2.88 | | | | | | | (201) ordered_pair(all_206_4, all_206_5) = all_248_1 &
% 15.39/2.88 | | | | | | | in(all_248_1, all_34_10) = all_248_0 & in(all_206_3,
% 15.39/2.88 | | | | | | | all_34_10) = all_248_2 & in(all_206_4, all_34_8) =
% 15.39/2.88 | | | | | | | all_248_3 & in(all_206_5, all_34_8) = all_248_4 &
% 15.39/2.88 | | | | | | | $i(all_248_1) & ( ~ (all_248_3 = 0) | ~ (all_248_4 = 0)
% 15.39/2.88 | | | | | | | | all_248_0 = 0 | all_248_2 = 0)
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | ALPHA: (201) implies:
% 15.39/2.88 | | | | | | | (202) in(all_206_5, all_34_8) = all_248_4
% 15.39/2.88 | | | | | | | (203) in(all_206_4, all_34_8) = all_248_3
% 15.39/2.88 | | | | | | | (204) in(all_206_3, all_34_10) = all_248_2
% 15.39/2.88 | | | | | | | (205) in(all_248_1, all_34_10) = all_248_0
% 15.39/2.88 | | | | | | | (206) ordered_pair(all_206_4, all_206_5) = all_248_1
% 15.39/2.88 | | | | | | | (207) ~ (all_248_3 = 0) | ~ (all_248_4 = 0) | all_248_0 = 0 |
% 15.39/2.88 | | | | | | | all_248_2 = 0
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | GROUND_INST: instantiating (18) with 0, all_248_4, all_34_8,
% 15.39/2.88 | | | | | | | all_206_5, simplifying with (189), (202) gives:
% 15.39/2.88 | | | | | | | (208) all_248_4 = 0
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | GROUND_INST: instantiating (18) with 0, all_248_3, all_34_8,
% 15.39/2.88 | | | | | | | all_206_4, simplifying with (190), (203) gives:
% 15.39/2.88 | | | | | | | (209) all_248_3 = 0
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | GROUND_INST: instantiating (18) with all_206_2, all_248_2,
% 15.39/2.88 | | | | | | | all_34_10, all_206_3, simplifying with (191), (204)
% 15.39/2.88 | | | | | | | gives:
% 15.39/2.88 | | | | | | | (210) all_248_2 = all_206_2
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | GROUND_INST: instantiating (20) with all_206_1, all_248_1,
% 15.39/2.88 | | | | | | | all_206_5, all_206_4, simplifying with (194), (206)
% 15.39/2.88 | | | | | | | gives:
% 15.39/2.88 | | | | | | | (211) all_248_1 = all_206_1
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | REDUCE: (205), (211) imply:
% 15.39/2.88 | | | | | | | (212) in(all_206_1, all_34_10) = all_248_0
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | BETA: splitting (197) gives:
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | | Case 1:
% 15.39/2.88 | | | | | | | |
% 15.39/2.88 | | | | | | | | (213) all_206_4 = all_206_5
% 15.39/2.88 | | | | | | | |
% 15.39/2.88 | | | | | | | | REDUCE: (184), (213) imply:
% 15.39/2.88 | | | | | | | | (214) $false
% 15.39/2.88 | | | | | | | |
% 15.39/2.88 | | | | | | | | CLOSE: (214) is inconsistent.
% 15.39/2.88 | | | | | | | |
% 15.39/2.88 | | | | | | | Case 2:
% 15.39/2.88 | | | | | | | |
% 15.39/2.88 | | | | | | | | (215) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 15.39/2.88 | | | | | | | | $i] : ? [v4: any] : (ordered_pair(all_206_5,
% 15.39/2.88 | | | | | | | | all_206_4) = v3 & in(v3, all_34_10) = v4 &
% 15.39/2.88 | | | | | | | | in(all_206_1, all_34_10) = v2 & in(all_206_4,
% 15.39/2.88 | | | | | | | | all_34_8) = v0 & in(all_206_5, all_34_8) = v1 &
% 15.39/2.88 | | | | | | | | $i(v3) & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 =
% 15.39/2.88 | | | | | | | | 0))
% 15.39/2.88 | | | | | | | |
% 15.39/2.88 | | | | | | | | DELTA: instantiating (215) with fresh symbols all_269_0,
% 15.39/2.88 | | | | | | | | all_269_1, all_269_2, all_269_3, all_269_4 gives:
% 15.39/2.88 | | | | | | | | (216) ordered_pair(all_206_5, all_206_4) = all_269_1 &
% 15.39/2.88 | | | | | | | | in(all_269_1, all_34_10) = all_269_0 & in(all_206_1,
% 15.39/2.88 | | | | | | | | all_34_10) = all_269_2 & in(all_206_4, all_34_8) =
% 15.39/2.88 | | | | | | | | all_269_4 & in(all_206_5, all_34_8) = all_269_3 &
% 15.39/2.88 | | | | | | | | $i(all_269_1) & ( ~ (all_269_3 = 0) | ~ (all_269_4 =
% 15.39/2.88 | | | | | | | | 0) | all_269_0 = 0 | all_269_2 = 0)
% 15.39/2.88 | | | | | | | |
% 15.39/2.88 | | | | | | | | ALPHA: (216) implies:
% 15.39/2.88 | | | | | | | | (217) in(all_206_1, all_34_10) = all_269_2
% 15.39/2.88 | | | | | | | |
% 15.39/2.88 | | | | | | | | BETA: splitting (196) gives:
% 15.39/2.88 | | | | | | | |
% 15.39/2.88 | | | | | | | | Case 1:
% 15.39/2.88 | | | | | | | | |
% 15.39/2.88 | | | | | | | | | (218) all_206_4 = all_206_5
% 15.39/2.88 | | | | | | | | |
% 15.39/2.88 | | | | | | | | | REDUCE: (184), (218) imply:
% 15.39/2.88 | | | | | | | | | (219) $false
% 15.39/2.88 | | | | | | | | |
% 15.39/2.88 | | | | | | | | | CLOSE: (219) is inconsistent.
% 15.39/2.88 | | | | | | | | |
% 15.39/2.88 | | | | | | | | Case 2:
% 15.39/2.88 | | | | | | | | |
% 15.39/2.88 | | | | | | | | | (220) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3:
% 15.39/2.88 | | | | | | | | | any] : ? [v4: any] : (ordered_pair(all_206_5,
% 15.39/2.88 | | | | | | | | | all_206_4) = v2 & in(v2, all_34_10) = v3 &
% 15.39/2.88 | | | | | | | | | in(all_206_1, all_34_10) = v4 & in(all_206_4,
% 15.39/2.88 | | | | | | | | | all_34_8) = v1 & in(all_206_5, all_34_8) = v0 &
% 15.39/2.88 | | | | | | | | | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v3 =
% 15.39/2.88 | | | | | | | | | 0))
% 15.39/2.88 | | | | | | | | |
% 15.39/2.88 | | | | | | | | | DELTA: instantiating (220) with fresh symbols all_275_0,
% 15.39/2.88 | | | | | | | | | all_275_1, all_275_2, all_275_3, all_275_4 gives:
% 15.39/2.88 | | | | | | | | | (221) ordered_pair(all_206_5, all_206_4) = all_275_2 &
% 15.39/2.88 | | | | | | | | | in(all_275_2, all_34_10) = all_275_1 & in(all_206_1,
% 15.39/2.88 | | | | | | | | | all_34_10) = all_275_0 & in(all_206_4, all_34_8) =
% 15.39/2.88 | | | | | | | | | all_275_3 & in(all_206_5, all_34_8) = all_275_4 &
% 15.39/2.88 | | | | | | | | | $i(all_275_2) & ( ~ (all_275_3 = 0) | ~ (all_275_4 =
% 15.39/2.88 | | | | | | | | | 0) | all_275_0 = 0 | all_275_1 = 0)
% 15.39/2.88 | | | | | | | | |
% 15.39/2.88 | | | | | | | | | ALPHA: (221) implies:
% 15.39/2.88 | | | | | | | | | (222) in(all_206_1, all_34_10) = all_275_0
% 15.39/2.88 | | | | | | | | |
% 15.39/2.88 | | | | | | | | | BETA: splitting (207) gives:
% 15.39/2.88 | | | | | | | | |
% 15.39/2.88 | | | | | | | | | Case 1:
% 15.39/2.88 | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | (223) ~ (all_248_3 = 0)
% 15.39/2.88 | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | REDUCE: (209), (223) imply:
% 15.39/2.88 | | | | | | | | | | (224) $false
% 15.39/2.88 | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | CLOSE: (224) is inconsistent.
% 15.39/2.88 | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | Case 2:
% 15.39/2.88 | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | (225) ~ (all_248_4 = 0) | all_248_0 = 0 | all_248_2 = 0
% 15.39/2.88 | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | BETA: splitting (225) gives:
% 15.39/2.88 | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | Case 1:
% 15.39/2.88 | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | (226) ~ (all_248_4 = 0)
% 15.39/2.88 | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | REDUCE: (208), (226) imply:
% 15.39/2.88 | | | | | | | | | | | (227) $false
% 15.39/2.88 | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | CLOSE: (227) is inconsistent.
% 15.39/2.88 | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | Case 2:
% 15.39/2.88 | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | (228) all_248_0 = 0 | all_248_2 = 0
% 15.39/2.88 | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | BETA: splitting (228) gives:
% 15.39/2.88 | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | Case 1:
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | (229) all_248_0 = 0
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | REDUCE: (212), (229) imply:
% 15.39/2.88 | | | | | | | | | | | | (230) in(all_206_1, all_34_10) = 0
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_269_2, all_34_10,
% 15.39/2.88 | | | | | | | | | | | | all_206_1, simplifying with (217), (230) gives:
% 15.39/2.88 | | | | | | | | | | | | (231) all_269_2 = 0
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_206_0, all_275_0,
% 15.39/2.88 | | | | | | | | | | | | all_34_10, all_206_1, simplifying with (192),
% 15.39/2.88 | | | | | | | | | | | | (222) gives:
% 15.39/2.88 | | | | | | | | | | | | (232) all_275_0 = all_206_0
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_269_2, all_275_0,
% 15.39/2.88 | | | | | | | | | | | | all_34_10, all_206_1, simplifying with (217),
% 15.39/2.88 | | | | | | | | | | | | (222) gives:
% 15.39/2.88 | | | | | | | | | | | | (233) all_275_0 = all_269_2
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | COMBINE_EQS: (232), (233) imply:
% 15.39/2.88 | | | | | | | | | | | | (234) all_269_2 = all_206_0
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | SIMP: (234) implies:
% 15.39/2.88 | | | | | | | | | | | | (235) all_269_2 = all_206_0
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | COMBINE_EQS: (231), (235) imply:
% 15.39/2.88 | | | | | | | | | | | | (236) all_206_0 = 0
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | REDUCE: (186), (236) imply:
% 15.39/2.88 | | | | | | | | | | | | (237) $false
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | CLOSE: (237) is inconsistent.
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | Case 2:
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | (238) all_248_2 = 0
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | COMBINE_EQS: (210), (238) imply:
% 15.39/2.88 | | | | | | | | | | | | (239) all_206_2 = 0
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | REDUCE: (185), (239) imply:
% 15.39/2.88 | | | | | | | | | | | | (240) $false
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 15.39/2.88 | | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | | End of split
% 15.39/2.88 | | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | | End of split
% 15.39/2.88 | | | | | | | | | |
% 15.39/2.88 | | | | | | | | | End of split
% 15.39/2.88 | | | | | | | | |
% 15.39/2.88 | | | | | | | | End of split
% 15.39/2.88 | | | | | | | |
% 15.39/2.88 | | | | | | | End of split
% 15.39/2.88 | | | | | | |
% 15.39/2.88 | | | | | | End of split
% 15.39/2.88 | | | | | |
% 15.39/2.88 | | | | | End of split
% 15.39/2.88 | | | | |
% 15.39/2.88 | | | | Case 2:
% 15.39/2.88 | | | | |
% 15.39/2.88 | | | | | (241) all_72_1 = 0
% 15.39/2.88 | | | | |
% 15.39/2.88 | | | | | COMBINE_EQS: (80), (241) imply:
% 15.39/2.88 | | | | | (242) all_34_9 = 0
% 15.39/2.88 | | | | |
% 15.39/2.88 | | | | | SIMP: (242) implies:
% 15.39/2.88 | | | | | (243) all_34_9 = 0
% 15.39/2.88 | | | | |
% 15.39/2.88 | | | | | REDUCE: (172), (243) imply:
% 15.39/2.88 | | | | | (244) $false
% 15.39/2.88 | | | | |
% 15.39/2.88 | | | | | CLOSE: (244) is inconsistent.
% 15.39/2.88 | | | | |
% 15.39/2.88 | | | | End of split
% 15.39/2.88 | | | |
% 15.39/2.88 | | | End of split
% 15.39/2.88 | | |
% 15.39/2.88 | | End of split
% 15.39/2.88 | |
% 15.39/2.88 | End of split
% 15.39/2.88 |
% 15.39/2.88 End of proof
% 15.39/2.89 % SZS output end Proof for theBenchmark
% 15.39/2.89
% 15.39/2.89 2258ms
%------------------------------------------------------------------------------