TSTP Solution File: SEU048+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU048+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:42:24 EDT 2023
% Result : Theorem 32.26s 5.21s
% Output : Proof 36.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU048+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 15:47:20 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.66/1.11 Prover 4: Preprocessing ...
% 2.66/1.11 Prover 1: Preprocessing ...
% 2.66/1.15 Prover 2: Preprocessing ...
% 2.66/1.15 Prover 0: Preprocessing ...
% 2.66/1.15 Prover 3: Preprocessing ...
% 2.66/1.15 Prover 5: Preprocessing ...
% 3.28/1.15 Prover 6: Preprocessing ...
% 6.94/1.70 Prover 3: Warning: ignoring some quantifiers
% 6.94/1.70 Prover 1: Warning: ignoring some quantifiers
% 6.94/1.71 Prover 5: Proving ...
% 6.94/1.72 Prover 1: Constructing countermodel ...
% 6.94/1.73 Prover 3: Constructing countermodel ...
% 6.94/1.74 Prover 6: Proving ...
% 7.41/1.80 Prover 2: Proving ...
% 12.13/2.39 Prover 4: Warning: ignoring some quantifiers
% 12.13/2.43 Prover 4: Constructing countermodel ...
% 12.56/2.57 Prover 0: Proving ...
% 12.56/2.58 Prover 3: gave up
% 12.56/2.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.43/2.63 Prover 7: Preprocessing ...
% 14.78/2.76 Prover 7: Warning: ignoring some quantifiers
% 14.78/2.76 Prover 7: Constructing countermodel ...
% 15.49/2.87 Prover 7: gave up
% 15.49/2.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.95/2.92 Prover 8: Preprocessing ...
% 17.10/3.05 Prover 8: Warning: ignoring some quantifiers
% 17.10/3.06 Prover 8: Constructing countermodel ...
% 17.43/3.11 Prover 1: gave up
% 17.43/3.11 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 17.75/3.16 Prover 9: Preprocessing ...
% 20.03/3.48 Prover 8: gave up
% 20.03/3.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 20.74/3.55 Prover 10: Preprocessing ...
% 20.74/3.59 Prover 10: Warning: ignoring some quantifiers
% 21.15/3.61 Prover 10: Constructing countermodel ...
% 21.15/3.61 Prover 9: Warning: ignoring some quantifiers
% 21.15/3.63 Prover 9: Constructing countermodel ...
% 21.62/3.66 Prover 10: gave up
% 21.62/3.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.62/3.69 Prover 11: Preprocessing ...
% 24.29/4.02 Prover 11: Warning: ignoring some quantifiers
% 24.29/4.03 Prover 11: Constructing countermodel ...
% 32.26/5.20 Prover 2: proved (4562ms)
% 32.26/5.21
% 32.26/5.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.26/5.21
% 32.26/5.21 Prover 9: stopped
% 32.26/5.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 32.26/5.21 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 32.26/5.21 Prover 6: stopped
% 32.26/5.22 Prover 0: stopped
% 32.26/5.22 Prover 5: stopped
% 32.26/5.22 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 32.26/5.23 Prover 13: Preprocessing ...
% 33.32/5.25 Prover 16: Preprocessing ...
% 33.32/5.26 Prover 19: Preprocessing ...
% 33.90/5.29 Prover 16: Warning: ignoring some quantifiers
% 33.90/5.33 Prover 16: Constructing countermodel ...
% 33.90/5.33 Prover 19: Warning: ignoring some quantifiers
% 33.90/5.33 Prover 13: Warning: ignoring some quantifiers
% 34.26/5.33 Prover 19: Constructing countermodel ...
% 34.26/5.33 Prover 13: Constructing countermodel ...
% 35.93/5.56 Prover 13: Found proof (size 120)
% 35.93/5.56 Prover 13: proved (343ms)
% 35.93/5.56 Prover 19: stopped
% 35.93/5.56 Prover 16: stopped
% 35.93/5.56 Prover 4: stopped
% 36.12/5.59 Prover 11: stopped
% 36.12/5.59
% 36.12/5.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.12/5.59
% 36.12/5.61 % SZS output start Proof for theBenchmark
% 36.12/5.61 Assumptions after simplification:
% 36.12/5.61 ---------------------------------
% 36.12/5.61
% 36.12/5.61 (cc1_funct_1)
% 36.12/5.61 ! [v0: $i] : ( ~ $i(v0) | ~ empty(v0) | function(v0))
% 36.12/5.61
% 36.12/5.61 (cc1_relat_1)
% 36.12/5.61 ! [v0: $i] : ( ~ $i(v0) | ~ empty(v0) | relation(v0))
% 36.12/5.61
% 36.12/5.61 (d8_funct_1)
% 36.35/5.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2
% 36.35/5.64 | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v3) = v4) | ~ (apply(v0, v2) =
% 36.35/5.64 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ one_to_one(v0) | ~
% 36.35/5.64 relation(v0) | ~ function(v0) | ~ in(v3, v1) | ~ in(v2, v1)) & ! [v0:
% 36.35/5.64 $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~
% 36.35/5.64 relation(v0) | ~ function(v0) | one_to_one(v0) | ? [v2: $i] : ? [v3: $i]
% 36.35/5.64 : ? [v4: $i] : ( ~ (v3 = v2) & apply(v0, v3) = v4 & apply(v0, v2) = v4 &
% 36.35/5.64 $i(v4) & $i(v3) & $i(v2) & in(v3, v1) & in(v2, v1))) & ! [v0: $i] : ( ~
% 36.35/5.64 $i(v0) | ~ relation(v0) | ~ function(v0) | ? [v1: $i] : ? [v2: $i] : ?
% 36.35/5.64 [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v1 & $i(v3) &
% 36.35/5.64 $i(v2) & $i(v1) & ( ~ one_to_one(v0) | ! [v6: $i] : ! [v7: $i] : (v7 =
% 36.35/5.64 v6 | ~ $i(v7) | ~ $i(v6) | ~ in(v7, v1) | ~ in(v6, v1) | ? [v8:
% 36.35/5.64 $i] : ? [v9: $i] : ( ~ (v9 = v8) & apply(v0, v7) = v9 & apply(v0,
% 36.35/5.64 v6) = v8 & $i(v9) & $i(v8)))) & (one_to_one(v0) | (v5 = v4 & ~
% 36.35/5.64 (v3 = v2) & apply(v0, v3) = v4 & apply(v0, v2) = v4 & $i(v4) & in(v3,
% 36.35/5.64 v1) & in(v2, v1)))))
% 36.35/5.64
% 36.35/5.64 (dt_k8_relat_1)
% 36.35/5.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 36.35/5.64 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | relation(v2)) & ?
% 36.35/5.64 [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v2:
% 36.35/5.64 $i] : (relation_rng_restriction(v0, v1) = v2 & $i(v2) & relation(v2)))
% 36.35/5.64
% 36.35/5.64 (fc4_relat_1)
% 36.35/5.64 $i(empty_set) & relation(empty_set) & empty(empty_set)
% 36.35/5.64
% 36.35/5.64 (fc5_funct_1)
% 36.35/5.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 36.35/5.64 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) |
% 36.35/5.64 relation(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 36.35/5.64 (relation_rng_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 36.35/5.64 relation(v1) | ~ function(v1) | function(v2)) & ? [v0: $i] : ! [v1: $i] :
% 36.35/5.64 ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ? [v2: $i] :
% 36.35/5.64 (relation_rng_restriction(v0, v1) = v2 & $i(v2) & relation(v2) &
% 36.35/5.64 function(v2)))
% 36.35/5.64
% 36.35/5.64 (fc7_relat_1)
% 36.35/5.64 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~
% 36.35/5.64 empty(v0) | relation(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 36.35/5.64 (relation_dom(v0) = v1) | ~ $i(v0) | ~ empty(v0) | empty(v1)) & ! [v0:
% 36.35/5.64 $i] : ( ~ $i(v0) | ~ empty(v0) | ? [v1: $i] : (relation_dom(v0) = v1 &
% 36.35/5.64 $i(v1) & relation(v1) & empty(v1)))
% 36.35/5.64
% 36.35/5.64 (rc1_funct_1)
% 36.35/5.65 ? [v0: $i] : ($i(v0) & relation(v0) & function(v0))
% 36.35/5.65
% 36.35/5.65 (rc1_relat_1)
% 36.35/5.65 ? [v0: $i] : ($i(v0) & relation(v0) & empty(v0))
% 36.35/5.65
% 36.35/5.65 (rc1_xboole_0)
% 36.35/5.65 ? [v0: $i] : ($i(v0) & empty(v0))
% 36.35/5.65
% 36.35/5.65 (rc2_funct_1)
% 36.35/5.65 ? [v0: $i] : ($i(v0) & relation(v0) & function(v0) & empty(v0))
% 36.35/5.65
% 36.35/5.65 (rc3_funct_1)
% 36.35/5.65 ? [v0: $i] : ($i(v0) & one_to_one(v0) & relation(v0) & function(v0))
% 36.35/5.65
% 36.35/5.65 (t6_boole)
% 36.35/5.65 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 36.35/5.65
% 36.35/5.65 (t85_funct_1)
% 36.44/5.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 36.44/5.65 (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) = v2) | ~
% 36.44/5.65 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v3) | ~ relation(v1) | ~
% 36.44/5.65 function(v3) | ~ function(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 36.44/5.65 ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : (relation_dom(v3) = v5 & $i(v9) &
% 36.44/5.65 $i(v6) & $i(v5) & ( ~ (v4 = v1) | ( ! [v11: $i] : ! [v12: $i] : ( ~
% 36.44/5.65 (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v12, v0) | ~ in(v11,
% 36.44/5.65 v5) | in(v11, v2)) & ! [v11: $i] : ! [v12: $i] : ( ~ (apply(v3,
% 36.44/5.65 v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | in(v12, v0)) & !
% 36.44/5.65 [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~ $i(v11) |
% 36.44/5.65 ~ in(v11, v2) | in(v11, v5)) & ! [v11: $i] : ! [v12: $i] : ( ~
% 36.44/5.65 (apply(v1, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | (apply(v3,
% 36.44/5.65 v11) = v12 & $i(v12))))) & (v4 = v1 | ( ~ (v8 = v7) & apply(v3,
% 36.44/5.65 v6) = v8 & apply(v1, v6) = v7 & $i(v8) & $i(v7) & in(v6, v2)) |
% 36.44/5.65 (apply(v3, v9) = v10 & $i(v10) & ( ~ in(v10, v0) | ~ in(v9, v5) | ~
% 36.44/5.65 in(v9, v2)) & (in(v9, v2) | (in(v10, v0) & in(v9, v5))))))) & ?
% 36.44/5.65 [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~
% 36.44/5.65 function(v1) | ? [v2: $i] : (relation_dom(v1) = v2 & $i(v2) & ! [v3: $i] :
% 36.44/5.65 ( ~ $i(v3) | ~ relation(v3) | ~ function(v3) | ? [v4: $i] : ? [v5: $i]
% 36.44/5.65 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 36.44/5.65 (relation_rng_restriction(v0, v3) = v4 & relation_dom(v3) = v5 & $i(v9)
% 36.44/5.65 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v4 = v1) | ( ! [v11: $i] : ( ~
% 36.44/5.65 $i(v11) | ~ in(v11, v5) | in(v11, v2) | ? [v12: $i] :
% 36.44/5.65 (apply(v3, v11) = v12 & $i(v12) & ~ in(v12, v0))) & ! [v11:
% 36.44/5.65 $i] : ( ~ $i(v11) | ~ in(v11, v2) | in(v11, v5)) & ! [v11: $i]
% 36.44/5.65 : ( ~ $i(v11) | ~ in(v11, v2) | ? [v12: $i] : (apply(v3, v11) =
% 36.44/5.65 v12 & apply(v1, v11) = v12 & $i(v12))) & ! [v11: $i] : ( ~
% 36.44/5.65 $i(v11) | ~ in(v11, v2) | ? [v12: $i] : (apply(v3, v11) = v12
% 36.44/5.65 & $i(v12) & in(v12, v0))))) & (v4 = v1 | ( ~ (v8 = v7) &
% 36.44/5.65 apply(v3, v6) = v8 & apply(v1, v6) = v7 & $i(v8) & $i(v7) & in(v6,
% 36.44/5.65 v2)) | (apply(v3, v9) = v10 & $i(v10) & ( ~ in(v10, v0) | ~
% 36.44/5.65 in(v9, v5) | ~ in(v9, v2)) & (in(v9, v2) | (in(v10, v0) &
% 36.44/5.65 in(v9, v5)))))))))
% 36.44/5.65
% 36.44/5.65 (t8_boole)
% 36.44/5.66 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ empty(v1) |
% 36.44/5.66 ~ empty(v0))
% 36.44/5.66
% 36.44/5.66 (t99_funct_1)
% 36.44/5.66 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng_restriction(v0, v1) =
% 36.44/5.66 v2 & $i(v2) & $i(v1) & $i(v0) & one_to_one(v1) & relation(v1) & function(v1)
% 36.44/5.66 & ~ one_to_one(v2))
% 36.44/5.66
% 36.44/5.66 (function-axioms)
% 36.44/5.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 36.44/5.66 (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3,
% 36.44/5.66 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 36.44/5.66 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : !
% 36.44/5.66 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 36.44/5.66 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 36.44/5.66 (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 36.44/5.66
% 36.44/5.66 Further assumptions not needed in the proof:
% 36.44/5.66 --------------------------------------------
% 36.44/5.66 antisymmetry_r2_hidden, cc2_funct_1, existence_m1_subset_1, fc12_relat_1,
% 36.44/5.66 fc1_subset_1, fc1_xboole_0, fc5_relat_1, rc1_subset_1, rc2_relat_1,
% 36.44/5.66 rc2_subset_1, rc2_xboole_0, rc3_relat_1, reflexivity_r1_tarski, t1_subset,
% 36.44/5.66 t2_subset, t3_subset, t4_subset, t5_subset, t7_boole
% 36.44/5.66
% 36.44/5.66 Those formulas are unsatisfiable:
% 36.44/5.66 ---------------------------------
% 36.44/5.66
% 36.44/5.66 Begin of proof
% 36.44/5.66 |
% 36.44/5.66 | ALPHA: (d8_funct_1) implies:
% 36.44/5.66 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ relation(v0) | ~ function(v0) | ? [v1:
% 36.44/5.66 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 36.44/5.66 | (relation_dom(v0) = v1 & $i(v3) & $i(v2) & $i(v1) & ( ~
% 36.44/5.66 | one_to_one(v0) | ! [v6: $i] : ! [v7: $i] : (v7 = v6 | ~ $i(v7)
% 36.44/5.66 | | ~ $i(v6) | ~ in(v7, v1) | ~ in(v6, v1) | ? [v8: $i] : ?
% 36.44/5.66 | [v9: $i] : ( ~ (v9 = v8) & apply(v0, v7) = v9 & apply(v0, v6) =
% 36.44/5.66 | v8 & $i(v9) & $i(v8)))) & (one_to_one(v0) | (v5 = v4 & ~ (v3
% 36.44/5.66 | = v2) & apply(v0, v3) = v4 & apply(v0, v2) = v4 & $i(v4) &
% 36.44/5.66 | in(v3, v1) & in(v2, v1)))))
% 36.44/5.66 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 36.44/5.66 | (v3 = v2 | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v3) = v4) | ~
% 36.44/5.66 | (apply(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 36.44/5.66 | one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ~ in(v3, v1) |
% 36.44/5.66 | ~ in(v2, v1))
% 36.44/5.66 |
% 36.44/5.66 | ALPHA: (dt_k8_relat_1) implies:
% 36.44/5.66 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 36.44/5.66 | (relation_rng_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 36.44/5.66 | relation(v1) | relation(v2))
% 36.44/5.66 |
% 36.44/5.66 | ALPHA: (fc4_relat_1) implies:
% 36.44/5.66 | (4) empty(empty_set)
% 36.44/5.66 |
% 36.44/5.66 | ALPHA: (fc5_funct_1) implies:
% 36.44/5.67 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 36.44/5.67 | (relation_rng_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 36.44/5.67 | relation(v1) | ~ function(v1) | function(v2))
% 36.44/5.67 |
% 36.44/5.67 | ALPHA: (fc7_relat_1) implies:
% 36.44/5.67 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ empty(v0) | ? [v1: $i] :
% 36.44/5.67 | (relation_dom(v0) = v1 & $i(v1) & relation(v1) & empty(v1)))
% 36.44/5.67 |
% 36.44/5.67 | ALPHA: (t6_boole) implies:
% 36.44/5.67 | (7) $i(empty_set)
% 36.44/5.67 | (8) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 36.44/5.67 |
% 36.44/5.67 | ALPHA: (t85_funct_1) implies:
% 36.44/5.67 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 36.44/5.67 | ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) =
% 36.44/5.67 | v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v3) | ~
% 36.44/5.67 | relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5: $i] : ?
% 36.44/5.67 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 36.44/5.67 | (relation_dom(v3) = v5 & $i(v9) & $i(v6) & $i(v5) & ( ~ (v4 = v1) | (
% 36.44/5.67 | ! [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~
% 36.44/5.67 | $i(v11) | ~ in(v12, v0) | ~ in(v11, v5) | in(v11, v2)) & !
% 36.44/5.67 | [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~
% 36.44/5.67 | $i(v11) | ~ in(v11, v2) | in(v12, v0)) & ! [v11: $i] : !
% 36.44/5.67 | [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~ $i(v11) | ~
% 36.44/5.67 | in(v11, v2) | in(v11, v5)) & ! [v11: $i] : ! [v12: $i] : (
% 36.44/5.67 | ~ (apply(v1, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) |
% 36.44/5.67 | (apply(v3, v11) = v12 & $i(v12))))) & (v4 = v1 | ( ~ (v8 =
% 36.44/5.67 | v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & $i(v8) &
% 36.44/5.67 | $i(v7) & in(v6, v2)) | (apply(v3, v9) = v10 & $i(v10) & ( ~
% 36.44/5.67 | in(v10, v0) | ~ in(v9, v5) | ~ in(v9, v2)) & (in(v9, v2) |
% 36.44/5.67 | (in(v10, v0) & in(v9, v5)))))))
% 36.44/5.67 |
% 36.44/5.67 | ALPHA: (function-axioms) implies:
% 36.44/5.67 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 36.44/5.67 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 36.44/5.67 |
% 36.44/5.67 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_28_0 gives:
% 36.44/5.67 | (11) $i(all_28_0) & empty(all_28_0)
% 36.44/5.67 |
% 36.44/5.67 | ALPHA: (11) implies:
% 36.44/5.67 | (12) empty(all_28_0)
% 36.44/5.67 | (13) $i(all_28_0)
% 36.44/5.67 |
% 36.44/5.67 | DELTA: instantiating (rc1_funct_1) with fresh symbol all_31_0 gives:
% 36.44/5.67 | (14) $i(all_31_0) & relation(all_31_0) & function(all_31_0)
% 36.44/5.67 |
% 36.44/5.67 | ALPHA: (14) implies:
% 36.44/5.67 | (15) function(all_31_0)
% 36.44/5.67 | (16) relation(all_31_0)
% 36.44/5.67 | (17) $i(all_31_0)
% 36.44/5.67 |
% 36.44/5.67 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_33_0 gives:
% 36.44/5.67 | (18) $i(all_33_0) & relation(all_33_0) & empty(all_33_0)
% 36.44/5.67 |
% 36.44/5.67 | ALPHA: (18) implies:
% 36.44/5.67 | (19) empty(all_33_0)
% 36.44/5.67 | (20) $i(all_33_0)
% 36.44/5.67 |
% 36.44/5.67 | DELTA: instantiating (rc3_funct_1) with fresh symbol all_39_0 gives:
% 36.44/5.67 | (21) $i(all_39_0) & one_to_one(all_39_0) & relation(all_39_0) &
% 36.44/5.67 | function(all_39_0)
% 36.44/5.67 |
% 36.44/5.67 | ALPHA: (21) implies:
% 36.44/5.67 | (22) function(all_39_0)
% 36.44/5.67 | (23) relation(all_39_0)
% 36.44/5.67 | (24) $i(all_39_0)
% 36.44/5.67 |
% 36.44/5.67 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_41_0 gives:
% 36.44/5.67 | (25) $i(all_41_0) & relation(all_41_0) & function(all_41_0) &
% 36.44/5.67 | empty(all_41_0)
% 36.44/5.67 |
% 36.44/5.67 | ALPHA: (25) implies:
% 36.44/5.67 | (26) empty(all_41_0)
% 36.44/5.67 | (27) function(all_41_0)
% 36.44/5.68 | (28) relation(all_41_0)
% 36.44/5.68 | (29) $i(all_41_0)
% 36.44/5.68 |
% 36.44/5.68 | DELTA: instantiating (t99_funct_1) with fresh symbols all_46_0, all_46_1,
% 36.44/5.68 | all_46_2 gives:
% 36.44/5.68 | (30) relation_rng_restriction(all_46_2, all_46_1) = all_46_0 & $i(all_46_0)
% 36.44/5.68 | & $i(all_46_1) & $i(all_46_2) & one_to_one(all_46_1) &
% 36.44/5.68 | relation(all_46_1) & function(all_46_1) & ~ one_to_one(all_46_0)
% 36.44/5.68 |
% 36.44/5.68 | ALPHA: (30) implies:
% 36.44/5.68 | (31) ~ one_to_one(all_46_0)
% 36.44/5.68 | (32) function(all_46_1)
% 36.44/5.68 | (33) relation(all_46_1)
% 36.44/5.68 | (34) one_to_one(all_46_1)
% 36.44/5.68 | (35) $i(all_46_2)
% 36.44/5.68 | (36) $i(all_46_1)
% 36.44/5.68 | (37) $i(all_46_0)
% 36.44/5.68 | (38) relation_rng_restriction(all_46_2, all_46_1) = all_46_0
% 36.44/5.68 |
% 36.44/5.68 | GROUND_INST: instantiating (6) with empty_set, simplifying with (4), (7)
% 36.44/5.68 | gives:
% 36.44/5.68 | (39) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & relation(v0) &
% 36.44/5.68 | empty(v0))
% 36.44/5.68 |
% 36.44/5.68 | GROUND_INST: instantiating (cc1_relat_1) with all_28_0, simplifying with (12),
% 36.44/5.68 | (13) gives:
% 36.44/5.68 | (40) relation(all_28_0)
% 36.44/5.68 |
% 36.44/5.68 | GROUND_INST: instantiating (cc1_funct_1) with all_28_0, simplifying with (12),
% 36.44/5.68 | (13) gives:
% 36.44/5.68 | (41) function(all_28_0)
% 36.44/5.68 |
% 36.44/5.68 | GROUND_INST: instantiating (6) with all_28_0, simplifying with (12), (13)
% 36.44/5.68 | gives:
% 36.44/5.68 | (42) ? [v0: $i] : (relation_dom(all_28_0) = v0 & $i(v0) & relation(v0) &
% 36.44/5.68 | empty(v0))
% 36.44/5.68 |
% 36.44/5.68 | GROUND_INST: instantiating (t8_boole) with all_28_0, all_33_0, simplifying
% 36.44/5.68 | with (12), (13), (19), (20) gives:
% 36.44/5.68 | (43) all_33_0 = all_28_0
% 36.44/5.68 |
% 36.44/5.68 | GROUND_INST: instantiating (6) with all_33_0, simplifying with (19), (20)
% 36.44/5.68 | gives:
% 36.44/5.68 | (44) ? [v0: $i] : (relation_dom(all_33_0) = v0 & $i(v0) & relation(v0) &
% 36.44/5.68 | empty(v0))
% 36.44/5.68 |
% 36.44/5.68 | GROUND_INST: instantiating (t8_boole) with all_33_0, all_41_0, simplifying
% 36.44/5.68 | with (19), (20), (26), (29) gives:
% 36.44/5.68 | (45) all_41_0 = all_33_0
% 36.44/5.68 |
% 36.44/5.68 | GROUND_INST: instantiating (8) with all_41_0, simplifying with (26), (29)
% 36.44/5.68 | gives:
% 36.44/5.68 | (46) all_41_0 = empty_set
% 36.44/5.68 |
% 36.44/5.68 | GROUND_INST: instantiating (6) with all_41_0, simplifying with (26), (29)
% 36.44/5.68 | gives:
% 36.44/5.68 | (47) ? [v0: $i] : (relation_dom(all_41_0) = v0 & $i(v0) & relation(v0) &
% 36.44/5.68 | empty(v0))
% 36.44/5.68 |
% 36.44/5.68 | GROUND_INST: instantiating (1) with all_31_0, simplifying with (15), (16),
% 36.44/5.68 | (17) gives:
% 36.44/5.68 | (48) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 36.44/5.68 | (relation_dom(all_31_0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~
% 36.44/5.68 | one_to_one(all_31_0) | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~
% 36.44/5.68 | $i(v6) | ~ $i(v5) | ~ in(v6, v0) | ~ in(v5, v0) | ? [v7: $i]
% 36.44/5.68 | : ? [v8: $i] : ( ~ (v8 = v7) & apply(all_31_0, v6) = v8 &
% 36.44/5.68 | apply(all_31_0, v5) = v7 & $i(v8) & $i(v7)))) &
% 36.44/5.68 | (one_to_one(all_31_0) | (v4 = v3 & ~ (v2 = v1) & apply(all_31_0,
% 36.44/5.68 | v2) = v3 & apply(all_31_0, v1) = v3 & $i(v3) & in(v2, v0) &
% 36.44/5.68 | in(v1, v0))))
% 36.44/5.68 |
% 36.44/5.69 | GROUND_INST: instantiating (1) with all_39_0, simplifying with (22), (23),
% 36.44/5.69 | (24) gives:
% 36.44/5.69 | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 36.44/5.69 | (relation_dom(all_39_0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~
% 36.44/5.69 | one_to_one(all_39_0) | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~
% 36.44/5.69 | $i(v6) | ~ $i(v5) | ~ in(v6, v0) | ~ in(v5, v0) | ? [v7: $i]
% 36.44/5.69 | : ? [v8: $i] : ( ~ (v8 = v7) & apply(all_39_0, v6) = v8 &
% 36.44/5.69 | apply(all_39_0, v5) = v7 & $i(v8) & $i(v7)))) &
% 36.44/5.69 | (one_to_one(all_39_0) | (v4 = v3 & ~ (v2 = v1) & apply(all_39_0,
% 36.44/5.69 | v2) = v3 & apply(all_39_0, v1) = v3 & $i(v3) & in(v2, v0) &
% 36.44/5.69 | in(v1, v0))))
% 36.44/5.69 |
% 36.44/5.69 | GROUND_INST: instantiating (1) with all_41_0, simplifying with (27), (28),
% 36.44/5.69 | (29) gives:
% 36.44/5.69 | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 36.44/5.69 | (relation_dom(all_41_0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~
% 36.44/5.69 | one_to_one(all_41_0) | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~
% 36.44/5.69 | $i(v6) | ~ $i(v5) | ~ in(v6, v0) | ~ in(v5, v0) | ? [v7: $i]
% 36.44/5.69 | : ? [v8: $i] : ( ~ (v8 = v7) & apply(all_41_0, v6) = v8 &
% 36.44/5.69 | apply(all_41_0, v5) = v7 & $i(v8) & $i(v7)))) &
% 36.44/5.69 | (one_to_one(all_41_0) | (v4 = v3 & ~ (v2 = v1) & apply(all_41_0,
% 36.44/5.69 | v2) = v3 & apply(all_41_0, v1) = v3 & $i(v3) & in(v2, v0) &
% 36.44/5.69 | in(v1, v0))))
% 36.44/5.69 |
% 36.44/5.69 | GROUND_INST: instantiating (1) with all_46_1, simplifying with (32), (33),
% 36.44/5.69 | (36) gives:
% 36.44/5.69 | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 36.44/5.69 | (relation_dom(all_46_1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~
% 36.44/5.69 | one_to_one(all_46_1) | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~
% 36.44/5.69 | $i(v6) | ~ $i(v5) | ~ in(v6, v0) | ~ in(v5, v0) | ? [v7: $i]
% 36.44/5.69 | : ? [v8: $i] : ( ~ (v8 = v7) & apply(all_46_1, v6) = v8 &
% 36.44/5.69 | apply(all_46_1, v5) = v7 & $i(v8) & $i(v7)))) &
% 36.44/5.69 | (one_to_one(all_46_1) | (v4 = v3 & ~ (v2 = v1) & apply(all_46_1,
% 36.44/5.69 | v2) = v3 & apply(all_46_1, v1) = v3 & $i(v3) & in(v2, v0) &
% 36.44/5.69 | in(v1, v0))))
% 36.44/5.69 |
% 36.44/5.69 | GROUND_INST: instantiating (5) with all_46_2, all_46_1, all_46_0, simplifying
% 36.44/5.69 | with (32), (33), (35), (36), (38) gives:
% 36.44/5.69 | (52) function(all_46_0)
% 36.44/5.69 |
% 36.44/5.69 | GROUND_INST: instantiating (3) with all_46_2, all_46_1, all_46_0, simplifying
% 36.44/5.69 | with (33), (35), (36), (38) gives:
% 36.44/5.69 | (53) relation(all_46_0)
% 36.44/5.69 |
% 36.44/5.69 | COMBINE_EQS: (45), (46) imply:
% 36.44/5.69 | (54) all_33_0 = empty_set
% 36.44/5.69 |
% 36.44/5.69 | SIMP: (54) implies:
% 36.44/5.69 | (55) all_33_0 = empty_set
% 36.44/5.69 |
% 36.44/5.69 | COMBINE_EQS: (43), (55) imply:
% 36.44/5.69 | (56) all_28_0 = empty_set
% 36.44/5.69 |
% 36.44/5.69 | SIMP: (56) implies:
% 36.44/5.69 | (57) all_28_0 = empty_set
% 36.44/5.69 |
% 36.44/5.69 | DELTA: instantiating (47) with fresh symbol all_60_0 gives:
% 36.44/5.69 | (58) relation_dom(all_41_0) = all_60_0 & $i(all_60_0) & relation(all_60_0)
% 36.44/5.69 | & empty(all_60_0)
% 36.44/5.69 |
% 36.44/5.69 | ALPHA: (58) implies:
% 36.44/5.69 | (59) relation_dom(all_41_0) = all_60_0
% 36.44/5.69 |
% 36.44/5.69 | DELTA: instantiating (42) with fresh symbol all_62_0 gives:
% 36.44/5.69 | (60) relation_dom(all_28_0) = all_62_0 & $i(all_62_0) & relation(all_62_0)
% 36.44/5.69 | & empty(all_62_0)
% 36.44/5.69 |
% 36.44/5.69 | ALPHA: (60) implies:
% 36.44/5.69 | (61) relation_dom(all_28_0) = all_62_0
% 36.44/5.69 |
% 36.44/5.69 | DELTA: instantiating (44) with fresh symbol all_64_0 gives:
% 36.44/5.69 | (62) relation_dom(all_33_0) = all_64_0 & $i(all_64_0) & relation(all_64_0)
% 36.44/5.69 | & empty(all_64_0)
% 36.44/5.69 |
% 36.44/5.69 | ALPHA: (62) implies:
% 36.44/5.69 | (63) relation_dom(all_33_0) = all_64_0
% 36.44/5.69 |
% 36.44/5.69 | DELTA: instantiating (39) with fresh symbol all_66_0 gives:
% 36.44/5.70 | (64) relation_dom(empty_set) = all_66_0 & $i(all_66_0) & relation(all_66_0)
% 36.44/5.70 | & empty(all_66_0)
% 36.44/5.70 |
% 36.44/5.70 | ALPHA: (64) implies:
% 36.44/5.70 | (65) relation_dom(empty_set) = all_66_0
% 36.44/5.70 |
% 36.44/5.70 | DELTA: instantiating (51) with fresh symbols all_68_0, all_68_1, all_68_2,
% 36.44/5.70 | all_68_3, all_68_4 gives:
% 36.44/5.70 | (66) relation_dom(all_46_1) = all_68_4 & $i(all_68_2) & $i(all_68_3) &
% 36.44/5.70 | $i(all_68_4) & ( ~ one_to_one(all_46_1) | ! [v0: $i] : ! [v1: $i] :
% 36.44/5.70 | (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ in(v1, all_68_4) | ~ in(v0,
% 36.44/5.70 | all_68_4) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 36.44/5.70 | apply(all_46_1, v1) = v3 & apply(all_46_1, v0) = v2 & $i(v3) &
% 36.44/5.70 | $i(v2)))) & (one_to_one(all_46_1) | (all_68_0 = all_68_1 & ~
% 36.44/5.70 | (all_68_2 = all_68_3) & apply(all_46_1, all_68_2) = all_68_1 &
% 36.44/5.70 | apply(all_46_1, all_68_3) = all_68_1 & $i(all_68_1) & in(all_68_2,
% 36.44/5.70 | all_68_4) & in(all_68_3, all_68_4)))
% 36.44/5.70 |
% 36.44/5.70 | ALPHA: (66) implies:
% 36.44/5.70 | (67) relation_dom(all_46_1) = all_68_4
% 36.44/5.70 |
% 36.44/5.70 | DELTA: instantiating (49) with fresh symbols all_70_0, all_70_1, all_70_2,
% 36.44/5.70 | all_70_3, all_70_4 gives:
% 36.44/5.70 | (68) relation_dom(all_39_0) = all_70_4 & $i(all_70_2) & $i(all_70_3) &
% 36.44/5.70 | $i(all_70_4) & ( ~ one_to_one(all_39_0) | ! [v0: $i] : ! [v1: $i] :
% 36.44/5.70 | (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ in(v1, all_70_4) | ~ in(v0,
% 36.44/5.70 | all_70_4) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 36.44/5.70 | apply(all_39_0, v1) = v3 & apply(all_39_0, v0) = v2 & $i(v3) &
% 36.44/5.70 | $i(v2)))) & (one_to_one(all_39_0) | (all_70_0 = all_70_1 & ~
% 36.44/5.70 | (all_70_2 = all_70_3) & apply(all_39_0, all_70_2) = all_70_1 &
% 36.44/5.70 | apply(all_39_0, all_70_3) = all_70_1 & $i(all_70_1) & in(all_70_2,
% 36.44/5.70 | all_70_4) & in(all_70_3, all_70_4)))
% 36.44/5.70 |
% 36.44/5.70 | ALPHA: (68) implies:
% 36.44/5.70 | (69) relation_dom(all_39_0) = all_70_4
% 36.44/5.70 |
% 36.44/5.70 | DELTA: instantiating (50) with fresh symbols all_72_0, all_72_1, all_72_2,
% 36.44/5.70 | all_72_3, all_72_4 gives:
% 36.44/5.70 | (70) relation_dom(all_41_0) = all_72_4 & $i(all_72_2) & $i(all_72_3) &
% 36.44/5.70 | $i(all_72_4) & ( ~ one_to_one(all_41_0) | ! [v0: $i] : ! [v1: $i] :
% 36.44/5.70 | (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ in(v1, all_72_4) | ~ in(v0,
% 36.44/5.70 | all_72_4) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 36.44/5.70 | apply(all_41_0, v1) = v3 & apply(all_41_0, v0) = v2 & $i(v3) &
% 36.44/5.70 | $i(v2)))) & (one_to_one(all_41_0) | (all_72_0 = all_72_1 & ~
% 36.44/5.70 | (all_72_2 = all_72_3) & apply(all_41_0, all_72_2) = all_72_1 &
% 36.44/5.70 | apply(all_41_0, all_72_3) = all_72_1 & $i(all_72_1) & in(all_72_2,
% 36.44/5.70 | all_72_4) & in(all_72_3, all_72_4)))
% 36.44/5.70 |
% 36.44/5.70 | ALPHA: (70) implies:
% 36.44/5.70 | (71) relation_dom(all_41_0) = all_72_4
% 36.44/5.70 |
% 36.44/5.70 | DELTA: instantiating (48) with fresh symbols all_74_0, all_74_1, all_74_2,
% 36.44/5.70 | all_74_3, all_74_4 gives:
% 36.44/5.70 | (72) relation_dom(all_31_0) = all_74_4 & $i(all_74_2) & $i(all_74_3) &
% 36.44/5.70 | $i(all_74_4) & ( ~ one_to_one(all_31_0) | ! [v0: $i] : ! [v1: $i] :
% 36.44/5.70 | (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ in(v1, all_74_4) | ~ in(v0,
% 36.44/5.70 | all_74_4) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 36.44/5.70 | apply(all_31_0, v1) = v3 & apply(all_31_0, v0) = v2 & $i(v3) &
% 36.44/5.70 | $i(v2)))) & (one_to_one(all_31_0) | (all_74_0 = all_74_1 & ~
% 36.44/5.70 | (all_74_2 = all_74_3) & apply(all_31_0, all_74_2) = all_74_1 &
% 36.44/5.70 | apply(all_31_0, all_74_3) = all_74_1 & $i(all_74_1) & in(all_74_2,
% 36.44/5.70 | all_74_4) & in(all_74_3, all_74_4)))
% 36.44/5.70 |
% 36.44/5.70 | ALPHA: (72) implies:
% 36.44/5.70 | (73) relation_dom(all_31_0) = all_74_4
% 36.44/5.70 |
% 36.44/5.70 | REDUCE: (46), (71) imply:
% 36.44/5.70 | (74) relation_dom(empty_set) = all_72_4
% 36.44/5.70 |
% 36.44/5.70 | REDUCE: (46), (59) imply:
% 36.44/5.70 | (75) relation_dom(empty_set) = all_60_0
% 36.44/5.70 |
% 36.44/5.70 | REDUCE: (55), (63) imply:
% 36.44/5.70 | (76) relation_dom(empty_set) = all_64_0
% 36.44/5.70 |
% 36.44/5.70 | REDUCE: (57), (61) imply:
% 36.44/5.70 | (77) relation_dom(empty_set) = all_62_0
% 36.44/5.70 |
% 36.44/5.70 | REDUCE: (40), (57) imply:
% 36.44/5.70 | (78) relation(empty_set)
% 36.44/5.70 |
% 36.44/5.70 | REDUCE: (41), (57) imply:
% 36.44/5.70 | (79) function(empty_set)
% 36.44/5.70 |
% 36.44/5.70 | GROUND_INST: instantiating (10) with all_64_0, all_66_0, empty_set,
% 36.44/5.70 | simplifying with (65), (76) gives:
% 36.44/5.70 | (80) all_66_0 = all_64_0
% 36.44/5.70 |
% 36.44/5.70 | GROUND_INST: instantiating (10) with all_62_0, all_66_0, empty_set,
% 36.44/5.70 | simplifying with (65), (77) gives:
% 36.44/5.70 | (81) all_66_0 = all_62_0
% 36.44/5.70 |
% 36.44/5.70 | GROUND_INST: instantiating (10) with all_66_0, all_72_4, empty_set,
% 36.44/5.71 | simplifying with (65), (74) gives:
% 36.44/5.71 | (82) all_72_4 = all_66_0
% 36.44/5.71 |
% 36.44/5.71 | GROUND_INST: instantiating (10) with all_60_0, all_72_4, empty_set,
% 36.44/5.71 | simplifying with (74), (75) gives:
% 36.44/5.71 | (83) all_72_4 = all_60_0
% 36.44/5.71 |
% 36.44/5.71 | COMBINE_EQS: (82), (83) imply:
% 36.44/5.71 | (84) all_66_0 = all_60_0
% 36.44/5.71 |
% 36.44/5.71 | SIMP: (84) implies:
% 36.44/5.71 | (85) all_66_0 = all_60_0
% 36.44/5.71 |
% 36.44/5.71 | COMBINE_EQS: (80), (85) imply:
% 36.44/5.71 | (86) all_64_0 = all_60_0
% 36.44/5.71 |
% 36.44/5.71 | COMBINE_EQS: (80), (81) imply:
% 36.44/5.71 | (87) all_64_0 = all_62_0
% 36.44/5.71 |
% 36.44/5.71 | COMBINE_EQS: (86), (87) imply:
% 36.44/5.71 | (88) all_62_0 = all_60_0
% 36.44/5.71 |
% 36.44/5.71 | SIMP: (88) implies:
% 36.44/5.71 | (89) all_62_0 = all_60_0
% 36.44/5.71 |
% 36.44/5.71 | GROUND_INST: instantiating (1) with all_46_0, simplifying with (37), (52),
% 36.44/5.71 | (53) gives:
% 36.44/5.71 | (90) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 36.44/5.71 | (relation_dom(all_46_0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~
% 36.44/5.71 | one_to_one(all_46_0) | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~
% 36.44/5.71 | $i(v6) | ~ $i(v5) | ~ in(v6, v0) | ~ in(v5, v0) | ? [v7: $i]
% 36.44/5.71 | : ? [v8: $i] : ( ~ (v8 = v7) & apply(all_46_0, v6) = v8 &
% 36.44/5.71 | apply(all_46_0, v5) = v7 & $i(v8) & $i(v7)))) &
% 36.44/5.71 | (one_to_one(all_46_0) | (v4 = v3 & ~ (v2 = v1) & apply(all_46_0,
% 36.44/5.71 | v2) = v3 & apply(all_46_0, v1) = v3 & $i(v3) & in(v2, v0) &
% 36.44/5.71 | in(v1, v0))))
% 36.44/5.71 |
% 36.44/5.71 | GROUND_INST: instantiating (9) with all_46_2, empty_set, all_60_0, all_46_1,
% 36.44/5.71 | all_46_0, simplifying with (7), (32), (33), (35), (36), (38),
% 36.44/5.71 | (75), (78), (79) gives:
% 36.44/5.71 | (91) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 36.44/5.71 | ? [v5: $i] : (relation_dom(all_46_1) = v0 & $i(v4) & $i(v1) & $i(v0) &
% 36.44/5.71 | ( ~ (all_46_0 = empty_set) | ( ! [v6: $i] : ! [v7: $i] : ( ~
% 36.44/5.71 | (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v7, all_46_2) |
% 36.44/5.71 | ~ in(v6, v0) | in(v6, all_60_0)) & ! [v6: $i] : ! [v7: $i]
% 36.44/5.71 | : ( ~ (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v6,
% 36.44/5.71 | all_60_0) | in(v7, all_46_2)) & ! [v6: $i] : ! [v7: $i] :
% 36.44/5.71 | ( ~ (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v6, all_60_0)
% 36.44/5.71 | | in(v6, v0)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 36.44/5.71 | (apply(empty_set, v6) = v7) | ~ $i(v6) | ~ in(v6, all_60_0)
% 36.44/5.71 | | (apply(all_46_1, v6) = v7 & $i(v7))))) & (all_46_0 =
% 36.44/5.71 | empty_set | ( ~ (v3 = v2) & apply(all_46_1, v1) = v3 &
% 36.44/5.71 | apply(empty_set, v1) = v2 & $i(v3) & $i(v2) & in(v1, all_60_0))
% 36.44/5.71 | | (apply(all_46_1, v4) = v5 & $i(v5) & ( ~ in(v5, all_46_2) | ~
% 36.44/5.71 | in(v4, v0) | ~ in(v4, all_60_0)) & (in(v4, all_60_0) |
% 36.44/5.71 | (in(v5, all_46_2) & in(v4, v0))))))
% 36.44/5.71 |
% 36.44/5.71 | GROUND_INST: instantiating (9) with all_46_2, all_31_0, all_74_4, all_46_1,
% 36.44/5.71 | all_46_0, simplifying with (15), (16), (17), (32), (33), (35),
% 36.44/5.71 | (36), (38), (73) gives:
% 36.44/5.71 | (92) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 36.44/5.71 | ? [v5: $i] : (relation_dom(all_46_1) = v0 & $i(v4) & $i(v1) & $i(v0) &
% 36.44/5.71 | ( ~ (all_46_0 = all_31_0) | ( ! [v6: $i] : ! [v7: $i] : ( ~
% 36.44/5.71 | (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v7, all_46_2) |
% 36.44/5.71 | ~ in(v6, v0) | in(v6, all_74_4)) & ! [v6: $i] : ! [v7: $i]
% 36.44/5.71 | : ( ~ (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v6,
% 36.44/5.71 | all_74_4) | in(v7, all_46_2)) & ! [v6: $i] : ! [v7: $i] :
% 36.44/5.71 | ( ~ (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v6, all_74_4)
% 36.44/5.71 | | in(v6, v0)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 36.44/5.71 | (apply(all_31_0, v6) = v7) | ~ $i(v6) | ~ in(v6, all_74_4) |
% 36.44/5.71 | (apply(all_46_1, v6) = v7 & $i(v7))))) & (all_46_0 = all_31_0
% 36.44/5.71 | | ( ~ (v3 = v2) & apply(all_46_1, v1) = v3 & apply(all_31_0, v1) =
% 36.44/5.71 | v2 & $i(v3) & $i(v2) & in(v1, all_74_4)) | (apply(all_46_1, v4)
% 36.44/5.71 | = v5 & $i(v5) & ( ~ in(v5, all_46_2) | ~ in(v4, v0) | ~ in(v4,
% 36.44/5.71 | all_74_4)) & (in(v4, all_74_4) | (in(v5, all_46_2) & in(v4,
% 36.44/5.71 | v0))))))
% 36.44/5.71 |
% 36.44/5.71 | GROUND_INST: instantiating (9) with all_46_2, all_39_0, all_70_4, all_46_1,
% 36.44/5.71 | all_46_0, simplifying with (22), (23), (24), (32), (33), (35),
% 36.44/5.71 | (36), (38), (69) gives:
% 36.77/5.72 | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 36.77/5.72 | ? [v5: $i] : (relation_dom(all_46_1) = v0 & $i(v4) & $i(v1) & $i(v0) &
% 36.77/5.72 | ( ~ (all_46_0 = all_39_0) | ( ! [v6: $i] : ! [v7: $i] : ( ~
% 36.77/5.72 | (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v7, all_46_2) |
% 36.77/5.72 | ~ in(v6, v0) | in(v6, all_70_4)) & ! [v6: $i] : ! [v7: $i]
% 36.77/5.72 | : ( ~ (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v6,
% 36.77/5.72 | all_70_4) | in(v7, all_46_2)) & ! [v6: $i] : ! [v7: $i] :
% 36.77/5.72 | ( ~ (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v6, all_70_4)
% 36.77/5.72 | | in(v6, v0)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 36.77/5.72 | (apply(all_39_0, v6) = v7) | ~ $i(v6) | ~ in(v6, all_70_4) |
% 36.77/5.72 | (apply(all_46_1, v6) = v7 & $i(v7))))) & (all_46_0 = all_39_0
% 36.77/5.72 | | ( ~ (v3 = v2) & apply(all_46_1, v1) = v3 & apply(all_39_0, v1) =
% 36.77/5.72 | v2 & $i(v3) & $i(v2) & in(v1, all_70_4)) | (apply(all_46_1, v4)
% 36.77/5.72 | = v5 & $i(v5) & ( ~ in(v5, all_46_2) | ~ in(v4, v0) | ~ in(v4,
% 36.77/5.72 | all_70_4)) & (in(v4, all_70_4) | (in(v5, all_46_2) & in(v4,
% 36.77/5.72 | v0))))))
% 36.77/5.72 |
% 36.77/5.72 | GROUND_INST: instantiating (9) with all_46_2, all_46_1, all_68_4, all_46_1,
% 36.77/5.72 | all_46_0, simplifying with (32), (33), (35), (36), (38), (67)
% 36.77/5.72 | gives:
% 36.77/5.72 | (94) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 36.77/5.72 | ? [v5: $i] : (relation_dom(all_46_1) = v0 & $i(v4) & $i(v1) & $i(v0) &
% 36.77/5.72 | ( ~ (all_46_0 = all_46_1) | ( ! [v6: $i] : ! [v7: $i] : ( ~
% 36.77/5.72 | (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v7, all_46_2) |
% 36.77/5.72 | ~ in(v6, v0) | in(v6, all_68_4)) & ! [v6: $i] : ! [v7: $i]
% 36.77/5.72 | : ( ~ (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v6,
% 36.77/5.72 | all_68_4) | $i(v7)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 36.77/5.72 | (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v6, all_68_4) |
% 36.77/5.72 | in(v7, all_46_2)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 36.77/5.72 | (apply(all_46_1, v6) = v7) | ~ $i(v6) | ~ in(v6, all_68_4) |
% 36.77/5.72 | in(v6, v0)))) & (all_46_0 = all_46_1 | ( ~ (v3 = v2) &
% 36.77/5.72 | apply(all_46_1, v1) = v3 & apply(all_46_1, v1) = v2 & $i(v3) &
% 36.77/5.72 | $i(v2) & in(v1, all_68_4)) | (apply(all_46_1, v4) = v5 & $i(v5)
% 36.77/5.72 | & ( ~ in(v5, all_46_2) | ~ in(v4, v0) | ~ in(v4, all_68_4)) &
% 36.77/5.72 | (in(v4, all_68_4) | (in(v5, all_46_2) & in(v4, v0))))))
% 36.77/5.72 |
% 36.77/5.72 | DELTA: instantiating (90) with fresh symbols all_101_0, all_101_1, all_101_2,
% 36.77/5.72 | all_101_3, all_101_4 gives:
% 36.77/5.72 | (95) relation_dom(all_46_0) = all_101_4 & $i(all_101_2) & $i(all_101_3) &
% 36.77/5.72 | $i(all_101_4) & ( ~ one_to_one(all_46_0) | ! [v0: $i] : ! [v1: $i] :
% 36.77/5.72 | (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ in(v1, all_101_4) | ~ in(v0,
% 36.77/5.72 | all_101_4) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 36.77/5.72 | apply(all_46_0, v1) = v3 & apply(all_46_0, v0) = v2 & $i(v3) &
% 36.77/5.72 | $i(v2)))) & (one_to_one(all_46_0) | (all_101_0 = all_101_1 & ~
% 36.77/5.72 | (all_101_2 = all_101_3) & apply(all_46_0, all_101_2) = all_101_1 &
% 36.77/5.72 | apply(all_46_0, all_101_3) = all_101_1 & $i(all_101_1) &
% 36.77/5.72 | in(all_101_2, all_101_4) & in(all_101_3, all_101_4)))
% 36.77/5.72 |
% 36.77/5.72 | ALPHA: (95) implies:
% 36.77/5.72 | (96) $i(all_101_3)
% 36.77/5.72 | (97) $i(all_101_2)
% 36.77/5.72 | (98) relation_dom(all_46_0) = all_101_4
% 36.77/5.72 | (99) one_to_one(all_46_0) | (all_101_0 = all_101_1 & ~ (all_101_2 =
% 36.77/5.72 | all_101_3) & apply(all_46_0, all_101_2) = all_101_1 &
% 36.77/5.72 | apply(all_46_0, all_101_3) = all_101_1 & $i(all_101_1) &
% 36.77/5.72 | in(all_101_2, all_101_4) & in(all_101_3, all_101_4))
% 36.77/5.72 |
% 36.77/5.72 | DELTA: instantiating (94) with fresh symbols all_103_0, all_103_1, all_103_2,
% 36.77/5.72 | all_103_3, all_103_4, all_103_5 gives:
% 36.77/5.72 | (100) relation_dom(all_46_1) = all_103_5 & $i(all_103_1) & $i(all_103_4) &
% 36.77/5.72 | $i(all_103_5) & ( ~ (all_46_0 = all_46_1) | ( ! [v0: $i] : ! [v1:
% 36.77/5.72 | $i] : ( ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~ in(v1,
% 36.77/5.72 | all_46_2) | ~ in(v0, all_103_5) | in(v0, all_68_4)) & !
% 36.77/5.72 | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_46_1, v0) = v1) | ~
% 36.77/5.72 | $i(v0) | ~ in(v0, all_68_4) | $i(v1)) & ! [v0: $i] : ! [v1:
% 36.77/5.72 | $i] : ( ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~ in(v0,
% 36.77/5.72 | all_68_4) | in(v1, all_46_2)) & ! [v0: $i] : ! [v1: $i] : (
% 36.77/5.72 | ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~ in(v0, all_68_4)
% 36.77/5.72 | | in(v0, all_103_5)))) & (all_46_0 = all_46_1 | ( ~ (all_103_2
% 36.77/5.72 | = all_103_3) & apply(all_46_1, all_103_4) = all_103_2 &
% 36.77/5.72 | apply(all_46_1, all_103_4) = all_103_3 & $i(all_103_2) &
% 36.77/5.72 | $i(all_103_3) & in(all_103_4, all_68_4)) | (apply(all_46_1,
% 36.77/5.72 | all_103_1) = all_103_0 & $i(all_103_0) & ( ~ in(all_103_0,
% 36.77/5.72 | all_46_2) | ~ in(all_103_1, all_103_5) | ~ in(all_103_1,
% 36.77/5.72 | all_68_4)) & (in(all_103_1, all_68_4) | (in(all_103_0,
% 36.77/5.72 | all_46_2) & in(all_103_1, all_103_5)))))
% 36.77/5.72 |
% 36.77/5.72 | ALPHA: (100) implies:
% 36.77/5.72 | (101) relation_dom(all_46_1) = all_103_5
% 36.77/5.72 |
% 36.77/5.72 | DELTA: instantiating (93) with fresh symbols all_105_0, all_105_1, all_105_2,
% 36.77/5.72 | all_105_3, all_105_4, all_105_5 gives:
% 36.77/5.73 | (102) relation_dom(all_46_1) = all_105_5 & $i(all_105_1) & $i(all_105_4) &
% 36.77/5.73 | $i(all_105_5) & ( ~ (all_46_0 = all_39_0) | ( ! [v0: $i] : ! [v1:
% 36.77/5.73 | $i] : ( ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~ in(v1,
% 36.77/5.73 | all_46_2) | ~ in(v0, all_105_5) | in(v0, all_70_4)) & !
% 36.77/5.73 | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_46_1, v0) = v1) | ~
% 36.77/5.73 | $i(v0) | ~ in(v0, all_70_4) | in(v1, all_46_2)) & ! [v0: $i]
% 36.77/5.73 | : ! [v1: $i] : ( ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~
% 36.77/5.73 | in(v0, all_70_4) | in(v0, all_105_5)) & ! [v0: $i] : ! [v1:
% 36.77/5.73 | $i] : ( ~ (apply(all_39_0, v0) = v1) | ~ $i(v0) | ~ in(v0,
% 36.77/5.73 | all_70_4) | (apply(all_46_1, v0) = v1 & $i(v1))))) &
% 36.77/5.73 | (all_46_0 = all_39_0 | ( ~ (all_105_2 = all_105_3) & apply(all_46_1,
% 36.77/5.73 | all_105_4) = all_105_2 & apply(all_39_0, all_105_4) = all_105_3
% 36.77/5.73 | & $i(all_105_2) & $i(all_105_3) & in(all_105_4, all_70_4)) |
% 36.77/5.73 | (apply(all_46_1, all_105_1) = all_105_0 & $i(all_105_0) & ( ~
% 36.77/5.73 | in(all_105_0, all_46_2) | ~ in(all_105_1, all_105_5) | ~
% 36.77/5.73 | in(all_105_1, all_70_4)) & (in(all_105_1, all_70_4) |
% 36.77/5.73 | (in(all_105_0, all_46_2) & in(all_105_1, all_105_5)))))
% 36.77/5.73 |
% 36.77/5.73 | ALPHA: (102) implies:
% 36.77/5.73 | (103) relation_dom(all_46_1) = all_105_5
% 36.77/5.73 |
% 36.77/5.73 | DELTA: instantiating (92) with fresh symbols all_107_0, all_107_1, all_107_2,
% 36.77/5.73 | all_107_3, all_107_4, all_107_5 gives:
% 36.77/5.73 | (104) relation_dom(all_46_1) = all_107_5 & $i(all_107_1) & $i(all_107_4) &
% 36.77/5.73 | $i(all_107_5) & ( ~ (all_46_0 = all_31_0) | ( ! [v0: $i] : ! [v1:
% 36.77/5.73 | $i] : ( ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~ in(v1,
% 36.77/5.73 | all_46_2) | ~ in(v0, all_107_5) | in(v0, all_74_4)) & !
% 36.77/5.73 | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_46_1, v0) = v1) | ~
% 36.77/5.73 | $i(v0) | ~ in(v0, all_74_4) | in(v1, all_46_2)) & ! [v0: $i]
% 36.77/5.73 | : ! [v1: $i] : ( ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~
% 36.77/5.73 | in(v0, all_74_4) | in(v0, all_107_5)) & ! [v0: $i] : ! [v1:
% 36.77/5.73 | $i] : ( ~ (apply(all_31_0, v0) = v1) | ~ $i(v0) | ~ in(v0,
% 36.77/5.73 | all_74_4) | (apply(all_46_1, v0) = v1 & $i(v1))))) &
% 36.77/5.73 | (all_46_0 = all_31_0 | ( ~ (all_107_2 = all_107_3) & apply(all_46_1,
% 36.77/5.73 | all_107_4) = all_107_2 & apply(all_31_0, all_107_4) = all_107_3
% 36.77/5.73 | & $i(all_107_2) & $i(all_107_3) & in(all_107_4, all_74_4)) |
% 36.77/5.73 | (apply(all_46_1, all_107_1) = all_107_0 & $i(all_107_0) & ( ~
% 36.77/5.73 | in(all_107_0, all_46_2) | ~ in(all_107_1, all_107_5) | ~
% 36.77/5.73 | in(all_107_1, all_74_4)) & (in(all_107_1, all_74_4) |
% 36.77/5.73 | (in(all_107_0, all_46_2) & in(all_107_1, all_107_5)))))
% 36.77/5.73 |
% 36.77/5.73 | ALPHA: (104) implies:
% 36.77/5.73 | (105) relation_dom(all_46_1) = all_107_5
% 36.77/5.73 |
% 36.77/5.73 | DELTA: instantiating (91) with fresh symbols all_109_0, all_109_1, all_109_2,
% 36.77/5.73 | all_109_3, all_109_4, all_109_5 gives:
% 36.77/5.73 | (106) relation_dom(all_46_1) = all_109_5 & $i(all_109_1) & $i(all_109_4) &
% 36.77/5.73 | $i(all_109_5) & ( ~ (all_46_0 = empty_set) | ( ! [v0: $i] : ! [v1:
% 36.77/5.73 | $i] : ( ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~ in(v1,
% 36.77/5.73 | all_46_2) | ~ in(v0, all_109_5) | in(v0, all_60_0)) & !
% 36.77/5.73 | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_46_1, v0) = v1) | ~
% 36.77/5.73 | $i(v0) | ~ in(v0, all_60_0) | in(v1, all_46_2)) & ! [v0: $i]
% 36.77/5.73 | : ! [v1: $i] : ( ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~
% 36.77/5.73 | in(v0, all_60_0) | in(v0, all_109_5)) & ! [v0: $i] : ! [v1:
% 36.77/5.73 | $i] : ( ~ (apply(empty_set, v0) = v1) | ~ $i(v0) | ~ in(v0,
% 36.77/5.73 | all_60_0) | (apply(all_46_1, v0) = v1 & $i(v1))))) &
% 36.77/5.73 | (all_46_0 = empty_set | ( ~ (all_109_2 = all_109_3) & apply(all_46_1,
% 36.77/5.73 | all_109_4) = all_109_2 & apply(empty_set, all_109_4) =
% 36.77/5.73 | all_109_3 & $i(all_109_2) & $i(all_109_3) & in(all_109_4,
% 36.77/5.73 | all_60_0)) | (apply(all_46_1, all_109_1) = all_109_0 &
% 36.77/5.73 | $i(all_109_0) & ( ~ in(all_109_0, all_46_2) | ~ in(all_109_1,
% 36.77/5.73 | all_109_5) | ~ in(all_109_1, all_60_0)) & (in(all_109_1,
% 36.77/5.73 | all_60_0) | (in(all_109_0, all_46_2) & in(all_109_1,
% 36.77/5.73 | all_109_5)))))
% 36.77/5.73 |
% 36.77/5.73 | ALPHA: (106) implies:
% 36.77/5.73 | (107) relation_dom(all_46_1) = all_109_5
% 36.77/5.73 |
% 36.77/5.73 | BETA: splitting (99) gives:
% 36.77/5.73 |
% 36.77/5.73 | Case 1:
% 36.77/5.73 | |
% 36.77/5.73 | | (108) one_to_one(all_46_0)
% 36.77/5.73 | |
% 36.77/5.73 | | PRED_UNIFY: (31), (108) imply:
% 36.77/5.73 | | (109) $false
% 36.77/5.73 | |
% 36.77/5.73 | | CLOSE: (109) is inconsistent.
% 36.77/5.73 | |
% 36.77/5.73 | Case 2:
% 36.77/5.73 | |
% 36.77/5.73 | | (110) all_101_0 = all_101_1 & ~ (all_101_2 = all_101_3) &
% 36.77/5.73 | | apply(all_46_0, all_101_2) = all_101_1 & apply(all_46_0, all_101_3)
% 36.77/5.73 | | = all_101_1 & $i(all_101_1) & in(all_101_2, all_101_4) &
% 36.77/5.73 | | in(all_101_3, all_101_4)
% 36.77/5.73 | |
% 36.77/5.73 | | ALPHA: (110) implies:
% 36.77/5.73 | | (111) ~ (all_101_2 = all_101_3)
% 36.77/5.73 | | (112) in(all_101_3, all_101_4)
% 36.77/5.73 | | (113) in(all_101_2, all_101_4)
% 36.77/5.73 | | (114) apply(all_46_0, all_101_3) = all_101_1
% 36.77/5.73 | | (115) apply(all_46_0, all_101_2) = all_101_1
% 36.77/5.73 | |
% 36.77/5.73 | | GROUND_INST: instantiating (10) with all_68_4, all_107_5, all_46_1,
% 36.77/5.73 | | simplifying with (67), (105) gives:
% 36.77/5.73 | | (116) all_107_5 = all_68_4
% 36.77/5.73 | |
% 36.77/5.73 | | GROUND_INST: instantiating (10) with all_105_5, all_107_5, all_46_1,
% 36.77/5.73 | | simplifying with (103), (105) gives:
% 36.77/5.73 | | (117) all_107_5 = all_105_5
% 36.77/5.73 | |
% 36.77/5.73 | | GROUND_INST: instantiating (10) with all_107_5, all_109_5, all_46_1,
% 36.77/5.73 | | simplifying with (105), (107) gives:
% 36.77/5.73 | | (118) all_109_5 = all_107_5
% 36.77/5.73 | |
% 36.77/5.73 | | GROUND_INST: instantiating (10) with all_103_5, all_109_5, all_46_1,
% 36.77/5.73 | | simplifying with (101), (107) gives:
% 36.77/5.73 | | (119) all_109_5 = all_103_5
% 36.77/5.73 | |
% 36.77/5.73 | | COMBINE_EQS: (118), (119) imply:
% 36.77/5.73 | | (120) all_107_5 = all_103_5
% 36.77/5.73 | |
% 36.77/5.73 | | SIMP: (120) implies:
% 36.77/5.73 | | (121) all_107_5 = all_103_5
% 36.77/5.73 | |
% 36.77/5.73 | | COMBINE_EQS: (116), (117) imply:
% 36.77/5.73 | | (122) all_105_5 = all_68_4
% 36.77/5.73 | |
% 36.77/5.73 | | COMBINE_EQS: (117), (121) imply:
% 36.77/5.73 | | (123) all_105_5 = all_103_5
% 36.77/5.73 | |
% 36.77/5.73 | | COMBINE_EQS: (122), (123) imply:
% 36.77/5.73 | | (124) all_103_5 = all_68_4
% 36.77/5.73 | |
% 36.77/5.73 | | GROUND_INST: instantiating (9) with all_46_2, all_46_0, all_101_4, all_46_1,
% 36.77/5.73 | | all_46_0, simplifying with (32), (33), (35), (36), (37), (38),
% 36.77/5.73 | | (52), (53), (98) gives:
% 36.77/5.74 | | (125) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_46_1) =
% 36.77/5.74 | | v0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 36.77/5.74 | | (apply(all_46_0, v3) = v4) | ~ $i(v3) | ~ in(v3, all_101_4) |
% 36.77/5.74 | | (apply(all_46_1, v3) = v4 & $i(v4))) & ! [v3: $i] : ! [v4:
% 36.77/5.74 | | $i] : ( ~ (apply(all_46_1, v3) = v4) | ~ $i(v3) | ~ in(v4,
% 36.77/5.74 | | all_46_2) | ~ in(v3, v0) | in(v3, all_101_4)) & ! [v3: $i]
% 36.77/5.74 | | : ! [v4: $i] : ( ~ (apply(all_46_1, v3) = v4) | ~ $i(v3) | ~
% 36.77/5.74 | | in(v3, all_101_4) | in(v4, all_46_2)) & ! [v3: $i] : ! [v4:
% 36.77/5.74 | | $i] : ( ~ (apply(all_46_1, v3) = v4) | ~ $i(v3) | ~ in(v3,
% 36.77/5.74 | | all_101_4) | in(v3, v0)))
% 36.77/5.74 | |
% 36.77/5.74 | | DELTA: instantiating (125) with fresh symbols all_127_0, all_127_1,
% 36.77/5.74 | | all_127_2 gives:
% 36.77/5.74 | | (126) relation_dom(all_46_1) = all_127_2 & $i(all_127_0) & $i(all_127_1)
% 36.77/5.74 | | & $i(all_127_2) & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_46_0,
% 36.77/5.74 | | v0) = v1) | ~ $i(v0) | ~ in(v0, all_101_4) |
% 36.77/5.74 | | (apply(all_46_1, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i]
% 36.77/5.74 | | : ( ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~ in(v1, all_46_2)
% 36.77/5.74 | | | ~ in(v0, all_127_2) | in(v0, all_101_4)) & ! [v0: $i] : !
% 36.77/5.74 | | [v1: $i] : ( ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~ in(v0,
% 36.77/5.74 | | all_101_4) | in(v1, all_46_2)) & ! [v0: $i] : ! [v1: $i] : (
% 36.77/5.74 | | ~ (apply(all_46_1, v0) = v1) | ~ $i(v0) | ~ in(v0, all_101_4) |
% 36.77/5.74 | | in(v0, all_127_2))
% 36.77/5.74 | |
% 36.77/5.74 | | ALPHA: (126) implies:
% 36.77/5.74 | | (127) relation_dom(all_46_1) = all_127_2
% 36.77/5.74 | | (128) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_46_1, v0) = v1) | ~
% 36.77/5.74 | | $i(v0) | ~ in(v0, all_101_4) | in(v0, all_127_2))
% 36.77/5.74 | | (129) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_46_0, v0) = v1) | ~
% 36.77/5.74 | | $i(v0) | ~ in(v0, all_101_4) | (apply(all_46_1, v0) = v1 &
% 36.77/5.74 | | $i(v1)))
% 36.77/5.74 | |
% 36.77/5.74 | | GROUND_INST: instantiating (129) with all_101_3, all_101_1, simplifying with
% 36.77/5.74 | | (96), (112), (114) gives:
% 36.77/5.74 | | (130) apply(all_46_1, all_101_3) = all_101_1 & $i(all_101_1)
% 36.77/5.74 | |
% 36.77/5.74 | | ALPHA: (130) implies:
% 36.77/5.74 | | (131) apply(all_46_1, all_101_3) = all_101_1
% 36.77/5.74 | |
% 36.77/5.74 | | GROUND_INST: instantiating (129) with all_101_2, all_101_1, simplifying with
% 36.77/5.74 | | (97), (113), (115) gives:
% 36.77/5.74 | | (132) apply(all_46_1, all_101_2) = all_101_1 & $i(all_101_1)
% 36.77/5.74 | |
% 36.77/5.74 | | ALPHA: (132) implies:
% 36.77/5.74 | | (133) apply(all_46_1, all_101_2) = all_101_1
% 36.77/5.74 | |
% 36.77/5.74 | | GROUND_INST: instantiating (10) with all_68_4, all_127_2, all_46_1,
% 36.77/5.74 | | simplifying with (67), (127) gives:
% 36.77/5.74 | | (134) all_127_2 = all_68_4
% 36.77/5.74 | |
% 36.77/5.74 | | GROUND_INST: instantiating (128) with all_101_3, all_101_1, simplifying with
% 36.77/5.74 | | (96), (112), (131) gives:
% 36.77/5.74 | | (135) in(all_101_3, all_127_2)
% 36.77/5.74 | |
% 36.77/5.74 | | GROUND_INST: instantiating (128) with all_101_2, all_101_1, simplifying with
% 36.77/5.74 | | (97), (113), (133) gives:
% 36.77/5.74 | | (136) in(all_101_2, all_127_2)
% 36.77/5.74 | |
% 36.77/5.74 | | REDUCE: (134), (136) imply:
% 36.77/5.74 | | (137) in(all_101_2, all_68_4)
% 36.77/5.74 | |
% 36.77/5.74 | | REDUCE: (134), (135) imply:
% 36.77/5.74 | | (138) in(all_101_3, all_68_4)
% 36.77/5.74 | |
% 36.77/5.74 | | GROUND_INST: instantiating (2) with all_46_1, all_68_4, all_101_3,
% 36.77/5.74 | | all_101_2, all_101_1, simplifying with (32), (33), (34), (36),
% 36.77/5.74 | | (67), (96), (97), (131), (133), (137), (138) gives:
% 36.77/5.74 | | (139) all_101_2 = all_101_3
% 36.77/5.74 | |
% 36.77/5.74 | | REDUCE: (111), (139) imply:
% 36.77/5.74 | | (140) $false
% 36.77/5.74 | |
% 36.77/5.74 | | CLOSE: (140) is inconsistent.
% 36.77/5.74 | |
% 36.77/5.74 | End of split
% 36.77/5.74 |
% 36.77/5.74 End of proof
% 36.77/5.74 % SZS output end Proof for theBenchmark
% 36.77/5.74
% 36.77/5.74 5124ms
%------------------------------------------------------------------------------