TSTP Solution File: ITP322_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ITP322_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n018.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 04:11:44 EDT 2023
% Result : Theorem 47.90s 7.31s
% Output : Proof 79.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : ITP322_1 : TPTP v8.1.2. Released v8.0.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 10:16:16 EDT 2023
% 0.23/0.37 % CPUTime :
% 0.23/0.71 ________ _____
% 0.23/0.71 ___ __ \_________(_)________________________________
% 0.23/0.71 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.23/0.71 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.23/0.71 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.23/0.71
% 0.23/0.71 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.23/0.71 (2023-06-19)
% 0.23/0.71
% 0.23/0.71 (c) Philipp Rümmer, 2009-2023
% 0.23/0.71 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.23/0.71 Amanda Stjerna.
% 0.23/0.71 Free software under BSD-3-Clause.
% 0.23/0.71
% 0.23/0.71 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.23/0.71
% 0.23/0.71 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.23/0.72 Running up to 7 provers in parallel.
% 0.70/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.70/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.70/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.70/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.70/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.70/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.70/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 15.39/3.00 Prover 1: Preprocessing ...
% 16.18/3.04 Prover 4: Preprocessing ...
% 16.18/3.05 Prover 3: Preprocessing ...
% 16.18/3.05 Prover 6: Preprocessing ...
% 16.18/3.05 Prover 2: Preprocessing ...
% 16.18/3.05 Prover 5: Preprocessing ...
% 16.18/3.05 Prover 0: Preprocessing ...
% 37.31/5.86 Prover 3: Warning: ignoring some quantifiers
% 38.03/5.95 Prover 3: Constructing countermodel ...
% 38.42/6.01 Prover 1: Warning: ignoring some quantifiers
% 38.42/6.01 Prover 6: Proving ...
% 39.58/6.18 Prover 1: Constructing countermodel ...
% 47.90/7.31 Prover 3: proved (6575ms)
% 47.90/7.31
% 47.90/7.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.90/7.31
% 47.90/7.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 47.90/7.33 Prover 6: stopped
% 47.90/7.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 49.78/7.54 Prover 4: Warning: ignoring some quantifiers
% 51.23/7.70 Prover 0: Proving ...
% 51.23/7.70 Prover 0: stopped
% 51.23/7.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 51.23/7.80 Prover 4: Constructing countermodel ...
% 53.01/7.95 Prover 5: Proving ...
% 53.01/7.95 Prover 5: stopped
% 53.01/7.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 54.11/8.13 Prover 2: Proving ...
% 54.11/8.13 Prover 2: stopped
% 54.58/8.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 55.23/8.23 Prover 7: Preprocessing ...
% 55.23/8.24 Prover 8: Preprocessing ...
% 56.75/8.55 Prover 10: Preprocessing ...
% 60.25/8.91 Prover 13: Preprocessing ...
% 60.25/8.94 Prover 11: Preprocessing ...
% 65.87/9.65 Prover 10: Warning: ignoring some quantifiers
% 67.20/9.83 Prover 10: Constructing countermodel ...
% 67.91/9.92 Prover 8: Warning: ignoring some quantifiers
% 68.98/10.08 Prover 8: Constructing countermodel ...
% 69.60/10.12 Prover 7: Warning: ignoring some quantifiers
% 71.32/10.35 Prover 7: Constructing countermodel ...
% 76.11/11.02 Prover 13: Warning: ignoring some quantifiers
% 77.63/11.22 Prover 11: Warning: ignoring some quantifiers
% 77.63/11.24 Prover 1: Found proof (size 20)
% 77.63/11.24 Prover 1: proved (10515ms)
% 77.63/11.25 Prover 4: stopped
% 77.63/11.25 Prover 8: stopped
% 77.63/11.25 Prover 7: stopped
% 77.63/11.25 Prover 13: Constructing countermodel ...
% 77.63/11.26 Prover 10: stopped
% 78.92/11.37 Prover 11: Constructing countermodel ...
% 78.92/11.41 Prover 13: stopped
% 78.92/11.44 Prover 11: stopped
% 78.92/11.44
% 78.92/11.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 78.92/11.44
% 79.33/11.45 % SZS output start Proof for theBenchmark
% 79.33/11.47 Assumptions after simplification:
% 79.33/11.47 ---------------------------------
% 79.33/11.47
% 79.33/11.47 (axiom138)
% 79.46/11.50 B_set_b_set_b_set_fun_fun$(sup$) & ! [v0: B_set$] : ! [v1: B_set$] : ! [v2:
% 79.46/11.50 B_set_b_set_fun$] : ! [v3: B_set$] : ( ~ (fun_app$c(sup$, v0) = v2) | ~
% 79.46/11.50 (fun_app$b(v2, v1) = v3) | ~ B_set$(v1) | ~ B_set$(v0) | ? [v4:
% 79.46/11.50 B_set_b_set_fun$] : (fun_app$c(sup$, v1) = v4 & fun_app$b(v4, v0) = v3 &
% 79.46/11.50 B_set_b_set_fun$(v4) & B_set$(v3)))
% 79.46/11.50
% 79.46/11.50 (axiom144)
% 79.46/11.50 B_set_b_set_b_set_fun_fun$(sup$) & ! [v0: B_set$] : ! [v1: B_set$] : ! [v2:
% 79.46/11.50 B_set_b_set_fun$] : ! [v3: B_set$] : ( ~ (fun_app$c(sup$, v0) = v2) | ~
% 79.46/11.50 (fun_app$b(v2, v1) = v3) | ~ B_set$(v1) | ~ B_set$(v0) | ? [v4:
% 79.46/11.50 B_set_b_set_fun$] : (fun_app$c(sup$, v1) = v4 & fun_app$b(v4, v0) = v3 &
% 79.46/11.50 B_set_b_set_fun$(v4) & B_set$(v3)))
% 79.46/11.50
% 79.46/11.50 (axiom146)
% 79.46/11.50 B_set_b_set_b_set_fun_fun$(sup$) & ! [v0: B_set$] : ! [v1: B_set$] : ! [v2:
% 79.46/11.50 B_set_b_set_fun$] : ! [v3: B_set$] : ( ~ (fun_app$c(sup$, v0) = v2) | ~
% 79.46/11.50 (fun_app$b(v2, v1) = v3) | ~ B_set$(v1) | ~ B_set$(v0) | ? [v4:
% 79.46/11.50 B_set_b_set_fun$] : (fun_app$c(sup$, v1) = v4 & fun_app$b(v4, v0) = v3 &
% 79.46/11.50 B_set_b_set_fun$(v4) & B_set$(v3)))
% 79.46/11.50
% 79.46/11.50 (axiom403)
% 79.46/11.50 B_set_b_set_fun$(uminus$) & B_set$(top$) & B_set_b_set_b_set_fun_fun$(sup$) &
% 79.46/11.50 ! [v0: B_set$] : ! [v1: B_set_b_set_fun$] : ! [v2: B_set$] : ! [v3: B_set$]
% 79.46/11.50 : (v3 = top$ | ~ (fun_app$c(sup$, v0) = v1) | ~ (fun_app$b(v1, v2) = v3) |
% 79.46/11.50 ~ (fun_app$b(uminus$, v0) = v2) | ~ B_set$(v0))
% 79.46/11.50
% 79.46/11.50 (axiom46)
% 79.46/11.51 B_set_b_set_b_set_fun_fun$(sup$) & ! [v0: B_set$] : ! [v1: B_set$] : ! [v2:
% 79.46/11.51 B_set_b_set_fun$] : ! [v3: B_set$] : ( ~ (fun_app$c(sup$, v0) = v2) | ~
% 79.46/11.51 (fun_app$b(v2, v1) = v3) | ~ B_set$(v1) | ~ B_set$(v0) | ? [v4:
% 79.46/11.51 B_set_b_set_fun$] : (fun_app$c(sup$, v1) = v4 & fun_app$b(v4, v0) = v3 &
% 79.46/11.51 B_set_b_set_fun$(v4) & B_set$(v3)))
% 79.46/11.51
% 79.46/11.51 (axiom562)
% 79.46/11.51 B_set_b_set_fun$(uminus$) & B_set$(top$) & B_set_b_set_b_set_fun_fun$(sup$) &
% 79.46/11.51 ! [v0: B_set$] : ! [v1: B_set_b_set_fun$] : ! [v2: B_set$] : ! [v3: B_set$]
% 79.46/11.51 : (v3 = top$ | ~ (fun_app$c(sup$, v0) = v1) | ~ (fun_app$b(v1, v2) = v3) |
% 79.46/11.51 ~ (fun_app$b(uminus$, v0) = v2) | ~ B_set$(v0))
% 79.46/11.51
% 79.46/11.51 (axiom564)
% 79.46/11.51 B_set_b_set_fun$(uminus$) & B_set$(top$) & B_set_b_set_b_set_fun_fun$(minus$)
% 79.46/11.51 & ? [v0: B_set_b_set_fun$] : (fun_app$c(minus$, top$) = v0 &
% 79.46/11.51 B_set_b_set_fun$(v0) & ! [v1: B_set$] : ! [v2: B_set$] : ( ~
% 79.46/11.51 (fun_app$b(v0, v1) = v2) | ~ B_set$(v1) | (fun_app$b(uminus$, v1) = v2 &
% 79.46/11.51 B_set$(v2))))
% 79.46/11.51
% 79.46/11.51 (conjecture1)
% 79.46/11.51 B_set$(bot$) & B_set$(top$) & B_set_b_set_b_set_fun_fun$(sup$) &
% 79.46/11.51 B_set_b_set_b_set_fun_fun$(minus$) & B$(a$) & ? [v0: B_set_b_set_fun$] : ?
% 79.46/11.51 [v1: B_set_b_set_fun$] : ? [v2: B_set$] : ? [v3: B_set$] : ? [v4:
% 79.46/11.51 B_set_b_set_fun$] : ? [v5: B_set$] : ( ~ (v5 = top$) & insert$(a$) = v1 &
% 79.46/11.51 fun_app$c(sup$, v3) = v4 & fun_app$c(minus$, top$) = v0 & fun_app$b(v4, v2)
% 79.46/11.51 = v5 & fun_app$b(v1, bot$) = v2 & fun_app$b(v0, v2) = v3 &
% 79.46/11.51 B_set_b_set_fun$(v4) & B_set_b_set_fun$(v1) & B_set_b_set_fun$(v0) &
% 79.46/11.51 B_set$(v5) & B_set$(v3) & B_set$(v2))
% 79.46/11.51
% 79.46/11.51 (function-axioms)
% 79.71/11.54 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: B_set$] : !
% 79.71/11.54 [v3: B_set_b_set_bool_fun_fun$] : ! [v4: B_set_b_set_bool_fun_fun$] : (v1 =
% 79.71/11.54 v0 | ~ (ordering_top$a(v4, v3, v2) = v1) | ~ (ordering_top$a(v4, v3, v2) =
% 79.71/11.54 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 79.71/11.54 B_bool_fun$] : ! [v3: B_bool_fun_b_bool_fun_bool_fun_fun$] : ! [v4:
% 79.71/11.54 B_bool_fun_b_bool_fun_bool_fun_fun$] : (v1 = v0 | ~ (ordering_top$(v4, v3,
% 79.71/11.54 v2) = v1) | ~ (ordering_top$(v4, v3, v2) = v0)) & ! [v0:
% 79.71/11.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: B_set$] : ! [v3:
% 79.71/11.54 B_set_b_set_bool_fun_fun$] : (v1 = v0 | ~ (ordering_top_axioms$(v3, v2) =
% 79.71/11.54 v1) | ~ (ordering_top_axioms$(v3, v2) = v0)) & ! [v0: tlbool] : ! [v1:
% 79.71/11.54 tlbool] : ! [v2: B$] : ! [v3: B_bool_fun$] : (v1 = v0 | ~ (def_41(v3, v2)
% 79.71/11.54 = v1) | ~ (def_41(v3, v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : !
% 79.71/11.54 [v2: tlbool] : ! [v3: tlbool] : (v1 = v0 | ~ (def_38(v3, v2) = v1) | ~
% 79.71/11.54 (def_38(v3, v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: tlbool]
% 79.71/11.54 : ! [v3: tlbool] : (v1 = v0 | ~ (def_37(v3, v2) = v1) | ~ (def_37(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_33(v3, v2) = v1) | ~ (def_33(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_25(v3, v2) = v1) | ~ (def_25(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_26(v3, v2) = v1) | ~ (def_26(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_23(v3, v2) = v1) | ~ (def_23(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_24(v3, v2) = v1) | ~ (def_24(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_21(v3, v2) = v1) | ~ (def_21(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_22(v3, v2) = v1) | ~ (def_22(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_19(v3, v2) = v1) | ~ (def_19(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_20(v3, v2) = v1) | ~ (def_20(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 79.71/11.54 tlbool] : ! [v3: tlbool] : (v1 = v0 | ~ (less_eq$b(v3, v2) = v1) | ~
% 79.71/11.54 (less_eq$b(v3, v2) = v0)) & ! [v0: B_bool_fun_bool_fun$] : ! [v1:
% 79.71/11.54 B_bool_fun_bool_fun$] : ! [v2: B_bool_fun$] : ! [v3:
% 79.71/11.54 B_bool_fun_b_bool_fun_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$m(v3, v2) =
% 79.71/11.54 v1) | ~ (fun_app$m(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 79.71/11.54 MultipleValueBool] : ! [v2: B_bool_fun$] : ! [v3: B_bool_fun_bool_fun$] :
% 79.71/11.54 (v1 = v0 | ~ (fun_app$l(v3, v2) = v1) | ~ (fun_app$l(v3, v2) = v0)) & !
% 79.71/11.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: B_set$] : !
% 79.71/11.54 [v3: B_set_b_set_b_set_fun_fun$] : (v1 = v0 | ~ (semilattice_neutr$b(v3, v2)
% 79.71/11.54 = v1) | ~ (semilattice_neutr$b(v3, v2) = v0)) & ! [v0:
% 79.71/11.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: B_bool_fun$] : !
% 79.71/11.54 [v3: B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$] : (v1 = v0 | ~
% 79.71/11.54 (semilattice_neutr$a(v3, v2) = v1) | ~ (semilattice_neutr$a(v3, v2) = v0))
% 79.71/11.54 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: tlbool] :
% 79.71/11.54 ! [v3: Bool_bool_bool_fun_fun$] : (v1 = v0 | ~ (semilattice_neutr$(v3, v2) =
% 79.71/11.54 v1) | ~ (semilattice_neutr$(v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 79.71/11.54 ! [v1: MultipleValueBool] : ! [v2: B_set$] : ! [v3: B_b_bool_fun_fun$] :
% 79.71/11.54 (v1 = v0 | ~ (pairwise$(v3, v2) = v1) | ~ (pairwise$(v3, v2) = v0)) & !
% 79.71/11.54 [v0: B_bool_fun$] : ! [v1: B_bool_fun$] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_b_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$k(v3, v2) = v1) | ~
% 79.71/11.54 (fun_app$k(v3, v2) = v0)) & ! [v0: B_set_bool_fun$] : ! [v1:
% 79.71/11.54 B_set_bool_fun$] : ! [v2: B_set$] : ! [v3: B_set_b_set_bool_fun_fun$] :
% 79.71/11.54 (v1 = v0 | ~ (fun_app$j(v3, v2) = v1) | ~ (fun_app$j(v3, v2) = v0)) & !
% 79.71/11.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: B_set$] : !
% 79.71/11.54 [v3: B_set_bool_fun$] : (v1 = v0 | ~ (fun_app$i(v3, v2) = v1) | ~
% 79.71/11.54 (fun_app$i(v3, v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$]
% 79.71/11.54 : ! [v3: B_bool_fun$] : (v1 = v0 | ~ (def_15(v3, v2) = v1) | ~ (def_15(v3,
% 79.71/11.54 v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_16(v3, v2) = v1) | ~ (def_16(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_13(v3, v2) = v1) | ~ (def_13(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_14(v3, v2) = v1) | ~ (def_14(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_10(v3, v2) = v1) | ~ (def_10(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_11(v3, v2) = v1) | ~ (def_11(v3, v2) =
% 79.71/11.54 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3:
% 79.71/11.54 B_bool_fun$] : (v1 = v0 | ~ (def_8(v3, v2) = v1) | ~ (def_8(v3, v2) = v0))
% 79.71/11.54 & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: B$] : ! [v3: B_bool_fun$] : (v1
% 79.71/11.54 = v0 | ~ (def_9(v3, v2) = v1) | ~ (def_9(v3, v2) = v0)) & ! [v0:
% 79.71/11.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: tlbool] : ! [v3:
% 79.71/11.54 tlbool] : (v1 = v0 | ~ (minus$b(v3, v2) = v1) | ~ (minus$b(v3, v2) = v0))
% 79.71/11.54 & ! [v0: B_bool_fun_b_bool_fun_fun$] : ! [v1: B_bool_fun_b_bool_fun_fun$] :
% 79.71/11.54 ! [v2: B_bool_fun$] : ! [v3: B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$] : (v1
% 79.71/11.54 = v0 | ~ (fun_app$h(v3, v2) = v1) | ~ (fun_app$h(v3, v2) = v0)) & ! [v0:
% 79.71/11.54 B_bool_fun$] : ! [v1: B_bool_fun$] : ! [v2: B_bool_fun$] : ! [v3:
% 79.71/11.54 B_bool_fun_b_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$g(v3, v2) = v1) | ~
% 79.71/11.54 (fun_app$g(v3, v2) = v0)) & ! [v0: Bool_bool_fun$] : ! [v1:
% 79.71/11.54 Bool_bool_fun$] : ! [v2: tlbool] : ! [v3: Bool_bool_bool_fun_fun$] : (v1 =
% 79.71/11.54 v0 | ~ (fun_app$f(v3, v2) = v1) | ~ (fun_app$f(v3, v2) = v0)) & ! [v0:
% 79.71/11.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: tlbool] : ! [v3:
% 79.71/11.54 Bool_bool_fun$] : (v1 = v0 | ~ (fun_app$e(v3, v2) = v1) | ~ (fun_app$e(v3,
% 79.71/11.54 v2) = v0)) & ! [v0: B_set$] : ! [v1: B_set$] : ! [v2: B_bool_fun$] :
% 79.71/11.54 ! [v3: B_bool_fun_b_set_fun$] : (v1 = v0 | ~ (fun_app$d(v3, v2) = v1) | ~
% 79.71/11.54 (fun_app$d(v3, v2) = v0)) & ! [v0: B_set_b_set_fun$] : ! [v1:
% 79.71/11.54 B_set_b_set_fun$] : ! [v2: B_set$] : ! [v3: B_set_b_set_b_set_fun_fun$] :
% 79.71/11.54 (v1 = v0 | ~ (fun_app$c(v3, v2) = v1) | ~ (fun_app$c(v3, v2) = v0)) & !
% 79.71/11.54 [v0: B_set$] : ! [v1: B_set$] : ! [v2: B_set$] : ! [v3: B_set_b_set_fun$] :
% 79.71/11.54 (v1 = v0 | ~ (fun_app$b(v3, v2) = v1) | ~ (fun_app$b(v3, v2) = v0)) & !
% 79.71/11.54 [v0: B_bool_fun$] : ! [v1: B_bool_fun$] : ! [v2: B_set$] : ! [v3:
% 79.71/11.54 B_set_b_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$a(v3, v2) = v1) | ~
% 79.71/11.54 (fun_app$a(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 79.71/11.54 MultipleValueBool] : ! [v2: B$] : ! [v3: B_bool_fun$] : (v1 = v0 | ~
% 79.71/11.54 (fun_app$(v3, v2) = v1) | ~ (fun_app$(v3, v2) = v0)) & ! [v0:
% 79.71/11.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: B_set$] : ! [v3:
% 79.71/11.54 B$] : (v1 = v0 | ~ (member$(v3, v2) = v1) | ~ (member$(v3, v2) = v0)) & !
% 79.71/11.54 [v0: tlbool] : ! [v1: tlbool] : ! [v2: tlbool] : (v1 = v0 | ~ (def_42(v2) =
% 79.71/11.54 v1) | ~ (def_42(v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2:
% 79.71/11.54 tlbool] : (v1 = v0 | ~ (def_40(v2) = v1) | ~ (def_40(v2) = v0)) & ! [v0:
% 79.71/11.54 tlbool] : ! [v1: tlbool] : ! [v2: tlbool] : (v1 = v0 | ~ (def_39(v2) =
% 79.71/11.54 v1) | ~ (def_39(v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2:
% 79.71/11.54 tlbool] : (v1 = v0 | ~ (def_36(v2) = v1) | ~ (def_36(v2) = v0)) & ! [v0:
% 79.71/11.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: tlbool] : (v1 = v0
% 79.71/11.54 | ~ (uminus$b(v2) = v1) | ~ (uminus$b(v2) = v0)) & ! [v0:
% 79.71/11.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: B_set$] : (v1 = v0
% 79.71/11.54 | ~ (is_empty$(v2) = v1) | ~ (is_empty$(v2) = v0)) & ! [v0:
% 79.71/11.54 B_set_b_set_fun$] : ! [v1: B_set_b_set_fun$] : ! [v2: B$] : (v1 = v0 | ~
% 79.71/11.54 (remove$(v2) = v1) | ~ (remove$(v2) = v0)) & ! [v0: MultipleValueBool] :
% 79.71/11.54 ! [v1: MultipleValueBool] : ! [v2: B_set$] : (v1 = v0 | ~ (is_singleton$(v2)
% 79.71/11.54 = v1) | ~ (is_singleton$(v2) = v0)) & ! [v0: B$] : ! [v1: B$] : ! [v2:
% 79.71/11.54 B_set$] : (v1 = v0 | ~ (the_elem$(v2) = v1) | ~ (the_elem$(v2) = v0)) & !
% 79.71/11.54 [v0: B_set_b_set_fun$] : ! [v1: B_set_b_set_fun$] : ! [v2: B$] : (v1 = v0 |
% 79.71/11.54 ~ (insert$(v2) = v1) | ~ (insert$(v2) = v0))
% 79.71/11.54
% 79.71/11.54 Further assumptions not needed in the proof:
% 79.71/11.54 --------------------------------------------
% 79.71/11.54 axiom0, axiom10, axiom100, axiom101, axiom102, axiom103, axiom104, axiom105,
% 79.71/11.54 axiom106, axiom107, axiom108, axiom109, axiom11, axiom110, axiom111, axiom112,
% 79.71/11.54 axiom113, axiom114, axiom115, axiom116, axiom117, axiom118, axiom119, axiom12,
% 79.71/11.54 axiom120, axiom121, axiom122, axiom123, axiom124, axiom125, axiom126, axiom127,
% 79.71/11.54 axiom128, axiom129, axiom13, axiom130, axiom131, axiom132, axiom133, axiom134,
% 79.71/11.54 axiom135, axiom136, axiom137, axiom139, axiom14, axiom140, axiom141, axiom142,
% 79.71/11.54 axiom143, axiom145, axiom147, axiom148, axiom149, axiom15, axiom150, axiom151,
% 79.71/11.54 axiom152, axiom153, axiom154, axiom155, axiom156, axiom157, axiom158, axiom159,
% 79.71/11.54 axiom16, axiom160, axiom161, axiom162, axiom163, axiom164, axiom165, axiom166,
% 79.71/11.54 axiom167, axiom168, axiom169, axiom17, axiom170, axiom171, axiom172, axiom173,
% 79.71/11.54 axiom174, axiom175, axiom176, axiom177, axiom178, axiom179, axiom18, axiom180,
% 79.71/11.54 axiom181, axiom182, axiom183, axiom184, axiom185, axiom186, axiom187, axiom188,
% 79.71/11.54 axiom189, axiom19, axiom190, axiom191, axiom192, axiom193, axiom194, axiom195,
% 79.71/11.54 axiom196, axiom197, axiom198, axiom199, axiom2, axiom20, axiom200, axiom201,
% 79.71/11.54 axiom202, axiom203, axiom204, axiom205, axiom206, axiom207, axiom208, axiom209,
% 79.71/11.54 axiom21, axiom210, axiom211, axiom212, axiom213, axiom214, axiom215, axiom216,
% 79.71/11.54 axiom217, axiom218, axiom219, axiom22, axiom220, axiom221, axiom222, axiom223,
% 79.71/11.54 axiom224, axiom225, axiom226, axiom227, axiom228, axiom229, axiom23, axiom230,
% 79.71/11.54 axiom231, axiom232, axiom233, axiom234, axiom235, axiom236, axiom237, axiom238,
% 79.71/11.54 axiom239, axiom24, axiom240, axiom241, axiom242, axiom243, axiom244, axiom245,
% 79.71/11.54 axiom246, axiom247, axiom248, axiom249, axiom25, axiom250, axiom251, axiom252,
% 79.71/11.54 axiom253, axiom254, axiom255, axiom256, axiom257, axiom258, axiom259, axiom26,
% 79.71/11.54 axiom260, axiom261, axiom262, axiom263, axiom264, axiom265, axiom266, axiom267,
% 79.71/11.54 axiom268, axiom269, axiom27, axiom270, axiom271, axiom272, axiom273, axiom274,
% 79.71/11.54 axiom275, axiom276, axiom277, axiom278, axiom279, axiom28, axiom280, axiom281,
% 79.71/11.54 axiom282, axiom283, axiom284, axiom285, axiom286, axiom287, axiom288, axiom289,
% 79.71/11.54 axiom29, axiom290, axiom291, axiom292, axiom293, axiom294, axiom295, axiom296,
% 79.71/11.54 axiom297, axiom298, axiom299, axiom3, axiom30, axiom300, axiom301, axiom302,
% 79.71/11.54 axiom303, axiom304, axiom305, axiom306, axiom307, axiom308, axiom309, axiom31,
% 79.71/11.54 axiom310, axiom311, axiom312, axiom313, axiom314, axiom315, axiom316, axiom317,
% 79.71/11.54 axiom318, axiom319, axiom32, axiom320, axiom321, axiom322, axiom323, axiom324,
% 79.71/11.54 axiom325, axiom326, axiom327, axiom328, axiom329, axiom33, axiom330, axiom331,
% 79.71/11.54 axiom332, axiom333, axiom334, axiom335, axiom336, axiom337, axiom338, axiom339,
% 79.71/11.54 axiom34, axiom340, axiom341, axiom342, axiom343, axiom344, axiom345, axiom346,
% 79.71/11.54 axiom347, axiom348, axiom349, axiom35, axiom350, axiom351, axiom352, axiom353,
% 79.71/11.54 axiom354, axiom355, axiom356, axiom357, axiom358, axiom359, axiom36, axiom360,
% 79.71/11.54 axiom361, axiom362, axiom363, axiom364, axiom365, axiom366, axiom367, axiom368,
% 79.71/11.54 axiom369, axiom37, axiom370, axiom371, axiom372, axiom373, axiom374, axiom375,
% 79.71/11.54 axiom376, axiom377, axiom378, axiom379, axiom38, axiom380, axiom381, axiom382,
% 79.71/11.54 axiom383, axiom384, axiom385, axiom386, axiom387, axiom388, axiom389, axiom39,
% 79.71/11.54 axiom390, axiom391, axiom392, axiom393, axiom394, axiom395, axiom396, axiom397,
% 79.71/11.54 axiom398, axiom399, axiom4, axiom40, axiom400, axiom401, axiom402, axiom404,
% 79.71/11.54 axiom405, axiom406, axiom407, axiom408, axiom409, axiom41, axiom410, axiom411,
% 79.71/11.54 axiom412, axiom413, axiom414, axiom415, axiom416, axiom417, axiom418, axiom419,
% 79.71/11.54 axiom42, axiom420, axiom421, axiom422, axiom423, axiom424, axiom425, axiom426,
% 79.71/11.54 axiom427, axiom428, axiom429, axiom43, axiom430, axiom431, axiom432, axiom433,
% 79.71/11.54 axiom434, axiom435, axiom436, axiom437, axiom438, axiom439, axiom44, axiom440,
% 79.71/11.54 axiom441, axiom442, axiom443, axiom444, axiom445, axiom446, axiom447, axiom448,
% 79.71/11.54 axiom449, axiom45, axiom450, axiom451, axiom452, axiom453, axiom454, axiom455,
% 79.71/11.54 axiom456, axiom457, axiom458, axiom459, axiom460, axiom461, axiom462, axiom463,
% 79.71/11.54 axiom464, axiom465, axiom466, axiom467, axiom468, axiom469, axiom47, axiom470,
% 79.71/11.54 axiom471, axiom472, axiom473, axiom474, axiom475, axiom476, axiom477, axiom478,
% 79.71/11.54 axiom479, axiom48, axiom480, axiom481, axiom482, axiom483, axiom484, axiom485,
% 79.71/11.54 axiom486, axiom487, axiom488, axiom489, axiom49, axiom490, axiom491, axiom492,
% 79.71/11.54 axiom493, axiom494, axiom495, axiom496, axiom497, axiom498, axiom499, axiom5,
% 79.71/11.54 axiom50, axiom500, axiom501, axiom502, axiom503, axiom504, axiom505, axiom506,
% 79.71/11.54 axiom507, axiom508, axiom509, axiom51, axiom510, axiom511, axiom512, axiom513,
% 79.71/11.54 axiom514, axiom515, axiom516, axiom517, axiom518, axiom519, axiom52, axiom520,
% 79.71/11.54 axiom521, axiom522, axiom523, axiom524, axiom525, axiom526, axiom527, axiom528,
% 79.71/11.54 axiom529, axiom53, axiom530, axiom531, axiom532, axiom533, axiom534, axiom535,
% 79.71/11.54 axiom536, axiom537, axiom538, axiom539, axiom54, axiom540, axiom541, axiom542,
% 79.71/11.54 axiom543, axiom544, axiom545, axiom546, axiom547, axiom548, axiom549, axiom55,
% 79.71/11.54 axiom550, axiom551, axiom552, axiom553, axiom554, axiom555, axiom556, axiom557,
% 79.71/11.54 axiom558, axiom559, axiom56, axiom560, axiom561, axiom563, axiom565, axiom566,
% 79.71/11.54 axiom567, axiom568, axiom569, axiom57, axiom570, axiom571, axiom572, axiom573,
% 79.71/11.54 axiom574, axiom575, axiom576, axiom577, axiom578, axiom579, axiom58, axiom580,
% 79.71/11.55 axiom581, axiom582, axiom583, axiom584, axiom585, axiom586, axiom587, axiom588,
% 79.71/11.55 axiom589, axiom59, axiom590, axiom591, axiom592, axiom593, axiom594, axiom595,
% 79.71/11.55 axiom596, axiom597, axiom598, axiom599, axiom6, axiom60, axiom600, axiom601,
% 79.71/11.55 axiom602, axiom603, axiom604, axiom605, axiom606, axiom607, axiom608, axiom609,
% 79.71/11.55 axiom61, axiom610, axiom611, axiom612, axiom613, axiom614, axiom615, axiom616,
% 79.71/11.55 axiom617, axiom618, axiom619, axiom62, axiom620, axiom621, axiom622, axiom623,
% 79.71/11.55 axiom624, axiom625, axiom626, axiom627, axiom628, axiom629, axiom63, axiom630,
% 79.71/11.55 axiom631, axiom632, axiom633, axiom634, axiom64, axiom65, axiom66, axiom67,
% 79.71/11.55 axiom68, axiom69, axiom7, axiom70, axiom71, axiom72, axiom73, axiom74, axiom75,
% 79.71/11.55 axiom76, axiom77, axiom78, axiom79, axiom8, axiom80, axiom81, axiom82, axiom83,
% 79.71/11.55 axiom84, axiom85, axiom86, axiom87, axiom88, axiom89, axiom9, axiom90, axiom91,
% 79.71/11.55 axiom92, axiom93, axiom94, axiom95, axiom96, axiom97, axiom98, axiom99,
% 79.71/11.55 formula_636, formula_637, formula_638, formula_639, formula_640, formula_641,
% 79.71/11.55 formula_642, formula_643, formula_644, formula_645, formula_646, formula_647,
% 79.71/11.55 formula_648, formula_649, formula_650, formula_651, formula_652, formula_653,
% 79.71/11.55 formula_654, formula_655, formula_656, formula_657, formula_658, formula_659,
% 79.71/11.55 formula_660, formula_661, formula_662, formula_663, formula_664, formula_665,
% 79.71/11.55 formula_666, formula_667, formula_668, formula_669, formula_670, formula_671,
% 79.71/11.55 formula_672, formula_673, formula_674, formula_675, formula_676, formula_677,
% 79.71/11.55 formula_678, formula_679
% 79.71/11.55
% 79.71/11.55 Those formulas are unsatisfiable:
% 79.71/11.55 ---------------------------------
% 79.71/11.55
% 79.71/11.55 Begin of proof
% 79.71/11.55 |
% 79.71/11.55 | ALPHA: (axiom46) implies:
% 79.71/11.55 | (1) ! [v0: B_set$] : ! [v1: B_set$] : ! [v2: B_set_b_set_fun$] : ! [v3:
% 79.71/11.55 | B_set$] : ( ~ (fun_app$c(sup$, v0) = v2) | ~ (fun_app$b(v2, v1) =
% 79.71/11.55 | v3) | ~ B_set$(v1) | ~ B_set$(v0) | ? [v4: B_set_b_set_fun$] :
% 79.71/11.55 | (fun_app$c(sup$, v1) = v4 & fun_app$b(v4, v0) = v3 &
% 79.71/11.55 | B_set_b_set_fun$(v4) & B_set$(v3)))
% 79.71/11.55 |
% 79.71/11.55 | ALPHA: (axiom562) implies:
% 79.71/11.55 | (2) ! [v0: B_set$] : ! [v1: B_set_b_set_fun$] : ! [v2: B_set$] : ! [v3:
% 79.71/11.55 | B_set$] : (v3 = top$ | ~ (fun_app$c(sup$, v0) = v1) | ~
% 79.71/11.55 | (fun_app$b(v1, v2) = v3) | ~ (fun_app$b(uminus$, v0) = v2) | ~
% 79.71/11.55 | B_set$(v0))
% 79.71/11.55 |
% 79.71/11.55 | ALPHA: (axiom564) implies:
% 79.71/11.55 | (3) ? [v0: B_set_b_set_fun$] : (fun_app$c(minus$, top$) = v0 &
% 79.71/11.55 | B_set_b_set_fun$(v0) & ! [v1: B_set$] : ! [v2: B_set$] : ( ~
% 79.79/11.55 | (fun_app$b(v0, v1) = v2) | ~ B_set$(v1) | (fun_app$b(uminus$, v1)
% 79.79/11.55 | = v2 & B_set$(v2))))
% 79.79/11.55 |
% 79.79/11.55 | ALPHA: (conjecture1) implies:
% 79.79/11.55 | (4) ? [v0: B_set_b_set_fun$] : ? [v1: B_set_b_set_fun$] : ? [v2: B_set$]
% 79.79/11.55 | : ? [v3: B_set$] : ? [v4: B_set_b_set_fun$] : ? [v5: B_set$] : ( ~
% 79.79/11.55 | (v5 = top$) & insert$(a$) = v1 & fun_app$c(sup$, v3) = v4 &
% 79.79/11.55 | fun_app$c(minus$, top$) = v0 & fun_app$b(v4, v2) = v5 & fun_app$b(v1,
% 79.79/11.55 | bot$) = v2 & fun_app$b(v0, v2) = v3 & B_set_b_set_fun$(v4) &
% 79.79/11.55 | B_set_b_set_fun$(v1) & B_set_b_set_fun$(v0) & B_set$(v5) & B_set$(v3)
% 79.79/11.55 | & B_set$(v2))
% 79.79/11.55 |
% 79.79/11.55 | ALPHA: (function-axioms) implies:
% 79.79/11.55 | (5) ! [v0: B_set_b_set_fun$] : ! [v1: B_set_b_set_fun$] : ! [v2: B_set$]
% 79.79/11.55 | : ! [v3: B_set_b_set_b_set_fun_fun$] : (v1 = v0 | ~ (fun_app$c(v3,
% 79.79/11.55 | v2) = v1) | ~ (fun_app$c(v3, v2) = v0))
% 79.79/11.55 |
% 79.79/11.55 | DELTA: instantiating (3) with fresh symbol all_718_0 gives:
% 79.79/11.55 | (6) fun_app$c(minus$, top$) = all_718_0 & B_set_b_set_fun$(all_718_0) & !
% 79.79/11.55 | [v0: B_set$] : ! [v1: B_set$] : ( ~ (fun_app$b(all_718_0, v0) = v1) |
% 79.79/11.55 | ~ B_set$(v0) | (fun_app$b(uminus$, v0) = v1 & B_set$(v1)))
% 79.79/11.55 |
% 79.79/11.55 | ALPHA: (6) implies:
% 79.79/11.55 | (7) fun_app$c(minus$, top$) = all_718_0
% 79.79/11.56 | (8) ! [v0: B_set$] : ! [v1: B_set$] : ( ~ (fun_app$b(all_718_0, v0) = v1)
% 79.79/11.56 | | ~ B_set$(v0) | (fun_app$b(uminus$, v0) = v1 & B_set$(v1)))
% 79.79/11.56 |
% 79.79/11.56 | DELTA: instantiating (4) with fresh symbols all_749_0, all_749_1, all_749_2,
% 79.79/11.56 | all_749_3, all_749_4, all_749_5 gives:
% 79.79/11.56 | (9) ~ (all_749_0 = top$) & insert$(a$) = all_749_4 & fun_app$c(sup$,
% 79.79/11.56 | all_749_2) = all_749_1 & fun_app$c(minus$, top$) = all_749_5 &
% 79.79/11.56 | fun_app$b(all_749_1, all_749_3) = all_749_0 & fun_app$b(all_749_4,
% 79.79/11.56 | bot$) = all_749_3 & fun_app$b(all_749_5, all_749_3) = all_749_2 &
% 79.79/11.56 | B_set_b_set_fun$(all_749_1) & B_set_b_set_fun$(all_749_4) &
% 79.79/11.56 | B_set_b_set_fun$(all_749_5) & B_set$(all_749_0) & B_set$(all_749_2) &
% 79.79/11.56 | B_set$(all_749_3)
% 79.79/11.56 |
% 79.79/11.56 | ALPHA: (9) implies:
% 79.79/11.56 | (10) ~ (all_749_0 = top$)
% 79.79/11.56 | (11) B_set$(all_749_3)
% 79.79/11.56 | (12) fun_app$b(all_749_5, all_749_3) = all_749_2
% 79.79/11.56 | (13) fun_app$b(all_749_1, all_749_3) = all_749_0
% 79.79/11.56 | (14) fun_app$c(minus$, top$) = all_749_5
% 79.79/11.56 | (15) fun_app$c(sup$, all_749_2) = all_749_1
% 79.79/11.56 |
% 79.79/11.56 | GROUND_INST: instantiating (5) with all_718_0, all_749_5, top$, minus$,
% 79.79/11.56 | simplifying with (7), (14) gives:
% 79.79/11.56 | (16) all_749_5 = all_718_0
% 79.79/11.56 |
% 79.79/11.56 | REDUCE: (12), (16) imply:
% 79.79/11.56 | (17) fun_app$b(all_718_0, all_749_3) = all_749_2
% 79.79/11.56 |
% 79.79/11.56 | GROUND_INST: instantiating (8) with all_749_3, all_749_2, simplifying with
% 79.79/11.56 | (11), (17) gives:
% 79.79/11.56 | (18) fun_app$b(uminus$, all_749_3) = all_749_2 & B_set$(all_749_2)
% 79.79/11.56 |
% 79.79/11.56 | ALPHA: (18) implies:
% 79.79/11.56 | (19) B_set$(all_749_2)
% 79.79/11.56 | (20) fun_app$b(uminus$, all_749_3) = all_749_2
% 79.79/11.56 |
% 79.79/11.56 | GROUND_INST: instantiating (1) with all_749_2, all_749_3, all_749_1,
% 79.79/11.56 | all_749_0, simplifying with (11), (13), (15), (19) gives:
% 79.79/11.56 | (21) ? [v0: B_set_b_set_fun$] : (fun_app$c(sup$, all_749_3) = v0 &
% 79.79/11.56 | fun_app$b(v0, all_749_2) = all_749_0 & B_set_b_set_fun$(v0) &
% 79.79/11.56 | B_set$(all_749_0))
% 79.79/11.56 |
% 79.79/11.56 | DELTA: instantiating (21) with fresh symbol all_792_0 gives:
% 79.79/11.56 | (22) fun_app$c(sup$, all_749_3) = all_792_0 & fun_app$b(all_792_0,
% 79.79/11.56 | all_749_2) = all_749_0 & B_set_b_set_fun$(all_792_0) &
% 79.79/11.56 | B_set$(all_749_0)
% 79.79/11.56 |
% 79.79/11.56 | ALPHA: (22) implies:
% 79.79/11.56 | (23) fun_app$b(all_792_0, all_749_2) = all_749_0
% 79.79/11.56 | (24) fun_app$c(sup$, all_749_3) = all_792_0
% 79.79/11.56 |
% 79.79/11.56 | GROUND_INST: instantiating (2) with all_749_3, all_792_0, all_749_2,
% 79.79/11.56 | all_749_0, simplifying with (11), (20), (23), (24) gives:
% 79.79/11.56 | (25) all_749_0 = top$
% 79.79/11.56 |
% 79.79/11.56 | REDUCE: (10), (25) imply:
% 79.79/11.56 | (26) $false
% 79.79/11.56 |
% 79.79/11.56 | CLOSE: (26) is inconsistent.
% 79.79/11.56 |
% 79.79/11.56 End of proof
% 79.79/11.56 % SZS output end Proof for theBenchmark
% 79.79/11.56
% 79.79/11.56 10855ms
%------------------------------------------------------------------------------