TSTP Solution File: SEU226+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU226+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n017.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 17:43:28 EDT 2023
% Result : Theorem 10.80s 2.30s
% Output : Proof 15.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU226+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 23:01:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.62 Loading /export/starexec/sandbox/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 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 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 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
% 2.55/1.07 Prover 1: Preprocessing ...
% 2.55/1.07 Prover 4: Preprocessing ...
% 2.87/1.11 Prover 2: Preprocessing ...
% 2.87/1.11 Prover 5: Preprocessing ...
% 2.87/1.11 Prover 6: Preprocessing ...
% 2.87/1.11 Prover 0: Preprocessing ...
% 2.87/1.11 Prover 3: Preprocessing ...
% 6.54/1.61 Prover 1: Warning: ignoring some quantifiers
% 6.54/1.66 Prover 5: Proving ...
% 6.54/1.67 Prover 1: Constructing countermodel ...
% 6.54/1.70 Prover 6: Proving ...
% 7.15/1.74 Prover 3: Warning: ignoring some quantifiers
% 7.15/1.76 Prover 3: Constructing countermodel ...
% 7.76/1.80 Prover 2: Proving ...
% 8.72/1.93 Prover 4: Warning: ignoring some quantifiers
% 8.72/2.02 Prover 4: Constructing countermodel ...
% 8.72/2.03 Prover 0: Proving ...
% 10.80/2.30 Prover 3: proved (1658ms)
% 10.80/2.30
% 10.80/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.80/2.30
% 10.80/2.30 Prover 5: stopped
% 10.80/2.30 Prover 2: stopped
% 11.54/2.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.54/2.31 Prover 0: stopped
% 11.54/2.31 Prover 6: stopped
% 11.54/2.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.54/2.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.54/2.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.54/2.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.54/2.35 Prover 7: Preprocessing ...
% 11.54/2.36 Prover 10: Preprocessing ...
% 11.54/2.37 Prover 11: Preprocessing ...
% 11.54/2.39 Prover 13: Preprocessing ...
% 12.24/2.40 Prover 8: Preprocessing ...
% 12.24/2.43 Prover 7: Warning: ignoring some quantifiers
% 12.24/2.44 Prover 7: Constructing countermodel ...
% 12.24/2.47 Prover 10: Warning: ignoring some quantifiers
% 12.24/2.48 Prover 13: Warning: ignoring some quantifiers
% 12.24/2.49 Prover 8: Warning: ignoring some quantifiers
% 12.97/2.49 Prover 13: Constructing countermodel ...
% 12.97/2.50 Prover 10: Constructing countermodel ...
% 12.97/2.50 Prover 8: Constructing countermodel ...
% 13.82/2.61 Prover 10: gave up
% 13.82/2.63 Prover 7: gave up
% 13.82/2.63 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.82/2.63 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 13.82/2.68 Prover 16: Preprocessing ...
% 13.82/2.69 Prover 19: Preprocessing ...
% 14.43/2.70 Prover 1: Found proof (size 62)
% 14.43/2.70 Prover 1: proved (2069ms)
% 14.43/2.71 Prover 4: stopped
% 14.43/2.71 Prover 8: stopped
% 14.43/2.71 Prover 13: stopped
% 14.43/2.72 Prover 16: stopped
% 14.43/2.75 Prover 11: Warning: ignoring some quantifiers
% 14.43/2.76 Prover 11: Constructing countermodel ...
% 14.43/2.78 Prover 11: stopped
% 15.00/2.80 Prover 19: Warning: ignoring some quantifiers
% 15.00/2.81 Prover 19: Constructing countermodel ...
% 15.00/2.82 Prover 19: stopped
% 15.00/2.82
% 15.00/2.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.00/2.82
% 15.00/2.83 % SZS output start Proof for theBenchmark
% 15.00/2.84 Assumptions after simplification:
% 15.00/2.84 ---------------------------------
% 15.00/2.84
% 15.00/2.84 (d12_funct_1)
% 15.00/2.87 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 15.00/2.87 : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ?
% 15.00/2.87 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~
% 15.00/2.87 (relation_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i]
% 15.00/2.87 : ? [v7: any] : (in(v6, v3) = v7 & $i(v6) & ( ~ (v7 = 0) | ! [v8:
% 15.00/2.87 $i] : ( ~ (in(v8, v2) = 0) | ~ $i(v8) | ? [v9: any] : ?
% 15.00/2.87 [v10: $i] : (apply(v0, v8) = v10 & in(v8, v4) = v9 & $i(v10) &
% 15.00/2.87 ( ~ (v10 = v6) | ~ (v9 = 0))))) & (v7 = 0 | ? [v8: $i] :
% 15.00/2.87 (apply(v0, v8) = v6 & in(v8, v4) = 0 & in(v8, v2) = 0 &
% 15.00/2.87 $i(v8))))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 15.00/2.87 (relation_image(v0, v3) = v4) | ~ $i(v4) | ~ $i(v3) | ( ! [v5: $i]
% 15.00/2.87 : ! [v6: int] : (v6 = 0 | ~ (in(v5, v4) = v6) | ~ $i(v5) | !
% 15.00/2.87 [v7: $i] : ( ~ (in(v7, v2) = 0) | ~ $i(v7) | ? [v8: any] : ?
% 15.00/2.87 [v9: $i] : (apply(v0, v7) = v9 & in(v7, v3) = v8 & $i(v9) & (
% 15.00/2.87 ~ (v9 = v5) | ~ (v8 = 0))))) & ! [v5: $i] : ( ~ (in(v5,
% 15.00/2.87 v4) = 0) | ~ $i(v5) | ? [v6: $i] : (apply(v0, v6) = v5 &
% 15.00/2.87 in(v6, v3) = 0 & in(v6, v2) = 0 & $i(v6)))))))))
% 15.00/2.87
% 15.00/2.87 (d13_funct_1)
% 15.00/2.87 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 15.00/2.87 : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ?
% 15.00/2.87 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~
% 15.00/2.87 (relation_inverse_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ?
% 15.00/2.87 [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any]
% 15.00/2.87 : (apply(v0, v6) = v9 & in(v9, v4) = v10 & in(v6, v3) = v7 & in(v6,
% 15.00/2.87 v2) = v8 & $i(v9) & $i(v6) & ( ~ (v10 = 0) | ~ (v8 = 0) | ~
% 15.00/2.87 (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = 0)))) & ! [v3: $i] : !
% 15.00/2.87 [v4: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ $i(v4) | ~
% 15.00/2.87 $i(v3) | ( ! [v5: $i] : ! [v6: $i] : ! [v7: any] : ( ~ (apply(v0,
% 15.00/2.87 v5) = v6) | ~ (in(v6, v3) = v7) | ~ $i(v5) | ? [v8: any]
% 15.00/2.87 : ? [v9: any] : (in(v5, v4) = v8 & in(v5, v2) = v9 & ( ~ (v8 =
% 15.00/2.87 0) | (v9 = 0 & v7 = 0)))) & ! [v5: $i] : ! [v6: $i] : (
% 15.00/2.87 ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = 0) | ~ $i(v5) | ?
% 15.00/2.87 [v7: any] : ? [v8: any] : (in(v5, v4) = v8 & in(v5, v2) = v7 &
% 15.00/2.87 ( ~ (v7 = 0) | v8 = 0)))))))))
% 15.00/2.87
% 15.00/2.87 (d3_tarski)
% 15.00/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 15.00/2.88 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 15.00/2.88 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 15.00/2.88 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 15.00/2.88 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 15.00/2.88
% 15.00/2.88 (rc3_funct_1)
% 15.00/2.88 ? [v0: $i] : (one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0 &
% 15.00/2.88 $i(v0))
% 15.00/2.88
% 15.00/2.88 (t145_funct_1)
% 15.00/2.88 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 15.00/2.88 = 0) & subset(v3, v0) = v4 & relation_inverse_image(v1, v0) = v2 &
% 15.00/2.88 relation_image(v1, v2) = v3 & relation(v1) = 0 & function(v1) = 0 & $i(v3) &
% 15.00/2.88 $i(v2) & $i(v1) & $i(v0))
% 15.00/2.88
% 15.00/2.88 (function-axioms)
% 15.00/2.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 15.00/2.88 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 15.00/2.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 15.00/2.88 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 15.00/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.00/2.88 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) =
% 15.00/2.88 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 15.00/2.88 ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & !
% 15.00/2.88 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3,
% 15.00/2.88 v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 15.00/2.88 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3,
% 15.00/2.88 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 15.00/2.88 $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0:
% 15.00/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 15.00/2.88 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) =
% 15.00/2.88 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.00/2.88 (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0:
% 15.00/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 15.00/2.88 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0:
% 15.00/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 15.00/2.88 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 15.00/2.88 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1)
% 15.00/2.88 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.00/2.88 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 15.00/2.88 (empty(v2) = v0))
% 15.00/2.88
% 15.00/2.88 Further assumptions not needed in the proof:
% 15.00/2.88 --------------------------------------------
% 15.00/2.88 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1,
% 15.00/2.88 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1,
% 15.00/2.88 fc5_relat_1, fc7_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0,
% 15.00/2.88 rc2_funct_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_relat_1,
% 15.00/2.88 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 15.00/2.88 t6_boole, t7_boole, t8_boole
% 15.00/2.88
% 15.00/2.88 Those formulas are unsatisfiable:
% 15.00/2.88 ---------------------------------
% 15.00/2.88
% 15.00/2.88 Begin of proof
% 15.00/2.88 |
% 15.00/2.88 | ALPHA: (d3_tarski) implies:
% 15.00/2.88 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 15.00/2.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 15.00/2.88 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 15.00/2.88 |
% 15.00/2.88 | ALPHA: (function-axioms) implies:
% 15.00/2.89 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 15.00/2.89 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 15.00/2.89 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 15.00/2.89 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 15.00/2.89 |
% 15.00/2.89 | DELTA: instantiating (rc3_funct_1) with fresh symbol all_39_0 gives:
% 15.00/2.89 | (4) one_to_one(all_39_0) = 0 & relation(all_39_0) = 0 & function(all_39_0)
% 15.00/2.89 | = 0 & $i(all_39_0)
% 15.00/2.89 |
% 15.00/2.89 | ALPHA: (4) implies:
% 15.00/2.89 | (5) $i(all_39_0)
% 15.00/2.89 | (6) function(all_39_0) = 0
% 15.00/2.89 | (7) relation(all_39_0) = 0
% 15.00/2.89 |
% 15.00/2.89 | DELTA: instantiating (t145_funct_1) with fresh symbols all_43_0, all_43_1,
% 15.00/2.89 | all_43_2, all_43_3, all_43_4 gives:
% 15.00/2.89 | (8) ~ (all_43_0 = 0) & subset(all_43_1, all_43_4) = all_43_0 &
% 15.00/2.89 | relation_inverse_image(all_43_3, all_43_4) = all_43_2 &
% 15.00/2.89 | relation_image(all_43_3, all_43_2) = all_43_1 & relation(all_43_3) = 0
% 15.00/2.89 | & function(all_43_3) = 0 & $i(all_43_1) & $i(all_43_2) & $i(all_43_3) &
% 15.00/2.89 | $i(all_43_4)
% 15.00/2.89 |
% 15.00/2.89 | ALPHA: (8) implies:
% 15.00/2.89 | (9) ~ (all_43_0 = 0)
% 15.00/2.89 | (10) $i(all_43_4)
% 15.00/2.89 | (11) $i(all_43_3)
% 15.00/2.89 | (12) $i(all_43_2)
% 15.00/2.89 | (13) $i(all_43_1)
% 15.00/2.89 | (14) function(all_43_3) = 0
% 15.00/2.89 | (15) relation(all_43_3) = 0
% 15.00/2.89 | (16) relation_image(all_43_3, all_43_2) = all_43_1
% 15.00/2.89 | (17) relation_inverse_image(all_43_3, all_43_4) = all_43_2
% 15.00/2.89 | (18) subset(all_43_1, all_43_4) = all_43_0
% 15.00/2.89 |
% 15.00/2.89 | GROUND_INST: instantiating (d13_funct_1) with all_39_0, simplifying with (5),
% 15.00/2.89 | (6) gives:
% 15.00/2.89 | (19) ? [v0: any] : ? [v1: $i] : (relation_dom(all_39_0) = v1 &
% 15.00/2.89 | relation(all_39_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 15.00/2.89 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 15.00/2.89 | (relation_inverse_image(all_39_0, v3) = v4) | ~ $i(v3) | ~
% 15.00/2.89 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8:
% 15.00/2.89 | $i] : ? [v9: any] : (apply(all_39_0, v5) = v8 & in(v8, v3)
% 15.00/2.89 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) &
% 15.00/2.89 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 =
% 15.00/2.89 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 15.00/2.89 | (relation_inverse_image(all_39_0, v2) = v3) | ~ $i(v3) | ~
% 15.00/2.89 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 15.00/2.89 | (apply(all_39_0, v4) = v5) | ~ (in(v5, v2) = v6) | ~
% 15.00/2.89 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 &
% 15.00/2.89 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) &
% 15.00/2.89 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(all_39_0, v4) = v5) |
% 15.00/2.89 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 15.00/2.89 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0)
% 15.00/2.89 | | v7 = 0))))))))
% 15.00/2.89 |
% 15.00/2.89 | GROUND_INST: instantiating (d12_funct_1) with all_39_0, simplifying with (5),
% 15.00/2.89 | (6) gives:
% 15.00/2.90 | (20) ? [v0: any] : ? [v1: $i] : (relation_dom(all_39_0) = v1 &
% 15.00/2.90 | relation(all_39_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 15.00/2.90 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (relation_image(all_39_0,
% 15.00/2.90 | v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? [v6:
% 15.00/2.90 | any] : (in(v5, v2) = v6 & $i(v5) & ( ~ (v6 = 0) | ! [v7:
% 15.00/2.90 | $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7) | ? [v8: any] :
% 15.00/2.90 | ? [v9: $i] : (apply(all_39_0, v7) = v9 & in(v7, v3) = v8
% 15.00/2.90 | & $i(v9) & ( ~ (v9 = v5) | ~ (v8 = 0))))) & (v6 = 0 |
% 15.00/2.90 | ? [v7: $i] : (apply(all_39_0, v7) = v5 & in(v7, v3) = 0 &
% 15.00/2.90 | in(v7, v1) = 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i]
% 15.00/2.90 | : ( ~ (relation_image(all_39_0, v2) = v3) | ~ $i(v3) | ~
% 15.00/2.90 | $i(v2) | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4,
% 15.00/2.90 | v3) = v5) | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1)
% 15.00/2.90 | = 0) | ~ $i(v6) | ? [v7: any] : ? [v8: $i] :
% 15.00/2.90 | (apply(all_39_0, v6) = v8 & in(v6, v2) = v7 & $i(v8) & (
% 15.00/2.90 | ~ (v8 = v4) | ~ (v7 = 0))))) & ! [v4: $i] : ( ~
% 15.00/2.90 | (in(v4, v3) = 0) | ~ $i(v4) | ? [v5: $i] :
% 15.00/2.90 | (apply(all_39_0, v5) = v4 & in(v5, v2) = 0 & in(v5, v1) =
% 15.00/2.90 | 0 & $i(v5))))))))
% 15.00/2.90 |
% 15.00/2.90 | GROUND_INST: instantiating (d13_funct_1) with all_43_3, simplifying with (11),
% 15.00/2.90 | (14) gives:
% 15.00/2.90 | (21) ? [v0: any] : ? [v1: $i] : (relation_dom(all_43_3) = v1 &
% 15.00/2.90 | relation(all_43_3) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 15.00/2.90 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 15.00/2.90 | (relation_inverse_image(all_43_3, v3) = v4) | ~ $i(v3) | ~
% 15.00/2.90 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8:
% 15.00/2.90 | $i] : ? [v9: any] : (apply(all_43_3, v5) = v8 & in(v8, v3)
% 15.00/2.90 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) &
% 15.00/2.90 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 =
% 15.00/2.90 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 15.00/2.90 | (relation_inverse_image(all_43_3, v2) = v3) | ~ $i(v3) | ~
% 15.00/2.90 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 15.00/2.90 | (apply(all_43_3, v4) = v5) | ~ (in(v5, v2) = v6) | ~
% 15.00/2.90 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 &
% 15.00/2.90 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) &
% 15.00/2.90 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(all_43_3, v4) = v5) |
% 15.00/2.90 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 15.00/2.90 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0)
% 15.00/2.90 | | v7 = 0))))))))
% 15.00/2.90 |
% 15.00/2.90 | GROUND_INST: instantiating (d12_funct_1) with all_43_3, simplifying with (11),
% 15.00/2.90 | (14) gives:
% 15.00/2.90 | (22) ? [v0: any] : ? [v1: $i] : (relation_dom(all_43_3) = v1 &
% 15.00/2.90 | relation(all_43_3) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 15.00/2.90 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (relation_image(all_43_3,
% 15.00/2.90 | v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? [v6:
% 15.00/2.90 | any] : (in(v5, v2) = v6 & $i(v5) & ( ~ (v6 = 0) | ! [v7:
% 15.00/2.90 | $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7) | ? [v8: any] :
% 15.00/2.90 | ? [v9: $i] : (apply(all_43_3, v7) = v9 & in(v7, v3) = v8
% 15.00/2.90 | & $i(v9) & ( ~ (v9 = v5) | ~ (v8 = 0))))) & (v6 = 0 |
% 15.00/2.90 | ? [v7: $i] : (apply(all_43_3, v7) = v5 & in(v7, v3) = 0 &
% 15.00/2.90 | in(v7, v1) = 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i]
% 15.00/2.90 | : ( ~ (relation_image(all_43_3, v2) = v3) | ~ $i(v3) | ~
% 15.00/2.90 | $i(v2) | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4,
% 15.00/2.90 | v3) = v5) | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1)
% 15.00/2.90 | = 0) | ~ $i(v6) | ? [v7: any] : ? [v8: $i] :
% 15.00/2.90 | (apply(all_43_3, v6) = v8 & in(v6, v2) = v7 & $i(v8) & (
% 15.00/2.90 | ~ (v8 = v4) | ~ (v7 = 0))))) & ! [v4: $i] : ( ~
% 15.00/2.91 | (in(v4, v3) = 0) | ~ $i(v4) | ? [v5: $i] :
% 15.00/2.91 | (apply(all_43_3, v5) = v4 & in(v5, v2) = 0 & in(v5, v1) =
% 15.00/2.91 | 0 & $i(v5))))))))
% 15.00/2.91 |
% 15.00/2.91 | GROUND_INST: instantiating (1) with all_43_1, all_43_4, all_43_0, simplifying
% 15.00/2.91 | with (10), (13), (18) gives:
% 15.00/2.91 | (23) all_43_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 15.00/2.91 | all_43_1) = 0 & in(v0, all_43_4) = v1 & $i(v0))
% 15.00/2.91 |
% 15.00/2.91 | DELTA: instantiating (21) with fresh symbols all_53_0, all_53_1 gives:
% 15.00/2.91 | (24) relation_dom(all_43_3) = all_53_0 & relation(all_43_3) = all_53_1 &
% 15.00/2.91 | $i(all_53_0) & ( ~ (all_53_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : !
% 15.00/2.91 | [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_43_3, v1) =
% 15.00/2.91 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ?
% 15.00/2.91 | [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(all_43_3, v3) =
% 15.00/2.91 | v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_53_0) = v5
% 15.00/2.91 | & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0))
% 15.00/2.91 | & (v4 = 0 | (v7 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] :
% 15.00/2.91 | ( ~ (relation_inverse_image(all_43_3, v0) = v1) | ~ $i(v1) | ~
% 15.00/2.91 | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 15.00/2.91 | (apply(all_43_3, v2) = v3) | ~ (in(v3, v0) = v4) | ~
% 15.00/2.91 | $i(v2) | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 &
% 15.00/2.91 | in(v2, all_53_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 15.00/2.91 | 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 15.00/2.91 | (apply(all_43_3, v2) = v3) | ~ (in(v3, v0) = 0) | ~ $i(v2)
% 15.00/2.91 | | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 & in(v2,
% 15.00/2.91 | all_53_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))))
% 15.00/2.91 |
% 15.00/2.91 | ALPHA: (24) implies:
% 15.00/2.91 | (25) relation(all_43_3) = all_53_1
% 15.00/2.91 | (26) ~ (all_53_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 =
% 15.00/2.91 | v0 | ~ (relation_inverse_image(all_43_3, v1) = v2) | ~ $i(v1) |
% 15.00/2.91 | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: $i]
% 15.00/2.91 | : ? [v7: any] : (apply(all_43_3, v3) = v6 & in(v6, v1) = v7 &
% 15.00/2.91 | in(v3, v0) = v4 & in(v3, all_53_0) = v5 & $i(v6) & $i(v3) & ( ~
% 15.00/2.91 | (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5
% 15.00/2.91 | = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 15.00/2.91 | (relation_inverse_image(all_43_3, v0) = v1) | ~ $i(v1) | ~
% 15.00/2.91 | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 15.00/2.91 | (apply(all_43_3, v2) = v3) | ~ (in(v3, v0) = v4) | ~ $i(v2)
% 15.00/2.91 | | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 & in(v2,
% 15.00/2.91 | all_53_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & !
% 15.00/2.91 | [v2: $i] : ! [v3: $i] : ( ~ (apply(all_43_3, v2) = v3) | ~
% 15.00/2.91 | (in(v3, v0) = 0) | ~ $i(v2) | ? [v4: any] : ? [v5: any] :
% 15.00/2.91 | (in(v2, v1) = v5 & in(v2, all_53_0) = v4 & ( ~ (v4 = 0) | v5 =
% 15.00/2.91 | 0))))))
% 15.00/2.91 |
% 15.00/2.91 | DELTA: instantiating (19) with fresh symbols all_57_0, all_57_1 gives:
% 15.00/2.92 | (27) relation_dom(all_39_0) = all_57_0 & relation(all_39_0) = all_57_1 &
% 15.00/2.92 | $i(all_57_0) & ( ~ (all_57_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : !
% 15.00/2.92 | [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_39_0, v1) =
% 15.00/2.92 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ?
% 15.00/2.92 | [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(all_39_0, v3) =
% 15.00/2.92 | v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_57_0) = v5
% 15.00/2.92 | & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0))
% 15.00/2.92 | & (v4 = 0 | (v7 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] :
% 15.00/2.92 | ( ~ (relation_inverse_image(all_39_0, v0) = v1) | ~ $i(v1) | ~
% 15.00/2.92 | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 15.00/2.92 | (apply(all_39_0, v2) = v3) | ~ (in(v3, v0) = v4) | ~
% 15.00/2.92 | $i(v2) | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 &
% 15.00/2.92 | in(v2, all_57_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 15.00/2.92 | 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 15.00/2.92 | (apply(all_39_0, v2) = v3) | ~ (in(v3, v0) = 0) | ~ $i(v2)
% 15.00/2.92 | | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 & in(v2,
% 15.00/2.92 | all_57_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))))
% 15.00/2.92 |
% 15.00/2.92 | ALPHA: (27) implies:
% 15.00/2.92 | (28) relation(all_39_0) = all_57_1
% 15.00/2.92 |
% 15.00/2.92 | DELTA: instantiating (22) with fresh symbols all_61_0, all_61_1 gives:
% 15.00/2.92 | (29) relation_dom(all_43_3) = all_61_0 & relation(all_43_3) = all_61_1 &
% 15.00/2.92 | $i(all_61_0) & ( ~ (all_61_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : !
% 15.00/2.92 | [v2: $i] : (v2 = v0 | ~ (relation_image(all_43_3, v1) = v2) | ~
% 15.00/2.92 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) =
% 15.00/2.92 | v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v5,
% 15.00/2.92 | all_61_0) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7:
% 15.00/2.92 | $i] : (apply(all_43_3, v5) = v7 & in(v5, v1) = v6 &
% 15.00/2.92 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ?
% 15.00/2.92 | [v5: $i] : (apply(all_43_3, v5) = v3 & in(v5, v1) = 0 &
% 15.00/2.92 | in(v5, all_61_0) = 0 & $i(v5))))) & ! [v0: $i] : ! [v1:
% 15.00/2.92 | $i] : ( ~ (relation_image(all_43_3, v0) = v1) | ~ $i(v1) | ~
% 15.00/2.92 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1)
% 15.00/2.92 | = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4, all_61_0) =
% 15.00/2.92 | 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] :
% 15.00/2.92 | (apply(all_43_3, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( ~
% 15.00/2.92 | (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] : ( ~
% 15.00/2.92 | (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 15.00/2.92 | (apply(all_43_3, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 15.00/2.92 | all_61_0) = 0 & $i(v3)))))))
% 15.00/2.92 |
% 15.00/2.92 | ALPHA: (29) implies:
% 15.00/2.92 | (30) relation(all_43_3) = all_61_1
% 15.00/2.92 | (31) ~ (all_61_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 =
% 15.00/2.92 | v0 | ~ (relation_image(all_43_3, v1) = v2) | ~ $i(v1) | ~
% 15.00/2.92 | $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) &
% 15.00/2.92 | ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v5, all_61_0) = 0) | ~
% 15.00/2.92 | $i(v5) | ? [v6: any] : ? [v7: $i] : (apply(all_43_3, v5) =
% 15.00/2.92 | v7 & in(v5, v1) = v6 & $i(v7) & ( ~ (v7 = v3) | ~ (v6 =
% 15.00/2.92 | 0))))) & (v4 = 0 | ? [v5: $i] : (apply(all_43_3, v5)
% 15.00/2.92 | = v3 & in(v5, v1) = 0 & in(v5, all_61_0) = 0 & $i(v5))))) &
% 15.00/2.92 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_image(all_43_3, v0) = v1) |
% 15.00/2.92 | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 15.00/2.92 | (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4,
% 15.00/2.92 | all_61_0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i]
% 15.00/2.92 | : (apply(all_43_3, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( ~
% 15.00/2.92 | (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] : ( ~ (in(v2,
% 15.00/2.92 | v1) = 0) | ~ $i(v2) | ? [v3: $i] : (apply(all_43_3, v3)
% 15.00/2.92 | = v2 & in(v3, v0) = 0 & in(v3, all_61_0) = 0 & $i(v3))))))
% 15.00/2.92 |
% 15.00/2.92 | DELTA: instantiating (20) with fresh symbols all_63_0, all_63_1 gives:
% 15.00/2.92 | (32) relation_dom(all_39_0) = all_63_0 & relation(all_39_0) = all_63_1 &
% 15.00/2.92 | $i(all_63_0) & ( ~ (all_63_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : !
% 15.00/2.92 | [v2: $i] : (v2 = v0 | ~ (relation_image(all_39_0, v1) = v2) | ~
% 15.00/2.92 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) =
% 15.00/2.92 | v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v5,
% 15.00/2.92 | all_63_0) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7:
% 15.00/2.92 | $i] : (apply(all_39_0, v5) = v7 & in(v5, v1) = v6 &
% 15.00/2.92 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ?
% 15.00/2.92 | [v5: $i] : (apply(all_39_0, v5) = v3 & in(v5, v1) = 0 &
% 15.00/2.92 | in(v5, all_63_0) = 0 & $i(v5))))) & ! [v0: $i] : ! [v1:
% 15.00/2.92 | $i] : ( ~ (relation_image(all_39_0, v0) = v1) | ~ $i(v1) | ~
% 15.00/2.92 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1)
% 15.00/2.92 | = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4, all_63_0) =
% 15.00/2.93 | 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] :
% 15.00/2.93 | (apply(all_39_0, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( ~
% 15.00/2.93 | (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] : ( ~
% 15.00/2.93 | (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 15.00/2.93 | (apply(all_39_0, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 15.00/2.93 | all_63_0) = 0 & $i(v3)))))))
% 15.00/2.93 |
% 15.00/2.93 | ALPHA: (32) implies:
% 15.00/2.93 | (33) relation(all_39_0) = all_63_1
% 15.00/2.93 | (34) ~ (all_63_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 =
% 15.00/2.93 | v0 | ~ (relation_image(all_39_0, v1) = v2) | ~ $i(v1) | ~
% 15.00/2.93 | $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) &
% 15.00/2.93 | ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v5, all_63_0) = 0) | ~
% 15.00/2.93 | $i(v5) | ? [v6: any] : ? [v7: $i] : (apply(all_39_0, v5) =
% 15.00/2.93 | v7 & in(v5, v1) = v6 & $i(v7) & ( ~ (v7 = v3) | ~ (v6 =
% 15.00/2.93 | 0))))) & (v4 = 0 | ? [v5: $i] : (apply(all_39_0, v5)
% 15.00/2.93 | = v3 & in(v5, v1) = 0 & in(v5, all_63_0) = 0 & $i(v5))))) &
% 15.00/2.93 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_image(all_39_0, v0) = v1) |
% 15.00/2.93 | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 15.00/2.93 | (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4,
% 15.00/2.93 | all_63_0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i]
% 15.00/2.93 | : (apply(all_39_0, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( ~
% 15.00/2.93 | (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] : ( ~ (in(v2,
% 15.00/2.93 | v1) = 0) | ~ $i(v2) | ? [v3: $i] : (apply(all_39_0, v3)
% 15.00/2.93 | = v2 & in(v3, v0) = 0 & in(v3, all_63_0) = 0 & $i(v3))))))
% 15.00/2.93 |
% 15.00/2.93 | BETA: splitting (23) gives:
% 15.00/2.93 |
% 15.00/2.93 | Case 1:
% 15.00/2.93 | |
% 15.00/2.93 | | (35) all_43_0 = 0
% 15.00/2.93 | |
% 15.00/2.93 | | REDUCE: (9), (35) imply:
% 15.00/2.93 | | (36) $false
% 15.00/2.93 | |
% 15.00/2.93 | | CLOSE: (36) is inconsistent.
% 15.00/2.93 | |
% 15.00/2.93 | Case 2:
% 15.00/2.93 | |
% 15.00/2.93 | | (37) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_43_1) = 0 &
% 15.00/2.93 | | in(v0, all_43_4) = v1 & $i(v0))
% 15.00/2.93 | |
% 15.00/2.93 | | DELTA: instantiating (37) with fresh symbols all_73_0, all_73_1 gives:
% 15.00/2.93 | | (38) ~ (all_73_0 = 0) & in(all_73_1, all_43_1) = 0 & in(all_73_1,
% 15.00/2.93 | | all_43_4) = all_73_0 & $i(all_73_1)
% 15.00/2.93 | |
% 15.00/2.93 | | ALPHA: (38) implies:
% 15.00/2.93 | | (39) ~ (all_73_0 = 0)
% 15.00/2.93 | | (40) $i(all_73_1)
% 15.00/2.93 | | (41) in(all_73_1, all_43_4) = all_73_0
% 15.00/2.93 | | (42) in(all_73_1, all_43_1) = 0
% 15.00/2.93 | |
% 15.00/2.93 | | GROUND_INST: instantiating (2) with 0, all_63_1, all_39_0, simplifying with
% 15.00/2.93 | | (7), (33) gives:
% 15.00/2.93 | | (43) all_63_1 = 0
% 15.00/2.93 | |
% 15.00/2.93 | | GROUND_INST: instantiating (2) with all_57_1, all_63_1, all_39_0,
% 15.00/2.93 | | simplifying with (28), (33) gives:
% 15.00/2.93 | | (44) all_63_1 = all_57_1
% 15.00/2.93 | |
% 15.00/2.93 | | GROUND_INST: instantiating (2) with 0, all_61_1, all_43_3, simplifying with
% 15.00/2.93 | | (15), (30) gives:
% 15.00/2.93 | | (45) all_61_1 = 0
% 15.00/2.93 | |
% 15.00/2.93 | | GROUND_INST: instantiating (2) with all_53_1, all_61_1, all_43_3,
% 15.00/2.93 | | simplifying with (25), (30) gives:
% 15.00/2.93 | | (46) all_61_1 = all_53_1
% 15.00/2.93 | |
% 15.00/2.93 | | COMBINE_EQS: (43), (44) imply:
% 15.00/2.93 | | (47) all_57_1 = 0
% 15.00/2.93 | |
% 15.00/2.93 | | COMBINE_EQS: (45), (46) imply:
% 15.00/2.93 | | (48) all_53_1 = 0
% 15.00/2.93 | |
% 15.00/2.93 | | BETA: splitting (26) gives:
% 15.00/2.93 | |
% 15.00/2.93 | | Case 1:
% 15.00/2.93 | | |
% 15.00/2.93 | | | (49) ~ (all_53_1 = 0)
% 15.00/2.93 | | |
% 15.00/2.93 | | | REDUCE: (48), (49) imply:
% 15.00/2.93 | | | (50) $false
% 15.00/2.93 | | |
% 15.00/2.93 | | | CLOSE: (50) is inconsistent.
% 15.00/2.93 | | |
% 15.00/2.93 | | Case 2:
% 15.00/2.93 | | |
% 15.00/2.94 | | | (51) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 15.00/2.94 | | | (relation_inverse_image(all_43_3, v1) = v2) | ~ $i(v1) | ~
% 15.00/2.94 | | | $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: $i]
% 15.00/2.94 | | | : ? [v7: any] : (apply(all_43_3, v3) = v6 & in(v6, v1) = v7 &
% 15.00/2.94 | | | in(v3, v0) = v4 & in(v3, all_53_0) = v5 & $i(v6) & $i(v3) & (
% 15.00/2.94 | | | ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0
% 15.00/2.94 | | | & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 15.00/2.94 | | | (relation_inverse_image(all_43_3, v0) = v1) | ~ $i(v1) | ~
% 15.00/2.94 | | | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 15.00/2.94 | | | (apply(all_43_3, v2) = v3) | ~ (in(v3, v0) = v4) | ~
% 15.00/2.94 | | | $i(v2) | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 &
% 15.00/2.94 | | | in(v2, all_53_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 15.00/2.94 | | | 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 15.00/2.94 | | | (apply(all_43_3, v2) = v3) | ~ (in(v3, v0) = 0) | ~ $i(v2)
% 15.00/2.94 | | | | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 & in(v2,
% 15.00/2.94 | | | all_53_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))
% 15.00/2.94 | | |
% 15.00/2.94 | | | ALPHA: (51) implies:
% 15.00/2.94 | | | (52) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse_image(all_43_3,
% 15.00/2.94 | | | v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3:
% 15.00/2.94 | | | $i] : ! [v4: any] : ( ~ (apply(all_43_3, v2) = v3) | ~
% 15.00/2.94 | | | (in(v3, v0) = v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any]
% 15.00/2.94 | | | : (in(v2, v1) = v5 & in(v2, all_53_0) = v6 & ( ~ (v5 = 0) |
% 15.00/2.94 | | | (v6 = 0 & v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 15.00/2.94 | | | (apply(all_43_3, v2) = v3) | ~ (in(v3, v0) = 0) | ~ $i(v2)
% 15.00/2.94 | | | | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 & in(v2,
% 15.00/2.94 | | | all_53_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))
% 15.00/2.94 | | |
% 15.00/2.94 | | | GROUND_INST: instantiating (52) with all_43_4, all_43_2, simplifying with
% 15.00/2.94 | | | (10), (12), (17) gives:
% 15.00/2.94 | | | (53) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_43_3,
% 15.00/2.94 | | | v0) = v1) | ~ (in(v1, all_43_4) = v2) | ~ $i(v0) | ? [v3:
% 15.00/2.94 | | | any] : ? [v4: any] : (in(v0, all_53_0) = v4 & in(v0,
% 15.00/2.94 | | | all_43_2) = v3 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & !
% 15.00/2.94 | | | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_43_3, v0) = v1) | ~
% 15.00/2.94 | | | (in(v1, all_43_4) = 0) | ~ $i(v0) | ? [v2: any] : ? [v3: any]
% 15.00/2.94 | | | : (in(v0, all_53_0) = v2 & in(v0, all_43_2) = v3 & ( ~ (v2 = 0)
% 15.00/2.94 | | | | v3 = 0)))
% 15.00/2.94 | | |
% 15.00/2.94 | | | ALPHA: (53) implies:
% 15.00/2.94 | | | (54) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_43_3,
% 15.00/2.94 | | | v0) = v1) | ~ (in(v1, all_43_4) = v2) | ~ $i(v0) | ? [v3:
% 15.00/2.94 | | | any] : ? [v4: any] : (in(v0, all_53_0) = v4 & in(v0,
% 15.00/2.94 | | | all_43_2) = v3 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0))))
% 15.00/2.94 | | |
% 15.00/2.94 | | | BETA: splitting (31) gives:
% 15.00/2.94 | | |
% 15.00/2.94 | | | Case 1:
% 15.00/2.94 | | | |
% 15.00/2.94 | | | | (55) ~ (all_61_1 = 0)
% 15.00/2.94 | | | |
% 15.00/2.94 | | | | REDUCE: (45), (55) imply:
% 15.00/2.94 | | | | (56) $false
% 15.00/2.94 | | | |
% 15.00/2.94 | | | | CLOSE: (56) is inconsistent.
% 15.00/2.94 | | | |
% 15.00/2.94 | | | Case 2:
% 15.00/2.94 | | | |
% 15.00/2.94 | | | | (57) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 15.00/2.94 | | | | (relation_image(all_43_3, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 15.00/2.94 | | | | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~
% 15.00/2.94 | | | | (v4 = 0) | ! [v5: $i] : ( ~ (in(v5, all_61_0) = 0) | ~
% 15.00/2.94 | | | | $i(v5) | ? [v6: any] : ? [v7: $i] : (apply(all_43_3,
% 15.00/2.94 | | | | v5) = v7 & in(v5, v1) = v6 & $i(v7) & ( ~ (v7 = v3)
% 15.00/2.94 | | | | | ~ (v6 = 0))))) & (v4 = 0 | ? [v5: $i] :
% 15.00/2.94 | | | | (apply(all_43_3, v5) = v3 & in(v5, v1) = 0 & in(v5,
% 15.00/2.94 | | | | all_61_0) = 0 & $i(v5))))) & ! [v0: $i] : ! [v1: $i]
% 15.00/2.94 | | | | : ( ~ (relation_image(all_43_3, v0) = v1) | ~ $i(v1) | ~
% 15.00/2.94 | | | | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2,
% 15.00/2.94 | | | | v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4,
% 15.00/2.94 | | | | all_61_0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 15.00/2.94 | | | | $i] : (apply(all_43_3, v4) = v6 & in(v4, v0) = v5 &
% 15.00/2.94 | | | | $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i]
% 15.00/2.94 | | | | : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 15.00/2.94 | | | | (apply(all_43_3, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 15.00/2.94 | | | | all_61_0) = 0 & $i(v3)))))
% 15.00/2.94 | | | |
% 15.00/2.94 | | | | ALPHA: (57) implies:
% 15.00/2.94 | | | | (58) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_image(all_43_3, v0) =
% 15.00/2.94 | | | | v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] :
% 15.00/2.94 | | | | (v3 = 0 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : (
% 15.00/2.94 | | | | ~ (in(v4, all_61_0) = 0) | ~ $i(v4) | ? [v5: any] : ?
% 15.00/2.94 | | | | [v6: $i] : (apply(all_43_3, v4) = v6 & in(v4, v0) = v5 &
% 15.00/2.94 | | | | $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i]
% 15.00/2.94 | | | | : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 15.00/2.94 | | | | (apply(all_43_3, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 15.00/2.94 | | | | all_61_0) = 0 & $i(v3)))))
% 15.00/2.94 | | | |
% 15.00/2.94 | | | | GROUND_INST: instantiating (58) with all_43_2, all_43_1, simplifying
% 15.00/2.94 | | | | with (12), (13), (16) gives:
% 15.00/2.94 | | | | (59) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_43_1) =
% 15.00/2.94 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, all_61_0) = 0) |
% 15.00/2.94 | | | | ~ $i(v2) | ? [v3: any] : ? [v4: $i] : (apply(all_43_3,
% 15.00/2.94 | | | | v2) = v4 & in(v2, all_43_2) = v3 & $i(v4) & ( ~ (v4 =
% 15.00/2.94 | | | | v0) | ~ (v3 = 0))))) & ! [v0: $i] : ( ~ (in(v0,
% 15.00/2.94 | | | | all_43_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 15.00/2.94 | | | | (apply(all_43_3, v1) = v0 & in(v1, all_61_0) = 0 & in(v1,
% 15.00/2.94 | | | | all_43_2) = 0 & $i(v1)))
% 15.00/2.94 | | | |
% 15.00/2.94 | | | | ALPHA: (59) implies:
% 15.00/2.94 | | | | (60) ! [v0: $i] : ( ~ (in(v0, all_43_1) = 0) | ~ $i(v0) | ? [v1:
% 15.00/2.94 | | | | $i] : (apply(all_43_3, v1) = v0 & in(v1, all_61_0) = 0 &
% 15.00/2.94 | | | | in(v1, all_43_2) = 0 & $i(v1)))
% 15.00/2.94 | | | |
% 15.00/2.94 | | | | BETA: splitting (34) gives:
% 15.00/2.94 | | | |
% 15.00/2.94 | | | | Case 1:
% 15.00/2.94 | | | | |
% 15.00/2.94 | | | | | (61) ~ (all_63_1 = 0)
% 15.00/2.94 | | | | |
% 15.00/2.94 | | | | | REDUCE: (43), (61) imply:
% 15.00/2.94 | | | | | (62) $false
% 15.00/2.94 | | | | |
% 15.00/2.94 | | | | | CLOSE: (62) is inconsistent.
% 15.00/2.94 | | | | |
% 15.00/2.94 | | | | Case 2:
% 15.00/2.94 | | | | |
% 15.00/2.94 | | | | |
% 15.00/2.94 | | | | | GROUND_INST: instantiating (60) with all_73_1, simplifying with (40),
% 15.00/2.94 | | | | | (42) gives:
% 15.00/2.94 | | | | | (63) ? [v0: $i] : (apply(all_43_3, v0) = all_73_1 & in(v0,
% 15.00/2.94 | | | | | all_61_0) = 0 & in(v0, all_43_2) = 0 & $i(v0))
% 15.00/2.94 | | | | |
% 15.00/2.94 | | | | | DELTA: instantiating (63) with fresh symbol all_139_0 gives:
% 15.00/2.95 | | | | | (64) apply(all_43_3, all_139_0) = all_73_1 & in(all_139_0,
% 15.00/2.95 | | | | | all_61_0) = 0 & in(all_139_0, all_43_2) = 0 & $i(all_139_0)
% 15.00/2.95 | | | | |
% 15.00/2.95 | | | | | ALPHA: (64) implies:
% 15.00/2.95 | | | | | (65) $i(all_139_0)
% 15.00/2.95 | | | | | (66) in(all_139_0, all_43_2) = 0
% 15.00/2.95 | | | | | (67) apply(all_43_3, all_139_0) = all_73_1
% 15.00/2.95 | | | | |
% 15.00/2.95 | | | | | GROUND_INST: instantiating (54) with all_139_0, all_73_1, all_73_0,
% 15.00/2.95 | | | | | simplifying with (41), (65), (67) gives:
% 15.00/2.95 | | | | | (68) ? [v0: any] : ? [v1: any] : (in(all_139_0, all_53_0) = v1 &
% 15.00/2.95 | | | | | in(all_139_0, all_43_2) = v0 & ( ~ (v0 = 0) | (v1 = 0 &
% 15.00/2.95 | | | | | all_73_0 = 0)))
% 15.00/2.95 | | | | |
% 15.00/2.95 | | | | | DELTA: instantiating (68) with fresh symbols all_185_0, all_185_1
% 15.00/2.95 | | | | | gives:
% 15.00/2.95 | | | | | (69) in(all_139_0, all_53_0) = all_185_0 & in(all_139_0, all_43_2)
% 15.00/2.95 | | | | | = all_185_1 & ( ~ (all_185_1 = 0) | (all_185_0 = 0 & all_73_0
% 15.00/2.95 | | | | | = 0))
% 15.00/2.95 | | | | |
% 15.00/2.95 | | | | | ALPHA: (69) implies:
% 15.00/2.95 | | | | | (70) in(all_139_0, all_43_2) = all_185_1
% 15.00/2.95 | | | | | (71) ~ (all_185_1 = 0) | (all_185_0 = 0 & all_73_0 = 0)
% 15.00/2.95 | | | | |
% 15.00/2.95 | | | | | BETA: splitting (71) gives:
% 15.00/2.95 | | | | |
% 15.00/2.95 | | | | | Case 1:
% 15.00/2.95 | | | | | |
% 15.00/2.95 | | | | | | (72) ~ (all_185_1 = 0)
% 15.00/2.95 | | | | | |
% 15.00/2.95 | | | | | | GROUND_INST: instantiating (3) with 0, all_185_1, all_43_2,
% 15.00/2.95 | | | | | | all_139_0, simplifying with (66), (70) gives:
% 15.00/2.95 | | | | | | (73) all_185_1 = 0
% 15.00/2.95 | | | | | |
% 15.00/2.95 | | | | | | REDUCE: (72), (73) imply:
% 15.00/2.95 | | | | | | (74) $false
% 15.00/2.95 | | | | | |
% 15.00/2.95 | | | | | | CLOSE: (74) is inconsistent.
% 15.00/2.95 | | | | | |
% 15.00/2.95 | | | | | Case 2:
% 15.00/2.95 | | | | | |
% 15.00/2.95 | | | | | | (75) all_185_0 = 0 & all_73_0 = 0
% 15.00/2.95 | | | | | |
% 15.00/2.95 | | | | | | ALPHA: (75) implies:
% 15.00/2.95 | | | | | | (76) all_73_0 = 0
% 15.00/2.95 | | | | | |
% 15.00/2.95 | | | | | | REDUCE: (39), (76) imply:
% 15.00/2.95 | | | | | | (77) $false
% 15.00/2.95 | | | | | |
% 15.00/2.95 | | | | | | CLOSE: (77) is inconsistent.
% 15.00/2.95 | | | | | |
% 15.00/2.95 | | | | | End of split
% 15.00/2.95 | | | | |
% 15.00/2.95 | | | | End of split
% 15.00/2.95 | | | |
% 15.00/2.95 | | | End of split
% 15.00/2.95 | | |
% 15.00/2.95 | | End of split
% 15.00/2.95 | |
% 15.00/2.95 | End of split
% 15.00/2.95 |
% 15.00/2.95 End of proof
% 15.00/2.95 % SZS output end Proof for theBenchmark
% 15.00/2.95
% 15.00/2.95 2333ms
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