TSTP Solution File: ITP199^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP199^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.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 : Mon May 20 22:56:08 EDT 2024
% Result : Theorem 0.23s 0.70s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP199^2 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.37 % Computer : n019.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat May 18 15:41:23 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 % (5585)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.41 % (5588)WARNING: value z3 for option sas not known
% 0.23/0.41 % (5586)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.41 % (5588)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.23/0.41 % (5590)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.23/0.41 % (5591)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.23/0.41 % (5587)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.42 % (5592)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.23/0.43 % (5589)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.45 % Exception at run slice level
% 0.23/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.45 % Exception at run slice level
% 0.23/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.45 % (5592)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.46 % (5593)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.23/0.46 % (5594)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.23/0.48 % Exception at run slice level
% 0.23/0.49 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.49 % (5595)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.23/0.50 % (5593)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.50 % (5594)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.51 % Exception at run slice level
% 0.23/0.51 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.52 % (5596)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.23/0.67 % (5590)First to succeed.
% 0.23/0.70 % (5590)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5585"
% 0.23/0.70 % (5590)Refutation found. Thanks to Tanya!
% 0.23/0.70 % SZS status Theorem for theBenchmark
% 0.23/0.70 % SZS output start Proof for theBenchmark
% 0.23/0.70 thf(type_def_5, type, variable: $tType).
% 0.23/0.70 thf(type_def_6, type, real: $tType).
% 0.23/0.70 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.70 thf(type_def_8, type, set: $tType > $tType).
% 0.23/0.70 thf(type_def_9, type, denotational_interp: $tType).
% 0.23/0.70 thf(type_def_10, type, char: $tType).
% 0.23/0.70 thf(type_def_11, type, trm: $tType).
% 0.23/0.70 thf(type_def_12, type, nat: $tType).
% 0.23/0.70 thf(type_def_13, type, option: $tType > $tType).
% 0.23/0.70 thf(type_def_14, type, fml: $tType).
% 0.23/0.70 thf(type_def_15, type, game: $tType).
% 0.23/0.70 thf(type_def_16, type, product_prod: ($tType * $tType) > $tType).
% 0.23/0.70 thf(func_def_0, type, denotational_interp: $tType).
% 0.23/0.70 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 0.23/0.70 thf(func_def_2, type, variable: $tType).
% 0.23/0.70 thf(func_def_3, type, option: $tType > $tType).
% 0.23/0.70 thf(func_def_4, type, game: $tType).
% 0.23/0.70 thf(func_def_5, type, char: $tType).
% 0.23/0.70 thf(func_def_6, type, trm: $tType).
% 0.23/0.70 thf(func_def_7, type, fml: $tType).
% 0.23/0.70 thf(func_def_8, type, real: $tType).
% 0.23/0.70 thf(func_def_9, type, set: $tType > $tType).
% 0.23/0.70 thf(func_def_10, type, nat: $tType).
% 0.23/0.70 thf(func_def_11, type, bounded_lattice: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_12, type, type: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_13, type, zero: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_14, type, uminus: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_15, type, bot: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_16, type, group_add: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_17, type, lattice: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_18, type, preorder: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_19, type, boolean_algebra: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_20, type, semilattice_inf: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_21, type, semilattice_sup: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_22, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_23, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_24, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_25, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.23/0.70 thf(func_def_26, type, statediff: (variable > real) > (variable > real) > set(variable)).
% 0.23/0.70 thf(func_def_27, type, stateinterpol: (variable > real) > (variable > real) > set(variable) > variable > real).
% 0.23/0.70 thf(func_def_28, type, denota1419872369iation: (variable > real) > (variable > real) > set(variable) > $o).
% 0.23/0.70 thf(func_def_29, type, denotational_Vagree: (variable > real) > (variable > real) > set(variable) > $o).
% 0.23/0.70 thf(func_def_30, type, denotational_repv: (variable > real) > variable > real > variable > real).
% 0.23/0.70 thf(func_def_31, type, denota1778088425es_ODE: denotational_interp > (real > variable > real) > char > trm > $o).
% 0.23/0.70 thf(func_def_32, type, denota1863255036rm_sem: denotational_interp > trm > (variable > real) > real).
% 0.23/0.70 thf(func_def_33, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 0.23/0.70 thf(func_def_34, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.23/0.70 thf(func_def_35, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 0.23/0.70 thf(func_def_36, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 0.23/0.70 thf(func_def_37, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 0.23/0.70 thf(func_def_38, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 0.23/0.70 thf(func_def_39, type, none: !>[X0: $tType]:(option(X0))).
% 0.23/0.70 thf(func_def_40, type, some: !>[X0: $tType]:(X0 > option(X0))).
% 0.23/0.70 thf(func_def_41, type, case_option: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > option(X1) > X0)).
% 0.23/0.70 thf(func_def_42, type, set_option: !>[X0: $tType]:(option(X0) > set(X0))).
% 0.23/0.70 thf(func_def_43, type, the: !>[X0: $tType]:(option(X0) > X0)).
% 0.23/0.70 thf(func_def_44, type, these: !>[X0: $tType]:(set(option(X0)) > set(X0))).
% 0.23/0.70 thf(func_def_45, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.23/0.70 thf(func_def_46, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.23/0.70 thf(func_def_47, type, collect: !>[X0: $tType]:((X0 > $o) > set(X0))).
% 0.23/0.70 thf(func_def_48, type, insert: !>[X0: $tType]:(X0 > set(X0) > set(X0))).
% 0.23/0.70 thf(func_def_49, type, is_empty: !>[X0: $tType]:(set(X0) > $o)).
% 0.23/0.70 thf(func_def_50, type, is_singleton: !>[X0: $tType]:(set(X0) > $o)).
% 0.23/0.70 thf(func_def_51, type, the_elem: !>[X0: $tType]:(set(X0) > X0)).
% 0.23/0.70 thf(func_def_52, type, static_FVT: trm > set(variable)).
% 0.23/0.70 thf(func_def_53, type, static_selectlike: set(sTfun(variable,real)) > (variable > real) > set(variable) > set(sTfun(variable,real))).
% 0.23/0.70 thf(func_def_54, type, times: trm > trm > trm).
% 0.23/0.70 thf(func_def_55, type, dVar: char > variable).
% 0.23/0.70 thf(func_def_56, type, rVar: char > variable).
% 0.23/0.70 thf(func_def_57, type, rec_variable: !>[X0: $tType]:((char > X0) > (char > X0) > variable > X0)).
% 0.23/0.70 thf(func_def_58, type, size_variable: variable > nat).
% 0.23/0.70 thf(func_def_59, type, uSubst277968634Timeso: option(trm) > option(trm) > option(trm)).
% 0.23/0.70 thf(func_def_60, type, uSubst2091380086djoint: product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))) > denotational_interp > (variable > real) > denotational_interp).
% 0.23/0.70 thf(func_def_61, type, uSubst95898992stappt: product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))) > set(variable) > trm > option(trm)).
% 0.23/0.70 thf(func_def_62, type, member: !>[X0: $tType]:(X0 > set(X0) > $o)).
% 0.23/0.70 thf(func_def_63, type, f: real > variable > real).
% 0.23/0.70 thf(func_def_64, type, i: denotational_interp).
% 0.23/0.70 thf(func_def_65, type, u: set(variable)).
% 0.23/0.70 thf(func_def_66, type, omega: variable > real).
% 0.23/0.70 thf(func_def_67, type, sigma: product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game)))))).
% 0.23/0.70 thf(func_def_68, type, theta: trm).
% 0.23/0.70 thf(func_def_69, type, rr: trm > denotational_interp > trm > denotational_interp > char > (real > variable > real) > variable > real).
% 0.23/0.70 thf(func_def_70, type, x: char).
% 0.23/0.70 thf(func_def_74, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 0.23/0.70 thf(func_def_75, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.23/0.70 thf(func_def_76, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.23/0.70 thf(func_def_77, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.23/0.70 thf(func_def_78, type, vIMP: $o > $o > $o).
% 0.23/0.70 thf(func_def_79, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
% 0.23/0.70 thf(func_def_80, type, vNOT: $o > $o).
% 0.23/0.70 thf(func_def_81, type, vAND: $o > $o > $o).
% 0.23/0.70 thf(func_def_82, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
% 0.23/0.70 thf(func_def_83, type, iCOMB: !>[X0: $tType]:(X0 > X0)).
% 0.23/0.70 thf(func_def_84, type, vOR: $o > $o > $o).
% 0.23/0.70 thf(func_def_85, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.23/0.70 thf(func_def_86, type, sP0: option(trm) > option(trm) > option(trm) > $o).
% 0.23/0.70 thf(func_def_87, type, sP1: option(trm) > option(trm) > option(trm) > $o).
% 0.23/0.70 thf(func_def_88, type, sP2: !>[X0: $tType, X1: $tType]:((option(X1) > option(X0) > $o) > option(X1) > option(X0) > $o)).
% 0.23/0.70 thf(func_def_89, type, sK3: trm > denotational_interp > trm > denotational_interp > char > (real > variable > real) > variable > real).
% 0.23/0.70 thf(func_def_90, type, sK4: variable > char).
% 0.23/0.70 thf(func_def_91, type, sK5: variable > char).
% 0.23/0.70 thf(func_def_92, type, sK6: option(trm) > trm).
% 0.23/0.70 thf(func_def_93, type, sK7: !>[X0: $tType]:(option(X0) > X0)).
% 0.23/0.70 thf(func_def_94, type, sK8: !>[X0: $tType]:(set(X0) > X0)).
% 0.23/0.70 thf(func_def_95, type, sK9: !>[X0: $tType]:(set(X0) > X0)).
% 0.23/0.70 thf(func_def_96, type, sK10: !>[X0: $tType]:(set(X0) > X0)).
% 0.23/0.70 thf(func_def_97, type, sK11: (variable > $o) > char).
% 0.23/0.70 thf(func_def_98, type, sK12: (variable > $o) > char).
% 0.23/0.70 thf(func_def_99, type, sK13: (option(trm) > $o) > trm).
% 0.23/0.70 thf(func_def_100, type, sK14: !>[X0: $tType]:(set(X0) > X0)).
% 0.23/0.70 thf(func_def_101, type, sK15: option(trm) > trm).
% 0.23/0.70 thf(func_def_102, type, sK16: option(trm) > option(trm) > option(trm) > trm).
% 0.23/0.70 thf(func_def_103, type, sK17: option(trm) > option(trm) > option(trm) > trm).
% 0.23/0.70 thf(func_def_104, type, sK18: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 0.23/0.70 thf(func_def_105, type, sK19: !>[X0: $tType]:(set(X0) > set(X0) > X0)).
% 0.23/0.70 thf(func_def_106, type, sK20: (char > option(trm) > $o) > char).
% 0.23/0.70 thf(func_def_107, type, sK21: (char > option(trm) > $o) > char).
% 0.23/0.70 thf(func_def_108, type, sK22: (char > option(trm) > $o) > trm).
% 0.23/0.70 thf(func_def_109, type, sK23: (variable > option(trm) > $o) > variable).
% 0.23/0.70 thf(func_def_110, type, sK24: (variable > option(trm) > $o) > variable).
% 0.23/0.70 thf(func_def_111, type, sK25: (variable > option(trm) > $o) > trm).
% 0.23/0.70 thf(func_def_112, type, sK26: (option(trm) > option(trm) > $o) > trm).
% 0.23/0.70 thf(func_def_113, type, sK27: (option(trm) > option(trm) > $o) > option(trm)).
% 0.23/0.70 thf(func_def_114, type, sK28: (option(trm) > option(trm) > $o) > trm).
% 0.23/0.70 thf(func_def_115, type, sK29: (option(trm) > option(trm) > $o) > trm).
% 0.23/0.70 thf(func_def_116, type, sK30: !>[X0: $tType]:((option(X0) > $o) > X0)).
% 0.23/0.70 thf(func_def_117, type, sK31: !>[X0: $tType]:(set(X0) > X0 > set(X0))).
% 0.23/0.70 thf(func_def_118, type, sK32: !>[X0: $tType]:(set(X0) > X0 > set(X0))).
% 0.23/0.70 thf(func_def_119, type, sK33: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 0.23/0.70 thf(func_def_120, type, sK34: !>[X0: $tType]:((X0 > $o) > option(X0) > X0)).
% 0.23/0.70 thf(func_def_121, type, sK35: set(sTfun(variable,real)) > set(sTfun(variable,real)) > set(variable) > (variable > real) > variable > real).
% 0.23/0.70 thf(func_def_122, type, sK36: set(sTfun(variable,real)) > set(sTfun(variable,real)) > set(variable) > (variable > real) > variable > real).
% 0.23/0.70 thf(func_def_123, type, sK37: !>[X0: $tType, X1: $tType]:((option(X1) > option(X0) > $o) > option(X1) > option(X0) > X1)).
% 0.23/0.70 thf(func_def_124, type, sK38: !>[X0: $tType, X1: $tType]:((option(X1) > option(X0) > $o) > option(X1) > option(X0) > X0)).
% 0.23/0.70 thf(func_def_125, type, sK39: trm > denotational_interp > trm > denotational_interp > char > (real > variable > real) > variable > real).
% 0.23/0.70 thf(func_def_127, type, sK41: denotational_interp > trm > (real > variable > real) > trm > char > denotational_interp > variable > real).
% 0.23/0.70 thf(func_def_128, type, sK42: !>[X0: $tType]:(X0 > set(X0) > X0 > set(X0) > set(X0))).
% 0.23/0.70 thf(func_def_129, type, sK43: !>[X0: $tType]:(set(X0) > (X0 > $o) > X0)).
% 0.23/0.70 thf(func_def_130, type, sK44: !>[X0: $tType]:(set(X0) > (X0 > $o) > X0)).
% 0.23/0.70 thf(func_def_131, type, sK45: !>[X0: $tType]:(set(X0) > (X0 > $o) > set(X0) > X0)).
% 0.23/0.70 thf(func_def_132, type, sK46: !>[X0: $tType]:(set(X0) > (X0 > $o) > set(X0) > X0)).
% 0.23/0.70 thf(func_def_133, type, sK47: !>[X0: $tType]:(set(X0) > (X0 > $o) > X0)).
% 0.23/0.70 thf(func_def_134, type, sK48: !>[X0: $tType]:(set(X0) > (X0 > $o) > X0)).
% 0.23/0.70 thf(func_def_135, type, sK49: !>[X0: $tType]:(X0 > (X0 > $o) > set(X0) > X0)).
% 0.23/0.70 thf(func_def_136, type, sK50: !>[X0: $tType]:(set(X0) > (X0 > $o) > X0)).
% 0.23/0.70 thf(func_def_137, type, sK51: (variable > real) > set(sTfun(variable,real)) > set(sTfun(variable,real)) > set(variable) > variable > real).
% 0.23/0.70 thf(func_def_138, type, sK52: (variable > real) > set(sTfun(variable,real)) > set(sTfun(variable,real)) > set(variable) > variable > real).
% 0.23/0.70 thf(func_def_139, type, sK53: !>[X0: $tType]:(set(X0) > X0)).
% 0.23/0.70 thf(func_def_140, type, sK54: !>[X0: $tType]:(set(X0) > X0)).
% 0.23/0.70 thf(func_def_141, type, sK55: !>[X0: $tType]:(option(X0) > X0)).
% 0.23/0.70 thf(func_def_142, type, sK56: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.23/0.70 thf(func_def_143, type, sK57: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.23/0.70 thf(func_def_144, type, sK58: !>[X0: $tType]:(option(X0) > X0)).
% 0.23/0.70 thf(func_def_145, type, sK59: option(trm) > trm).
% 0.23/0.70 thf(func_def_146, type, sK60: trm > trm > (real > variable > real) > denotational_interp > denotational_interp > char > variable > real).
% 0.23/0.70 thf(f4323,plain,(
% 0.23/0.70 $false),
% 0.23/0.70 inference(avatar_sat_refutation,[],[f2215,f2220,f2225,f2230,f2235,f2240,f2245,f2250,f2255,f2260,f2265,f2270,f2275,f2280,f2285,f2290,f2295,f2300,f2305,f2310,f2315,f2320,f2325,f2330,f2335,f2340,f2344,f2348,f2352,f2356,f2360,f2364,f2368,f2372,f2376,f2380,f2412,f2422,f2426,f2430,f2434,f2439,f2443,f2447,f2451,f2455,f2459,f2500,f2542,f2546,f2550,f2554,f2560,f2564,f2568,f2572,f2582,f2587,f2591,f2595,f2599,f2615,f2619,f2623,f2627,f2631,f2671,f2675,f2679,f2699,f2703,f2707,f2713,f2717,f2721,f2725,f2729,f2733,f2737,f2758,f2762,f2766,f2770,f2782,f2786,f2790,f2794,f2799,f2807,f2814,f2818,f2822,f2826,f2840,f2866,f2873,f2877,f2881,f2885,f2889,f2893,f2917,f2927,f2931,f2937,f2948,f2952,f3000,f3004,f3008,f3014,f3019,f3023,f3027,f3045,f3062,f3066,f3070,f3074,f3078,f3082,f3086,f3090,f3142,f3167,f3171,f3188,f3192,f3198,f3204,f3208,f3214,f3218,f3226,f3230,f3234,f3256,f3260,f3288,f3292,f3296,f3300,f3304,f3308,f3373,f3377,f3390,f3396,f3400,f3404,f3408,f3460,f3464,f3496,f3504,f3530,f3543,f3547,f3553,f3559,f3571,f3597,f3601,f3632,f3636,f3640,f3705,f3709,f3807,f3811,f3819,f3827,f3831,f3840,f3844,f3852,f3869,f3875,f3879,f3884,f3891,f3899,f3913,f3917,f3941,f3954,f3970,f3985,f3992,f3997,f4002,f4014,f4018,f4088,f4110,f4139,f4147,f4157,f4161,f4175,f4184,f4190,f4199,f4214,f4218,f4222,f4226,f4258,f4268,f4272,f4282,f4289,f4306,f4317,f4322])).
% 0.23/0.70 thf(f4322,plain,(
% 0.23/0.70 spl40_197),
% 0.23/0.70 inference(avatar_split_clause,[],[f2210,f4144])).
% 0.23/0.70 thf(f4144,plain,(
% 0.23/0.70 spl40_197 <=> ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),vAPP(option(variable),set(variable),set_option(variable),vAPP(variable,option(variable),some(variable),vAPP(char,variable,rVar,x)))))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_197])])).
% 0.23/0.70 thf(f2210,plain,(
% 0.23/0.70 ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),vAPP(option(variable),set(variable),set_option(variable),vAPP(variable,option(variable),some(variable),vAPP(char,variable,rVar,x)))))))),
% 0.23/0.70 inference(forward_demodulation,[],[f2209,f1199])).
% 0.23/0.70 thf(f1199,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0))) = vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f801])).
% 0.23/0.70 thf(f801,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0))) = vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1)))),
% 0.23/0.70 inference(rectify,[],[f166])).
% 0.23/0.70 thf(f166,axiom,(
% 0.23/0.70 ! [X0 : $tType,X54 : X0] : (vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X54)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X54),bot_bot(set(X0))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_option_Osimps_I15_J)).
% 0.23/0.70 thf(f2209,plain,(
% 0.23/0.70 ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),bot_bot(set(variable)))))))),
% 0.23/0.70 inference(forward_demodulation,[],[f1481,f1321])).
% 0.23/0.70 thf(f1321,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X3 : set(X0),X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f835])).
% 0.23/0.70 thf(f835,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3)))),
% 0.23/0.70 inference(rectify,[],[f35])).
% 0.23/0.70 thf(f35,axiom,(
% 0.23/0.70 ! [X0 : $tType,X8 : X0,X9 : X0,X7 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X8),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X9),X7)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X9),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X8),X7)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_insert__commute)).
% 0.23/0.70 thf(f1481,plain,(
% 0.23/0.70 ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable)))))))),
% 0.23/0.70 inference(definition_unfolding,[],[f1423,f1104])).
% 0.23/0.70 thf(f1104,plain,(
% 0.23/0.70 (denota1419872369iation = vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))))),
% 0.23/0.70 inference(cnf_transformation,[],[f321])).
% 0.23/0.70 thf(f321,plain,(
% 0.23/0.70 (denota1419872369iation = vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))))),
% 0.23/0.70 inference(fool_elimination,[],[f320])).
% 0.23/0.70 thf(f320,plain,(
% 0.23/0.70 (denota1419872369iation = (^[X0 : variable > real, X1 : variable > real, X2 : set(variable)] : (! [X3 : variable] : (~vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X3),X2) => (vAPP(variable,real,X0,X3) = vAPP(variable,real,X1,X3))))))),
% 0.23/0.70 inference(rectify,[],[f73])).
% 0.23/0.70 thf(f73,axiom,(
% 0.23/0.70 (denota1419872369iation = (^[X34 : variable > real, X35 : variable > real, X36 : set(variable)] : (! [X37 : variable] : (~vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X37),X36) => (vAPP(variable,real,X34,X37) = vAPP(variable,real,X35,X37))))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Uvariation__def)).
% 0.23/0.70 thf(f1423,plain,(
% 0.23/0.70 (vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable)))))) = $true)),
% 0.23/0.70 inference(cnf_transformation,[],[f783])).
% 0.23/0.70 thf(f783,plain,(
% 0.23/0.70 (vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable)))))) = $true)),
% 0.23/0.70 inference(fool_elimination,[],[f782])).
% 0.23/0.70 thf(f782,plain,(
% 0.23/0.70 vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))))),
% 0.23/0.70 inference(rectify,[],[f1])).
% 0.23/0.70 thf(f1,axiom,(
% 0.23/0.70 vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_uv)).
% 0.23/0.70 thf(f4317,plain,(
% 0.23/0.70 spl40_214),
% 0.23/0.70 inference(avatar_split_clause,[],[f2185,f4315])).
% 0.23/0.70 thf(f4315,plain,(
% 0.23/0.70 spl40_214 <=> ! [X4 : real,X0 : denotational_interp,X3 : trm,X2 : char,X1 : real > variable > real] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),X1,X4)),vAPP(real,sTfun(variable,real),X1,zero_zero(real))),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,X2)),vAPP(option(variable),set(variable),set_option(variable),vAPP(variable,option(variable),some(variable),vAPP(char,variable,rVar,X2))))))) | ($true != vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,X0),X1),X2),X3)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_214])])).
% 0.23/0.70 thf(f2185,plain,(
% 0.23/0.70 ( ! [X2 : char,X3 : trm,X0 : denotational_interp,X1 : real > variable > real,X4 : real] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),X1,X4)),vAPP(real,sTfun(variable,real),X1,zero_zero(real))),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,X2)),vAPP(option(variable),set(variable),set_option(variable),vAPP(variable,option(variable),some(variable),vAPP(char,variable,rVar,X2))))))) | ($true != vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,X0),X1),X2),X3))) )),
% 0.23/0.70 inference(forward_demodulation,[],[f2184,f1199])).
% 0.23/0.70 thf(f2184,plain,(
% 0.23/0.70 ( ! [X2 : char,X3 : trm,X0 : denotational_interp,X1 : real > variable > real,X4 : real] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),X1,X4)),vAPP(real,sTfun(variable,real),X1,zero_zero(real))),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,X2)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,X2)),bot_bot(set(variable))))))) | ($true != vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,X0),X1),X2),X3))) )),
% 0.23/0.70 inference(forward_demodulation,[],[f1472,f1321])).
% 0.23/0.70 thf(f1472,plain,(
% 0.23/0.70 ( ! [X2 : char,X3 : trm,X0 : denotational_interp,X1 : real > variable > real,X4 : real] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),X1,X4)),vAPP(real,sTfun(variable,real),X1,zero_zero(real))),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,X2)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,X2)),bot_bot(set(variable))))))) | ($true != vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,X0),X1),X2),X3))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1386,f1102])).
% 0.23/0.70 thf(f1102,plain,(
% 0.23/0.70 (denotational_Vagree = vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))))),
% 0.23/0.70 inference(cnf_transformation,[],[f317])).
% 0.23/0.70 thf(f317,plain,(
% 0.23/0.70 (denotational_Vagree = vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))))),
% 0.23/0.70 inference(fool_elimination,[],[f316])).
% 0.23/0.70 thf(f316,plain,(
% 0.23/0.70 (denotational_Vagree = (^[X0 : variable > real, X1 : variable > real, X2 : set(variable)] : (! [X3 : variable] : (vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X3),X2) => (vAPP(variable,real,X0,X3) = vAPP(variable,real,X1,X3))))))),
% 0.23/0.70 inference(rectify,[],[f178])).
% 0.23/0.70 thf(f178,axiom,(
% 0.23/0.70 (denotational_Vagree = (^[X34 : variable > real, X35 : variable > real, X93 : set(variable)] : (! [X37 : variable] : (vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X37),X93) => (vAPP(variable,real,X34,X37) = vAPP(variable,real,X35,X37))))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Vagree__def)).
% 0.23/0.70 thf(f1386,plain,(
% 0.23/0.70 ( ! [X2 : char,X3 : trm,X0 : denotational_interp,X1 : real > variable > real,X4 : real] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,vAPP(real,sTfun(variable,real),X1,X4)),vAPP(real,sTfun(variable,real),X1,zero_zero(real))),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,X2)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,X2)),bot_bot(set(variable))))))) | ($true != vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,X0),X1),X2),X3))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1014])).
% 0.23/0.70 thf(f1014,plain,(
% 0.23/0.70 ! [X0 : denotational_interp,X1 : real > variable > real,X2 : char,X3 : trm,X4 : real] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,vAPP(real,sTfun(variable,real),X1,X4)),vAPP(real,sTfun(variable,real),X1,zero_zero(real))),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,X2)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,X2)),bot_bot(set(variable))))))) | ($true != vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,X0),X1),X2),X3)))),
% 0.23/0.70 inference(ennf_transformation,[],[f713])).
% 0.23/0.70 thf(f713,plain,(
% 0.23/0.70 ! [X0 : denotational_interp,X1 : real > variable > real,X2 : char,X3 : trm,X4 : real] : (($true = vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,X0),X1),X2),X3)) => ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,vAPP(real,sTfun(variable,real),X1,X4)),vAPP(real,sTfun(variable,real),X1,zero_zero(real))),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,X2)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,X2)),bot_bot(set(variable))))))))),
% 0.23/0.70 inference(fool_elimination,[],[f712])).
% 0.23/0.70 thf(f712,plain,(
% 0.23/0.70 ! [X0 : denotational_interp,X1 : real > variable > real,X2 : char,X3 : trm,X4 : real] : (vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,X0),X1),X2),X3) => vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,vAPP(real,sTfun(variable,real),X1,X4)),vAPP(real,sTfun(variable,real),X1,zero_zero(real))),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,X2)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,X2)),bot_bot(set(variable)))))))),
% 0.23/0.70 inference(rectify,[],[f188])).
% 0.23/0.70 thf(f188,axiom,(
% 0.23/0.70 ! [X49 : denotational_interp,X48 : real > variable > real,X8 : char,X50 : trm,X51 : real] : (vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,X49),X48),X8),X50) => vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,vAPP(real,sTfun(variable,real),X48,X51)),vAPP(real,sTfun(variable,real),X48,zero_zero(real))),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,X8)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,X8)),bot_bot(set(variable)))))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_solves__Vagree)).
% 0.23/0.70 thf(f4306,plain,(
% 0.23/0.70 spl40_213),
% 0.23/0.70 inference(avatar_split_clause,[],[f1462,f4304])).
% 0.23/0.70 thf(f4304,plain,(
% 0.23/0.70 spl40_213 <=> ! [X0 : variable > real,X3 : set(sTfun(variable,real)),X2 : set(variable),X1 : variable > real] : ((vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X1),X2) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X0),X2)) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_213])])).
% 0.23/0.70 thf(f1462,plain,(
% 0.23/0.70 ( ! [X2 : set(variable),X3 : set(sTfun(variable,real)),X0 : variable > real,X1 : variable > real] : ((vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X1),X2) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X0),X2)) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X1),X2))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1364,f1102])).
% 0.23/0.70 thf(f1364,plain,(
% 0.23/0.70 ( ! [X2 : set(variable),X3 : set(sTfun(variable,real)),X0 : variable > real,X1 : variable > real] : ((vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X1),X2) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X0),X2)) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f994])).
% 0.23/0.70 thf(f994,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real,X2 : set(variable),X3 : set(sTfun(variable,real))] : ((vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X1),X2) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X0),X2)) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),X2)))),
% 0.23/0.70 inference(ennf_transformation,[],[f689])).
% 0.23/0.70 thf(f689,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real,X2 : set(variable),X3 : set(sTfun(variable,real))] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),X2)) => (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X1),X2) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X0),X2)))),
% 0.23/0.70 inference(fool_elimination,[],[f688])).
% 0.23/0.70 thf(f688,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real,X2 : set(variable),X3 : set(sTfun(variable,real))] : (vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),X2) => (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X1),X2) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X3),X0),X2)))),
% 0.23/0.70 inference(rectify,[],[f172])).
% 0.23/0.70 thf(f172,axiom,(
% 0.23/0.70 ! [X2 : variable > real,X30 : variable > real,X32 : set(variable),X76 : set(sTfun(variable,real))] : (vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X2),X30),X32) => (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X76),X2),X32) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X76),X30),X32)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_selectlike__Vagree)).
% 0.23/0.70 thf(f4289,plain,(
% 0.23/0.70 spl40_212),
% 0.23/0.70 inference(avatar_split_clause,[],[f1441,f4287])).
% 0.23/0.70 thf(f4287,plain,(
% 0.23/0.70 spl40_212 <=> ! [X0 : variable > real,X1 : set(variable)] : ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X0),X1))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_212])])).
% 0.23/0.70 thf(f1441,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : set(variable)] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X0),X1))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1256,f1104])).
% 0.23/0.70 thf(f1256,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : set(variable)] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,X0),X0),X1))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f563])).
% 0.23/0.70 thf(f563,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : set(variable)] : ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,X0),X0),X1))),
% 0.23/0.70 inference(fool_elimination,[],[f562])).
% 0.23/0.70 thf(f562,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : set(variable)] : vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,X0),X0),X1)),
% 0.23/0.70 inference(rectify,[],[f71])).
% 0.23/0.70 thf(f71,axiom,(
% 0.23/0.70 ! [X2 : variable > real,X32 : set(variable)] : vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,X2),X2),X32)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Uvariation__refl)).
% 0.23/0.70 thf(f4282,plain,(
% 0.23/0.70 spl40_211),
% 0.23/0.70 inference(avatar_split_clause,[],[f1465,f4280])).
% 0.23/0.70 thf(f4280,plain,(
% 0.23/0.70 spl40_211 <=> ! [X0 : variable > real,X3 : denotational_interp,X2 : trm,X1 : variable > real] : ((vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X0) = vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X1)) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X1),vAPP(trm,set(variable),static_FVT,X2))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_211])])).
% 0.23/0.70 thf(f1465,plain,(
% 0.23/0.70 ( ! [X2 : trm,X3 : denotational_interp,X0 : variable > real,X1 : variable > real] : ((vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X0) = vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X1)) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X1),vAPP(trm,set(variable),static_FVT,X2)))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1369,f1102])).
% 0.23/0.70 thf(f1369,plain,(
% 0.23/0.70 ( ! [X2 : trm,X3 : denotational_interp,X0 : variable > real,X1 : variable > real] : ((vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X0) = vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X1)) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),vAPP(trm,set(variable),static_FVT,X2)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1002])).
% 0.23/0.70 thf(f1002,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real,X2 : trm,X3 : denotational_interp] : ((vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X0) = vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X1)) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),vAPP(trm,set(variable),static_FVT,X2))))),
% 0.23/0.70 inference(ennf_transformation,[],[f699])).
% 0.23/0.70 thf(f699,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real,X2 : trm,X3 : denotational_interp] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),vAPP(trm,set(variable),static_FVT,X2))) => (vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X0) = vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X1)))),
% 0.23/0.70 inference(fool_elimination,[],[f698])).
% 0.23/0.70 thf(f698,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real,X2 : trm,X3 : denotational_interp] : (vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),vAPP(trm,set(variable),static_FVT,X2)) => (vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X0) = vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X3),X2),X1)))),
% 0.23/0.70 inference(rectify,[],[f231])).
% 0.23/0.70 thf(f231,axiom,(
% 0.23/0.70 ! [X30 : variable > real,X109 : variable > real,X50 : trm,X49 : denotational_interp] : (vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X30),X109),vAPP(trm,set(variable),static_FVT,X50)) => (vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X49),X50),X30) = vAPP(sTfun(variable,real),real,vAPP(trm,sTfun(sTfun(variable,real),real),vAPP(denotational_interp,sTfun(trm,sTfun(sTfun(variable,real),real)),denota1863255036rm_sem,X49),X50),X109)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_coincidence__term)).
% 0.23/0.70 thf(f4272,plain,(
% 0.23/0.70 spl40_210),
% 0.23/0.70 inference(avatar_split_clause,[],[f1446,f4270])).
% 0.23/0.70 thf(f4270,plain,(
% 0.23/0.70 spl40_210 <=> ! [X2 : set(variable),X0 : variable > real,X1 : variable > real] : (($true = vAPP(set(variable),$o,vAPP(set(variable),sTfun(set(variable),$o),ord_less_eq(set(variable)),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X0),X1)),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),X2))) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_210])])).
% 0.23/0.70 thf(f1446,plain,(
% 0.23/0.70 ( ! [X2 : set(variable),X0 : variable > real,X1 : variable > real] : (($true = vAPP(set(variable),$o,vAPP(set(variable),sTfun(set(variable),$o),ord_less_eq(set(variable)),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X0),X1)),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),X2))) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X1),X2))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1309,f1102])).
% 0.23/0.70 thf(f1309,plain,(
% 0.23/0.70 ( ! [X2 : set(variable),X0 : variable > real,X1 : variable > real] : (($true = vAPP(set(variable),$o,vAPP(set(variable),sTfun(set(variable),$o),ord_less_eq(set(variable)),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X0),X1)),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),X2))) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f970])).
% 0.23/0.70 thf(f970,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real,X2 : set(variable)] : (($true = vAPP(set(variable),$o,vAPP(set(variable),sTfun(set(variable),$o),ord_less_eq(set(variable)),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X0),X1)),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),X2))) | ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),X2)))),
% 0.23/0.70 inference(ennf_transformation,[],[f619])).
% 0.23/0.70 thf(f619,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real,X2 : set(variable)] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),X2)) => ($true = vAPP(set(variable),$o,vAPP(set(variable),sTfun(set(variable),$o),ord_less_eq(set(variable)),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X0),X1)),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),X2))))),
% 0.23/0.70 inference(fool_elimination,[],[f618])).
% 0.23/0.70 thf(f618,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real,X2 : set(variable)] : (vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),X2) => vAPP(set(variable),$o,vAPP(set(variable),sTfun(set(variable),$o),ord_less_eq(set(variable)),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X0),X1)),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),X2)))),
% 0.23/0.70 inference(rectify,[],[f233])).
% 0.23/0.70 thf(f233,axiom,(
% 0.23/0.70 ! [X30 : variable > real,X109 : variable > real,X101 : set(variable)] : (vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X30),X109),X101) => vAPP(set(variable),$o,vAPP(set(variable),sTfun(set(variable),$o),ord_less_eq(set(variable)),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X30),X109)),vAPP(set(variable),set(variable),uminus_uminus(set(variable)),X101)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_Vagree__statediff)).
% 0.23/0.70 thf(f4268,plain,(
% 0.23/0.70 spl40_209),
% 0.23/0.70 inference(avatar_split_clause,[],[f1442,f4266])).
% 0.23/0.70 thf(f4266,plain,(
% 0.23/0.70 spl40_209 <=> ! [X0 : variable > real,X1 : variable > real] : ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X1),bot_bot(set(variable))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_209])])).
% 0.23/0.70 thf(f1442,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : variable > real] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X1),bot_bot(set(variable))))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1257,f1102])).
% 0.23/0.70 thf(f1257,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : variable > real] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),bot_bot(set(variable))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f565])).
% 0.23/0.70 thf(f565,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real] : ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),bot_bot(set(variable))))),
% 0.23/0.70 inference(fool_elimination,[],[f564])).
% 0.23/0.70 thf(f564,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real] : vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X1),bot_bot(set(variable)))),
% 0.23/0.70 inference(rectify,[],[f182])).
% 0.23/0.70 thf(f182,axiom,(
% 0.23/0.70 ! [X2 : variable > real,X3 : variable > real] : vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X2),X3),bot_bot(set(variable)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Vagree__empty)).
% 0.23/0.70 thf(f4258,plain,(
% 0.23/0.70 spl40_208),
% 0.23/0.70 inference(avatar_split_clause,[],[f1440,f4256])).
% 0.23/0.70 thf(f4256,plain,(
% 0.23/0.70 spl40_208 <=> ! [X0 : variable > real,X1 : set(variable)] : ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X0),X1))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_208])])).
% 0.23/0.70 thf(f1440,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : set(variable)] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),X0),X0),X1))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1255,f1102])).
% 0.23/0.70 thf(f1255,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : set(variable)] : (($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X0),X1))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f561])).
% 0.23/0.70 thf(f561,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : set(variable)] : ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X0),X1))),
% 0.23/0.70 inference(fool_elimination,[],[f560])).
% 0.23/0.70 thf(f560,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : set(variable)] : vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X0),X0),X1)),
% 0.23/0.70 inference(rectify,[],[f180])).
% 0.23/0.70 thf(f180,axiom,(
% 0.23/0.70 ! [X2 : variable > real,X32 : set(variable)] : vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denotational_Vagree,X2),X2),X32)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Vagree__refl)).
% 0.23/0.70 thf(f4226,plain,(
% 0.23/0.70 spl40_207),
% 0.23/0.70 inference(avatar_split_clause,[],[f1461,f4224])).
% 0.23/0.70 thf(f4224,plain,(
% 0.23/0.70 spl40_207 <=> ! [X0 : variable,X3 : variable > real,X2 : variable > real,X1 : set(variable)] : ((vAPP(variable,real,X2,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real))))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),X2),X3),X1),X0)) | ($true != vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_207])])).
% 0.23/0.70 thf(f1461,plain,(
% 0.23/0.70 ( ! [X2 : variable > real,X3 : variable > real,X0 : variable,X1 : set(variable)] : ((vAPP(variable,real,X2,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real))))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),X2),X3),X1),X0)) | ($true != vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1359,f1098])).
% 0.23/0.70 thf(f1098,plain,(
% 0.23/0.70 (stateinterpol = vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real))))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))))),
% 0.23/0.70 inference(cnf_transformation,[],[f309])).
% 0.23/0.70 thf(f309,plain,(
% 0.23/0.70 (stateinterpol = vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real))))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))))),
% 0.23/0.70 inference(fool_elimination,[],[f308])).
% 0.23/0.70 thf(f308,plain,(
% 0.23/0.70 (stateinterpol = (^[X0 : variable > real, X1 : variable > real, X2 : set(variable), X3 : variable] : (vAPP(real,real,vAPP(real,sTfun(real,real),vAPP($o,sTfun(real,sTfun(real,real)),if(real),vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X3),X2)),vAPP(variable,real,X0,X3)),vAPP(variable,real,X1,X3)))))),
% 0.23/0.70 inference(rectify,[],[f224])).
% 0.23/0.70 thf(f224,axiom,(
% 0.23/0.70 (stateinterpol = (^[X34 : variable > real, X33 : variable > real, X107 : set(variable), X12 : variable] : (vAPP(real,real,vAPP(real,sTfun(real,real),vAPP($o,sTfun(real,sTfun(real,real)),if(real),vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X12),X107)),vAPP(variable,real,X34,X12)),vAPP(variable,real,X33,X12)))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_stateinterpol__def)).
% 0.23/0.70 thf(f1359,plain,(
% 0.23/0.70 ( ! [X2 : variable > real,X3 : variable > real,X0 : variable,X1 : set(variable)] : ((vAPP(variable,real,X2,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X3),X1),X0)) | ($true != vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f988])).
% 0.23/0.70 thf(f988,plain,(
% 0.23/0.70 ! [X0 : variable,X1 : set(variable),X2 : variable > real,X3 : variable > real] : ((vAPP(variable,real,X2,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X3),X1),X0)) | ($true != vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1)))),
% 0.23/0.70 inference(ennf_transformation,[],[f679])).
% 0.23/0.70 thf(f679,plain,(
% 0.23/0.70 ! [X0 : variable,X1 : set(variable),X2 : variable > real,X3 : variable > real] : (($true = vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1)) => (vAPP(variable,real,X2,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X3),X1),X0)))),
% 0.23/0.70 inference(fool_elimination,[],[f678])).
% 0.23/0.70 thf(f678,plain,(
% 0.23/0.70 ! [X0 : variable,X1 : set(variable),X2 : variable > real,X3 : variable > real] : (vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1) => (vAPP(variable,real,X2,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X3),X1),X0)))),
% 0.23/0.70 inference(rectify,[],[f219])).
% 0.23/0.70 thf(f219,axiom,(
% 0.23/0.70 ! [X8 : variable,X101 : set(variable),X2 : variable > real,X30 : variable > real] : (vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X8),X101) => (vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X30),X101),X8) = vAPP(variable,real,X2,X8)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_stateinterpol__left)).
% 0.23/0.70 thf(f4222,plain,(
% 0.23/0.70 spl40_206),
% 0.23/0.70 inference(avatar_split_clause,[],[f1458,f4220])).
% 0.23/0.70 thf(f4220,plain,(
% 0.23/0.70 spl40_206 <=> ! [X0 : variable,X3 : variable > real,X2 : variable > real,X1 : set(variable)] : ((vAPP(variable,real,X3,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real))))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),X2),X3),X1),X0)) | ($true = vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_206])])).
% 0.23/0.70 thf(f1458,plain,(
% 0.23/0.70 ( ! [X2 : variable > real,X3 : variable > real,X0 : variable,X1 : set(variable)] : ((vAPP(variable,real,X3,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real))))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),X2),X3),X1),X0)) | ($true = vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1350,f1098])).
% 0.23/0.70 thf(f1350,plain,(
% 0.23/0.70 ( ! [X2 : variable > real,X3 : variable > real,X0 : variable,X1 : set(variable)] : ((vAPP(variable,real,X3,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X3),X1),X0)) | ($true = vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f980])).
% 0.23/0.70 thf(f980,plain,(
% 0.23/0.70 ! [X0 : variable,X1 : set(variable),X2 : variable > real,X3 : variable > real] : ((vAPP(variable,real,X3,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X3),X1),X0)) | ($true = vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1)))),
% 0.23/0.70 inference(ennf_transformation,[],[f847])).
% 0.23/0.70 thf(f847,plain,(
% 0.23/0.70 ! [X0 : variable,X1 : set(variable),X2 : variable > real,X3 : variable > real] : (($true != vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1)) => (vAPP(variable,real,X3,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X3),X1),X0)))),
% 0.23/0.70 inference(flattening,[],[f669])).
% 0.23/0.70 thf(f669,plain,(
% 0.23/0.70 ! [X0 : variable,X1 : set(variable),X2 : variable > real,X3 : variable > real] : (~($true = vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1)) => (vAPP(variable,real,X3,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X3),X1),X0)))),
% 0.23/0.70 inference(fool_elimination,[],[f668])).
% 0.23/0.70 thf(f668,plain,(
% 0.23/0.70 ! [X0 : variable,X1 : set(variable),X2 : variable > real,X3 : variable > real] : (~vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),X1) => (vAPP(variable,real,X3,X0) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X3),X1),X0)))),
% 0.23/0.70 inference(rectify,[],[f220])).
% 0.23/0.70 thf(f220,axiom,(
% 0.23/0.70 ! [X8 : variable,X101 : set(variable),X2 : variable > real,X30 : variable > real] : (~vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X8),X101) => (vAPP(variable,real,X30,X8) = vAPP(variable,real,vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X30),X101),X8)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_stateinterpol__right)).
% 0.23/0.70 thf(f4218,plain,(
% 0.23/0.70 spl40_205),
% 0.23/0.70 inference(avatar_split_clause,[],[f1433,f4216])).
% 0.23/0.70 thf(f4216,plain,(
% 0.23/0.70 spl40_205 <=> ! [X0 : variable > real,X1 : variable > real] : (vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real))))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),X0),X1),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X0),X1)) = X0)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_205])])).
% 0.23/0.70 thf(f1433,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : variable > real] : ((vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real))))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),X0),X1),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X0),X1)) = X0)) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1205,f1098])).
% 0.23/0.70 thf(f1205,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : variable > real] : ((vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X0),X1),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X0),X1)) = X0)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f807])).
% 0.23/0.70 thf(f807,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real] : (vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X0),X1),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X0),X1)) = X0)),
% 0.23/0.70 inference(rectify,[],[f228])).
% 0.23/0.70 thf(f228,axiom,(
% 0.23/0.70 ! [X2 : variable > real,X30 : variable > real] : (vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X30),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X2),X30)) = X2)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_stateinterpol__diff)).
% 0.23/0.70 thf(f4214,plain,(
% 0.23/0.70 spl40_204),
% 0.23/0.70 inference(avatar_split_clause,[],[f1432,f4212])).
% 0.23/0.70 thf(f4212,plain,(
% 0.23/0.70 spl40_204 <=> ! [X0 : variable > real,X1 : variable > real] : (vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real))))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),X0),X1),bot_bot(set(variable))) = X1)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_204])])).
% 0.23/0.70 thf(f1432,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : variable > real] : ((vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,real))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,sTfun(real,real)))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(set(variable),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,real))))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable))))))),X0),X1),bot_bot(set(variable))) = X1)) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1201,f1098])).
% 0.23/0.70 thf(f1201,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : variable > real] : ((vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X0),X1),bot_bot(set(variable))) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f803])).
% 0.23/0.70 thf(f803,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable > real] : (vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X0),X1),bot_bot(set(variable))) = X1)),
% 0.23/0.70 inference(rectify,[],[f222])).
% 0.23/0.70 thf(f222,axiom,(
% 0.23/0.70 ! [X2 : variable > real,X30 : variable > real] : (vAPP(set(variable),sTfun(variable,real),vAPP(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,real))),stateinterpol,X2),X30),bot_bot(set(variable))) = X30)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_stateinterpol__empty)).
% 0.23/0.70 thf(f4199,plain,(
% 0.23/0.70 spl40_203),
% 0.23/0.70 inference(avatar_split_clause,[],[f1467,f4197])).
% 0.23/0.70 thf(f4197,plain,(
% 0.23/0.70 spl40_203 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1 > X0,X2 : X0] : (vAPP(X1,X0,X3,X4) = vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),vAPP(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0))),vAPP(sTfun(X0,sTfun(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(sTfun(X1,X0),sTfun(option(X1),X0)))),sTfun(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0))),sTfun(X0,sTfun(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(sTfun(X1,X0),sTfun(option(X1),X0)))),vAPP(sTfun(sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0)),sTfun(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(sTfun(X1,X0),sTfun(option(X1),X0)))),sTfun(sTfun(X0,sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0))),sTfun(X0,sTfun(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(sTfun(X1,X0),sTfun(option(X1),X0))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(option(X1),sTfun(X0,X0))),sTfun(X0,sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0))),vAPP(sTfun(sTfun(option(X1),sTfun(X0,X0)),sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0))),sTfun(sTfun(X0,sTfun(option(X1),sTfun(X0,X0))),sTfun(X0,sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0)))),bCOMB,sCOMB),vAPP(sTfun(option(X1),sTfun(X0,sTfun(X0,X0))),sTfun(X0,sTfun(option(X1),sTfun(X0,X0))),cCOMB,vAPP(sTfun(option(X1),$o),sTfun(option(X1),sTfun(X0,sTfun(X0,X0))),vAPP(sTfun($o,sTfun(X0,sTfun(X0,X0))),sTfun(sTfun(option(X1),$o),sTfun(option(X1),sTfun(X0,sTfun(X0,X0)))),bCOMB,if(X0)),vAPP(option(X1),sTfun(option(X1),$o),vEQ(option(X1)),none(X1))))))),vAPP(sTfun(option(X1),X1),sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),vAPP(sTfun(sTfun(X1,X0),sTfun(sTfun(option(X1),X1),sTfun(option(X1),X0))),sTfun(sTfun(option(X1),X1),sTfun(sTfun(X1,X0),sTfun(option(X1),X0))),cCOMB,bCOMB),the(X1))),X2),X3),vAPP(X1,option(X1),some(X1),X4)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_203])])).
% 0.23/0.70 thf(f1467,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1] : ((vAPP(X1,X0,X3,X4) = vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),vAPP(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0))),vAPP(sTfun(X0,sTfun(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(sTfun(X1,X0),sTfun(option(X1),X0)))),sTfun(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0))),sTfun(X0,sTfun(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(sTfun(X1,X0),sTfun(option(X1),X0)))),vAPP(sTfun(sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0)),sTfun(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(sTfun(X1,X0),sTfun(option(X1),X0)))),sTfun(sTfun(X0,sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0))),sTfun(X0,sTfun(sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),sTfun(sTfun(X1,X0),sTfun(option(X1),X0))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(option(X1),sTfun(X0,X0))),sTfun(X0,sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0))),vAPP(sTfun(sTfun(option(X1),sTfun(X0,X0)),sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0))),sTfun(sTfun(X0,sTfun(option(X1),sTfun(X0,X0))),sTfun(X0,sTfun(sTfun(option(X1),X0),sTfun(option(X1),X0)))),bCOMB,sCOMB),vAPP(sTfun(option(X1),sTfun(X0,sTfun(X0,X0))),sTfun(X0,sTfun(option(X1),sTfun(X0,X0))),cCOMB,vAPP(sTfun(option(X1),$o),sTfun(option(X1),sTfun(X0,sTfun(X0,X0))),vAPP(sTfun($o,sTfun(X0,sTfun(X0,X0))),sTfun(sTfun(option(X1),$o),sTfun(option(X1),sTfun(X0,sTfun(X0,X0)))),bCOMB,if(X0)),vAPP(option(X1),sTfun(option(X1),$o),vEQ(option(X1)),none(X1))))))),vAPP(sTfun(option(X1),X1),sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),vAPP(sTfun(sTfun(X1,X0),sTfun(sTfun(option(X1),X1),sTfun(option(X1),X0))),sTfun(sTfun(option(X1),X1),sTfun(sTfun(X1,X0),sTfun(option(X1),X0))),cCOMB,bCOMB),the(X1))),X2),X3),vAPP(X1,option(X1),some(X1),X4)))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1371,f1219])).
% 0.23/0.70 thf(f1219,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : ((case_option(X1,X0) = vAPP(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1))),vAPP(sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),cCOMB,vAPP(sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),vAPP(sTfun(sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1)),sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),sTfun(sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1))))),bCOMB,bCOMB),vAPP(sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),vAPP(sTfun(sTfun(option(X0),sTfun(X1,X1)),sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1)))),bCOMB,sCOMB),vAPP(sTfun(option(X0),sTfun(X1,sTfun(X1,X1))),sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),cCOMB,vAPP(sTfun(option(X0),$o),sTfun(option(X0),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun($o,sTfun(X1,sTfun(X1,X1))),sTfun(sTfun(option(X0),$o),sTfun(option(X0),sTfun(X1,sTfun(X1,X1)))),bCOMB,if(X1)),vAPP(option(X0),sTfun(option(X0),$o),vEQ(option(X0)),none(X0))))))),vAPP(sTfun(option(X0),X0),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),vAPP(sTfun(sTfun(X0,X1),sTfun(sTfun(option(X0),X0),sTfun(option(X0),X1))),sTfun(sTfun(option(X0),X0),sTfun(sTfun(X0,X1),sTfun(option(X0),X1))),cCOMB,bCOMB),the(X0))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f499])).
% 0.23/0.70 thf(f499,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : (case_option(X1,X0) = vAPP(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1))),vAPP(sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),cCOMB,vAPP(sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),vAPP(sTfun(sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1)),sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),sTfun(sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1))))),bCOMB,bCOMB),vAPP(sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),vAPP(sTfun(sTfun(option(X0),sTfun(X1,X1)),sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1)))),bCOMB,sCOMB),vAPP(sTfun(option(X0),sTfun(X1,sTfun(X1,X1))),sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),cCOMB,vAPP(sTfun(option(X0),$o),sTfun(option(X0),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun($o,sTfun(X1,sTfun(X1,X1))),sTfun(sTfun(option(X0),$o),sTfun(option(X0),sTfun(X1,sTfun(X1,X1)))),bCOMB,if(X1)),vAPP(option(X0),sTfun(option(X0),$o),vEQ(option(X0)),none(X0))))))),vAPP(sTfun(option(X0),X0),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),vAPP(sTfun(sTfun(X0,X1),sTfun(sTfun(option(X0),X0),sTfun(option(X0),X1))),sTfun(sTfun(option(X0),X0),sTfun(sTfun(X0,X1),sTfun(option(X0),X1))),cCOMB,bCOMB),the(X0))))),
% 0.23/0.70 inference(fool_elimination,[],[f498])).
% 0.23/0.70 thf(f498,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : (case_option(X1,X0) = (^[X2 : X1, X3 : X0 > X1, X4 : option(X0)] : (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP($o,sTfun(X1,sTfun(X1,X1)),if(X1),(none(X0) = X4)),X2),vAPP(X0,X1,X3,vAPP(option(X0),X0,the(X0),X4))))))),
% 0.23/0.70 inference(rectify,[],[f187])).
% 0.23/0.70 thf(f187,axiom,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : (case_option(X1,X0) = (^[X94 : X1, X95 : X0 > X1, X96 : option(X0)] : (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP($o,sTfun(X1,sTfun(X1,X1)),if(X1),(none(X0) = X96)),X94),vAPP(X0,X1,X95,vAPP(option(X0),X0,the(X0),X96))))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_option_Ocase__eq__if)).
% 0.23/0.70 thf(f1371,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1] : ((vAPP(X1,X0,X3,X4) = vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X2),X3),vAPP(X1,option(X1),some(X1),X4)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f851])).
% 0.23/0.70 thf(f851,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1] : (vAPP(X1,X0,X3,X4) = vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X2),X3),vAPP(X1,option(X1),some(X1),X4)))),
% 0.23/0.70 inference(rectify,[],[f184])).
% 0.23/0.70 thf(f184,axiom,(
% 0.23/0.70 ! [X1 : $tType,X0 : $tType,X73 : X1,X74 : X0 > X1,X54 : X0] : (vAPP(option(X0),X1,vAPP(sTfun(X0,X1),sTfun(option(X0),X1),vAPP(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),case_option(X1,X0),X73),X74),vAPP(X0,option(X0),some(X0),X54)) = vAPP(X0,X1,X74,X54))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_option_Osimps_I5_J)).
% 0.23/0.70 thf(f4190,plain,(
% 0.23/0.70 spl40_202),
% 0.23/0.70 inference(avatar_split_clause,[],[f1453,f4188])).
% 0.23/0.70 thf(f4188,plain,(
% 0.23/0.70 spl40_202 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > X1,X2 : X1] : (vAPP(option(X0),X1,vAPP(sTfun(X0,X1),sTfun(option(X0),X1),vAPP(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),vAPP(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1))),vAPP(sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),cCOMB,vAPP(sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),vAPP(sTfun(sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1)),sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),sTfun(sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1))))),bCOMB,bCOMB),vAPP(sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),vAPP(sTfun(sTfun(option(X0),sTfun(X1,X1)),sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1)))),bCOMB,sCOMB),vAPP(sTfun(option(X0),sTfun(X1,sTfun(X1,X1))),sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),cCOMB,vAPP(sTfun(option(X0),$o),sTfun(option(X0),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun($o,sTfun(X1,sTfun(X1,X1))),sTfun(sTfun(option(X0),$o),sTfun(option(X0),sTfun(X1,sTfun(X1,X1)))),bCOMB,if(X1)),vAPP(option(X0),sTfun(option(X0),$o),vEQ(option(X0)),none(X0))))))),vAPP(sTfun(option(X0),X0),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),vAPP(sTfun(sTfun(X0,X1),sTfun(sTfun(option(X0),X0),sTfun(option(X0),X1))),sTfun(sTfun(option(X0),X0),sTfun(sTfun(X0,X1),sTfun(option(X0),X1))),cCOMB,bCOMB),the(X0))),X2),X3),none(X0)) = X2)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_202])])).
% 0.23/0.70 thf(f1453,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0 > X1] : ((vAPP(option(X0),X1,vAPP(sTfun(X0,X1),sTfun(option(X0),X1),vAPP(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),vAPP(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1))),vAPP(sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),cCOMB,vAPP(sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),vAPP(sTfun(sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1)),sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)))),sTfun(sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(X1,sTfun(sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),sTfun(sTfun(X0,X1),sTfun(option(X0),X1))))),bCOMB,bCOMB),vAPP(sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),vAPP(sTfun(sTfun(option(X0),sTfun(X1,X1)),sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1))),sTfun(sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),sTfun(X1,sTfun(sTfun(option(X0),X1),sTfun(option(X0),X1)))),bCOMB,sCOMB),vAPP(sTfun(option(X0),sTfun(X1,sTfun(X1,X1))),sTfun(X1,sTfun(option(X0),sTfun(X1,X1))),cCOMB,vAPP(sTfun(option(X0),$o),sTfun(option(X0),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun($o,sTfun(X1,sTfun(X1,X1))),sTfun(sTfun(option(X0),$o),sTfun(option(X0),sTfun(X1,sTfun(X1,X1)))),bCOMB,if(X1)),vAPP(option(X0),sTfun(option(X0),$o),vEQ(option(X0)),none(X0))))))),vAPP(sTfun(option(X0),X0),sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),vAPP(sTfun(sTfun(X0,X1),sTfun(sTfun(option(X0),X0),sTfun(option(X0),X1))),sTfun(sTfun(option(X0),X0),sTfun(sTfun(X0,X1),sTfun(option(X0),X1))),cCOMB,bCOMB),the(X0))),X2),X3),none(X0)) = X2)) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1318,f1219])).
% 0.23/0.70 thf(f1318,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0 > X1] : ((vAPP(option(X0),X1,vAPP(sTfun(X0,X1),sTfun(option(X0),X1),vAPP(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),case_option(X1,X0),X2),X3),none(X0)) = X2)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f832])).
% 0.23/0.70 thf(f832,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X0 > X1] : (vAPP(option(X0),X1,vAPP(sTfun(X0,X1),sTfun(option(X0),X1),vAPP(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),case_option(X1,X0),X2),X3),none(X0)) = X2)),
% 0.23/0.70 inference(rectify,[],[f183])).
% 0.23/0.70 thf(f183,axiom,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X73 : X1,X74 : X0 > X1] : (vAPP(option(X0),X1,vAPP(sTfun(X0,X1),sTfun(option(X0),X1),vAPP(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),case_option(X1,X0),X73),X74),none(X0)) = X73)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_option_Osimps_I4_J)).
% 0.23/0.70 thf(f4184,plain,(
% 0.23/0.70 spl40_201),
% 0.23/0.70 inference(avatar_split_clause,[],[f1431,f4182])).
% 0.23/0.70 thf(f4182,plain,(
% 0.23/0.70 spl40_201 <=> ! [X0 : variable > real,X1 : variable] : (vAPP(real,sTfun(variable,real),vAPP(variable,sTfun(real,sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(variable,sTfun(real,sTfun(variable,real))),vAPP(sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,sTfun(variable,real)))),cCOMB,vAPP(sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),vAPP(sTfun(sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),sTfun(sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(real,sTfun(variable,sTfun(real,real))),sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(real,sTfun(variable,sTfun(real,real))),sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real))))),bCOMB,cCOMB),vAPP(sTfun(variable,sTfun(variable,$o)),sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(variable,sTfun(variable,$o)),sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vEQ(variable)))))),X0),X1),vAPP(variable,real,X0,X1)) = X0)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_201])])).
% 0.23/0.70 thf(f1431,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : variable] : ((vAPP(real,sTfun(variable,real),vAPP(variable,sTfun(real,sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(variable,sTfun(real,sTfun(variable,real))),vAPP(sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,sTfun(variable,real)))),cCOMB,vAPP(sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),vAPP(sTfun(sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),sTfun(sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(real,sTfun(variable,sTfun(real,real))),sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(real,sTfun(variable,sTfun(real,real))),sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real))))),bCOMB,cCOMB),vAPP(sTfun(variable,sTfun(variable,$o)),sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(variable,sTfun(variable,$o)),sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vEQ(variable)))))),X0),X1),vAPP(variable,real,X0,X1)) = X0)) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1200,f1099])).
% 0.23/0.70 thf(f1099,plain,(
% 0.23/0.70 (denotational_repv = vAPP(sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,sTfun(variable,real)))),cCOMB,vAPP(sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),vAPP(sTfun(sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),sTfun(sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(real,sTfun(variable,sTfun(real,real))),sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(real,sTfun(variable,sTfun(real,real))),sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real))))),bCOMB,cCOMB),vAPP(sTfun(variable,sTfun(variable,$o)),sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(variable,sTfun(variable,$o)),sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vEQ(variable)))))))),
% 0.23/0.70 inference(cnf_transformation,[],[f311])).
% 0.23/0.70 thf(f311,plain,(
% 0.23/0.70 (denotational_repv = vAPP(sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,sTfun(variable,real)))),cCOMB,vAPP(sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),vAPP(sTfun(sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real)))),sTfun(sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(variable,sTfun(sTfun(variable,real),sTfun(real,sTfun(variable,real))))),bCOMB,cCOMB),vAPP(sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),vAPP(sTfun(sTfun(real,sTfun(variable,sTfun(real,real))),sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),sTfun(sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real))))),bCOMB,vAPP(sTfun(sTfun(variable,sTfun(real,real)),sTfun(sTfun(variable,real),sTfun(variable,real))),sTfun(sTfun(real,sTfun(variable,sTfun(real,real))),sTfun(real,sTfun(sTfun(variable,real),sTfun(variable,real)))),bCOMB,sCOMB)),vAPP(sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,sTfun(real,sTfun(real,real))),sTfun(real,sTfun(variable,sTfun(real,real)))),sTfun(sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(variable,sTfun(real,sTfun(variable,sTfun(real,real))))),bCOMB,cCOMB),vAPP(sTfun(variable,sTfun(variable,$o)),sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real)))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),sTfun(sTfun(variable,sTfun(variable,$o)),sTfun(variable,sTfun(variable,sTfun(real,sTfun(real,real))))),bCOMB,vAPP(sTfun($o,sTfun(real,sTfun(real,real))),sTfun(sTfun(variable,$o),sTfun(variable,sTfun(real,sTfun(real,real)))),bCOMB,if(real))),vEQ(variable)))))))),
% 0.23/0.70 inference(fool_elimination,[],[f310])).
% 0.23/0.70 thf(f310,plain,(
% 0.23/0.70 (denotational_repv = (^[X0 : variable > real, X1 : variable, X2 : real, X3 : variable] : (vAPP(real,real,vAPP(real,sTfun(real,real),vAPP($o,sTfun(real,sTfun(real,real)),if(real),(X1 = X3)),X2),vAPP(variable,real,X0,X3)))))),
% 0.23/0.70 inference(rectify,[],[f134])).
% 0.23/0.70 thf(f134,axiom,(
% 0.23/0.70 (denotational_repv = (^[X33 : variable > real, X12 : variable, X75 : real, X20 : variable] : (vAPP(real,real,vAPP(real,sTfun(real,real),vAPP($o,sTfun(real,sTfun(real,real)),if(real),(X12 = X20)),X75),vAPP(variable,real,X33,X20)))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_repv__def__correct)).
% 0.23/0.70 thf(f1200,plain,(
% 0.23/0.70 ( ! [X0 : variable > real,X1 : variable] : ((vAPP(real,sTfun(variable,real),vAPP(variable,sTfun(real,sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(variable,sTfun(real,sTfun(variable,real))),denotational_repv,X0),X1),vAPP(variable,real,X0,X1)) = X0)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f802])).
% 0.23/0.70 thf(f802,plain,(
% 0.23/0.70 ! [X0 : variable > real,X1 : variable] : (vAPP(real,sTfun(variable,real),vAPP(variable,sTfun(real,sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(variable,sTfun(real,sTfun(variable,real))),denotational_repv,X0),X1),vAPP(variable,real,X0,X1)) = X0)),
% 0.23/0.70 inference(rectify,[],[f130])).
% 0.23/0.70 thf(f130,axiom,(
% 0.23/0.70 ! [X30 : variable > real,X8 : variable] : (vAPP(real,sTfun(variable,real),vAPP(variable,sTfun(real,sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(variable,sTfun(real,sTfun(variable,real))),denotational_repv,X30),X8),vAPP(variable,real,X30,X8)) = X30)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_repv__self)).
% 0.23/0.70 thf(f4175,plain,(
% 0.23/0.70 spl40_200),
% 0.23/0.70 inference(avatar_split_clause,[],[f1429,f4173])).
% 0.23/0.70 thf(f4173,plain,(
% 0.23/0.70 spl40_200 <=> ! [X0 : $tType] : (vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),$o),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),$o)),sCOMB,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(set(X0),set(X0)),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,vAPP(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0))),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0)))),bCOMB,insert(X0)),the_elem(X0))),bot_bot(set(X0))))),iCOMB) = vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_200])])).
% 0.23/0.70 thf(f1429,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : ((vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),$o),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),$o)),sCOMB,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(set(X0),set(X0)),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,vAPP(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0))),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0)))),bCOMB,insert(X0)),the_elem(X0))),bot_bot(set(X0))))),iCOMB) = vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1121,f1120])).
% 0.23/0.70 thf(f1120,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : ((is_singleton(X0) = vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),$o),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),$o)),sCOMB,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(set(X0),set(X0)),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,vAPP(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0))),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0)))),bCOMB,insert(X0)),the_elem(X0))),bot_bot(set(X0))))),iCOMB))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f335])).
% 0.23/0.70 thf(f335,plain,(
% 0.23/0.70 ! [X0 : $tType] : (is_singleton(X0) = vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),$o),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),$o)),sCOMB,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(set(X0),set(X0)),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,vAPP(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0))),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0)))),bCOMB,insert(X0)),the_elem(X0))),bot_bot(set(X0))))),iCOMB))),
% 0.23/0.70 inference(fool_elimination,[],[f334])).
% 0.23/0.70 thf(f334,plain,(
% 0.23/0.70 ! [X0 : $tType] : (is_singleton(X0) = (^[X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),vAPP(set(X0),X0,the_elem(X0),X1)),bot_bot(set(X0))) = X1))))),
% 0.23/0.70 inference(rectify,[],[f105])).
% 0.23/0.70 thf(f105,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (is_singleton(X0) = (^[X28 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),vAPP(set(X0),X0,the_elem(X0),X28)),bot_bot(set(X0))) = X28))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_is__singleton__the__elem)).
% 0.23/0.70 thf(f1121,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : ((is_singleton(X0) = vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f337])).
% 0.23/0.70 thf(f337,plain,(
% 0.23/0.70 ! [X0 : $tType] : (is_singleton(X0) = vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))))),
% 0.23/0.70 inference(fool_elimination,[],[f336])).
% 0.23/0.70 thf(f336,plain,(
% 0.23/0.70 ! [X0 : $tType] : (is_singleton(X0) = (^[X1 : set(X0)] : (? [X2 : X0] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0))) = X1))))),
% 0.23/0.70 inference(rectify,[],[f110])).
% 0.23/0.70 thf(f110,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (is_singleton(X0) = (^[X28 : set(X0)] : (? [X12 : X0] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X12),bot_bot(set(X0))) = X28))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_is__singleton__def)).
% 0.23/0.70 thf(f4161,plain,(
% 0.23/0.70 spl40_199),
% 0.23/0.70 inference(avatar_split_clause,[],[f1118,f4159])).
% 0.23/0.70 thf(f4159,plain,(
% 0.23/0.70 spl40_199 <=> ! [X0 : $tType] : (vSIGMA(option(X0)) = vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o)),sCOMB,vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o))),bCOMB,vOR),vAPP(option(X0),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun(option(X0),$o)),sTfun(option(X0),sTfun(sTfun(option(X0),$o),$o)),cCOMB,iCOMB),none(X0)))),vAPP(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(option(X0),$o),sTfun(sTfun(X0,option(X0)),sTfun(X0,$o))),sTfun(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o))),cCOMB,bCOMB),some(X0)))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_199])])).
% 0.23/0.70 thf(f1118,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : ((vSIGMA(option(X0)) = vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o)),sCOMB,vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o))),bCOMB,vOR),vAPP(option(X0),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun(option(X0),$o)),sTfun(option(X0),sTfun(sTfun(option(X0),$o),$o)),cCOMB,iCOMB),none(X0)))),vAPP(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(option(X0),$o),sTfun(sTfun(X0,option(X0)),sTfun(X0,$o))),sTfun(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o))),cCOMB,bCOMB),some(X0)))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f331])).
% 0.23/0.70 thf(f331,plain,(
% 0.23/0.70 ! [X0 : $tType] : (vSIGMA(option(X0)) = vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o)),sCOMB,vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o))),bCOMB,vOR),vAPP(option(X0),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun(option(X0),$o)),sTfun(option(X0),sTfun(sTfun(option(X0),$o),$o)),cCOMB,iCOMB),none(X0)))),vAPP(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(option(X0),$o),sTfun(sTfun(X0,option(X0)),sTfun(X0,$o))),sTfun(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o))),cCOMB,bCOMB),some(X0)))))),
% 0.23/0.70 inference(fool_elimination,[],[f330])).
% 0.23/0.70 thf(f330,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((^[X1 : option(X0) > $o] : (? [X2 : option(X0)] : vAPP(option(X0),$o,X1,X2))) = (^[X3 : option(X0) > $o] : (? [X4 : X0] : vAPP(option(X0),$o,X3,vAPP(X0,option(X0),some(X0),X4)) | vAPP(option(X0),$o,X3,none(X0)))))),
% 0.23/0.70 inference(rectify,[],[f154])).
% 0.23/0.70 thf(f154,axiom,(
% 0.23/0.70 ! [X0 : $tType] : ((^[X79 : option(X0) > $o] : (? [X80 : option(X0)] : vAPP(option(X0),$o,X79,X80))) = (^[X81 : option(X0) > $o] : (? [X12 : X0] : vAPP(option(X0),$o,X81,vAPP(X0,option(X0),some(X0),X12)) | vAPP(option(X0),$o,X81,none(X0)))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_split__option__ex)).
% 0.23/0.70 thf(f4157,plain,(
% 0.23/0.70 spl40_198),
% 0.23/0.70 inference(avatar_split_clause,[],[f1117,f4155])).
% 0.23/0.70 thf(f4155,plain,(
% 0.23/0.70 spl40_198 <=> ! [X0 : $tType] : (vPI(option(X0)) = vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o)),sCOMB,vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o))),bCOMB,vAND),vAPP(option(X0),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun(option(X0),$o)),sTfun(option(X0),sTfun(sTfun(option(X0),$o),$o)),cCOMB,iCOMB),none(X0)))),vAPP(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o)),bCOMB,vPI(X0)),vAPP(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(option(X0),$o),sTfun(sTfun(X0,option(X0)),sTfun(X0,$o))),sTfun(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o))),cCOMB,bCOMB),some(X0)))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_198])])).
% 0.23/0.70 thf(f1117,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : ((vPI(option(X0)) = vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o)),sCOMB,vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o))),bCOMB,vAND),vAPP(option(X0),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun(option(X0),$o)),sTfun(option(X0),sTfun(sTfun(option(X0),$o),$o)),cCOMB,iCOMB),none(X0)))),vAPP(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o)),bCOMB,vPI(X0)),vAPP(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(option(X0),$o),sTfun(sTfun(X0,option(X0)),sTfun(X0,$o))),sTfun(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o))),cCOMB,bCOMB),some(X0)))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f329])).
% 0.23/0.70 thf(f329,plain,(
% 0.23/0.70 ! [X0 : $tType] : (vPI(option(X0)) = vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),$o)),sCOMB,vAPP(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(sTfun(option(X0),$o),$o),sTfun(sTfun(option(X0),$o),sTfun($o,$o))),bCOMB,vAND),vAPP(option(X0),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(option(X0),$o),sTfun(option(X0),$o)),sTfun(option(X0),sTfun(sTfun(option(X0),$o),$o)),cCOMB,iCOMB),none(X0)))),vAPP(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),sTfun(sTfun(option(X0),$o),$o)),bCOMB,vPI(X0)),vAPP(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(option(X0),$o),sTfun(sTfun(X0,option(X0)),sTfun(X0,$o))),sTfun(sTfun(X0,option(X0)),sTfun(sTfun(option(X0),$o),sTfun(X0,$o))),cCOMB,bCOMB),some(X0)))))),
% 0.23/0.70 inference(fool_elimination,[],[f328])).
% 0.23/0.70 thf(f328,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((^[X1 : option(X0) > $o] : (! [X2 : option(X0)] : vAPP(option(X0),$o,X1,X2))) = (^[X3 : option(X0) > $o] : (! [X4 : X0] : vAPP(option(X0),$o,X3,vAPP(X0,option(X0),some(X0),X4)) & vAPP(option(X0),$o,X3,none(X0)))))),
% 0.23/0.70 inference(rectify,[],[f155])).
% 0.23/0.70 thf(f155,axiom,(
% 0.23/0.70 ! [X0 : $tType] : ((^[X79 : option(X0) > $o] : (! [X80 : option(X0)] : vAPP(option(X0),$o,X79,X80))) = (^[X81 : option(X0) > $o] : (! [X12 : X0] : vAPP(option(X0),$o,X81,vAPP(X0,option(X0),some(X0),X12)) & vAPP(option(X0),$o,X81,none(X0)))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_split__option__all)).
% 0.23/0.70 thf(f4147,plain,(
% 0.23/0.70 ~spl40_197 | ~spl40_84 | ~spl40_103 | ~spl40_161 | ~spl40_167 | spl40_196),
% 0.23/0.70 inference(avatar_split_clause,[],[f4142,f4136,f3703,f3569,f2925,f2780,f4144])).
% 0.23/0.70 thf(f2780,plain,(
% 0.23/0.70 spl40_84 <=> ! [X0 : $tType,X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),bot_bot(set(X0))) = X1)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_84])])).
% 0.23/0.70 thf(f2925,plain,(
% 0.23/0.70 spl40_103 <=> ! [X0 : $tType,X1 : X0] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0))) = vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_103])])).
% 0.23/0.70 thf(f3569,plain,(
% 0.23/0.70 spl40_161 <=> ! [X0 : $tType,X3 : set(X0),X2 : X0,X1 : X0] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_161])])).
% 0.23/0.70 thf(f3703,plain,(
% 0.23/0.70 spl40_167 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X3)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_167])])).
% 0.23/0.70 thf(f4136,plain,(
% 0.23/0.70 spl40_196 <=> ($true = vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))),u)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_196])])).
% 0.23/0.70 thf(f4142,plain,(
% 0.23/0.70 ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),vAPP(option(variable),set(variable),set_option(variable),vAPP(variable,option(variable),some(variable),vAPP(char,variable,rVar,x))))))) | (~spl40_84 | ~spl40_103 | ~spl40_161 | ~spl40_167 | spl40_196)),
% 0.23/0.70 inference(forward_demodulation,[],[f4141,f2926])).
% 0.23/0.70 thf(f2926,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0))) = vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1)))) ) | ~spl40_103),
% 0.23/0.70 inference(avatar_component_clause,[],[f2925])).
% 0.23/0.70 thf(f4141,plain,(
% 0.23/0.70 ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),bot_bot(set(variable))))))) | (~spl40_84 | ~spl40_161 | ~spl40_167 | spl40_196)),
% 0.23/0.70 inference(forward_demodulation,[],[f4140,f3570])).
% 0.23/0.70 thf(f3570,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X3 : set(X0),X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3)))) ) | ~spl40_161),
% 0.23/0.70 inference(avatar_component_clause,[],[f3569])).
% 0.23/0.70 thf(f4140,plain,(
% 0.23/0.70 ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))))) | (~spl40_84 | ~spl40_167 | spl40_196)),
% 0.23/0.70 inference(forward_demodulation,[],[f4138,f3744])).
% 0.23/0.70 thf(f3744,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X1) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X2))) ) | (~spl40_84 | ~spl40_167)),
% 0.23/0.70 inference(forward_demodulation,[],[f3711,f2781])).
% 0.23/0.70 thf(f2781,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),bot_bot(set(X0))) = X1)) ) | ~spl40_84),
% 0.23/0.70 inference(avatar_component_clause,[],[f2780])).
% 0.23/0.70 thf(f3711,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X1) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),bot_bot(set(X0)))))) ) | (~spl40_84 | ~spl40_167)),
% 0.23/0.70 inference(superposition,[],[f3704,f2781])).
% 0.23/0.70 thf(f3704,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X3)))) ) | ~spl40_167),
% 0.23/0.70 inference(avatar_component_clause,[],[f3703])).
% 0.23/0.70 thf(f4138,plain,(
% 0.23/0.70 ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))),u))) | spl40_196),
% 0.23/0.70 inference(avatar_component_clause,[],[f4136])).
% 0.23/0.70 thf(f4139,plain,(
% 0.23/0.70 ~spl40_196),
% 0.23/0.70 inference(avatar_split_clause,[],[f1424,f4136])).
% 0.23/0.70 thf(f1424,plain,(
% 0.23/0.70 ($true != vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)))),bCOMB,vAPP(sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),sTfun(sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(set(variable),$o))),bCOMB,vAPP(sTfun(sTfun(variable,$o),$o),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),$o)),bCOMB,vPI(variable)))),vAPP(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),vAPP(sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),sTfun(sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o))))),bCOMB,vAPP(sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,$o)),sTfun(sTfun(variable,real),sTfun(set(variable),sTfun(variable,$o)))),bCOMB,vAPP(sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(variable,$o),sTfun(set(variable),sTfun(variable,$o))),cCOMB,vAPP(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,$o))),sTfun(sTfun(set(variable),sTfun(variable,sTfun($o,$o))),sTfun(set(variable),sTfun(sTfun(variable,$o),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o))),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(variable,$o),sTfun(variable,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o)),vAPP(sTfun(sTfun(variable,$o),sTfun(variable,$o)),sTfun(sTfun(set(variable),sTfun(variable,$o)),sTfun(set(variable),sTfun(variable,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(variable,$o),sTfun(variable,$o)),bCOMB,vNOT)),vAPP(sTfun(variable,sTfun(set(variable),$o)),sTfun(set(variable),sTfun(variable,$o)),cCOMB,member(variable)))))))),vAPP(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o))),vAPP(sTfun(sTfun(variable,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,$o))),sTfun(sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),sTfun(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(variable,$o)))),bCOMB,sCOMB),vAPP(sTfun(real,sTfun(real,$o)),sTfun(sTfun(variable,real),sTfun(variable,sTfun(real,$o))),bCOMB,vEQ(real))))),vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))),u)))),
% 0.23/0.70 inference(definition_unfolding,[],[f1094,f1104])).
% 0.23/0.70 thf(f1094,plain,(
% 0.23/0.70 (vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))),u)) != $true)),
% 0.23/0.70 inference(cnf_transformation,[],[f784])).
% 0.23/0.70 thf(f784,plain,(
% 0.23/0.70 (vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))),u)) != $true)),
% 0.23/0.70 inference(flattening,[],[f307])).
% 0.23/0.70 thf(f307,plain,(
% 0.23/0.70 ~(vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))),u)) = $true)),
% 0.23/0.70 inference(fool_elimination,[],[f306])).
% 0.23/0.70 thf(f306,plain,(
% 0.23/0.70 ~vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))),u))),
% 0.23/0.70 inference(rectify,[],[f303])).
% 0.23/0.70 thf(f303,negated_conjecture,(
% 0.23/0.70 ~vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))),u))),
% 0.23/0.70 inference(negated_conjecture,[],[f302])).
% 0.23/0.70 thf(f302,conjecture,(
% 0.23/0.70 vAPP(set(variable),$o,vAPP(sTfun(variable,real),sTfun(set(variable),$o),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),sTfun(set(variable),$o)),denota1419872369iation,vAPP(real,sTfun(variable,real),f,zero_zero(real))),omega),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable))))),u))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.23/0.70 thf(f4110,plain,(
% 0.23/0.70 spl40_195),
% 0.23/0.70 inference(avatar_split_clause,[],[f1343,f4108])).
% 0.23/0.70 thf(f4108,plain,(
% 0.23/0.70 spl40_195 <=> ! [X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X3 : set(variable),X2 : trm,X1 : set(variable)] : ((vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X3),X2)) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X3),X2)) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_195])])).
% 0.23/0.70 thf(f1343,plain,(
% 0.23/0.70 ( ! [X2 : trm,X3 : set(variable),X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X1 : set(variable)] : ((vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X3),X2)) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X3),X2)) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f976])).
% 0.23/0.70 thf(f976,plain,(
% 0.23/0.70 ! [X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X1 : set(variable),X2 : trm,X3 : set(variable)] : ((vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X3),X2)) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X3),X2)) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2)))),
% 0.23/0.70 inference(flattening,[],[f975])).
% 0.23/0.70 thf(f975,plain,(
% 0.23/0.70 ! [X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X1 : set(variable),X2 : trm,X3 : set(variable)] : (((vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X3),X2)) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X3),X2))) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2)))),
% 0.23/0.70 inference(ennf_transformation,[],[f843])).
% 0.23/0.70 thf(f843,plain,(
% 0.23/0.70 ! [X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X1 : set(variable),X2 : trm,X3 : set(variable)] : ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2)) => ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X3),X2)) => (vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X3),X2))))),
% 0.23/0.70 inference(rectify,[],[f118])).
% 0.23/0.70 thf(f118,axiom,(
% 0.23/0.70 ! [X70 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X31 : set(variable),X50 : trm,X32 : set(variable)] : ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X70),X31),X50)) => ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X70),X32),X50)) => (vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X70),X31),X50) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X70),X32),X50))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_usubstappt__det)).
% 0.23/0.70 thf(f4088,plain,(
% 0.23/0.70 spl40_194),
% 0.23/0.70 inference(avatar_split_clause,[],[f1328,f4086])).
% 0.23/0.70 thf(f4086,plain,(
% 0.23/0.70 spl40_194 <=> ! [X0 : set(sTfun(variable,real)),X3 : set(variable),X2 : variable > real,X1 : set(sTfun(variable,real))] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),vAPP(set(sTfun(variable,real)),sTfun(set(sTfun(variable,real)),set(sTfun(variable,real))),sup_sup(set(sTfun(variable,real))),X0),X1)),X2),X3) = vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),vAPP(set(sTfun(variable,real)),sTfun(set(sTfun(variable,real)),set(sTfun(variable,real))),sup_sup(set(sTfun(variable,real))),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X2),X3)),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X1),X2),X3)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_194])])).
% 0.23/0.70 thf(f1328,plain,(
% 0.23/0.70 ( ! [X2 : variable > real,X3 : set(variable),X0 : set(sTfun(variable,real)),X1 : set(sTfun(variable,real))] : ((vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),vAPP(set(sTfun(variable,real)),sTfun(set(sTfun(variable,real)),set(sTfun(variable,real))),sup_sup(set(sTfun(variable,real))),X0),X1)),X2),X3) = vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),vAPP(set(sTfun(variable,real)),sTfun(set(sTfun(variable,real)),set(sTfun(variable,real))),sup_sup(set(sTfun(variable,real))),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X2),X3)),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X1),X2),X3)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f842])).
% 0.23/0.70 thf(f842,plain,(
% 0.23/0.70 ! [X0 : set(sTfun(variable,real)),X1 : set(sTfun(variable,real)),X2 : variable > real,X3 : set(variable)] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),vAPP(set(sTfun(variable,real)),sTfun(set(sTfun(variable,real)),set(sTfun(variable,real))),sup_sup(set(sTfun(variable,real))),X0),X1)),X2),X3) = vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),vAPP(set(sTfun(variable,real)),sTfun(set(sTfun(variable,real)),set(sTfun(variable,real))),sup_sup(set(sTfun(variable,real))),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X2),X3)),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X1),X2),X3)))),
% 0.23/0.70 inference(rectify,[],[f148])).
% 0.23/0.70 thf(f148,axiom,(
% 0.23/0.70 ! [X76 : set(sTfun(variable,real)),X78 : set(sTfun(variable,real)),X2 : variable > real,X32 : set(variable)] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),vAPP(set(sTfun(variable,real)),sTfun(set(sTfun(variable,real)),set(sTfun(variable,real))),sup_sup(set(sTfun(variable,real))),X76),X78)),X2),X32) = vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),vAPP(set(sTfun(variable,real)),sTfun(set(sTfun(variable,real)),set(sTfun(variable,real))),sup_sup(set(sTfun(variable,real))),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X76),X2),X32)),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X78),X2),X32)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_selectlike__union)).
% 0.23/0.70 thf(f4018,plain,(
% 0.23/0.70 spl40_193),
% 0.23/0.70 inference(avatar_split_clause,[],[f2136,f4016])).
% 0.23/0.70 thf(f4016,plain,(
% 0.23/0.70 spl40_193 <=> ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),X1)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK8(X0),X1)),X1)) | (bot_bot(set(X0)) = X1))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_193])])).
% 0.23/0.70 thf(f2136,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),X1)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK8(X0),X1)),X1)) | (bot_bot(set(X0)) = X1)) )),
% 0.23/0.70 inference(forward_demodulation,[],[f1437,f1429])).
% 0.23/0.70 thf(f1437,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),$o),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),$o)),sCOMB,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(set(X0),set(X0)),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,vAPP(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0))),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0)))),bCOMB,insert(X0)),the_elem(X0))),bot_bot(set(X0))))),iCOMB),X1)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK8(X0),X1)),X1)) | (bot_bot(set(X0)) = X1)) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1227,f1120])).
% 0.23/0.70 thf(f1227,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,is_singleton(X0),X1)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK8(X0),X1)),X1)) | (bot_bot(set(X0)) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1037])).
% 0.23/0.70 thf(f1037,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,is_singleton(X0),X1)) | ((vAPP(set(X0),X0,sK8(X0),X1) != vAPP(set(X0),X0,sK9(X0),X1)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK9(X0),X1)),X1)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK8(X0),X1)),X1))) | (bot_bot(set(X0)) = X1))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f920,f1036])).
% 0.23/0.70 thf(f1036,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1))) => ((vAPP(set(X0),X0,sK8(X0),X1) != vAPP(set(X0),X0,sK9(X0),X1)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK9(X0),X1)),X1)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK8(X0),X1)),X1))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f920,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,is_singleton(X0),X1)) | ? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1))) | (bot_bot(set(X0)) = X1))),
% 0.23/0.70 inference(flattening,[],[f919])).
% 0.23/0.70 thf(f919,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : ((($true = vAPP(set(X0),$o,is_singleton(X0),X1)) | ? [X2 : X0,X3 : X0] : (((X2 != X3) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1))) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)))) | (bot_bot(set(X0)) = X1))),
% 0.23/0.70 inference(ennf_transformation,[],[f509])).
% 0.23/0.70 thf(f509,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : ((bot_bot(set(X0)) != X1) => (! [X2 : X0,X3 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) => (X2 = X3))) => ($true = vAPP(set(X0),$o,is_singleton(X0),X1))))),
% 0.23/0.70 inference(fool_elimination,[],[f508])).
% 0.23/0.70 thf(f508,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : ((bot_bot(set(X0)) != X1) => (! [X2 : X0,X3 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1) => (X2 = X3))) => vAPP(set(X0),$o,is_singleton(X0),X1)))),
% 0.23/0.70 inference(rectify,[],[f109])).
% 0.23/0.70 thf(f109,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0)] : ((bot_bot(set(X0)) != X7) => (! [X22 : X0,X16 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X22),X7) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X16),X7) => (X16 = X22))) => vAPP(set(X0),$o,is_singleton(X0),X7)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_is__singletonI_H)).
% 0.23/0.70 thf(f4014,plain,(
% 0.23/0.70 spl40_192),
% 0.23/0.70 inference(avatar_split_clause,[],[f2135,f4012])).
% 0.23/0.70 thf(f4012,plain,(
% 0.23/0.70 spl40_192 <=> ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),X1)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK9(X0),X1)),X1)) | (bot_bot(set(X0)) = X1))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_192])])).
% 0.23/0.70 thf(f2135,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),X1)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK9(X0),X1)),X1)) | (bot_bot(set(X0)) = X1)) )),
% 0.23/0.70 inference(forward_demodulation,[],[f1436,f1429])).
% 0.23/0.70 thf(f1436,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),$o),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),$o)),sCOMB,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(set(X0),set(X0)),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,vAPP(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0))),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0)))),bCOMB,insert(X0)),the_elem(X0))),bot_bot(set(X0))))),iCOMB),X1)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK9(X0),X1)),X1)) | (bot_bot(set(X0)) = X1)) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1228,f1120])).
% 0.23/0.70 thf(f1228,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,is_singleton(X0),X1)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK9(X0),X1)),X1)) | (bot_bot(set(X0)) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1037])).
% 0.23/0.70 thf(f4002,plain,(
% 0.23/0.70 spl40_191),
% 0.23/0.70 inference(avatar_split_clause,[],[f2138,f4000])).
% 0.23/0.70 thf(f4000,plain,(
% 0.23/0.70 spl40_191 <=> ! [X0 : $tType,X1 : set(X0)] : (($true != vAPP(set(X0),$o,vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),X1)) | (vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),vAPP(set(X0),X0,sK14(X0),X1))) = X1))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_191])])).
% 0.23/0.70 thf(f2138,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : (($true != vAPP(set(X0),$o,vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),X1)) | (vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),vAPP(set(X0),X0,sK14(X0),X1))) = X1)) )),
% 0.23/0.70 inference(forward_demodulation,[],[f2137,f1429])).
% 0.23/0.70 thf(f2137,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),vAPP(set(X0),X0,sK14(X0),X1))) = X1) | ($true != vAPP(set(X0),$o,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),$o),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),$o)),sCOMB,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(set(X0),set(X0)),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,vAPP(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0))),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0)))),bCOMB,insert(X0)),the_elem(X0))),bot_bot(set(X0))))),iCOMB),X1))) )),
% 0.23/0.70 inference(forward_demodulation,[],[f1438,f1199])).
% 0.23/0.70 thf(f1438,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),vAPP(set(X0),X0,sK14(X0),X1)),bot_bot(set(X0))) = X1) | ($true != vAPP(set(X0),$o,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),$o),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),$o)),sCOMB,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(set(X0),set(X0)),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,vAPP(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0))),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0)))),bCOMB,insert(X0)),the_elem(X0))),bot_bot(set(X0))))),iCOMB),X1))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1249,f1120])).
% 0.23/0.70 thf(f1249,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),vAPP(set(X0),X0,sK14(X0),X1)),bot_bot(set(X0))) = X1) | ($true != vAPP(set(X0),$o,is_singleton(X0),X1))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1047])).
% 0.23/0.70 thf(f1047,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),vAPP(set(X0),X0,sK14(X0),X1)),bot_bot(set(X0))) = X1) | ($true != vAPP(set(X0),$o,is_singleton(X0),X1)))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f942,f1046])).
% 0.23/0.70 thf(f1046,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (? [X2 : X0] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0))) = X1) => (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),vAPP(set(X0),X0,sK14(X0),X1)),bot_bot(set(X0))) = X1))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f942,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (? [X2 : X0] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0))) = X1) | ($true != vAPP(set(X0),$o,is_singleton(X0),X1)))),
% 0.23/0.70 inference(ennf_transformation,[],[f549])).
% 0.23/0.70 thf(f549,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,is_singleton(X0),X1)) => ~! [X2 : X0] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0))) != X1))),
% 0.23/0.70 inference(fool_elimination,[],[f548])).
% 0.23/0.70 thf(f548,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (vAPP(set(X0),$o,is_singleton(X0),X1) => ~! [X2 : X0] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0))) != X1))),
% 0.23/0.70 inference(rectify,[],[f111])).
% 0.23/0.70 thf(f111,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0)] : (vAPP(set(X0),$o,is_singleton(X0),X7) => ~! [X22 : X0] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X22),bot_bot(set(X0))) != X7))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_is__singletonE)).
% 0.23/0.70 thf(f3997,plain,(
% 0.23/0.70 spl40_190),
% 0.23/0.70 inference(avatar_split_clause,[],[f2134,f3995])).
% 0.23/0.70 thf(f3995,plain,(
% 0.23/0.70 spl40_190 <=> ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),X1)) | (vAPP(set(X0),X0,sK8(X0),X1) != vAPP(set(X0),X0,sK9(X0),X1)) | (bot_bot(set(X0)) = X1))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_190])])).
% 0.23/0.70 thf(f2134,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),X1)) | (vAPP(set(X0),X0,sK8(X0),X1) != vAPP(set(X0),X0,sK9(X0),X1)) | (bot_bot(set(X0)) = X1)) )),
% 0.23/0.70 inference(forward_demodulation,[],[f1435,f1429])).
% 0.23/0.70 thf(f1435,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),$o),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),$o)),sCOMB,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(set(X0),set(X0)),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,vAPP(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0))),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0)))),bCOMB,insert(X0)),the_elem(X0))),bot_bot(set(X0))))),iCOMB),X1)) | (vAPP(set(X0),X0,sK8(X0),X1) != vAPP(set(X0),X0,sK9(X0),X1)) | (bot_bot(set(X0)) = X1)) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1229,f1120])).
% 0.23/0.70 thf(f1229,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,is_singleton(X0),X1)) | (vAPP(set(X0),X0,sK8(X0),X1) != vAPP(set(X0),X0,sK9(X0),X1)) | (bot_bot(set(X0)) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1037])).
% 0.23/0.70 thf(f3992,plain,(
% 0.23/0.70 spl40_189),
% 0.23/0.70 inference(avatar_split_clause,[],[f1327,f3990])).
% 0.23/0.70 thf(f3990,plain,(
% 0.23/0.70 spl40_189 <=> ! [X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X3 : trm,X2 : trm,X1 : set(variable)] : (vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2)),vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X3)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_189])])).
% 0.23/0.70 thf(f1327,plain,(
% 0.23/0.70 ( ! [X2 : trm,X3 : trm,X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X1 : set(variable)] : ((vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2)),vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X3)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f841])).
% 0.23/0.70 thf(f841,plain,(
% 0.23/0.70 ! [X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X1 : set(variable),X2 : trm,X3 : trm] : (vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2)),vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X3)))),
% 0.23/0.70 inference(rectify,[],[f226])).
% 0.23/0.70 thf(f226,axiom,(
% 0.23/0.70 ! [X70 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X31 : set(variable),X50 : trm,X65 : trm] : (vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X70),X31),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X50),X65)) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X70),X31),X50)),vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X70),X31),X65)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_usubstappt_Osimps_I6_J)).
% 0.23/0.70 thf(f3985,plain,(
% 0.23/0.70 spl40_188),
% 0.23/0.70 inference(avatar_split_clause,[],[f2140,f3983])).
% 0.23/0.70 thf(f3983,plain,(
% 0.23/0.70 spl40_188 <=> ! [X0 : $tType,X1 : X0] : ($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_188])])).
% 0.23/0.70 thf(f2140,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(set(X0),sTfun(X0,$o)),sTfun(set(X0),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1))))) )),
% 0.23/0.70 inference(forward_demodulation,[],[f2139,f1429])).
% 0.23/0.70 thf(f2139,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),$o),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),$o)),sCOMB,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(set(X0),set(X0)),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,vAPP(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0))),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0)))),bCOMB,insert(X0)),the_elem(X0))),bot_bot(set(X0))))),iCOMB),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1))))) )),
% 0.23/0.70 inference(forward_demodulation,[],[f1439,f1199])).
% 0.23/0.70 thf(f1439,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),$o),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),$o)),sCOMB,vAPP(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o)),vAPP(sTfun(set(X0),sTfun(set(X0),$o)),sTfun(sTfun(set(X0),set(X0)),sTfun(set(X0),sTfun(set(X0),$o))),bCOMB,vEQ(set(X0))),vAPP(set(X0),sTfun(set(X0),set(X0)),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,vAPP(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0))),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(sTfun(set(X0),X0),sTfun(set(X0),sTfun(set(X0),set(X0)))),bCOMB,insert(X0)),the_elem(X0))),bot_bot(set(X0))))),iCOMB),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0)))))) )),
% 0.23/0.70 inference(definition_unfolding,[],[f1253,f1120])).
% 0.23/0.70 thf(f1253,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(set(X0),$o,is_singleton(X0),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0)))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f557])).
% 0.23/0.70 thf(f557,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0] : ($true = vAPP(set(X0),$o,is_singleton(X0),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0)))))),
% 0.23/0.70 inference(fool_elimination,[],[f556])).
% 0.23/0.70 thf(f556,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0] : vAPP(set(X0),$o,is_singleton(X0),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0))))),
% 0.23/0.70 inference(rectify,[],[f107])).
% 0.23/0.70 thf(f107,axiom,(
% 0.23/0.70 ! [X0 : $tType,X8 : X0] : vAPP(set(X0),$o,is_singleton(X0),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X8),bot_bot(set(X0))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_is__singletonI)).
% 0.23/0.70 thf(f3970,plain,(
% 0.23/0.70 spl40_187),
% 0.23/0.70 inference(avatar_split_clause,[],[f1267,f3968])).
% 0.23/0.70 thf(f3968,plain,(
% 0.23/0.70 spl40_187 <=> ! [X2 : set(variable),X0 : set(sTfun(variable,real)),X1 : variable > real] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),uminus_uminus(set(sTfun(variable,real))),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),X2))),X1),X2) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),uminus_uminus(set(sTfun(variable,real))),X0)),X1),X2))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_187])])).
% 0.23/0.70 thf(f1267,plain,(
% 0.23/0.70 ( ! [X2 : set(variable),X0 : set(sTfun(variable,real)),X1 : variable > real] : ((vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),uminus_uminus(set(sTfun(variable,real))),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),X2))),X1),X2) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),uminus_uminus(set(sTfun(variable,real))),X0)),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f822])).
% 0.23/0.70 thf(f822,plain,(
% 0.23/0.70 ! [X0 : set(sTfun(variable,real)),X1 : variable > real,X2 : set(variable)] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),uminus_uminus(set(sTfun(variable,real))),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),X2))),X1),X2) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),uminus_uminus(set(sTfun(variable,real))),X0)),X1),X2))),
% 0.23/0.70 inference(rectify,[],[f221])).
% 0.23/0.70 thf(f221,axiom,(
% 0.23/0.70 ! [X76 : set(sTfun(variable,real)),X2 : variable > real,X32 : set(variable)] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),uminus_uminus(set(sTfun(variable,real))),vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X76),X2),X32))),X2),X32) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(sTfun(variable,real)),set(sTfun(variable,real)),uminus_uminus(set(sTfun(variable,real))),X76)),X2),X32))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_selectlike__co__selectlike)).
% 0.23/0.70 thf(f3954,plain,(
% 0.23/0.70 spl40_186),
% 0.23/0.70 inference(avatar_split_clause,[],[f1326,f3952])).
% 0.23/0.70 thf(f3952,plain,(
% 0.23/0.70 spl40_186 <=> ! [X0 : set(sTfun(variable,real)),X3 : set(variable),X2 : set(variable),X1 : variable > real] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),X2)),X1),X3) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),X2),X3)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_186])])).
% 0.23/0.70 thf(f1326,plain,(
% 0.23/0.70 ( ! [X2 : set(variable),X3 : set(variable),X0 : set(sTfun(variable,real)),X1 : variable > real] : ((vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),X2)),X1),X3) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),X2),X3)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f840])).
% 0.23/0.70 thf(f840,plain,(
% 0.23/0.70 ! [X0 : set(sTfun(variable,real)),X1 : variable > real,X2 : set(variable),X3 : set(variable)] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),X2)),X1),X3) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),X2),X3)))),
% 0.23/0.70 inference(rectify,[],[f145])).
% 0.23/0.70 thf(f145,axiom,(
% 0.23/0.70 ! [X76 : set(sTfun(variable,real)),X2 : variable > real,X32 : set(variable),X77 : set(variable)] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X76),X2),X32)),X2),X77) = vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X76),X2),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),X32),X77)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_selectlike__compose)).
% 0.23/0.70 thf(f3941,plain,(
% 0.23/0.70 spl40_185),
% 0.23/0.70 inference(avatar_split_clause,[],[f1298,f3939])).
% 0.23/0.70 thf(f3939,plain,(
% 0.23/0.70 spl40_185 <=> ! [X2 : option(trm),X0 : option(trm) > option(trm) > $o,X1 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,X1),X2)) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK26,X0))),none(trm))) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,none(trm)),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),option(trm),sK27,X0))) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK28,X0))),vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK29,X0)))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_185])])).
% 0.23/0.70 thf(f1298,plain,(
% 0.23/0.70 ( ! [X2 : option(trm),X0 : option(trm) > option(trm) > $o,X1 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,X1),X2)) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK26,X0))),none(trm))) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,none(trm)),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),option(trm),sK27,X0))) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK28,X0))),vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK29,X0))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1073])).
% 0.23/0.70 thf(f1073,plain,(
% 0.23/0.70 ! [X0 : option(trm) > option(trm) > $o,X1 : option(trm),X2 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,X1),X2)) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK26,X0))),none(trm))) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,none(trm)),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),option(trm),sK27,X0))) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK28,X0))),vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK29,X0)))))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27,sK28,sK29])],[f1069,f1072,f1071,f1070])).
% 0.23/0.70 thf(f1070,plain,(
% 0.23/0.70 ! [X0 : option(trm) > option(trm) > $o] : (? [X3 : trm] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X3)),none(trm))) => ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK26,X0))),none(trm))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1071,plain,(
% 0.23/0.70 ! [X0 : option(trm) > option(trm) > $o] : (? [X4 : option(trm)] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,none(trm)),X4)) => ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,none(trm)),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),option(trm),sK27,X0))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1072,plain,(
% 0.23/0.70 ! [X0 : option(trm) > option(trm) > $o] : (? [X5 : trm,X6 : trm] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X5)),vAPP(trm,option(trm),some(trm),X6))) => ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK28,X0))),vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),sTfun(option(trm),$o)),trm,sK29,X0)))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1069,plain,(
% 0.23/0.70 ! [X0 : option(trm) > option(trm) > $o,X1 : option(trm),X2 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,X1),X2)) | ? [X3 : trm] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X3)),none(trm))) | ? [X4 : option(trm)] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,none(trm)),X4)) | ? [X5 : trm,X6 : trm] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X5)),vAPP(trm,option(trm),some(trm),X6))))),
% 0.23/0.70 inference(rectify,[],[f959])).
% 0.23/0.70 thf(f959,plain,(
% 0.23/0.70 ! [X0 : option(trm) > option(trm) > $o,X1 : option(trm),X2 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,X1),X2)) | ? [X6 : trm] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X6)),none(trm))) | ? [X5 : option(trm)] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,none(trm)),X5)) | ? [X3 : trm,X4 : trm] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X3)),vAPP(trm,option(trm),some(trm),X4))))),
% 0.23/0.70 inference(flattening,[],[f958])).
% 0.23/0.70 thf(f958,plain,(
% 0.23/0.70 ! [X0 : option(trm) > option(trm) > $o,X1 : option(trm),X2 : option(trm)] : (((($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,X1),X2)) | ? [X6 : trm] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X6)),none(trm)))) | ? [X5 : option(trm)] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,none(trm)),X5))) | ? [X3 : trm,X4 : trm] : ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X3)),vAPP(trm,option(trm),some(trm),X4))))),
% 0.23/0.70 inference(ennf_transformation,[],[f601])).
% 0.23/0.70 thf(f601,plain,(
% 0.23/0.70 ! [X0 : option(trm) > option(trm) > $o,X1 : option(trm),X2 : option(trm)] : (! [X3 : trm,X4 : trm] : ($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X3)),vAPP(trm,option(trm),some(trm),X4))) => (! [X5 : option(trm)] : ($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,none(trm)),X5)) => (! [X6 : trm] : ($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X6)),none(trm))) => ($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,X1),X2)))))),
% 0.23/0.70 inference(fool_elimination,[],[f600])).
% 0.23/0.70 thf(f600,plain,(
% 0.23/0.70 ! [X0 : option(trm) > option(trm) > $o,X1 : option(trm),X2 : option(trm)] : (! [X3 : trm,X4 : trm] : vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X3)),vAPP(trm,option(trm),some(trm),X4)) => (! [X5 : option(trm)] : vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,none(trm)),X5) => (! [X6 : trm] : vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,vAPP(trm,option(trm),some(trm),X6)),none(trm)) => vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X0,X1),X2))))),
% 0.23/0.70 inference(rectify,[],[f159])).
% 0.23/0.70 thf(f159,axiom,(
% 0.23/0.70 ! [X11 : option(trm) > option(trm) > $o,X84 : option(trm),X85 : option(trm)] : (! [X86 : trm,X88 : trm] : vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X11,vAPP(trm,option(trm),some(trm),X86)),vAPP(trm,option(trm),some(trm),X88)) => (! [X89 : option(trm)] : vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X11,none(trm)),X89) => (! [X90 : trm] : vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X11,vAPP(trm,option(trm),some(trm),X90)),none(trm)) => vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),X11,X84),X85))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_Timeso_Oinduct)).
% 0.23/0.70 thf(f3917,plain,(
% 0.23/0.70 spl40_184),
% 0.23/0.70 inference(avatar_split_clause,[],[f1246,f3915])).
% 0.23/0.70 thf(f3915,plain,(
% 0.23/0.70 spl40_184 <=> ! [X1 : $tType,X0 : $tType] : ((sup_sup(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0))),vAPP(sTfun(sTfun(X1,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,X0))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),bCOMB,sup_sup(X0)))) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_184])])).
% 0.23/0.70 thf(f1246,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : ((sup_sup(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0))),vAPP(sTfun(sTfun(X1,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,X0))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),bCOMB,sup_sup(X0)))) | (semilattice_sup(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f939])).
% 0.23/0.70 thf(f939,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : ((sup_sup(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0))),vAPP(sTfun(sTfun(X1,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,X0))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),bCOMB,sup_sup(X0)))) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f543])).
% 0.23/0.70 thf(f543,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : ((semilattice_sup(X0) = $true) => (sup_sup(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0))),vAPP(sTfun(sTfun(X1,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,X0))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),bCOMB,sup_sup(X0)))))),
% 0.23/0.70 inference(fool_elimination,[],[f542])).
% 0.23/0.70 thf(f542,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : (semilattice_sup(X0) => (sup_sup(sTfun(X1,X0)) = (^[X2 : X1 > X0, X3 : X1 > X0, X4 : X1] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))))))),
% 0.23/0.70 inference(rectify,[],[f26])).
% 0.23/0.70 thf(f26,axiom,(
% 0.23/0.70 ! [X1 : $tType,X0 : $tType] : (semilattice_sup(X1) => (sup_sup(sTfun(X0,X1)) = (^[X14 : X0 > X1, X15 : X0 > X1, X12 : X0] : (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),sup_sup(X1),vAPP(X0,X1,X14,X12)),vAPP(X0,X1,X15,X12))))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_sup__apply)).
% 0.23/0.70 thf(f3913,plain,(
% 0.23/0.70 spl40_183),
% 0.23/0.70 inference(avatar_split_clause,[],[f1244,f3911])).
% 0.23/0.70 thf(f3911,plain,(
% 0.23/0.70 spl40_183 <=> ! [X1 : $tType,X0 : $tType] : ((inf_inf(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0))),vAPP(sTfun(sTfun(X1,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,X0))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),bCOMB,inf_inf(X0)))) | (semilattice_inf(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_183])])).
% 0.23/0.70 thf(f1244,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : ((inf_inf(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0))),vAPP(sTfun(sTfun(X1,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,X0))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),bCOMB,inf_inf(X0)))) | (semilattice_inf(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f937])).
% 0.23/0.70 thf(f937,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : ((inf_inf(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0))),vAPP(sTfun(sTfun(X1,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,X0))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),bCOMB,inf_inf(X0)))) | (semilattice_inf(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f539])).
% 0.23/0.70 thf(f539,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : ((semilattice_inf(X0) = $true) => (inf_inf(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0))),vAPP(sTfun(sTfun(X1,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,X0))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,X0))),bCOMB,inf_inf(X0)))))),
% 0.23/0.70 inference(fool_elimination,[],[f538])).
% 0.23/0.70 thf(f538,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : (semilattice_inf(X0) => (inf_inf(sTfun(X1,X0)) = (^[X2 : X1 > X0, X3 : X1 > X0, X4 : X1] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))))))),
% 0.23/0.70 inference(rectify,[],[f237])).
% 0.23/0.70 thf(f237,axiom,(
% 0.23/0.70 ! [X1 : $tType,X0 : $tType] : (semilattice_inf(X1) => (inf_inf(sTfun(X0,X1)) = (^[X14 : X0 > X1, X15 : X0 > X1, X12 : X0] : (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),inf_inf(X1),vAPP(X0,X1,X14,X12)),vAPP(X0,X1,X15,X12))))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_inf__apply)).
% 0.23/0.70 thf(f3899,plain,(
% 0.23/0.70 spl40_182),
% 0.23/0.70 inference(avatar_split_clause,[],[f1486,f3897])).
% 0.23/0.70 thf(f3897,plain,(
% 0.23/0.70 spl40_182 <=> ! [X0 : option(trm),X1 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X0),X1),vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1))) | (none(trm) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1)) | ($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X0),X1),vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_182])])).
% 0.23/0.70 thf(f1486,plain,(
% 0.23/0.70 ( ! [X0 : option(trm),X1 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X0),X1),vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1))) | (none(trm) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1)) | ($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X0),X1),vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1)))) )),
% 0.23/0.70 inference(equality_resolution,[],[f1286])).
% 0.23/0.70 thf(f1286,plain,(
% 0.23/0.70 ( ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X0),X1),X2)) | (none(trm) = X2) | ($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X0),X1),X2)) | (vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1) != X2)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1023])).
% 0.23/0.70 thf(f1023,plain,(
% 0.23/0.70 ! [X0 : option(trm),X1 : option(trm),X2 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X0),X1),X2)) | ((none(trm) = X2) & (none(trm) = X0)) | ($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X0),X1),X2)) | (vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1) != X2))),
% 0.23/0.70 inference(definition_folding,[],[f946,f1022,f1021])).
% 0.23/0.70 thf(f1021,plain,(
% 0.23/0.70 ! [X2 : option(trm),X1 : option(trm),X0 : option(trm)] : (? [X3 : trm] : (? [X4 : trm] : ((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X2) & (vAPP(trm,option(trm),some(trm),X4) = X1)) & (vAPP(trm,option(trm),some(trm),X3) = X0)) | ~($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X0),X1),X2)))),
% 0.23/0.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.23/0.70 thf(f1022,plain,(
% 0.23/0.70 ! [X2 : option(trm),X1 : option(trm),X0 : option(trm)] : (((none(trm) = X2) & (none(trm) = X1) & ? [X5 : trm] : (vAPP(trm,option(trm),some(trm),X5) = X0)) | ~($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X0),X1),X2)))),
% 0.23/0.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.23/0.70 thf(f946,plain,(
% 0.23/0.70 ! [X0 : option(trm),X1 : option(trm),X2 : option(trm)] : (((none(trm) = X2) & (none(trm) = X1) & ? [X5 : trm] : (vAPP(trm,option(trm),some(trm),X5) = X0)) | ((none(trm) = X2) & (none(trm) = X0)) | ? [X3 : trm] : (? [X4 : trm] : ((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X2) & (vAPP(trm,option(trm),some(trm),X4) = X1)) & (vAPP(trm,option(trm),some(trm),X3) = X0)) | (vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1) != X2))),
% 0.23/0.70 inference(flattening,[],[f945])).
% 0.23/0.70 thf(f945,plain,(
% 0.23/0.70 ! [X0 : option(trm),X1 : option(trm),X2 : option(trm)] : ((((((none(trm) = X2) & (none(trm) = X1)) & ? [X5 : trm] : (vAPP(trm,option(trm),some(trm),X5) = X0)) | ((none(trm) = X2) & (none(trm) = X0))) | ? [X3 : trm] : (? [X4 : trm] : ((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X2) & (vAPP(trm,option(trm),some(trm),X4) = X1)) & (vAPP(trm,option(trm),some(trm),X3) = X0))) | (vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1) != X2))),
% 0.23/0.70 inference(ennf_transformation,[],[f825])).
% 0.23/0.70 thf(f825,plain,(
% 0.23/0.70 ! [X0 : option(trm),X1 : option(trm),X2 : option(trm)] : ((vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1) = X2) => (! [X3 : trm] : ((vAPP(trm,option(trm),some(trm),X3) = X0) => ! [X4 : trm] : ((vAPP(trm,option(trm),some(trm),X4) = X1) => (vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) != X2))) => (((none(trm) = X0) => (none(trm) != X2)) => ~(? [X5 : trm] : (vAPP(trm,option(trm),some(trm),X5) = X0) => ((none(trm) = X1) => (none(trm) != X2))))))),
% 0.23/0.70 inference(rectify,[],[f217])).
% 0.23/0.70 thf(f217,axiom,(
% 0.23/0.70 ! [X8 : option(trm),X102 : option(trm),X9 : option(trm)] : ((vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X8),X102) = X9) => (! [X86 : trm] : ((vAPP(trm,option(trm),some(trm),X86) = X8) => ! [X88 : trm] : ((vAPP(trm,option(trm),some(trm),X88) = X102) => (vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X86),X88)) != X9))) => (((none(trm) = X8) => (none(trm) != X9)) => ~(? [X90 : trm] : (vAPP(trm,option(trm),some(trm),X90) = X8) => ((none(trm) = X102) => (none(trm) != X9))))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_Timeso_Oelims)).
% 0.23/0.70 thf(f3891,plain,(
% 0.23/0.70 ~spl40_181 | ~spl40_103 | ~spl40_161 | spl40_180),
% 0.23/0.70 inference(avatar_split_clause,[],[f3886,f3881,f3569,f2925,f3888])).
% 0.23/0.70 thf(f3888,plain,(
% 0.23/0.70 spl40_181 <=> (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,sigma),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),vAPP(option(variable),set(variable),set_option(variable),vAPP(variable,option(variable),some(variable),vAPP(char,variable,rVar,x)))))),theta))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_181])])).
% 0.23/0.70 thf(f3881,plain,(
% 0.23/0.70 spl40_180 <=> (vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,sigma),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable)))))),theta) = none(trm))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_180])])).
% 0.23/0.70 thf(f3886,plain,(
% 0.23/0.70 (none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,sigma),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),vAPP(option(variable),set(variable),set_option(variable),vAPP(variable,option(variable),some(variable),vAPP(char,variable,rVar,x)))))),theta)) | (~spl40_103 | ~spl40_161 | spl40_180)),
% 0.23/0.70 inference(forward_demodulation,[],[f3885,f2926])).
% 0.23/0.70 thf(f3885,plain,(
% 0.23/0.70 (none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,sigma),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),bot_bot(set(variable)))))),theta)) | (~spl40_161 | spl40_180)),
% 0.23/0.70 inference(forward_demodulation,[],[f3883,f3570])).
% 0.23/0.70 thf(f3883,plain,(
% 0.23/0.70 (vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,sigma),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable)))))),theta) != none(trm)) | spl40_180),
% 0.23/0.70 inference(avatar_component_clause,[],[f3881])).
% 0.23/0.70 thf(f3884,plain,(
% 0.23/0.70 ~spl40_180),
% 0.23/0.70 inference(avatar_split_clause,[],[f1097,f3881])).
% 0.23/0.70 thf(f1097,plain,(
% 0.23/0.70 (vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,sigma),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable)))))),theta) != none(trm))),
% 0.23/0.70 inference(cnf_transformation,[],[f115])).
% 0.23/0.70 thf(f115,axiom,(
% 0.23/0.70 (vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,sigma),vAPP(set(variable),set(variable),vAPP(set(variable),sTfun(set(variable),set(variable)),sup_sup(set(variable)),u),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,rVar,x)),vAPP(set(variable),set(variable),vAPP(variable,sTfun(set(variable),set(variable)),insert(variable),vAPP(char,variable,dVar,x)),bot_bot(set(variable)))))),theta) != none(trm))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_subdef)).
% 0.23/0.70 thf(f3879,plain,(
% 0.23/0.70 spl40_179),
% 0.23/0.70 inference(avatar_split_clause,[],[f1345,f3877])).
% 0.23/0.70 thf(f3877,plain,(
% 0.23/0.70 spl40_179 <=> ! [X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X3 : trm,X2 : trm,X1 : set(variable)] : ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X3)) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_179])])).
% 0.23/0.70 thf(f1345,plain,(
% 0.23/0.70 ( ! [X2 : trm,X3 : trm,X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X1 : set(variable)] : ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X3)) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f977])).
% 0.23/0.70 thf(f977,plain,(
% 0.23/0.70 ! [X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X1 : set(variable),X2 : trm,X3 : trm] : (((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X3)) & (none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2))) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3))))),
% 0.23/0.70 inference(ennf_transformation,[],[f844])).
% 0.23/0.70 thf(f844,plain,(
% 0.23/0.70 ! [X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X1 : set(variable),X2 : trm,X3 : trm] : ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3))) => ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X3)) & (none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2))))),
% 0.23/0.70 inference(rectify,[],[f225])).
% 0.23/0.70 thf(f225,axiom,(
% 0.23/0.70 ! [X70 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X31 : set(variable),X50 : trm,X65 : trm] : ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X70),X31),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X50),X65))) => ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X70),X31),X65)) & (none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X70),X31),X50))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_usubstappt__times__conv)).
% 0.23/0.70 thf(f3875,plain,(
% 0.23/0.70 spl40_178),
% 0.23/0.70 inference(avatar_split_clause,[],[f1344,f3873])).
% 0.23/0.70 thf(f3873,plain,(
% 0.23/0.70 spl40_178 <=> ! [X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X3 : trm,X2 : trm,X1 : set(variable)] : ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2)) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_178])])).
% 0.23/0.70 thf(f1344,plain,(
% 0.23/0.70 ( ! [X2 : trm,X3 : trm,X0 : product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),X1 : set(variable)] : ((none(trm) != vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),X2)) | (none(trm) = vAPP(trm,option(trm),vAPP(set(variable),sTfun(trm,option(trm)),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(set(variable),sTfun(trm,option(trm))),uSubst95898992stappt,X0),X1),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X2),X3)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f977])).
% 0.23/0.70 thf(f3869,plain,(
% 0.23/0.70 spl40_177),
% 0.23/0.70 inference(avatar_split_clause,[],[f1284,f3867])).
% 0.23/0.70 thf(f3867,plain,(
% 0.23/0.70 spl40_177 <=> ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK16,X2),X1),X0)),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK17,X2),X1),X0))) = X0) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X2),X1),X0)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_177])])).
% 0.23/0.70 thf(f1284,plain,(
% 0.23/0.70 ( ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK16,X2),X1),X0)),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK17,X2),X1),X0))) = X0) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X2),X1),X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1056])).
% 0.23/0.70 thf(f1056,plain,(
% 0.23/0.70 ! [X0 : option(trm),X1 : option(trm),X2 : option(trm)] : ((((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK16,X2),X1),X0)),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK17,X2),X1),X0))) = X0) & (vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK17,X2),X1),X0)) = X1)) & (vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK16,X2),X1),X0)) = X2)) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X2),X1),X0)))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f1053,f1055,f1054])).
% 0.23/0.70 thf(f1054,plain,(
% 0.23/0.70 ! [X0 : option(trm),X1 : option(trm),X2 : option(trm)] : (? [X3 : trm] : (? [X4 : trm] : ((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X0) & (vAPP(trm,option(trm),some(trm),X4) = X1)) & (vAPP(trm,option(trm),some(trm),X3) = X2)) => (? [X4 : trm] : ((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK16,X2),X1),X0)),X4)) = X0) & (vAPP(trm,option(trm),some(trm),X4) = X1)) & (vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK16,X2),X1),X0)) = X2)))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1055,plain,(
% 0.23/0.70 ! [X0 : option(trm),X1 : option(trm),X2 : option(trm)] : (? [X4 : trm] : ((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK16,X2),X1),X0)),X4)) = X0) & (vAPP(trm,option(trm),some(trm),X4) = X1)) => ((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK16,X2),X1),X0)),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK17,X2),X1),X0))) = X0) & (vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK17,X2),X1),X0)) = X1)))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1053,plain,(
% 0.23/0.70 ! [X0 : option(trm),X1 : option(trm),X2 : option(trm)] : (? [X3 : trm] : (? [X4 : trm] : ((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X0) & (vAPP(trm,option(trm),some(trm),X4) = X1)) & (vAPP(trm,option(trm),some(trm),X3) = X2)) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X2),X1),X0)))),
% 0.23/0.70 inference(rectify,[],[f1052])).
% 0.23/0.70 thf(f1052,plain,(
% 0.23/0.70 ! [X2 : option(trm),X1 : option(trm),X0 : option(trm)] : (? [X3 : trm] : (? [X4 : trm] : ((vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X3),X4)) = X2) & (vAPP(trm,option(trm),some(trm),X4) = X1)) & (vAPP(trm,option(trm),some(trm),X3) = X0)) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X0),X1),X2)))),
% 0.23/0.70 inference(nnf_transformation,[],[f1021])).
% 0.23/0.70 thf(f3852,plain,(
% 0.23/0.70 spl40_176),
% 0.23/0.70 inference(avatar_split_clause,[],[f1487,f3850])).
% 0.23/0.70 thf(f3850,plain,(
% 0.23/0.70 spl40_176 <=> ! [X0 : option(trm),X1 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X0),X1),vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1))) | (none(trm) = X0) | ($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X0),X1),vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_176])])).
% 0.23/0.70 thf(f1487,plain,(
% 0.23/0.70 ( ! [X0 : option(trm),X1 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X0),X1),vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1))) | (none(trm) = X0) | ($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X0),X1),vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1)))) )),
% 0.23/0.70 inference(equality_resolution,[],[f1285])).
% 0.23/0.70 thf(f1285,plain,(
% 0.23/0.70 ( ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X0),X1),X2)) | (none(trm) = X0) | ($true = vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X0),X1),X2)) | (vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,X0),X1) != X2)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1023])).
% 0.23/0.70 thf(f3844,plain,(
% 0.23/0.70 spl40_175),
% 0.23/0.70 inference(avatar_split_clause,[],[f1122,f3842])).
% 0.23/0.70 thf(f3842,plain,(
% 0.23/0.70 spl40_175 <=> ! [X0 : $tType] : (insert(X0) = vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),set(X0))),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),set(X0)))),bCOMB,sup_sup(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_175])])).
% 0.23/0.70 thf(f1122,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : ((insert(X0) = vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),set(X0))),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),set(X0)))),bCOMB,sup_sup(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f339])).
% 0.23/0.70 thf(f339,plain,(
% 0.23/0.70 ! [X0 : $tType] : (insert(X0) = vAPP(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),set(X0))),vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(sTfun(X0,set(X0)),sTfun(X0,sTfun(set(X0),set(X0)))),bCOMB,sup_sup(set(X0))),vAPP(set(X0),sTfun(X0,set(X0)),vAPP(sTfun(X0,sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(X0,set(X0))),cCOMB,insert(X0)),bot_bot(set(X0)))))),
% 0.23/0.70 inference(fool_elimination,[],[f338])).
% 0.23/0.70 thf(f338,plain,(
% 0.23/0.70 ! [X0 : $tType] : (insert(X0) = (^[X1 : X0] : (vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0)))))))),
% 0.23/0.70 inference(rectify,[],[f84])).
% 0.23/0.70 thf(f84,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (insert(X0) = (^[X25 : X0] : (vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X25),bot_bot(set(X0)))))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_insert__is__Un)).
% 0.23/0.70 thf(f3840,plain,(
% 0.23/0.70 spl40_174),
% 0.23/0.70 inference(avatar_split_clause,[],[f1422,f3837])).
% 0.23/0.70 thf(f3837,plain,(
% 0.23/0.70 spl40_174 <=> (vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,vAPP(sTfun(variable,real),denotational_interp,vAPP(denotational_interp,sTfun(sTfun(variable,real),denotational_interp),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(denotational_interp,sTfun(sTfun(variable,real),denotational_interp)),uSubst2091380086djoint,sigma),i),omega)),f),x),theta) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_174])])).
% 0.23/0.70 thf(f1422,plain,(
% 0.23/0.70 (vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,vAPP(sTfun(variable,real),denotational_interp,vAPP(denotational_interp,sTfun(sTfun(variable,real),denotational_interp),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(denotational_interp,sTfun(sTfun(variable,real),denotational_interp)),uSubst2091380086djoint,sigma),i),omega)),f),x),theta) = $true)),
% 0.23/0.70 inference(cnf_transformation,[],[f781])).
% 0.23/0.70 thf(f781,plain,(
% 0.23/0.70 (vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,vAPP(sTfun(variable,real),denotational_interp,vAPP(denotational_interp,sTfun(sTfun(variable,real),denotational_interp),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(denotational_interp,sTfun(sTfun(variable,real),denotational_interp)),uSubst2091380086djoint,sigma),i),omega)),f),x),theta) = $true)),
% 0.23/0.70 inference(fool_elimination,[],[f780])).
% 0.23/0.70 thf(f780,plain,(
% 0.23/0.70 vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,vAPP(sTfun(variable,real),denotational_interp,vAPP(denotational_interp,sTfun(sTfun(variable,real),denotational_interp),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(denotational_interp,sTfun(sTfun(variable,real),denotational_interp)),uSubst2091380086djoint,sigma),i),omega)),f),x),theta)),
% 0.23/0.70 inference(rectify,[],[f108])).
% 0.23/0.70 thf(f108,axiom,(
% 0.23/0.70 vAPP(trm,$o,vAPP(char,sTfun(trm,$o),vAPP(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o)),vAPP(denotational_interp,sTfun(sTfun(real,sTfun(variable,real)),sTfun(char,sTfun(trm,$o))),denota1778088425es_ODE,vAPP(sTfun(variable,real),denotational_interp,vAPP(denotational_interp,sTfun(sTfun(variable,real),denotational_interp),vAPP(product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(trm)),product_prod(sTfun(char,option(fml)),sTfun(char,option(game))))),sTfun(denotational_interp,sTfun(sTfun(variable,real),denotational_interp)),uSubst2091380086djoint,sigma),i),omega)),f),x),theta)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_a1)).
% 0.23/0.70 thf(f3831,plain,(
% 0.23/0.70 spl40_173),
% 0.23/0.70 inference(avatar_split_clause,[],[f1297,f3829])).
% 0.23/0.70 thf(f3829,plain,(
% 0.23/0.70 spl40_173 <=> ! [X2 : option(trm),X0 : variable > option(trm) > $o,X1 : variable] : (($true = vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X1),X2)) | ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,vAPP(sTfun(variable,sTfun(option(trm),$o)),variable,sK23,X0)),none(trm))) | ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,vAPP(sTfun(variable,sTfun(option(trm),$o)),variable,sK24,X0)),vAPP(trm,option(trm),some(trm),vAPP(sTfun(variable,sTfun(option(trm),$o)),trm,sK25,X0)))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_173])])).
% 0.23/0.70 thf(f1297,plain,(
% 0.23/0.70 ( ! [X2 : option(trm),X0 : variable > option(trm) > $o,X1 : variable] : (($true = vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X1),X2)) | ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,vAPP(sTfun(variable,sTfun(option(trm),$o)),variable,sK23,X0)),none(trm))) | ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,vAPP(sTfun(variable,sTfun(option(trm),$o)),variable,sK24,X0)),vAPP(trm,option(trm),some(trm),vAPP(sTfun(variable,sTfun(option(trm),$o)),trm,sK25,X0))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1068])).
% 0.23/0.70 thf(f1068,plain,(
% 0.23/0.70 ! [X0 : variable > option(trm) > $o,X1 : variable,X2 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X1),X2)) | ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,vAPP(sTfun(variable,sTfun(option(trm),$o)),variable,sK23,X0)),none(trm))) | ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,vAPP(sTfun(variable,sTfun(option(trm),$o)),variable,sK24,X0)),vAPP(trm,option(trm),some(trm),vAPP(sTfun(variable,sTfun(option(trm),$o)),trm,sK25,X0)))))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24,sK25])],[f1065,f1067,f1066])).
% 0.23/0.70 thf(f1066,plain,(
% 0.23/0.70 ! [X0 : variable > option(trm) > $o] : (? [X3 : variable] : ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X3),none(trm))) => ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,vAPP(sTfun(variable,sTfun(option(trm),$o)),variable,sK23,X0)),none(trm))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1067,plain,(
% 0.23/0.70 ! [X0 : variable > option(trm) > $o] : (? [X4 : variable,X5 : trm] : ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X4),vAPP(trm,option(trm),some(trm),X5))) => ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,vAPP(sTfun(variable,sTfun(option(trm),$o)),variable,sK24,X0)),vAPP(trm,option(trm),some(trm),vAPP(sTfun(variable,sTfun(option(trm),$o)),trm,sK25,X0)))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1065,plain,(
% 0.23/0.70 ! [X0 : variable > option(trm) > $o,X1 : variable,X2 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X1),X2)) | ? [X3 : variable] : ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X3),none(trm))) | ? [X4 : variable,X5 : trm] : ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X4),vAPP(trm,option(trm),some(trm),X5))))),
% 0.23/0.70 inference(rectify,[],[f957])).
% 0.23/0.70 thf(f957,plain,(
% 0.23/0.70 ! [X0 : variable > option(trm) > $o,X1 : variable,X2 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X1),X2)) | ? [X5 : variable] : ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X5),none(trm))) | ? [X3 : variable,X4 : trm] : ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X3),vAPP(trm,option(trm),some(trm),X4))))),
% 0.23/0.70 inference(flattening,[],[f956])).
% 0.23/0.70 thf(f956,plain,(
% 0.23/0.70 ! [X0 : variable > option(trm) > $o,X1 : variable,X2 : option(trm)] : ((($true = vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X1),X2)) | ? [X5 : variable] : ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X5),none(trm)))) | ? [X3 : variable,X4 : trm] : ($true != vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X3),vAPP(trm,option(trm),some(trm),X4))))),
% 0.23/0.70 inference(ennf_transformation,[],[f599])).
% 0.23/0.70 thf(f599,plain,(
% 0.23/0.70 ! [X0 : variable > option(trm) > $o,X1 : variable,X2 : option(trm)] : (! [X3 : variable,X4 : trm] : ($true = vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X3),vAPP(trm,option(trm),some(trm),X4))) => (! [X5 : variable] : ($true = vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X5),none(trm))) => ($true = vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X1),X2))))),
% 0.23/0.70 inference(fool_elimination,[],[f598])).
% 0.23/0.70 thf(f598,plain,(
% 0.23/0.70 ! [X0 : variable > option(trm) > $o,X1 : variable,X2 : option(trm)] : (! [X3 : variable,X4 : trm] : vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X3),vAPP(trm,option(trm),some(trm),X4)) => (! [X5 : variable] : vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X5),none(trm)) => vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X0,X1),X2)))),
% 0.23/0.70 inference(rectify,[],[f160])).
% 0.23/0.70 thf(f160,axiom,(
% 0.23/0.70 ! [X11 : variable > option(trm) > $o,X84 : variable,X85 : option(trm)] : (! [X22 : variable,X86 : trm] : vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X11,X22),vAPP(trm,option(trm),some(trm),X86)) => (! [X22 : variable] : vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X11,X22),none(trm)) => vAPP(option(trm),$o,vAPP(variable,sTfun(option(trm),$o),X11,X84),X85)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Assigno_Oinduct)).
% 0.23/0.70 thf(f3827,plain,(
% 0.23/0.70 spl40_172),
% 0.23/0.70 inference(avatar_split_clause,[],[f1296,f3825])).
% 0.23/0.70 thf(f3825,plain,(
% 0.23/0.70 spl40_172 <=> ! [X2 : option(trm),X0 : char > option(trm) > $o,X1 : char] : (($true = vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X1),X2)) | ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,vAPP(sTfun(char,sTfun(option(trm),$o)),char,sK20,X0)),none(trm))) | ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,vAPP(sTfun(char,sTfun(option(trm),$o)),char,sK21,X0)),vAPP(trm,option(trm),some(trm),vAPP(sTfun(char,sTfun(option(trm),$o)),trm,sK22,X0)))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_172])])).
% 0.23/0.70 thf(f1296,plain,(
% 0.23/0.70 ( ! [X2 : option(trm),X0 : char > option(trm) > $o,X1 : char] : (($true = vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X1),X2)) | ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,vAPP(sTfun(char,sTfun(option(trm),$o)),char,sK20,X0)),none(trm))) | ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,vAPP(sTfun(char,sTfun(option(trm),$o)),char,sK21,X0)),vAPP(trm,option(trm),some(trm),vAPP(sTfun(char,sTfun(option(trm),$o)),trm,sK22,X0))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1064])).
% 0.23/0.70 thf(f1064,plain,(
% 0.23/0.70 ! [X0 : char > option(trm) > $o,X1 : char,X2 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X1),X2)) | ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,vAPP(sTfun(char,sTfun(option(trm),$o)),char,sK20,X0)),none(trm))) | ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,vAPP(sTfun(char,sTfun(option(trm),$o)),char,sK21,X0)),vAPP(trm,option(trm),some(trm),vAPP(sTfun(char,sTfun(option(trm),$o)),trm,sK22,X0)))))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f1061,f1063,f1062])).
% 0.23/0.70 thf(f1062,plain,(
% 0.23/0.70 ! [X0 : char > option(trm) > $o] : (? [X3 : char] : ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X3),none(trm))) => ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,vAPP(sTfun(char,sTfun(option(trm),$o)),char,sK20,X0)),none(trm))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1063,plain,(
% 0.23/0.70 ! [X0 : char > option(trm) > $o] : (? [X4 : char,X5 : trm] : ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X4),vAPP(trm,option(trm),some(trm),X5))) => ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,vAPP(sTfun(char,sTfun(option(trm),$o)),char,sK21,X0)),vAPP(trm,option(trm),some(trm),vAPP(sTfun(char,sTfun(option(trm),$o)),trm,sK22,X0)))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1061,plain,(
% 0.23/0.70 ! [X0 : char > option(trm) > $o,X1 : char,X2 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X1),X2)) | ? [X3 : char] : ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X3),none(trm))) | ? [X4 : char,X5 : trm] : ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X4),vAPP(trm,option(trm),some(trm),X5))))),
% 0.23/0.70 inference(rectify,[],[f955])).
% 0.23/0.70 thf(f955,plain,(
% 0.23/0.70 ! [X0 : char > option(trm) > $o,X1 : char,X2 : option(trm)] : (($true = vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X1),X2)) | ? [X5 : char] : ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X5),none(trm))) | ? [X3 : char,X4 : trm] : ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X3),vAPP(trm,option(trm),some(trm),X4))))),
% 0.23/0.70 inference(flattening,[],[f954])).
% 0.23/0.70 thf(f954,plain,(
% 0.23/0.70 ! [X0 : char > option(trm) > $o,X1 : char,X2 : option(trm)] : ((($true = vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X1),X2)) | ? [X5 : char] : ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X5),none(trm)))) | ? [X3 : char,X4 : trm] : ($true != vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X3),vAPP(trm,option(trm),some(trm),X4))))),
% 0.23/0.70 inference(ennf_transformation,[],[f597])).
% 0.23/0.70 thf(f597,plain,(
% 0.23/0.70 ! [X0 : char > option(trm) > $o,X1 : char,X2 : option(trm)] : (! [X3 : char,X4 : trm] : ($true = vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X3),vAPP(trm,option(trm),some(trm),X4))) => (! [X5 : char] : ($true = vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X5),none(trm))) => ($true = vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X1),X2))))),
% 0.23/0.70 inference(fool_elimination,[],[f596])).
% 0.23/0.70 thf(f596,plain,(
% 0.23/0.70 ! [X0 : char > option(trm) > $o,X1 : char,X2 : option(trm)] : (! [X3 : char,X4 : trm] : vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X3),vAPP(trm,option(trm),some(trm),X4)) => (! [X5 : char] : vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X5),none(trm)) => vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X0,X1),X2)))),
% 0.23/0.70 inference(rectify,[],[f157])).
% 0.23/0.70 thf(f157,axiom,(
% 0.23/0.70 ! [X11 : char > option(trm) > $o,X84 : char,X85 : option(trm)] : (! [X22 : char,X86 : trm] : vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X11,X22),vAPP(trm,option(trm),some(trm),X86)) => (! [X22 : char] : vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X11,X22),none(trm)) => vAPP(option(trm),$o,vAPP(char,sTfun(option(trm),$o),X11,X84),X85)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_ODEo_Oinduct)).
% 0.23/0.70 thf(f3819,plain,(
% 0.23/0.70 spl40_171 | ~spl40_25 | ~spl40_47),
% 0.23/0.70 inference(avatar_split_clause,[],[f2538,f2457,f2332,f3817])).
% 0.23/0.70 thf(f3817,plain,(
% 0.23/0.70 spl40_171 <=> ! [X0 : $tType] : ($true = semilattice_sup(sTfun(X0,$o)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_171])])).
% 0.23/0.70 thf(f2332,plain,(
% 0.23/0.70 spl40_25 <=> (semilattice_sup($o) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_25])])).
% 0.23/0.70 thf(f2457,plain,(
% 0.23/0.70 spl40_47 <=> ! [X1 : $tType,X0 : $tType] : (($true = semilattice_sup(sTfun(X0,X1))) | (semilattice_sup(X1) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_47])])).
% 0.23/0.70 thf(f2538,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = semilattice_sup(sTfun(X0,$o)))) ) | (~spl40_25 | ~spl40_47)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2529])).
% 0.23/0.70 thf(f2529,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = semilattice_sup(sTfun(X0,$o)))) ) | (~spl40_25 | ~spl40_47)),
% 0.23/0.70 inference(superposition,[],[f2458,f2334])).
% 0.23/0.70 thf(f2334,plain,(
% 0.23/0.70 (semilattice_sup($o) = $true) | ~spl40_25),
% 0.23/0.70 inference(avatar_component_clause,[],[f2332])).
% 0.23/0.70 thf(f2458,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : ((semilattice_sup(X1) != $true) | ($true = semilattice_sup(sTfun(X0,X1)))) ) | ~spl40_47),
% 0.23/0.70 inference(avatar_component_clause,[],[f2457])).
% 0.23/0.70 thf(f3811,plain,(
% 0.23/0.70 spl40_170),
% 0.23/0.70 inference(avatar_split_clause,[],[f1377,f3809])).
% 0.23/0.70 thf(f3809,plain,(
% 0.23/0.70 spl40_170 <=> ! [X3 : $tType,X4 : $tType,X0 : option(X3),X2 : option(X4) > option(X3) > $o,X1 : option(X4)] : ((vAPP(X3,option(X3),some(X3),vAPP(option(X3),X3,vAPP(option(X4),sTfun(option(X3),X3),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),X3)),sK38(X3,X4),X2),X1),X0)) = X0) | ($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),$o)),sP2(X3,X4),X2),X1),X0)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_170])])).
% 0.23/0.70 thf(f1377,plain,(
% 0.23/0.70 ( ! [X4 : $tType,X3 : $tType,X2 : option(X4) > option(X3) > $o,X0 : option(X3),X1 : option(X4)] : ((vAPP(X3,option(X3),some(X3),vAPP(option(X3),X3,vAPP(option(X4),sTfun(option(X3),X3),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),X3)),sK38(X3,X4),X2),X1),X0)) = X0) | ($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),$o)),sP2(X3,X4),X2),X1),X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1091])).
% 0.23/0.70 thf(f1091,plain,(
% 0.23/0.70 ! [X0 : option(X3),X1 : option(X4),X2 : option(X4) > option(X3) > $o,X3 : $tType,X4 : $tType] : ((($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),X2,X1),X0)) & (vAPP(X3,option(X3),some(X3),vAPP(option(X3),X3,vAPP(option(X4),sTfun(option(X3),X3),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),X3)),sK38(X3,X4),X2),X1),X0)) = X0) & (vAPP(X4,option(X4),some(X4),vAPP(option(X3),X4,vAPP(option(X4),sTfun(option(X3),X4),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),X4)),sK37(X3,X4),X2),X1),X0)) = X1)) | ($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),$o)),sP2(X3,X4),X2),X1),X0)))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f1089,f1090])).
% 0.23/0.70 thf(f1090,plain,(
% 0.23/0.70 ! [X4 : $tType,X3 : $tType,X0 : option(X3),X1 : option(X4),X2 : option(X4) > option(X3) > $o] : (? [X5 : X4,X6 : X3] : (($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),X2,X1),X0)) & (vAPP(X3,option(X3),some(X3),X6) = X0) & (vAPP(X4,option(X4),some(X4),X5) = X1)) => (($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),X2,X1),X0)) & (vAPP(X3,option(X3),some(X3),vAPP(option(X3),X3,vAPP(option(X4),sTfun(option(X3),X3),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),X3)),sK38(X3,X4),X2),X1),X0)) = X0) & (vAPP(X4,option(X4),some(X4),vAPP(option(X3),X4,vAPP(option(X4),sTfun(option(X3),X4),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),X4)),sK37(X3,X4),X2),X1),X0)) = X1)))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1089,plain,(
% 0.23/0.70 ! [X0 : option(X3),X1 : option(X4),X2 : option(X4) > option(X3) > $o,X3 : $tType,X4 : $tType] : (? [X5 : X4,X6 : X3] : (($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),X2,X1),X0)) & (vAPP(X3,option(X3),some(X3),X6) = X0) & (vAPP(X4,option(X4),some(X4),X5) = X1)) | ($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),$o)),sP2(X3,X4),X2),X1),X0)))),
% 0.23/0.70 inference(rectify,[],[f1088])).
% 0.23/0.70 thf(f1088,plain,(
% 0.23/0.70 ! [X4 : option(X1),X2 : option(X0),X3 : option(X0) > option(X1) > $o,X1 : $tType,X0 : $tType] : (? [X5 : X0,X6 : X1] : (($true != vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) & (vAPP(X1,option(X1),some(X1),X6) = X4) & (vAPP(X0,option(X0),some(X0),X5) = X2)) | ($true != vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),vAPP(sTfun(option(X0),sTfun(option(X1),$o)),sTfun(option(X0),sTfun(option(X1),$o)),sP2(X1,X0),X3),X2),X4)))),
% 0.23/0.70 inference(nnf_transformation,[],[f1024])).
% 0.23/0.70 thf(f1024,plain,(
% 0.23/0.70 ! [X4 : option(X1),X2 : option(X0),X3 : option(X0) > option(X1) > $o,X1 : $tType,X0 : $tType] : (? [X5 : X0,X6 : X1] : (($true != vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) & (vAPP(X1,option(X1),some(X1),X6) = X4) & (vAPP(X0,option(X0),some(X0),X5) = X2)) | ~($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),vAPP(sTfun(option(X0),sTfun(option(X1),$o)),sTfun(option(X0),sTfun(option(X1),$o)),sP2(X1,X0),X3),X2),X4)))),
% 0.23/0.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.23/0.70 thf(f3807,plain,(
% 0.23/0.70 spl40_169),
% 0.23/0.70 inference(avatar_split_clause,[],[f1376,f3805])).
% 0.23/0.70 thf(f3805,plain,(
% 0.23/0.70 spl40_169 <=> ! [X3 : $tType,X4 : $tType,X0 : option(X3),X2 : option(X4) > option(X3) > $o,X1 : option(X4)] : ((vAPP(X4,option(X4),some(X4),vAPP(option(X3),X4,vAPP(option(X4),sTfun(option(X3),X4),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),X4)),sK37(X3,X4),X2),X1),X0)) = X1) | ($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),$o)),sP2(X3,X4),X2),X1),X0)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_169])])).
% 0.23/0.70 thf(f1376,plain,(
% 0.23/0.70 ( ! [X4 : $tType,X3 : $tType,X2 : option(X4) > option(X3) > $o,X0 : option(X3),X1 : option(X4)] : ((vAPP(X4,option(X4),some(X4),vAPP(option(X3),X4,vAPP(option(X4),sTfun(option(X3),X4),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),X4)),sK37(X3,X4),X2),X1),X0)) = X1) | ($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),$o)),sP2(X3,X4),X2),X1),X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1091])).
% 0.23/0.70 thf(f3709,plain,(
% 0.23/0.70 spl40_168),
% 0.23/0.70 inference(avatar_split_clause,[],[f1325,f3707])).
% 0.23/0.70 thf(f3707,plain,(
% 0.23/0.70 spl40_168 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X2)),X3))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_168])])).
% 0.23/0.70 thf(f1325,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X2)),X3))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f839])).
% 0.23/0.70 thf(f839,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X2)),X3))),
% 0.23/0.70 inference(rectify,[],[f64])).
% 0.23/0.70 thf(f64,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0),X5 : set(X0),X6 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X5),X6)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),X5)),X6))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Un__assoc)).
% 0.23/0.70 thf(f3705,plain,(
% 0.23/0.70 spl40_167),
% 0.23/0.70 inference(avatar_split_clause,[],[f1324,f3703])).
% 0.23/0.70 thf(f1324,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X3)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f838])).
% 0.23/0.70 thf(f838,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X3)))),
% 0.23/0.70 inference(rectify,[],[f60])).
% 0.23/0.70 thf(f60,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0),X5 : set(X0),X6 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X5),X6)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X5),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),X6)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Un__left__commute)).
% 0.23/0.70 thf(f3640,plain,(
% 0.23/0.70 spl40_166),
% 0.23/0.70 inference(avatar_split_clause,[],[f1323,f3638])).
% 0.23/0.70 thf(f3638,plain,(
% 0.23/0.70 spl40_166 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : X0] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2)),X3) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_166])])).
% 0.23/0.70 thf(f1323,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2)),X3) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f837])).
% 0.23/0.70 thf(f837,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2)),X3) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)))),
% 0.23/0.70 inference(rectify,[],[f3])).
% 0.23/0.70 thf(f3,axiom,(
% 0.23/0.70 ! [X0 : $tType,X4 : X0,X5 : set(X0),X6 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X4),X5)),X6) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X4),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X5),X6)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Un__insert__left)).
% 0.23/0.70 thf(f3636,plain,(
% 0.23/0.70 spl40_165 | ~spl40_26 | ~spl40_47),
% 0.23/0.70 inference(avatar_split_clause,[],[f2537,f2457,f2337,f3634])).
% 0.23/0.70 thf(f3634,plain,(
% 0.23/0.70 spl40_165 <=> ! [X0 : $tType] : ($true = semilattice_sup(sTfun(X0,real)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_165])])).
% 0.23/0.70 thf(f2337,plain,(
% 0.23/0.70 spl40_26 <=> (semilattice_sup(real) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_26])])).
% 0.23/0.70 thf(f2537,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = semilattice_sup(sTfun(X0,real)))) ) | (~spl40_26 | ~spl40_47)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2530])).
% 0.23/0.70 thf(f2530,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = semilattice_sup(sTfun(X0,real)))) ) | (~spl40_26 | ~spl40_47)),
% 0.23/0.70 inference(superposition,[],[f2458,f2339])).
% 0.23/0.70 thf(f2339,plain,(
% 0.23/0.70 (semilattice_sup(real) = $true) | ~spl40_26),
% 0.23/0.70 inference(avatar_component_clause,[],[f2337])).
% 0.23/0.70 thf(f3632,plain,(
% 0.23/0.70 spl40_164),
% 0.23/0.70 inference(avatar_split_clause,[],[f1322,f3630])).
% 0.23/0.70 thf(f3630,plain,(
% 0.23/0.70 spl40_164 <=> ! [X0 : $tType,X3 : set(X0),X2 : X0,X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X3)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_164])])).
% 0.23/0.70 thf(f1322,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X3 : set(X0),X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X3)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f836])).
% 0.23/0.70 thf(f836,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : X0,X3 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X3)))),
% 0.23/0.70 inference(rectify,[],[f4])).
% 0.23/0.70 thf(f4,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0),X4 : X0,X5 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X4),X5)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X4),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),X5)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Un__insert__right)).
% 0.23/0.70 thf(f3601,plain,(
% 0.23/0.70 spl40_163),
% 0.23/0.70 inference(avatar_split_clause,[],[f1368,f3599])).
% 0.23/0.70 thf(f3599,plain,(
% 0.23/0.70 spl40_163 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_163])])).
% 0.23/0.70 thf(f1368,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1001])).
% 0.23/0.70 thf(f1001,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3))))),
% 0.23/0.70 inference(flattening,[],[f1000])).
% 0.23/0.70 thf(f1000,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : ((($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3))))),
% 0.23/0.70 inference(ennf_transformation,[],[f850])).
% 0.23/0.70 thf(f850,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3))) => (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3))))),
% 0.23/0.70 inference(flattening,[],[f697])).
% 0.23/0.70 thf(f697,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3))) => (~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3))))),
% 0.23/0.70 inference(fool_elimination,[],[f696])).
% 0.23/0.70 thf(f696,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X3)) => (~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)))),
% 0.23/0.70 inference(rectify,[],[f69])).
% 0.23/0.70 thf(f69,axiom,(
% 0.23/0.70 ! [X0 : $tType,X13 : X0,X7 : set(X0),X5 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),X5)) => (~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),X7) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),X5)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_UnE)).
% 0.23/0.70 thf(f3597,plain,(
% 0.23/0.70 spl40_162),
% 0.23/0.70 inference(avatar_split_clause,[],[f1360,f3595])).
% 0.23/0.70 thf(f3595,plain,(
% 0.23/0.70 spl40_162 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X2),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_162])])).
% 0.23/0.70 thf(f1360,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X2),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f990])).
% 0.23/0.70 thf(f990,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X2),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 inference(flattening,[],[f989])).
% 0.23/0.70 thf(f989,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : ((($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X2),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 inference(ennf_transformation,[],[f681])).
% 0.23/0.70 thf(f681,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X2),X3)))))),
% 0.23/0.70 inference(fool_elimination,[],[f680])).
% 0.23/0.70 thf(f680,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X2),X3))))),
% 0.23/0.70 inference(rectify,[],[f244])).
% 0.23/0.70 thf(f244,axiom,(
% 0.23/0.70 ! [X0 : $tType,X13 : X0,X7 : set(X0),X5 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),X7) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),X5) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X7),X5))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_IntI)).
% 0.23/0.70 thf(f3571,plain,(
% 0.23/0.70 spl40_161),
% 0.23/0.70 inference(avatar_split_clause,[],[f1321,f3569])).
% 0.23/0.70 thf(f3559,plain,(
% 0.23/0.70 spl40_160),
% 0.23/0.70 inference(avatar_split_clause,[],[f1264,f3557])).
% 0.23/0.70 thf(f3557,plain,(
% 0.23/0.70 spl40_160 <=> ! [X0 : $tType,X2 : set(option(X0)),X1 : X0] : (vAPP(set(option(X0)),set(X0),these(X0),vAPP(set(option(X0)),set(option(X0)),vAPP(option(X0),sTfun(set(option(X0)),set(option(X0))),insert(option(X0)),vAPP(X0,option(X0),some(X0),X1)),X2)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(option(X0)),set(X0),these(X0),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_160])])).
% 0.23/0.70 thf(f1264,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(option(X0)),X1 : X0] : ((vAPP(set(option(X0)),set(X0),these(X0),vAPP(set(option(X0)),set(option(X0)),vAPP(option(X0),sTfun(set(option(X0)),set(option(X0))),insert(option(X0)),vAPP(X0,option(X0),some(X0),X1)),X2)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(option(X0)),set(X0),these(X0),X2)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f819])).
% 0.23/0.70 thf(f819,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(option(X0))] : (vAPP(set(option(X0)),set(X0),these(X0),vAPP(set(option(X0)),set(option(X0)),vAPP(option(X0),sTfun(set(option(X0)),set(option(X0))),insert(option(X0)),vAPP(X0,option(X0),some(X0),X1)),X2)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(option(X0)),set(X0),these(X0),X2)))),
% 0.23/0.70 inference(rectify,[],[f136])).
% 0.23/0.70 thf(f136,axiom,(
% 0.23/0.70 ! [X0 : $tType,X8 : X0,X7 : set(option(X0))] : (vAPP(set(option(X0)),set(X0),these(X0),vAPP(set(option(X0)),set(option(X0)),vAPP(option(X0),sTfun(set(option(X0)),set(option(X0))),insert(option(X0)),vAPP(X0,option(X0),some(X0),X8)),X7)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X8),vAPP(set(option(X0)),set(X0),these(X0),X7)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_these__insert__Some)).
% 0.23/0.70 thf(f3553,plain,(
% 0.23/0.70 spl40_159 | ~spl40_24 | ~spl40_47),
% 0.23/0.70 inference(avatar_split_clause,[],[f2535,f2457,f2327,f3551])).
% 0.23/0.70 thf(f3551,plain,(
% 0.23/0.70 spl40_159 <=> ! [X0 : $tType] : ($true = semilattice_sup(sTfun(X0,nat)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_159])])).
% 0.23/0.70 thf(f2327,plain,(
% 0.23/0.70 spl40_24 <=> (semilattice_sup(nat) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_24])])).
% 0.23/0.70 thf(f2535,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = semilattice_sup(sTfun(X0,nat)))) ) | (~spl40_24 | ~spl40_47)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2532])).
% 0.23/0.70 thf(f2532,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = semilattice_sup(sTfun(X0,nat)))) ) | (~spl40_24 | ~spl40_47)),
% 0.23/0.70 inference(superposition,[],[f2458,f2329])).
% 0.23/0.70 thf(f2329,plain,(
% 0.23/0.70 (semilattice_sup(nat) = $true) | ~spl40_24),
% 0.23/0.70 inference(avatar_component_clause,[],[f2327])).
% 0.23/0.70 thf(f3547,plain,(
% 0.23/0.70 spl40_158),
% 0.23/0.70 inference(avatar_split_clause,[],[f1283,f3545])).
% 0.23/0.70 thf(f3545,plain,(
% 0.23/0.70 spl40_158 <=> ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK17,X2),X1),X0)) = X1) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X2),X1),X0)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_158])])).
% 0.23/0.70 thf(f1283,plain,(
% 0.23/0.70 ( ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK17,X2),X1),X0)) = X1) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X2),X1),X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1056])).
% 0.23/0.70 thf(f3543,plain,(
% 0.23/0.70 spl40_157),
% 0.23/0.70 inference(avatar_split_clause,[],[f1282,f3541])).
% 0.23/0.70 thf(f3541,plain,(
% 0.23/0.70 spl40_157 <=> ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK16,X2),X1),X0)) = X2) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X2),X1),X0)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_157])])).
% 0.23/0.70 thf(f1282,plain,(
% 0.23/0.70 ( ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,vAPP(option(trm),sTfun(option(trm),trm),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),trm)),sK16,X2),X1),X0)) = X2) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP0,X2),X1),X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1056])).
% 0.23/0.70 thf(f3530,plain,(
% 0.23/0.70 spl40_156),
% 0.23/0.70 inference(avatar_split_clause,[],[f1379,f3528])).
% 0.23/0.70 thf(f3528,plain,(
% 0.23/0.70 spl40_156 <=> ! [X1 : $tType,X0 : $tType,X4 : option(X1),X3 : option(X0) > option(X1) > $o,X2 : option(X0)] : (($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) | ($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),vAPP(sTfun(option(X0),sTfun(option(X1),$o)),sTfun(option(X0),sTfun(option(X1),$o)),sP2(X1,X0),X3),X2),X4)) | (none(X1) = X4) | (none(X0) = X2))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_156])])).
% 0.23/0.70 thf(f1379,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType,X2 : option(X0),X3 : option(X0) > option(X1) > $o,X4 : option(X1)] : (($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) | ($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),vAPP(sTfun(option(X0),sTfun(option(X1),$o)),sTfun(option(X0),sTfun(option(X1),$o)),sP2(X1,X0),X3),X2),X4)) | (none(X1) = X4) | (none(X0) = X2)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1025])).
% 0.23/0.70 thf(f1025,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X2 : option(X0),X3 : option(X0) > option(X1) > $o,X4 : option(X1)] : (($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) | ($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),vAPP(sTfun(option(X0),sTfun(option(X1),$o)),sTfun(option(X0),sTfun(option(X1),$o)),sP2(X1,X0),X3),X2),X4)) | (($true != vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) & (none(X1) = X4)) | (($true != vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) & (none(X0) = X2)))),
% 0.23/0.70 inference(definition_folding,[],[f1007,f1024])).
% 0.23/0.70 thf(f1007,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X2 : option(X0),X3 : option(X0) > option(X1) > $o,X4 : option(X1)] : (($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) | ? [X5 : X0,X6 : X1] : (($true != vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) & (vAPP(X1,option(X1),some(X1),X6) = X4) & (vAPP(X0,option(X0),some(X0),X5) = X2)) | (($true != vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) & (none(X1) = X4)) | (($true != vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) & (none(X0) = X2)))),
% 0.23/0.70 inference(flattening,[],[f1006])).
% 0.23/0.70 thf(f1006,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X2 : option(X0),X3 : option(X0) > option(X1) > $o,X4 : option(X1)] : (((($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) | ? [X5 : X0,X6 : X1] : ((($true != vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) & (vAPP(X1,option(X1),some(X1),X6) = X4)) & (vAPP(X0,option(X0),some(X0),X5) = X2))) | (($true != vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) & (none(X1) = X4))) | (($true != vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) & (none(X0) = X2)))),
% 0.23/0.70 inference(ennf_transformation,[],[f705])).
% 0.23/0.70 thf(f705,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X2 : option(X0),X3 : option(X0) > option(X1) > $o,X4 : option(X1)] : (((none(X0) = X2) => ($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4))) => (((none(X1) = X4) => ($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4))) => (! [X5 : X0,X6 : X1] : ((vAPP(X0,option(X0),some(X0),X5) = X2) => ((vAPP(X1,option(X1),some(X1),X6) = X4) => ($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)))) => ($true = vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)))))),
% 0.23/0.70 inference(fool_elimination,[],[f704])).
% 0.23/0.70 thf(f704,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X2 : option(X0),X3 : option(X0) > option(X1) > $o,X4 : option(X1)] : (((none(X0) = X2) => vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) => (((none(X1) = X4) => vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4)) => (! [X5 : X0,X6 : X1] : ((vAPP(X0,option(X0),some(X0),X5) = X2) => ((vAPP(X1,option(X1),some(X1),X6) = X4) => vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4))) => vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X3,X2),X4))))),
% 0.23/0.70 inference(rectify,[],[f156])).
% 0.23/0.70 thf(f156,axiom,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X8 : option(X0),X11 : option(X0) > option(X1) > $o,X9 : option(X1)] : (((none(X0) = X8) => vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X11,X8),X9)) => (((none(X1) = X9) => vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X11,X8),X9)) => (! [X82 : X0,X83 : X1] : ((vAPP(X0,option(X0),some(X0),X82) = X8) => ((vAPP(X1,option(X1),some(X1),X83) = X9) => vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X11,X8),X9))) => vAPP(option(X1),$o,vAPP(option(X0),sTfun(option(X1),$o),X11,X8),X9))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_combine__options__cases)).
% 0.23/0.70 thf(f3504,plain,(
% 0.23/0.70 spl40_155),
% 0.23/0.70 inference(avatar_split_clause,[],[f1492,f3502])).
% 0.23/0.70 thf(f3502,plain,(
% 0.23/0.70 spl40_155 <=> ! [X0 : $tType,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(option(X0),X0,vAPP(sTfun(X0,$o),sTfun(option(X0),X0),sK34(X0),X2),vAPP(X0,option(X0),some(X0),X3))),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X3)))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_155])])).
% 0.23/0.70 thf(f1492,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(option(X0),X0,vAPP(sTfun(X0,$o),sTfun(option(X0),X0),sK34(X0),X2),vAPP(X0,option(X0),some(X0),X3))),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X3))))) )),
% 0.23/0.70 inference(equality_resolution,[],[f1353])).
% 0.23/0.70 thf(f1353,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : option(X0)] : (($true = vAPP(X0,$o,X2,X3)) | (vAPP(X0,option(X0),some(X0),X3) != X1) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(option(X0),X0,vAPP(sTfun(X0,$o),sTfun(option(X0),X0),sK34(X0),X2),X1)),vAPP(option(X0),set(X0),set_option(X0),X1)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1083])).
% 0.23/0.70 thf(f1083,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0),X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | (vAPP(X0,option(X0),some(X0),X3) != X1) | (($true != vAPP(X0,$o,X2,vAPP(option(X0),X0,vAPP(sTfun(X0,$o),sTfun(option(X0),X0),sK34(X0),X2),X1))) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(option(X0),X0,vAPP(sTfun(X0,$o),sTfun(option(X0),X0),sK34(X0),X2),X1)),vAPP(option(X0),set(X0),set_option(X0),X1)))))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f985,f1082])).
% 0.23/0.70 thf(f1082,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0),X2 : X0 > $o] : (? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(option(X0),set(X0),set_option(X0),X1)))) => (($true != vAPP(X0,$o,X2,vAPP(option(X0),X0,vAPP(sTfun(X0,$o),sTfun(option(X0),X0),sK34(X0),X2),X1))) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(option(X0),X0,vAPP(sTfun(X0,$o),sTfun(option(X0),X0),sK34(X0),X2),X1)),vAPP(option(X0),set(X0),set_option(X0),X1)))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f985,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0),X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | (vAPP(X0,option(X0),some(X0),X3) != X1) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(option(X0),set(X0),set_option(X0),X1)))))),
% 0.23/0.70 inference(flattening,[],[f984])).
% 0.23/0.70 thf(f984,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0),X2 : X0 > $o,X3 : X0] : ((($true = vAPP(X0,$o,X2,X3)) | (vAPP(X0,option(X0),some(X0),X3) != X1)) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(option(X0),set(X0),set_option(X0),X1)))))),
% 0.23/0.70 inference(ennf_transformation,[],[f673])).
% 0.23/0.70 thf(f673,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0),X2 : X0 > $o,X3 : X0] : (! [X4 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(option(X0),set(X0),set_option(X0),X1))) => ($true = vAPP(X0,$o,X2,X4))) => ((vAPP(X0,option(X0),some(X0),X3) = X1) => ($true = vAPP(X0,$o,X2,X3))))),
% 0.23/0.70 inference(fool_elimination,[],[f672])).
% 0.23/0.70 thf(f672,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0),X2 : X0 > $o,X3 : X0] : (! [X4 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(option(X0),set(X0),set_option(X0),X1)) => vAPP(X0,$o,X2,X4)) => ((vAPP(X0,option(X0),some(X0),X3) = X1) => vAPP(X0,$o,X2,X3)))),
% 0.23/0.70 inference(rectify,[],[f176])).
% 0.23/0.70 thf(f176,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : option(X0),X11 : X0 > $o,X8 : X0] : (! [X22 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X22),vAPP(option(X0),set(X0),set_option(X0),X7)) => vAPP(X0,$o,X11,X22)) => ((vAPP(X0,option(X0),some(X0),X8) = X7) => vAPP(X0,$o,X11,X8)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_ospec)).
% 0.23/0.70 thf(f3496,plain,(
% 0.23/0.70 spl40_154),
% 0.23/0.70 inference(avatar_split_clause,[],[f1263,f3494])).
% 0.23/0.70 thf(f3494,plain,(
% 0.23/0.70 spl40_154 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X2) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_154])])).
% 0.23/0.70 thf(f1263,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X2) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X2)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f818])).
% 0.23/0.70 thf(f818,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X2) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X2)))),
% 0.23/0.70 inference(rectify,[],[f61])).
% 0.23/0.70 thf(f61,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0),X5 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),X5) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),X5)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Un__left__absorb)).
% 0.23/0.70 thf(f3464,plain,(
% 0.23/0.70 spl40_153 | ~spl40_22 | ~spl40_46),
% 0.23/0.70 inference(avatar_split_clause,[],[f2528,f2453,f2317,f3462])).
% 0.23/0.70 thf(f3462,plain,(
% 0.23/0.70 spl40_153 <=> ! [X0 : $tType] : ($true = semilattice_inf(sTfun(X0,$o)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_153])])).
% 0.23/0.70 thf(f2317,plain,(
% 0.23/0.70 spl40_22 <=> (semilattice_inf($o) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_22])])).
% 0.23/0.70 thf(f2453,plain,(
% 0.23/0.70 spl40_46 <=> ! [X1 : $tType,X0 : $tType] : (($true = semilattice_inf(sTfun(X0,X1))) | (semilattice_inf(X1) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_46])])).
% 0.23/0.70 thf(f2528,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = semilattice_inf(sTfun(X0,$o)))) ) | (~spl40_22 | ~spl40_46)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2519])).
% 0.23/0.70 thf(f2519,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = semilattice_inf(sTfun(X0,$o)))) ) | (~spl40_22 | ~spl40_46)),
% 0.23/0.70 inference(superposition,[],[f2454,f2319])).
% 0.23/0.70 thf(f2319,plain,(
% 0.23/0.70 (semilattice_inf($o) = $true) | ~spl40_22),
% 0.23/0.70 inference(avatar_component_clause,[],[f2317])).
% 0.23/0.70 thf(f2454,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : ((semilattice_inf(X1) != $true) | ($true = semilattice_inf(sTfun(X0,X1)))) ) | ~spl40_46),
% 0.23/0.70 inference(avatar_component_clause,[],[f2453])).
% 0.23/0.70 thf(f3460,plain,(
% 0.23/0.70 spl40_152),
% 0.23/0.70 inference(avatar_split_clause,[],[f1352,f3458])).
% 0.23/0.70 thf(f3458,plain,(
% 0.23/0.70 spl40_152 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X2 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK33(X0,X1),X3),X2)) != vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK33(X0,X1),X3),X2))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_152])])).
% 0.23/0.70 thf(f1352,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK33(X0,X1),X3),X2)) != vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK33(X0,X1),X3),X2)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1081])).
% 0.23/0.70 thf(f1081,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK33(X0,X1),X3),X2)) != vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK33(X0,X1),X3),X2))))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f983,f1080])).
% 0.23/0.70 thf(f1080,plain,(
% 0.23/0.70 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (? [X4 : X1] : (vAPP(X1,X0,X2,X4) != vAPP(X1,X0,X3,X4)) => (vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK33(X0,X1),X3),X2)) != vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK33(X0,X1),X3),X2))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f983,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | ? [X4 : X1] : (vAPP(X1,X0,X2,X4) != vAPP(X1,X0,X3,X4)))),
% 0.23/0.70 inference(ennf_transformation,[],[f849])).
% 0.23/0.70 thf(f849,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (! [X4 : X1] : (vAPP(X1,X0,X2,X4) = vAPP(X1,X0,X3,X4)) => (X2 = X3))),
% 0.23/0.70 inference(rectify,[],[f49])).
% 0.23/0.70 thf(f49,axiom,(
% 0.23/0.70 ! [X1 : $tType,X0 : $tType,X23 : X0 > X1,X24 : X0 > X1] : (! [X22 : X0] : (vAPP(X0,X1,X23,X22) = vAPP(X0,X1,X24,X22)) => (X23 = X24))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_ext)).
% 0.23/0.70 thf(f3408,plain,(
% 0.23/0.70 spl40_151),
% 0.23/0.70 inference(avatar_split_clause,[],[f1175,f3406])).
% 0.23/0.70 thf(f3406,plain,(
% 0.23/0.70 spl40_151 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X3)) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_151])])).
% 0.23/0.70 thf(f1175,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X3)) | (semilattice_sup(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f908])).
% 0.23/0.70 thf(f908,plain,(
% 0.23/0.70 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X3)) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f441])).
% 0.23/0.70 thf(f441,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((semilattice_sup(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X3)))),
% 0.23/0.70 inference(fool_elimination,[],[f440])).
% 0.23/0.70 thf(f440,plain,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_sup(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X3)))),
% 0.23/0.70 inference(rectify,[],[f52])).
% 0.23/0.70 thf(f52,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_sup(X0) => ! [X4 : X0,X10 : X0,X13 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X10),X13)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X4),X10)),X13)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_sup_Oassoc)).
% 0.23/0.70 thf(f3404,plain,(
% 0.23/0.70 spl40_150),
% 0.23/0.70 inference(avatar_split_clause,[],[f1173,f3402])).
% 0.23/0.70 thf(f3402,plain,(
% 0.23/0.70 spl40_150 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X3))) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_150])])).
% 0.23/0.70 thf(f1173,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X3))) | (semilattice_sup(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f906])).
% 0.23/0.70 thf(f906,plain,(
% 0.23/0.70 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X3))) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f437])).
% 0.23/0.70 thf(f437,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((semilattice_sup(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X3))))),
% 0.23/0.70 inference(fool_elimination,[],[f436])).
% 0.23/0.70 thf(f436,plain,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_sup(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X3))))),
% 0.23/0.70 inference(rectify,[],[f44])).
% 0.23/0.70 thf(f44,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_sup(X0) => ! [X10 : X0,X4 : X0,X13 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X10),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X4),X13)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X10),X13))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_sup_Oleft__commute)).
% 0.23/0.70 thf(f3400,plain,(
% 0.23/0.70 spl40_149),
% 0.23/0.70 inference(avatar_split_clause,[],[f1149,f3398])).
% 0.23/0.70 thf(f3398,plain,(
% 0.23/0.70 spl40_149 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X3)) | (lattice(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_149])])).
% 0.23/0.70 thf(f1149,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X3)) | (lattice(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f882])).
% 0.23/0.70 thf(f882,plain,(
% 0.23/0.70 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X3)) | (lattice(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f389])).
% 0.23/0.70 thf(f389,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((lattice(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X3)))),
% 0.23/0.70 inference(fool_elimination,[],[f388])).
% 0.23/0.70 thf(f388,plain,(
% 0.23/0.70 ! [X0 : $tType] : (lattice(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X3)))),
% 0.23/0.70 inference(rectify,[],[f57])).
% 0.23/0.70 thf(f57,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (lattice(X0) => ! [X8 : X0,X9 : X0,X19 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X9),X19)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),X9)),X19)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_inf__sup__aci_I6_J)).
% 0.23/0.70 thf(f3396,plain,(
% 0.23/0.70 spl40_148),
% 0.23/0.70 inference(avatar_split_clause,[],[f1148,f3394])).
% 0.23/0.70 thf(f3394,plain,(
% 0.23/0.70 spl40_148 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X3))) | (lattice(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_148])])).
% 0.23/0.70 thf(f1148,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X3))) | (lattice(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f881])).
% 0.23/0.70 thf(f881,plain,(
% 0.23/0.70 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X3))) | (lattice(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f387])).
% 0.23/0.70 thf(f387,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((lattice(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X3))))),
% 0.23/0.70 inference(fool_elimination,[],[f386])).
% 0.23/0.70 thf(f386,plain,(
% 0.23/0.70 ! [X0 : $tType] : (lattice(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X3))))),
% 0.23/0.70 inference(rectify,[],[f58])).
% 0.23/0.70 thf(f58,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (lattice(X0) => ! [X8 : X0,X9 : X0,X19 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X9),X19)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),X19))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_inf__sup__aci_I7_J)).
% 0.23/0.70 thf(f3390,plain,(
% 0.23/0.70 spl40_147 | ~spl40_23 | ~spl40_46),
% 0.23/0.70 inference(avatar_split_clause,[],[f2527,f2453,f2322,f3388])).
% 0.23/0.70 thf(f3388,plain,(
% 0.23/0.70 spl40_147 <=> ! [X0 : $tType] : ($true = semilattice_inf(sTfun(X0,real)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_147])])).
% 0.23/0.70 thf(f2322,plain,(
% 0.23/0.70 spl40_23 <=> (semilattice_inf(real) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_23])])).
% 0.23/0.70 thf(f2527,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = semilattice_inf(sTfun(X0,real)))) ) | (~spl40_23 | ~spl40_46)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2520])).
% 0.23/0.70 thf(f2520,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = semilattice_inf(sTfun(X0,real)))) ) | (~spl40_23 | ~spl40_46)),
% 0.23/0.70 inference(superposition,[],[f2454,f2324])).
% 0.23/0.70 thf(f2324,plain,(
% 0.23/0.70 (semilattice_inf(real) = $true) | ~spl40_23),
% 0.23/0.70 inference(avatar_component_clause,[],[f2322])).
% 0.23/0.70 thf(f3377,plain,(
% 0.23/0.70 spl40_146),
% 0.23/0.70 inference(avatar_split_clause,[],[f1378,f3375])).
% 0.23/0.70 thf(f3375,plain,(
% 0.23/0.70 spl40_146 <=> ! [X3 : $tType,X4 : $tType,X0 : option(X3),X2 : option(X4) > option(X3) > $o,X1 : option(X4)] : (($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),X2,X1),X0)) | ($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),$o)),sP2(X3,X4),X2),X1),X0)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_146])])).
% 0.23/0.70 thf(f1378,plain,(
% 0.23/0.70 ( ! [X4 : $tType,X3 : $tType,X2 : option(X4) > option(X3) > $o,X0 : option(X3),X1 : option(X4)] : (($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),X2,X1),X0)) | ($true != vAPP(option(X3),$o,vAPP(option(X4),sTfun(option(X3),$o),vAPP(sTfun(option(X4),sTfun(option(X3),$o)),sTfun(option(X4),sTfun(option(X3),$o)),sP2(X3,X4),X2),X1),X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1091])).
% 0.23/0.70 thf(f3373,plain,(
% 0.23/0.70 spl40_145),
% 0.23/0.70 inference(avatar_split_clause,[],[f1367,f3371])).
% 0.23/0.70 thf(f3371,plain,(
% 0.23/0.70 spl40_145 <=> ! [X0 : $tType,X3 : set(X0),X2 : X0,X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) | (X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_145])])).
% 0.23/0.70 thf(f1367,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X3 : set(X0),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) | (X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f999])).
% 0.23/0.70 thf(f999,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) | (X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3))))),
% 0.23/0.70 inference(flattening,[],[f998])).
% 0.23/0.70 thf(f998,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set(X0)] : ((($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) | (X1 = X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3))))),
% 0.23/0.70 inference(ennf_transformation,[],[f695])).
% 0.23/0.70 thf(f695,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3))) => ((X1 != X2) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3))))),
% 0.23/0.70 inference(fool_elimination,[],[f694])).
% 0.23/0.70 thf(f694,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),X3)) => ((X1 != X2) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)))),
% 0.23/0.70 inference(rectify,[],[f42])).
% 0.23/0.70 thf(f42,axiom,(
% 0.23/0.70 ! [X0 : $tType,X4 : X0,X10 : X0,X7 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X10),X7)) => ((X4 != X10) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),X7)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_insertE)).
% 0.23/0.70 thf(f3308,plain,(
% 0.23/0.70 spl40_144),
% 0.23/0.70 inference(avatar_split_clause,[],[f1349,f3306])).
% 0.23/0.70 thf(f3306,plain,(
% 0.23/0.70 spl40_144 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X3),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_144])])).
% 0.23/0.70 thf(f1349,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X3),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f979])).
% 0.23/0.70 thf(f979,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X3),X2))) | (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) & ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))))),
% 0.23/0.70 inference(ennf_transformation,[],[f846])).
% 0.23/0.70 thf(f846,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : ((($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3))) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X3),X2))))),
% 0.23/0.70 inference(flattening,[],[f667])).
% 0.23/0.70 thf(f667,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : ((~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3))) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X3),X2))))),
% 0.23/0.70 inference(fool_elimination,[],[f666])).
% 0.23/0.70 thf(f666,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : set(X0)] : ((~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X3),X2)))),
% 0.23/0.70 inference(rectify,[],[f27])).
% 0.23/0.70 thf(f27,axiom,(
% 0.23/0.70 ! [X0 : $tType,X13 : X0,X5 : set(X0),X7 : set(X0)] : ((~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),X5) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),X7)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),X5)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_UnCI)).
% 0.23/0.70 thf(f3304,plain,(
% 0.23/0.70 spl40_143),
% 0.23/0.70 inference(avatar_split_clause,[],[f1348,f3302])).
% 0.23/0.70 thf(f3302,plain,(
% 0.23/0.70 spl40_143 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X3),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_143])])).
% 0.23/0.70 thf(f1348,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X3),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f979])).
% 0.23/0.70 thf(f3300,plain,(
% 0.23/0.70 spl40_142 | ~spl40_21 | ~spl40_46),
% 0.23/0.70 inference(avatar_split_clause,[],[f2525,f2453,f2312,f3298])).
% 0.23/0.70 thf(f3298,plain,(
% 0.23/0.70 spl40_142 <=> ! [X0 : $tType] : ($true = semilattice_inf(sTfun(X0,nat)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_142])])).
% 0.23/0.70 thf(f2312,plain,(
% 0.23/0.70 spl40_21 <=> (semilattice_inf(nat) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_21])])).
% 0.23/0.70 thf(f2525,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = semilattice_inf(sTfun(X0,nat)))) ) | (~spl40_21 | ~spl40_46)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2522])).
% 0.23/0.70 thf(f2522,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = semilattice_inf(sTfun(X0,nat)))) ) | (~spl40_21 | ~spl40_46)),
% 0.23/0.70 inference(superposition,[],[f2454,f2314])).
% 0.23/0.70 thf(f2314,plain,(
% 0.23/0.70 (semilattice_inf(nat) = $true) | ~spl40_21),
% 0.23/0.70 inference(avatar_component_clause,[],[f2312])).
% 0.23/0.70 thf(f3296,plain,(
% 0.23/0.70 spl40_141),
% 0.23/0.70 inference(avatar_split_clause,[],[f1303,f3294])).
% 0.23/0.70 thf(f3294,plain,(
% 0.23/0.70 spl40_141 <=> ! [X0 : $tType,X2 : set(X0),X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK32(X0),X2),X1)) = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_141])])).
% 0.23/0.70 thf(f1303,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK32(X0),X2),X1)) = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1079])).
% 0.23/0.70 thf(f1079,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : ((($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK32(X0),X2),X1))) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK32(X0),X2),X1)) = X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f964,f1078])).
% 0.23/0.70 thf(f1078,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (? [X3 : set(X0)] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3) = X2)) => (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK32(X0),X2),X1))) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK32(X0),X2),X1)) = X2)))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f964,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (? [X3 : set(X0)] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3) = X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 inference(ennf_transformation,[],[f830])).
% 0.23/0.70 thf(f830,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) => ? [X3 : set(X0)] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3) = X2)))),
% 0.23/0.70 inference(flattening,[],[f609])).
% 0.23/0.70 thf(f609,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) => ? [X3 : set(X0)] : (~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3) = X2)))),
% 0.23/0.70 inference(fool_elimination,[],[f608])).
% 0.23/0.70 thf(f608,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2) => ? [X3 : set(X0)] : (~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3) = X2)))),
% 0.23/0.70 inference(rectify,[],[f34])).
% 0.23/0.70 thf(f34,axiom,(
% 0.23/0.70 ! [X0 : $tType,X4 : X0,X7 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),X7) => ? [X17 : set(X0)] : (~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),X17) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X4),X17) = X7)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_mk__disjoint__insert)).
% 0.23/0.70 thf(f3292,plain,(
% 0.23/0.70 spl40_140),
% 0.23/0.70 inference(avatar_split_clause,[],[f1301,f3290])).
% 0.23/0.70 thf(f3290,plain,(
% 0.23/0.70 spl40_140 <=> ! [X0 : $tType,X2 : set(X0),X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK31(X0),X2),X1)) = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_140])])).
% 0.23/0.70 thf(f1301,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK31(X0),X2),X1)) = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1077])).
% 0.23/0.70 thf(f1077,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : ((($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK31(X0),X2),X1))) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK31(X0),X2),X1)) = X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f963,f1076])).
% 0.23/0.70 thf(f1076,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (? [X3 : set(X0)] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3) = X2)) => (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK31(X0),X2),X1))) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK31(X0),X2),X1)) = X2)))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f963,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (? [X3 : set(X0)] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)) & (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3) = X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 inference(ennf_transformation,[],[f607])).
% 0.23/0.70 thf(f607,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) => ~! [X3 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3) = X2) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3))))),
% 0.23/0.70 inference(fool_elimination,[],[f606])).
% 0.23/0.70 thf(f606,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2) => ~! [X3 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X3) = X2) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X3)))),
% 0.23/0.70 inference(rectify,[],[f39])).
% 0.23/0.70 thf(f39,axiom,(
% 0.23/0.70 ! [X0 : $tType,X8 : X0,X7 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X8),X7) => ~! [X17 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X8),X17) = X7) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X8),X17)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_Set_Oset__insert)).
% 0.23/0.70 thf(f3288,plain,(
% 0.23/0.70 spl40_139),
% 0.23/0.70 inference(avatar_split_clause,[],[f1262,f3286])).
% 0.23/0.70 thf(f3286,plain,(
% 0.23/0.70 spl40_139 <=> ! [X0 : $tType,X2 : set(X0),X1 : X0] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_139])])).
% 0.23/0.70 thf(f1262,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f817])).
% 0.23/0.70 thf(f817,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2)))),
% 0.23/0.70 inference(rectify,[],[f18])).
% 0.23/0.70 thf(f18,axiom,(
% 0.23/0.70 ! [X0 : $tType,X8 : X0,X7 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X8),X7) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X8),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X8),X7)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_insert__absorb2)).
% 0.23/0.70 thf(f3260,plain,(
% 0.23/0.70 spl40_138),
% 0.23/0.70 inference(avatar_split_clause,[],[f1295,f3258])).
% 0.23/0.70 thf(f3258,plain,(
% 0.23/0.70 spl40_138 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK19(X0),X2),X1)),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_138])])).
% 0.23/0.70 thf(f1295,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK19(X0),X2),X1)),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1060])).
% 0.23/0.70 thf(f1060,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK19(X0),X2),X1)),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK19(X0),X2),X1)),X1))))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f953,f1059])).
% 0.23/0.70 thf(f1059,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (? [X3 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1))) => (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK19(X0),X2),X1)),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK19(X0),X2),X1)),X1))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f953,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ? [X3 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1))))),
% 0.23/0.70 inference(ennf_transformation,[],[f595])).
% 0.23/0.70 thf(f595,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (! [X3 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2))) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 0.23/0.70 inference(fool_elimination,[],[f594])).
% 0.23/0.70 thf(f594,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (! [X3 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))),
% 0.23/0.70 inference(rectify,[],[f235])).
% 0.23/0.70 thf(f235,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0),X5 : set(X0)] : (! [X22 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X22),X7) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X22),X5)) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X7),X5))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_subsetI)).
% 0.23/0.70 thf(f3256,plain,(
% 0.23/0.70 spl40_137),
% 0.23/0.70 inference(avatar_split_clause,[],[f1294,f3254])).
% 0.23/0.70 thf(f3254,plain,(
% 0.23/0.70 spl40_137 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK19(X0),X2),X1)),X1)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_137])])).
% 0.23/0.70 thf(f1294,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK19(X0),X2),X1)),X1))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1060])).
% 0.23/0.70 thf(f3234,plain,(
% 0.23/0.70 spl40_136),
% 0.23/0.70 inference(avatar_split_clause,[],[f1346,f3232])).
% 0.23/0.70 thf(f3232,plain,(
% 0.23/0.70 spl40_136 <=> ! [X0 : $tType,X3 : X0,X2 : set(X0),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X3),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_136])])).
% 0.23/0.70 thf(f1346,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X3 : X0,X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X3),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f978])).
% 0.23/0.70 thf(f978,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X3),X2))) | ((X1 != X3) & ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))))),
% 0.23/0.70 inference(ennf_transformation,[],[f845])).
% 0.23/0.70 thf(f845,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : X0] : ((($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) => (X1 = X3)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X3),X2))))),
% 0.23/0.70 inference(flattening,[],[f665])).
% 0.23/0.70 thf(f665,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : X0] : ((~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) => (X1 = X3)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X3),X2))))),
% 0.23/0.70 inference(fool_elimination,[],[f664])).
% 0.23/0.70 thf(f664,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0),X3 : X0] : ((~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2) => (X1 = X3)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X3),X2)))),
% 0.23/0.70 inference(rectify,[],[f20])).
% 0.23/0.70 thf(f20,axiom,(
% 0.23/0.70 ! [X0 : $tType,X4 : X0,X5 : set(X0),X10 : X0] : ((~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),X5) => (X4 = X10)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X10),X5)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_insertCI)).
% 0.23/0.70 thf(f3230,plain,(
% 0.23/0.70 spl40_135 | ~spl40_18 | ~spl40_45),
% 0.23/0.70 inference(avatar_split_clause,[],[f2518,f2449,f2297,f3228])).
% 0.23/0.70 thf(f3228,plain,(
% 0.23/0.70 spl40_135 <=> ! [X0 : $tType] : ($true = lattice(sTfun(X0,$o)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_135])])).
% 0.23/0.70 thf(f2297,plain,(
% 0.23/0.70 spl40_18 <=> (lattice($o) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_18])])).
% 0.23/0.70 thf(f2449,plain,(
% 0.23/0.70 spl40_45 <=> ! [X1 : $tType,X0 : $tType] : (($true = lattice(sTfun(X0,X1))) | ($true != lattice(X1)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_45])])).
% 0.23/0.70 thf(f2518,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = lattice(sTfun(X0,$o)))) ) | (~spl40_18 | ~spl40_45)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2509])).
% 0.23/0.70 thf(f2509,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = lattice(sTfun(X0,$o)))) ) | (~spl40_18 | ~spl40_45)),
% 0.23/0.70 inference(superposition,[],[f2450,f2299])).
% 0.23/0.70 thf(f2299,plain,(
% 0.23/0.70 (lattice($o) = $true) | ~spl40_18),
% 0.23/0.70 inference(avatar_component_clause,[],[f2297])).
% 0.23/0.70 thf(f2450,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : (($true != lattice(X1)) | ($true = lattice(sTfun(X0,X1)))) ) | ~spl40_45),
% 0.23/0.70 inference(avatar_component_clause,[],[f2449])).
% 0.23/0.70 thf(f3226,plain,(
% 0.23/0.70 spl40_134),
% 0.23/0.70 inference(avatar_split_clause,[],[f1204,f3224])).
% 0.23/0.70 thf(f3224,plain,(
% 0.23/0.70 spl40_134 <=> ! [X0 : trm,X1 : trm] : (vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),some(trm),X0)),vAPP(trm,option(trm),some(trm),X1)) = vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),X1)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_134])])).
% 0.23/0.70 thf(f1204,plain,(
% 0.23/0.70 ( ! [X0 : trm,X1 : trm] : ((vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),some(trm),X0)),vAPP(trm,option(trm),some(trm),X1)) = vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),X1)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f806])).
% 0.23/0.70 thf(f806,plain,(
% 0.23/0.70 ! [X0 : trm,X1 : trm] : (vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),some(trm),X0)),vAPP(trm,option(trm),some(trm),X1)) = vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X0),X1)))),
% 0.23/0.70 inference(rectify,[],[f227])).
% 0.23/0.70 thf(f227,axiom,(
% 0.23/0.70 ! [X50 : trm,X65 : trm] : (vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),some(trm),X50)),vAPP(trm,option(trm),some(trm),X65)) = vAPP(trm,option(trm),some(trm),vAPP(trm,trm,vAPP(trm,sTfun(trm,trm),times,X50),X65)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_Timeso_Osimps_I1_J)).
% 0.23/0.70 thf(f3218,plain,(
% 0.23/0.70 spl40_133),
% 0.23/0.70 inference(avatar_split_clause,[],[f1304,f3216])).
% 0.23/0.70 thf(f3216,plain,(
% 0.23/0.70 spl40_133 <=> ! [X0 : $tType,X2 : set(X0),X1 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK32(X0),X2),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_133])])).
% 0.23/0.70 thf(f1304,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK32(X0),X2),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1079])).
% 0.23/0.70 thf(f3214,plain,(
% 0.23/0.70 spl40_132),
% 0.23/0.70 inference(avatar_split_clause,[],[f1302,f3212])).
% 0.23/0.70 thf(f3212,plain,(
% 0.23/0.70 spl40_132 <=> ! [X0 : $tType,X2 : set(X0),X1 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK31(X0),X2),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_132])])).
% 0.23/0.70 thf(f1302,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(X0,set(X0),vAPP(set(X0),sTfun(X0,set(X0)),sK31(X0),X2),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1077])).
% 0.23/0.70 thf(f3208,plain,(
% 0.23/0.70 spl40_131),
% 0.23/0.70 inference(avatar_split_clause,[],[f1292,f3206])).
% 0.23/0.70 thf(f3206,plain,(
% 0.23/0.70 spl40_131 <=> ! [X2 : variable > real,X0 : variable,X1 : variable > real] : ((vAPP(variable,real,X2,X0) = vAPP(variable,real,X1,X0)) | ($true = vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X1),X2))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_131])])).
% 0.23/0.70 thf(f1292,plain,(
% 0.23/0.70 ( ! [X2 : variable > real,X0 : variable,X1 : variable > real] : ((vAPP(variable,real,X2,X0) = vAPP(variable,real,X1,X0)) | ($true = vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X1),X2)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f951])).
% 0.23/0.70 thf(f951,plain,(
% 0.23/0.70 ! [X0 : variable,X1 : variable > real,X2 : variable > real] : ((vAPP(variable,real,X2,X0) = vAPP(variable,real,X1,X0)) | ($true = vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X1),X2))))),
% 0.23/0.70 inference(ennf_transformation,[],[f828])).
% 0.23/0.70 thf(f828,plain,(
% 0.23/0.70 ! [X0 : variable,X1 : variable > real,X2 : variable > real] : (($true != vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X1),X2))) => (vAPP(variable,real,X2,X0) = vAPP(variable,real,X1,X0)))),
% 0.23/0.70 inference(flattening,[],[f593])).
% 0.23/0.70 thf(f593,plain,(
% 0.23/0.70 ! [X0 : variable,X1 : variable > real,X2 : variable > real] : (~($true = vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X1),X2))) => (vAPP(variable,real,X2,X0) = vAPP(variable,real,X1,X0)))),
% 0.23/0.70 inference(fool_elimination,[],[f592])).
% 0.23/0.70 thf(f592,plain,(
% 0.23/0.70 ! [X0 : variable,X1 : variable > real,X2 : variable > real] : (~vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X0),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X1),X2)) => (vAPP(variable,real,X2,X0) = vAPP(variable,real,X1,X0)))),
% 0.23/0.70 inference(rectify,[],[f230])).
% 0.23/0.70 thf(f230,axiom,(
% 0.23/0.70 ! [X8 : variable,X2 : variable > real,X30 : variable > real] : (~vAPP(set(variable),$o,vAPP(variable,sTfun(set(variable),$o),member(variable),X8),vAPP(sTfun(variable,real),set(variable),vAPP(sTfun(variable,real),sTfun(sTfun(variable,real),set(variable)),statediff,X2),X30)) => (vAPP(variable,real,X30,X8) = vAPP(variable,real,X2,X8)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_nostatediff)).
% 0.23/0.70 thf(f3204,plain,(
% 0.23/0.70 spl40_130),
% 0.23/0.70 inference(avatar_split_clause,[],[f1203,f3202])).
% 0.23/0.70 thf(f3202,plain,(
% 0.23/0.70 spl40_130 <=> ! [X0 : set(sTfun(variable,real)),X1 : variable > real] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),bot_bot(set(variable))) = X0)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_130])])).
% 0.23/0.70 thf(f1203,plain,(
% 0.23/0.70 ( ! [X0 : set(sTfun(variable,real)),X1 : variable > real] : ((vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),bot_bot(set(variable))) = X0)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f805])).
% 0.23/0.70 thf(f805,plain,(
% 0.23/0.70 ! [X0 : set(sTfun(variable,real)),X1 : variable > real] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X0),X1),bot_bot(set(variable))) = X0)),
% 0.23/0.70 inference(rectify,[],[f144])).
% 0.23/0.70 thf(f144,axiom,(
% 0.23/0.70 ! [X76 : set(sTfun(variable,real)),X2 : variable > real] : (vAPP(set(variable),set(sTfun(variable,real)),vAPP(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real))),vAPP(set(sTfun(variable,real)),sTfun(sTfun(variable,real),sTfun(set(variable),set(sTfun(variable,real)))),static_selectlike,X76),X2),bot_bot(set(variable))) = X76)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_selectlike__empty)).
% 0.23/0.70 thf(f3198,plain,(
% 0.23/0.70 spl40_129 | ~spl40_19 | ~spl40_45),
% 0.23/0.70 inference(avatar_split_clause,[],[f2517,f2449,f2302,f3196])).
% 0.23/0.70 thf(f3196,plain,(
% 0.23/0.70 spl40_129 <=> ! [X0 : $tType] : ($true = lattice(sTfun(X0,real)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_129])])).
% 0.23/0.70 thf(f2302,plain,(
% 0.23/0.70 spl40_19 <=> (lattice(real) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_19])])).
% 0.23/0.70 thf(f2517,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = lattice(sTfun(X0,real)))) ) | (~spl40_19 | ~spl40_45)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2510])).
% 0.23/0.70 thf(f2510,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = lattice(sTfun(X0,real)))) ) | (~spl40_19 | ~spl40_45)),
% 0.23/0.70 inference(superposition,[],[f2450,f2304])).
% 0.23/0.70 thf(f2304,plain,(
% 0.23/0.70 (lattice(real) = $true) | ~spl40_19),
% 0.23/0.70 inference(avatar_component_clause,[],[f2302])).
% 0.23/0.70 thf(f3192,plain,(
% 0.23/0.70 spl40_128),
% 0.23/0.70 inference(avatar_split_clause,[],[f1279,f3190])).
% 0.23/0.70 thf(f3190,plain,(
% 0.23/0.70 spl40_128 <=> ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,sK15,X2)) = X2) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X2),X1),X0)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_128])])).
% 0.23/0.70 thf(f1279,plain,(
% 0.23/0.70 ( ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,sK15,X2)) = X2) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X2),X1),X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1051])).
% 0.23/0.70 thf(f1051,plain,(
% 0.23/0.70 ! [X0 : option(trm),X1 : option(trm),X2 : option(trm)] : (((none(trm) = X0) & (none(trm) = X1) & (vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,sK15,X2)) = X2)) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X2),X1),X0)))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f1049,f1050])).
% 0.23/0.70 thf(f1050,plain,(
% 0.23/0.70 ! [X2 : option(trm)] : (? [X3 : trm] : (vAPP(trm,option(trm),some(trm),X3) = X2) => (vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,sK15,X2)) = X2))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1049,plain,(
% 0.23/0.70 ! [X0 : option(trm),X1 : option(trm),X2 : option(trm)] : (((none(trm) = X0) & (none(trm) = X1) & ? [X3 : trm] : (vAPP(trm,option(trm),some(trm),X3) = X2)) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X2),X1),X0)))),
% 0.23/0.70 inference(rectify,[],[f1048])).
% 0.23/0.70 thf(f1048,plain,(
% 0.23/0.70 ! [X2 : option(trm),X1 : option(trm),X0 : option(trm)] : (((none(trm) = X2) & (none(trm) = X1) & ? [X5 : trm] : (vAPP(trm,option(trm),some(trm),X5) = X0)) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X0),X1),X2)))),
% 0.23/0.70 inference(nnf_transformation,[],[f1022])).
% 0.23/0.70 thf(f3188,plain,(
% 0.23/0.70 spl40_127),
% 0.23/0.70 inference(avatar_split_clause,[],[f1202,f3186])).
% 0.23/0.70 thf(f3186,plain,(
% 0.23/0.70 spl40_127 <=> ! [X0 : $tType,X1 : set(option(X0))] : (vAPP(set(option(X0)),set(X0),these(X0),X1) = vAPP(set(option(X0)),set(X0),these(X0),vAPP(set(option(X0)),set(option(X0)),vAPP(option(X0),sTfun(set(option(X0)),set(option(X0))),insert(option(X0)),none(X0)),X1)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_127])])).
% 0.23/0.70 thf(f1202,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(option(X0))] : ((vAPP(set(option(X0)),set(X0),these(X0),X1) = vAPP(set(option(X0)),set(X0),these(X0),vAPP(set(option(X0)),set(option(X0)),vAPP(option(X0),sTfun(set(option(X0)),set(option(X0))),insert(option(X0)),none(X0)),X1)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f804])).
% 0.23/0.70 thf(f804,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(option(X0))] : (vAPP(set(option(X0)),set(X0),these(X0),X1) = vAPP(set(option(X0)),set(X0),these(X0),vAPP(set(option(X0)),set(option(X0)),vAPP(option(X0),sTfun(set(option(X0)),set(option(X0))),insert(option(X0)),none(X0)),X1)))),
% 0.23/0.70 inference(rectify,[],[f133])).
% 0.23/0.70 thf(f133,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(option(X0))] : (vAPP(set(option(X0)),set(X0),these(X0),vAPP(set(option(X0)),set(option(X0)),vAPP(option(X0),sTfun(set(option(X0)),set(option(X0))),insert(option(X0)),none(X0)),X7)) = vAPP(set(option(X0)),set(X0),these(X0),X7))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_these__insert__None)).
% 0.23/0.70 thf(f3171,plain,(
% 0.23/0.70 spl40_126),
% 0.23/0.70 inference(avatar_split_clause,[],[f1287,f3169])).
% 0.23/0.70 thf(f3169,plain,(
% 0.23/0.70 spl40_126 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0))) != vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0)))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_126])])).
% 0.23/0.70 thf(f1287,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0))) != vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f947])).
% 0.23/0.70 thf(f947,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0] : ((X1 = X2) | (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0))) != vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0)))))),
% 0.23/0.70 inference(ennf_transformation,[],[f826])).
% 0.23/0.70 thf(f826,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0))) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0)))) => (X1 = X2))),
% 0.23/0.70 inference(rectify,[],[f74])).
% 0.23/0.70 thf(f74,axiom,(
% 0.23/0.70 ! [X0 : $tType,X4 : X0,X10 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X4),bot_bot(set(X0))) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X10),bot_bot(set(X0)))) => (X4 = X10))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_singleton__inject)).
% 0.23/0.70 thf(f3167,plain,(
% 0.23/0.70 spl40_125),
% 0.23/0.70 inference(avatar_split_clause,[],[f1231,f3165])).
% 0.23/0.70 thf(f3165,plain,(
% 0.23/0.70 spl40_125 <=> ! [X0 : variable > $o,X1 : variable] : (($true = vAPP(variable,$o,X0,X1)) | ($true != vAPP(variable,$o,X0,vAPP(char,variable,dVar,vAPP(sTfun(variable,$o),char,sK11,X0)))) | ($true != vAPP(variable,$o,X0,vAPP(char,variable,rVar,vAPP(sTfun(variable,$o),char,sK12,X0)))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_125])])).
% 0.23/0.70 thf(f1231,plain,(
% 0.23/0.70 ( ! [X0 : variable > $o,X1 : variable] : (($true = vAPP(variable,$o,X0,X1)) | ($true != vAPP(variable,$o,X0,vAPP(char,variable,dVar,vAPP(sTfun(variable,$o),char,sK11,X0)))) | ($true != vAPP(variable,$o,X0,vAPP(char,variable,rVar,vAPP(sTfun(variable,$o),char,sK12,X0))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1043])).
% 0.23/0.70 thf(f1043,plain,(
% 0.23/0.70 ! [X0 : variable > $o,X1 : variable] : (($true = vAPP(variable,$o,X0,X1)) | ($true != vAPP(variable,$o,X0,vAPP(char,variable,dVar,vAPP(sTfun(variable,$o),char,sK11,X0)))) | ($true != vAPP(variable,$o,X0,vAPP(char,variable,rVar,vAPP(sTfun(variable,$o),char,sK12,X0)))))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f1040,f1042,f1041])).
% 0.23/0.70 thf(f1041,plain,(
% 0.23/0.70 ! [X0 : variable > $o] : (? [X2 : char] : ($true != vAPP(variable,$o,X0,vAPP(char,variable,dVar,X2))) => ($true != vAPP(variable,$o,X0,vAPP(char,variable,dVar,vAPP(sTfun(variable,$o),char,sK11,X0)))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1042,plain,(
% 0.23/0.70 ! [X0 : variable > $o] : (? [X3 : char] : ($true != vAPP(variable,$o,X0,vAPP(char,variable,rVar,X3))) => ($true != vAPP(variable,$o,X0,vAPP(char,variable,rVar,vAPP(sTfun(variable,$o),char,sK12,X0)))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1040,plain,(
% 0.23/0.70 ! [X0 : variable > $o,X1 : variable] : (($true = vAPP(variable,$o,X0,X1)) | ? [X2 : char] : ($true != vAPP(variable,$o,X0,vAPP(char,variable,dVar,X2))) | ? [X3 : char] : ($true != vAPP(variable,$o,X0,vAPP(char,variable,rVar,X3))))),
% 0.23/0.70 inference(rectify,[],[f923])).
% 0.23/0.70 thf(f923,plain,(
% 0.23/0.70 ! [X0 : variable > $o,X1 : variable] : (($true = vAPP(variable,$o,X0,X1)) | ? [X3 : char] : ($true != vAPP(variable,$o,X0,vAPP(char,variable,dVar,X3))) | ? [X2 : char] : ($true != vAPP(variable,$o,X0,vAPP(char,variable,rVar,X2))))),
% 0.23/0.70 inference(flattening,[],[f922])).
% 0.23/0.70 thf(f922,plain,(
% 0.23/0.70 ! [X0 : variable > $o,X1 : variable] : ((($true = vAPP(variable,$o,X0,X1)) | ? [X3 : char] : ($true != vAPP(variable,$o,X0,vAPP(char,variable,dVar,X3)))) | ? [X2 : char] : ($true != vAPP(variable,$o,X0,vAPP(char,variable,rVar,X2))))),
% 0.23/0.70 inference(ennf_transformation,[],[f513])).
% 0.23/0.70 thf(f513,plain,(
% 0.23/0.70 ! [X0 : variable > $o,X1 : variable] : (! [X2 : char] : ($true = vAPP(variable,$o,X0,vAPP(char,variable,rVar,X2))) => (! [X3 : char] : ($true = vAPP(variable,$o,X0,vAPP(char,variable,dVar,X3))) => ($true = vAPP(variable,$o,X0,X1))))),
% 0.23/0.70 inference(fool_elimination,[],[f512])).
% 0.23/0.70 thf(f512,plain,(
% 0.23/0.70 ! [X0 : variable > $o,X1 : variable] : (! [X2 : char] : vAPP(variable,$o,X0,vAPP(char,variable,rVar,X2)) => (! [X3 : char] : vAPP(variable,$o,X0,vAPP(char,variable,dVar,X3)) => vAPP(variable,$o,X0,X1)))),
% 0.23/0.70 inference(rectify,[],[f101])).
% 0.23/0.70 thf(f101,axiom,(
% 0.23/0.70 ! [X11 : variable > $o,X67 : variable] : (! [X22 : char] : vAPP(variable,$o,X11,vAPP(char,variable,rVar,X22)) => (! [X22 : char] : vAPP(variable,$o,X11,vAPP(char,variable,dVar,X22)) => vAPP(variable,$o,X11,X67)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_variable_Oinduct)).
% 0.23/0.70 thf(f3142,plain,(
% 0.23/0.70 spl40_124 | ~spl40_17 | ~spl40_45),
% 0.23/0.70 inference(avatar_split_clause,[],[f2515,f2449,f2292,f3140])).
% 0.23/0.70 thf(f3140,plain,(
% 0.23/0.70 spl40_124 <=> ! [X0 : $tType] : ($true = lattice(sTfun(X0,nat)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_124])])).
% 0.23/0.70 thf(f2292,plain,(
% 0.23/0.70 spl40_17 <=> (lattice(nat) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_17])])).
% 0.23/0.70 thf(f2515,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = lattice(sTfun(X0,nat)))) ) | (~spl40_17 | ~spl40_45)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2512])).
% 0.23/0.70 thf(f2512,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = lattice(sTfun(X0,nat)))) ) | (~spl40_17 | ~spl40_45)),
% 0.23/0.70 inference(superposition,[],[f2450,f2294])).
% 0.23/0.70 thf(f2294,plain,(
% 0.23/0.70 (lattice(nat) = $true) | ~spl40_17),
% 0.23/0.70 inference(avatar_component_clause,[],[f2292])).
% 0.23/0.70 thf(f3090,plain,(
% 0.23/0.70 spl40_123),
% 0.23/0.70 inference(avatar_split_clause,[],[f1307,f3088])).
% 0.23/0.70 thf(f3088,plain,(
% 0.23/0.70 spl40_123 <=> ! [X0 : $tType,X2 : set(X0),X1 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),uminus_uminus(set(X0)),X2))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_123])])).
% 0.23/0.70 thf(f1307,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),uminus_uminus(set(X0)),X2)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f968])).
% 0.23/0.70 thf(f968,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),uminus_uminus(set(X0)),X2))))),
% 0.23/0.70 inference(ennf_transformation,[],[f831])).
% 0.23/0.70 thf(f831,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),uminus_uminus(set(X0)),X2))) => ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 inference(flattening,[],[f615])).
% 0.23/0.70 thf(f615,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),uminus_uminus(set(X0)),X2))) => ~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 inference(fool_elimination,[],[f614])).
% 0.23/0.70 thf(f614,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),uminus_uminus(set(X0)),X2)) => ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))),
% 0.23/0.70 inference(rectify,[],[f209])).
% 0.23/0.70 thf(f209,axiom,(
% 0.23/0.70 ! [X0 : $tType,X13 : X0,X7 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(set(X0),set(X0),uminus_uminus(set(X0)),X7)) => ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),X7))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_ComplD)).
% 0.23/0.70 thf(f3086,plain,(
% 0.23/0.70 spl40_122),
% 0.23/0.70 inference(avatar_split_clause,[],[f1305,f3084])).
% 0.23/0.70 thf(f3084,plain,(
% 0.23/0.70 spl40_122 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : ((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_122])])).
% 0.23/0.70 thf(f1305,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : ((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f966])).
% 0.23/0.70 thf(f966,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : ((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 0.23/0.70 inference(flattening,[],[f965])).
% 0.23/0.70 thf(f965,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 0.23/0.70 inference(ennf_transformation,[],[f611])).
% 0.23/0.70 thf(f611,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) => (X1 = X2)))),
% 0.23/0.70 inference(fool_elimination,[],[f610])).
% 0.23/0.70 thf(f610,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1) => (X1 = X2)))),
% 0.23/0.70 inference(rectify,[],[f236])).
% 0.23/0.70 thf(f236,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0),X5 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X7),X5) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X5),X7) => (X5 = X7)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_subset__antisym)).
% 0.23/0.70 thf(f3082,plain,(
% 0.23/0.70 spl40_121),
% 0.23/0.70 inference(avatar_split_clause,[],[f1172,f3080])).
% 0.23/0.70 thf(f3080,plain,(
% 0.23/0.70 spl40_121 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X2)) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_121])])).
% 0.23/0.70 thf(f1172,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X2)) | (semilattice_sup(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f905])).
% 0.23/0.70 thf(f905,plain,(
% 0.23/0.70 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X2)) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f435])).
% 0.23/0.70 thf(f435,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((semilattice_sup(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X2)))),
% 0.23/0.70 inference(fool_elimination,[],[f434])).
% 0.23/0.70 thf(f434,plain,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_sup(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X2)))),
% 0.23/0.70 inference(rectify,[],[f21])).
% 0.23/0.70 thf(f21,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_sup(X0) => ! [X4 : X0,X10 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X4),X10) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X4),X10)),X10)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_sup_Oright__idem)).
% 0.23/0.70 thf(f3078,plain,(
% 0.23/0.70 spl40_120),
% 0.23/0.70 inference(avatar_split_clause,[],[f1170,f3076])).
% 0.23/0.70 thf(f3076,plain,(
% 0.23/0.70 spl40_120 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2))) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_120])])).
% 0.23/0.70 thf(f1170,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2))) | (semilattice_sup(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f903])).
% 0.23/0.70 thf(f903,plain,(
% 0.23/0.70 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2))) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f431])).
% 0.23/0.70 thf(f431,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((semilattice_sup(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2))))),
% 0.23/0.70 inference(fool_elimination,[],[f430])).
% 0.23/0.70 thf(f430,plain,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_sup(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2))))),
% 0.23/0.70 inference(rectify,[],[f22])).
% 0.23/0.70 thf(f22,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_sup(X0) => ! [X8 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),X9) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),X9))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_sup__left__idem)).
% 0.23/0.70 thf(f3074,plain,(
% 0.23/0.70 spl40_119),
% 0.23/0.70 inference(avatar_split_clause,[],[f1162,f3072])).
% 0.23/0.70 thf(f3072,plain,(
% 0.23/0.70 spl40_119 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)),X2)) | (semilattice_inf(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_119])])).
% 0.23/0.70 thf(f1162,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)),X2)) | (semilattice_inf(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f895])).
% 0.23/0.70 thf(f895,plain,(
% 0.23/0.70 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)),X2)) | (semilattice_inf(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f415])).
% 0.23/0.70 thf(f415,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((semilattice_inf(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)),X2)))),
% 0.23/0.70 inference(fool_elimination,[],[f414])).
% 0.23/0.70 thf(f414,plain,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_inf(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)),X2)))),
% 0.23/0.70 inference(rectify,[],[f243])).
% 0.23/0.70 thf(f243,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_inf(X0) => ! [X8 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X8),X9) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X8),X9)),X9)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_inf__right__idem)).
% 0.23/0.70 thf(f3070,plain,(
% 0.23/0.70 spl40_118),
% 0.23/0.70 inference(avatar_split_clause,[],[f1160,f3068])).
% 0.23/0.70 thf(f3068,plain,(
% 0.23/0.70 spl40_118 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2))) | (semilattice_inf(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_118])])).
% 0.23/0.70 thf(f1160,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2))) | (semilattice_inf(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f893])).
% 0.23/0.70 thf(f893,plain,(
% 0.23/0.70 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2))) | (semilattice_inf(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f411])).
% 0.23/0.70 thf(f411,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((semilattice_inf(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2))))),
% 0.23/0.70 inference(fool_elimination,[],[f410])).
% 0.23/0.70 thf(f410,plain,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_inf(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2))))),
% 0.23/0.70 inference(rectify,[],[f240])).
% 0.23/0.70 thf(f240,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_inf(X0) => ! [X4 : X0,X10 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X4),X10) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X4),X10))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_inf_Oleft__idem)).
% 0.23/0.70 thf(f3066,plain,(
% 0.23/0.70 spl40_117 | ~spl40_8 | ~spl40_44),
% 0.23/0.70 inference(avatar_split_clause,[],[f2508,f2445,f2247,f3064])).
% 0.23/0.70 thf(f3064,plain,(
% 0.23/0.70 spl40_117 <=> ! [X0 : $tType] : ($true = bot(sTfun(X0,nat)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_117])])).
% 0.23/0.70 thf(f2247,plain,(
% 0.23/0.70 spl40_8 <=> (bot(nat) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_8])])).
% 0.23/0.70 thf(f2445,plain,(
% 0.23/0.70 spl40_44 <=> ! [X1 : $tType,X0 : $tType] : (($true = bot(sTfun(X0,X1))) | (bot(X1) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_44])])).
% 0.23/0.70 thf(f2508,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = bot(sTfun(X0,nat)))) ) | (~spl40_8 | ~spl40_44)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2501])).
% 0.23/0.70 thf(f2501,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = bot(sTfun(X0,nat)))) ) | (~spl40_8 | ~spl40_44)),
% 0.23/0.70 inference(superposition,[],[f2446,f2249])).
% 0.23/0.70 thf(f2249,plain,(
% 0.23/0.70 (bot(nat) = $true) | ~spl40_8),
% 0.23/0.70 inference(avatar_component_clause,[],[f2247])).
% 0.23/0.70 thf(f2446,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : ((bot(X1) != $true) | ($true = bot(sTfun(X0,X1)))) ) | ~spl40_44),
% 0.23/0.70 inference(avatar_component_clause,[],[f2445])).
% 0.23/0.70 thf(f3062,plain,(
% 0.23/0.70 spl40_116),
% 0.23/0.70 inference(avatar_split_clause,[],[f1147,f3060])).
% 0.23/0.70 thf(f3060,plain,(
% 0.23/0.70 spl40_116 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2))) | (lattice(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_116])])).
% 0.23/0.70 thf(f1147,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2))) | (lattice(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f880])).
% 0.23/0.70 thf(f880,plain,(
% 0.23/0.70 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2))) | (lattice(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f385])).
% 0.23/0.70 thf(f385,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((lattice(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2))))),
% 0.23/0.70 inference(fool_elimination,[],[f384])).
% 0.23/0.70 thf(f384,plain,(
% 0.23/0.70 ! [X0 : $tType] : (lattice(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2))))),
% 0.23/0.70 inference(rectify,[],[f59])).
% 0.23/0.70 thf(f59,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (lattice(X0) => ! [X8 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),X9) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),X9))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_inf__sup__aci_I8_J)).
% 0.23/0.70 thf(f3045,plain,(
% 0.23/0.70 spl40_115),
% 0.23/0.70 inference(avatar_split_clause,[],[f1299,f3043])).
% 0.23/0.70 thf(f3043,plain,(
% 0.23/0.70 spl40_115 <=> ! [X0 : $tType,X2 : option(X0),X1 : option(X0) > $o] : (($true = vAPP(option(X0),$o,X1,X2)) | ($true != vAPP(option(X0),$o,X1,vAPP(X0,option(X0),some(X0),vAPP(sTfun(option(X0),$o),X0,sK30(X0),X1)))) | ($true != vAPP(option(X0),$o,X1,none(X0))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_115])])).
% 0.23/0.70 thf(f1299,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : option(X0),X1 : option(X0) > $o] : (($true = vAPP(option(X0),$o,X1,X2)) | ($true != vAPP(option(X0),$o,X1,vAPP(X0,option(X0),some(X0),vAPP(sTfun(option(X0),$o),X0,sK30(X0),X1)))) | ($true != vAPP(option(X0),$o,X1,none(X0)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1075])).
% 0.23/0.70 thf(f1075,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0) > $o,X2 : option(X0)] : (($true = vAPP(option(X0),$o,X1,X2)) | ($true != vAPP(option(X0),$o,X1,vAPP(X0,option(X0),some(X0),vAPP(sTfun(option(X0),$o),X0,sK30(X0),X1)))) | ($true != vAPP(option(X0),$o,X1,none(X0))))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f961,f1074])).
% 0.23/0.70 thf(f1074,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0) > $o] : (? [X3 : X0] : ($true != vAPP(option(X0),$o,X1,vAPP(X0,option(X0),some(X0),X3))) => ($true != vAPP(option(X0),$o,X1,vAPP(X0,option(X0),some(X0),vAPP(sTfun(option(X0),$o),X0,sK30(X0),X1)))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f961,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0) > $o,X2 : option(X0)] : (($true = vAPP(option(X0),$o,X1,X2)) | ? [X3 : X0] : ($true != vAPP(option(X0),$o,X1,vAPP(X0,option(X0),some(X0),X3))) | ($true != vAPP(option(X0),$o,X1,none(X0))))),
% 0.23/0.70 inference(flattening,[],[f960])).
% 0.23/0.70 thf(f960,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0) > $o,X2 : option(X0)] : ((($true = vAPP(option(X0),$o,X1,X2)) | ? [X3 : X0] : ($true != vAPP(option(X0),$o,X1,vAPP(X0,option(X0),some(X0),X3)))) | ($true != vAPP(option(X0),$o,X1,none(X0))))),
% 0.23/0.70 inference(ennf_transformation,[],[f603])).
% 0.23/0.70 thf(f603,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0) > $o,X2 : option(X0)] : (($true = vAPP(option(X0),$o,X1,none(X0))) => (! [X3 : X0] : ($true = vAPP(option(X0),$o,X1,vAPP(X0,option(X0),some(X0),X3))) => ($true = vAPP(option(X0),$o,X1,X2))))),
% 0.23/0.70 inference(fool_elimination,[],[f602])).
% 0.23/0.70 thf(f602,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0) > $o,X2 : option(X0)] : (vAPP(option(X0),$o,X1,none(X0)) => (! [X3 : X0] : vAPP(option(X0),$o,X1,vAPP(X0,option(X0),some(X0),X3)) => vAPP(option(X0),$o,X1,X2)))),
% 0.23/0.70 inference(rectify,[],[f153])).
% 0.23/0.70 thf(f153,axiom,(
% 0.23/0.70 ! [X0 : $tType,X11 : option(X0) > $o,X71 : option(X0)] : (vAPP(option(X0),$o,X11,none(X0)) => (! [X22 : X0] : vAPP(option(X0),$o,X11,vAPP(X0,option(X0),some(X0),X22)) => vAPP(option(X0),$o,X11,X71)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_option_Oinducts)).
% 0.23/0.70 thf(f3027,plain,(
% 0.23/0.70 spl40_114),
% 0.23/0.70 inference(avatar_split_clause,[],[f1232,f3025])).
% 0.23/0.70 thf(f3025,plain,(
% 0.23/0.70 spl40_114 <=> ! [X0 : option(trm) > $o,X1 : option(trm)] : (($true = vAPP(option(trm),$o,X0,X1)) | ($true != vAPP(option(trm),$o,X0,none(trm))) | ($true != vAPP(option(trm),$o,X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),$o),trm,sK13,X0)))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_114])])).
% 0.23/0.70 thf(f1232,plain,(
% 0.23/0.70 ( ! [X0 : option(trm) > $o,X1 : option(trm)] : (($true = vAPP(option(trm),$o,X0,X1)) | ($true != vAPP(option(trm),$o,X0,none(trm))) | ($true != vAPP(option(trm),$o,X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),$o),trm,sK13,X0))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1045])).
% 0.23/0.70 thf(f1045,plain,(
% 0.23/0.70 ! [X0 : option(trm) > $o,X1 : option(trm)] : (($true = vAPP(option(trm),$o,X0,X1)) | ($true != vAPP(option(trm),$o,X0,none(trm))) | ($true != vAPP(option(trm),$o,X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),$o),trm,sK13,X0)))))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f925,f1044])).
% 0.23/0.70 thf(f1044,plain,(
% 0.23/0.70 ! [X0 : option(trm) > $o] : (? [X2 : trm] : ($true != vAPP(option(trm),$o,X0,vAPP(trm,option(trm),some(trm),X2))) => ($true != vAPP(option(trm),$o,X0,vAPP(trm,option(trm),some(trm),vAPP(sTfun(option(trm),$o),trm,sK13,X0)))))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f925,plain,(
% 0.23/0.70 ! [X0 : option(trm) > $o,X1 : option(trm)] : (($true = vAPP(option(trm),$o,X0,X1)) | ($true != vAPP(option(trm),$o,X0,none(trm))) | ? [X2 : trm] : ($true != vAPP(option(trm),$o,X0,vAPP(trm,option(trm),some(trm),X2))))),
% 0.23/0.70 inference(flattening,[],[f924])).
% 0.23/0.70 thf(f924,plain,(
% 0.23/0.70 ! [X0 : option(trm) > $o,X1 : option(trm)] : ((($true = vAPP(option(trm),$o,X0,X1)) | ($true != vAPP(option(trm),$o,X0,none(trm)))) | ? [X2 : trm] : ($true != vAPP(option(trm),$o,X0,vAPP(trm,option(trm),some(trm),X2))))),
% 0.23/0.70 inference(ennf_transformation,[],[f515])).
% 0.23/0.70 thf(f515,plain,(
% 0.23/0.70 ! [X0 : option(trm) > $o,X1 : option(trm)] : (! [X2 : trm] : ($true = vAPP(option(trm),$o,X0,vAPP(trm,option(trm),some(trm),X2))) => (($true = vAPP(option(trm),$o,X0,none(trm))) => ($true = vAPP(option(trm),$o,X0,X1))))),
% 0.23/0.70 inference(fool_elimination,[],[f514])).
% 0.23/0.70 thf(f514,plain,(
% 0.23/0.70 ! [X0 : option(trm) > $o,X1 : option(trm)] : (! [X2 : trm] : vAPP(option(trm),$o,X0,vAPP(trm,option(trm),some(trm),X2)) => (vAPP(option(trm),$o,X0,none(trm)) => vAPP(option(trm),$o,X0,X1)))),
% 0.23/0.70 inference(rectify,[],[f162])).
% 0.23/0.70 thf(f162,axiom,(
% 0.23/0.70 ! [X11 : option(trm) > $o,X84 : option(trm)] : (! [X86 : trm] : vAPP(option(trm),$o,X11,vAPP(trm,option(trm),some(trm),X86)) => (vAPP(option(trm),$o,X11,none(trm)) => vAPP(option(trm),$o,X11,X84)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_Differentialo_Oinduct)).
% 0.23/0.70 thf(f3023,plain,(
% 0.23/0.70 spl40_113),
% 0.23/0.70 inference(avatar_split_clause,[],[f1222,f3021])).
% 0.23/0.70 thf(f3021,plain,(
% 0.23/0.70 spl40_113 <=> ! [X0 : $tType,X1 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_113])])).
% 0.23/0.70 thf(f1222,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f505])).
% 0.23/0.70 thf(f505,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1)),
% 0.23/0.70 inference(fool_elimination,[],[f504])).
% 0.23/0.70 thf(f504,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X2 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)))) = X1)),
% 0.23/0.70 inference(rectify,[],[f47])).
% 0.23/0.70 thf(f47,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X12 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X12),X7)))) = X7)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq)).
% 0.23/0.70 thf(f3019,plain,(
% 0.23/0.70 spl40_112),
% 0.23/0.70 inference(avatar_split_clause,[],[f1123,f3017])).
% 0.23/0.70 thf(f3017,plain,(
% 0.23/0.70 spl40_112 <=> ! [X0 : $tType] : (sup_sup(set(X0)) = vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,sup_sup(set(X0))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_112])])).
% 0.23/0.70 thf(f1123,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : ((sup_sup(set(X0)) = vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,sup_sup(set(X0))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f341])).
% 0.23/0.70 thf(f341,plain,(
% 0.23/0.70 ! [X0 : $tType] : (sup_sup(set(X0)) = vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,sup_sup(set(X0))))),
% 0.23/0.70 inference(fool_elimination,[],[f340])).
% 0.23/0.70 thf(f340,plain,(
% 0.23/0.70 ! [X0 : $tType] : (sup_sup(set(X0)) = (^[X1 : set(X0), X2 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X1))))),
% 0.23/0.70 inference(rectify,[],[f62])).
% 0.23/0.70 thf(f62,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (sup_sup(set(X0)) = (^[X28 : set(X0), X29 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X29),X28))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Un__commute)).
% 0.23/0.70 thf(f3014,plain,(
% 0.23/0.70 spl40_111 | ~spl40_11 | ~spl40_44),
% 0.23/0.70 inference(avatar_split_clause,[],[f2507,f2445,f2262,f3012])).
% 0.23/0.70 thf(f3012,plain,(
% 0.23/0.70 spl40_111 <=> ! [X0 : $tType] : ($true = bot(sTfun(X0,$o)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_111])])).
% 0.23/0.70 thf(f2262,plain,(
% 0.23/0.70 spl40_11 <=> (bot($o) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_11])])).
% 0.23/0.70 thf(f2507,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = bot(sTfun(X0,$o)))) ) | (~spl40_11 | ~spl40_44)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2502])).
% 0.23/0.70 thf(f2502,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = bot(sTfun(X0,$o)))) ) | (~spl40_11 | ~spl40_44)),
% 0.23/0.70 inference(superposition,[],[f2446,f2264])).
% 0.23/0.70 thf(f2264,plain,(
% 0.23/0.70 (bot($o) = $true) | ~spl40_11),
% 0.23/0.70 inference(avatar_component_clause,[],[f2262])).
% 0.23/0.70 thf(f3008,plain,(
% 0.23/0.70 spl40_110),
% 0.23/0.70 inference(avatar_split_clause,[],[f1320,f3006])).
% 0.23/0.70 thf(f3006,plain,(
% 0.23/0.70 spl40_110 <=> ! [X0 : $tType,X3 : char,X2 : char > X0,X1 : char > X0] : (vAPP(variable,X0,vAPP(sTfun(char,X0),sTfun(variable,X0),vAPP(sTfun(char,X0),sTfun(sTfun(char,X0),sTfun(variable,X0)),rec_variable(X0),X1),X2),vAPP(char,variable,dVar,X3)) = vAPP(char,X0,X2,X3))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_110])])).
% 0.23/0.70 thf(f1320,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : char > X0,X3 : char,X1 : char > X0] : ((vAPP(variable,X0,vAPP(sTfun(char,X0),sTfun(variable,X0),vAPP(sTfun(char,X0),sTfun(sTfun(char,X0),sTfun(variable,X0)),rec_variable(X0),X1),X2),vAPP(char,variable,dVar,X3)) = vAPP(char,X0,X2,X3))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f834])).
% 0.23/0.70 thf(f834,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : char > X0,X2 : char > X0,X3 : char] : (vAPP(variable,X0,vAPP(sTfun(char,X0),sTfun(variable,X0),vAPP(sTfun(char,X0),sTfun(sTfun(char,X0),sTfun(variable,X0)),rec_variable(X0),X1),X2),vAPP(char,variable,dVar,X3)) = vAPP(char,X0,X2,X3))),
% 0.23/0.70 inference(rectify,[],[f135])).
% 0.23/0.70 thf(f135,axiom,(
% 0.23/0.70 ! [X0 : $tType,X73 : char > X0,X74 : char > X0,X54 : char] : (vAPP(variable,X0,vAPP(sTfun(char,X0),sTfun(variable,X0),vAPP(sTfun(char,X0),sTfun(sTfun(char,X0),sTfun(variable,X0)),rec_variable(X0),X73),X74),vAPP(char,variable,dVar,X54)) = vAPP(char,X0,X74,X54))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_variable_Osimps_I8_J)).
% 0.23/0.70 thf(f3004,plain,(
% 0.23/0.70 spl40_109),
% 0.23/0.70 inference(avatar_split_clause,[],[f1319,f3002])).
% 0.23/0.70 thf(f3002,plain,(
% 0.23/0.70 spl40_109 <=> ! [X0 : $tType,X3 : char,X2 : char > X0,X1 : char > X0] : (vAPP(variable,X0,vAPP(sTfun(char,X0),sTfun(variable,X0),vAPP(sTfun(char,X0),sTfun(sTfun(char,X0),sTfun(variable,X0)),rec_variable(X0),X1),X2),vAPP(char,variable,rVar,X3)) = vAPP(char,X0,X1,X3))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_109])])).
% 0.23/0.70 thf(f1319,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : char > X0,X3 : char,X1 : char > X0] : ((vAPP(variable,X0,vAPP(sTfun(char,X0),sTfun(variable,X0),vAPP(sTfun(char,X0),sTfun(sTfun(char,X0),sTfun(variable,X0)),rec_variable(X0),X1),X2),vAPP(char,variable,rVar,X3)) = vAPP(char,X0,X1,X3))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f833])).
% 0.23/0.70 thf(f833,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : char > X0,X2 : char > X0,X3 : char] : (vAPP(variable,X0,vAPP(sTfun(char,X0),sTfun(variable,X0),vAPP(sTfun(char,X0),sTfun(sTfun(char,X0),sTfun(variable,X0)),rec_variable(X0),X1),X2),vAPP(char,variable,rVar,X3)) = vAPP(char,X0,X1,X3))),
% 0.23/0.70 inference(rectify,[],[f129])).
% 0.23/0.70 thf(f129,axiom,(
% 0.23/0.70 ! [X0 : $tType,X73 : char > X0,X74 : char > X0,X52 : char] : (vAPP(variable,X0,vAPP(sTfun(char,X0),sTfun(variable,X0),vAPP(sTfun(char,X0),sTfun(sTfun(char,X0),sTfun(variable,X0)),rec_variable(X0),X73),X74),vAPP(char,variable,rVar,X52)) = vAPP(char,X0,X73,X52))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_variable_Osimps_I7_J)).
% 0.23/0.70 thf(f3000,plain,(
% 0.23/0.70 spl40_108),
% 0.23/0.70 inference(avatar_split_clause,[],[f1124,f2998])).
% 0.23/0.70 thf(f2998,plain,(
% 0.23/0.70 spl40_108 <=> ! [X0 : $tType] : (bot_bot(sTfun(X0,$o)) = vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),bot_bot(set(X0))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_108])])).
% 0.23/0.70 thf(f1124,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : ((bot_bot(sTfun(X0,$o)) = vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),bot_bot(set(X0))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f343])).
% 0.23/0.70 thf(f343,plain,(
% 0.23/0.70 ! [X0 : $tType] : (bot_bot(sTfun(X0,$o)) = vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),bot_bot(set(X0))))),
% 0.23/0.70 inference(fool_elimination,[],[f342])).
% 0.23/0.70 thf(f342,plain,(
% 0.23/0.70 ! [X0 : $tType] : (bot_bot(sTfun(X0,$o)) = (^[X1 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0))))))),
% 0.23/0.70 inference(rectify,[],[f103])).
% 0.23/0.70 thf(f103,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (bot_bot(sTfun(X0,$o)) = (^[X12 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X12),bot_bot(set(X0))))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_bot__empty__eq)).
% 0.23/0.70 thf(f2952,plain,(
% 0.23/0.70 spl40_107),
% 0.23/0.70 inference(avatar_split_clause,[],[f1491,f2950])).
% 0.23/0.70 thf(f2950,plain,(
% 0.23/0.70 spl40_107 <=> ! [X0 : $tType,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP(option(X0),X0,vAPP(sTfun(X0,$o),sTfun(option(X0),X0),sK34(X0),X2),vAPP(X0,option(X0),some(X0),X3)))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_107])])).
% 0.23/0.70 thf(f1491,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP(option(X0),X0,vAPP(sTfun(X0,$o),sTfun(option(X0),X0),sK34(X0),X2),vAPP(X0,option(X0),some(X0),X3))))) )),
% 0.23/0.70 inference(equality_resolution,[],[f1354])).
% 0.23/0.70 thf(f1354,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : option(X0)] : (($true = vAPP(X0,$o,X2,X3)) | (vAPP(X0,option(X0),some(X0),X3) != X1) | ($true != vAPP(X0,$o,X2,vAPP(option(X0),X0,vAPP(sTfun(X0,$o),sTfun(option(X0),X0),sK34(X0),X2),X1)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1083])).
% 0.23/0.70 thf(f2948,plain,(
% 0.23/0.70 spl40_106),
% 0.23/0.70 inference(avatar_split_clause,[],[f1300,f2946])).
% 0.23/0.70 thf(f2946,plain,(
% 0.23/0.70 spl40_106 <=> ! [X0 : $tType,X2 : set(X0),X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2) = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_106])])).
% 0.23/0.70 thf(f1300,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : X0] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2) = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f962])).
% 0.23/0.70 thf(f962,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2) = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)))),
% 0.23/0.70 inference(ennf_transformation,[],[f605])).
% 0.23/0.70 thf(f605,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2)) => (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2) = X2))),
% 0.23/0.70 inference(fool_elimination,[],[f604])).
% 0.23/0.70 thf(f604,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),X2) => (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2) = X2))),
% 0.23/0.70 inference(rectify,[],[f37])).
% 0.23/0.70 thf(f37,axiom,(
% 0.23/0.70 ! [X0 : $tType,X4 : X0,X7 : set(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),X7) => (vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X4),X7) = X7))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_insert__absorb)).
% 0.23/0.70 thf(f2937,plain,(
% 0.23/0.70 spl40_105 | ~spl40_10 | ~spl40_43),
% 0.23/0.70 inference(avatar_split_clause,[],[f2495,f2441,f2257,f2935])).
% 0.23/0.70 thf(f2935,plain,(
% 0.23/0.70 spl40_105 <=> ! [X0 : $tType] : ($true = boolean_algebra(sTfun(X0,$o)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_105])])).
% 0.23/0.70 thf(f2257,plain,(
% 0.23/0.70 spl40_10 <=> (boolean_algebra($o) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_10])])).
% 0.23/0.70 thf(f2441,plain,(
% 0.23/0.70 spl40_43 <=> ! [X1 : $tType,X0 : $tType] : (($true = boolean_algebra(sTfun(X0,X1))) | ($true != boolean_algebra(X1)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_43])])).
% 0.23/0.70 thf(f2495,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = boolean_algebra(sTfun(X0,$o)))) ) | (~spl40_10 | ~spl40_43)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2490])).
% 0.23/0.70 thf(f2490,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = boolean_algebra(sTfun(X0,$o)))) ) | (~spl40_10 | ~spl40_43)),
% 0.23/0.70 inference(superposition,[],[f2442,f2259])).
% 0.23/0.70 thf(f2259,plain,(
% 0.23/0.70 (boolean_algebra($o) = $true) | ~spl40_10),
% 0.23/0.70 inference(avatar_component_clause,[],[f2257])).
% 0.23/0.70 thf(f2442,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : (($true != boolean_algebra(X1)) | ($true = boolean_algebra(sTfun(X0,X1)))) ) | ~spl40_43),
% 0.23/0.70 inference(avatar_component_clause,[],[f2441])).
% 0.23/0.70 thf(f2931,plain,(
% 0.23/0.70 spl40_104),
% 0.23/0.70 inference(avatar_split_clause,[],[f1226,f2929])).
% 0.23/0.70 thf(f2929,plain,(
% 0.23/0.70 spl40_104 <=> ! [X0 : $tType,X1 : option(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(option(X0),X0,the(X0),X1)),vAPP(option(X0),set(X0),set_option(X0),X1))) | (none(X0) = X1))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_104])])).
% 0.23/0.70 thf(f1226,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : option(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(option(X0),X0,the(X0),X1)),vAPP(option(X0),set(X0),set_option(X0),X1))) | (none(X0) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f918])).
% 0.23/0.70 thf(f918,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(option(X0),X0,the(X0),X1)),vAPP(option(X0),set(X0),set_option(X0),X1))) | (none(X0) = X1))),
% 0.23/0.70 inference(ennf_transformation,[],[f507])).
% 0.23/0.70 thf(f507,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0)] : ((none(X0) != X1) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(option(X0),X0,the(X0),X1)),vAPP(option(X0),set(X0),set_option(X0),X1))))),
% 0.23/0.70 inference(fool_elimination,[],[f506])).
% 0.23/0.70 thf(f506,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0)] : ((none(X0) != X1) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(option(X0),X0,the(X0),X1)),vAPP(option(X0),set(X0),set_option(X0),X1)))),
% 0.23/0.70 inference(rectify,[],[f186])).
% 0.23/0.70 thf(f186,axiom,(
% 0.23/0.70 ! [X0 : $tType,X4 : option(X0)] : ((none(X0) != X4) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(option(X0),X0,the(X0),X4)),vAPP(option(X0),set(X0),set_option(X0),X4)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_option_Oset__sel)).
% 0.23/0.70 thf(f2927,plain,(
% 0.23/0.70 spl40_103),
% 0.23/0.70 inference(avatar_split_clause,[],[f1199,f2925])).
% 0.23/0.70 thf(f2917,plain,(
% 0.23/0.70 spl40_102),
% 0.23/0.70 inference(avatar_split_clause,[],[f1306,f2915])).
% 0.23/0.70 thf(f2915,plain,(
% 0.23/0.70 spl40_102 <=> ! [X0 : $tType,X2 : option(X0),X1 : X0] : ((vAPP(X0,option(X0),some(X0),X1) = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(option(X0),set(X0),set_option(X0),X2))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_102])])).
% 0.23/0.70 thf(f1306,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : option(X0),X1 : X0] : ((vAPP(X0,option(X0),some(X0),X1) = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(option(X0),set(X0),set_option(X0),X2)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f967])).
% 0.23/0.70 thf(f967,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : option(X0)] : ((vAPP(X0,option(X0),some(X0),X1) = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(option(X0),set(X0),set_option(X0),X2))))),
% 0.23/0.70 inference(ennf_transformation,[],[f613])).
% 0.23/0.70 thf(f613,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : option(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(option(X0),set(X0),set_option(X0),X2))) => (vAPP(X0,option(X0),some(X0),X1) = X2))),
% 0.23/0.70 inference(fool_elimination,[],[f612])).
% 0.23/0.70 thf(f612,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : option(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(option(X0),set(X0),set_option(X0),X2)) => (vAPP(X0,option(X0),some(X0),X1) = X2))),
% 0.23/0.70 inference(rectify,[],[f175])).
% 0.23/0.70 thf(f175,axiom,(
% 0.23/0.70 ! [X0 : $tType,X92 : X0,X4 : option(X0)] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X92),vAPP(option(X0),set(X0),set_option(X0),X4)) => (vAPP(X0,option(X0),some(X0),X92) = X4))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_option_Oset__cases)).
% 0.23/0.70 thf(f2893,plain,(
% 0.23/0.70 spl40_101),
% 0.23/0.70 inference(avatar_split_clause,[],[f2146,f2891])).
% 0.23/0.70 thf(f2891,plain,(
% 0.23/0.70 spl40_101 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X2)))) | (X1 = X2))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_101])])).
% 0.23/0.70 thf(f2146,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X2)))) | (X1 = X2)) )),
% 0.23/0.70 inference(forward_demodulation,[],[f1311,f1199])).
% 0.23/0.70 thf(f1311,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0)))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f972])).
% 0.23/0.70 thf(f972,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0] : ((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0))))))),
% 0.23/0.70 inference(ennf_transformation,[],[f623])).
% 0.23/0.70 thf(f623,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0))))) => (X1 = X2))),
% 0.23/0.70 inference(fool_elimination,[],[f622])).
% 0.23/0.70 thf(f622,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X2),bot_bot(set(X0)))) => (X1 = X2))),
% 0.23/0.70 inference(rectify,[],[f78])).
% 0.23/0.70 thf(f78,axiom,(
% 0.23/0.70 ! [X0 : $tType,X10 : X0,X4 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X10),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X4),bot_bot(set(X0)))) => (X4 = X10))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_singletonD)).
% 0.23/0.70 thf(f2889,plain,(
% 0.23/0.70 spl40_100 | ~spl40_12 | ~spl40_41),
% 0.23/0.70 inference(avatar_split_clause,[],[f2489,f2432,f2267,f2887])).
% 0.23/0.70 thf(f2887,plain,(
% 0.23/0.70 spl40_100 <=> ! [X0 : $tType] : ($true = uminus(sTfun(X0,$o)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_100])])).
% 0.23/0.70 thf(f2267,plain,(
% 0.23/0.70 spl40_12 <=> (uminus($o) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_12])])).
% 0.23/0.70 thf(f2432,plain,(
% 0.23/0.70 spl40_41 <=> ! [X1 : $tType,X0 : $tType] : (($true = uminus(sTfun(X0,X1))) | (uminus(X1) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_41])])).
% 0.23/0.70 thf(f2489,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = uminus(sTfun(X0,$o)))) ) | (~spl40_12 | ~spl40_41)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2482])).
% 0.23/0.70 thf(f2482,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = uminus(sTfun(X0,$o)))) ) | (~spl40_12 | ~spl40_41)),
% 0.23/0.70 inference(superposition,[],[f2433,f2269])).
% 0.23/0.70 thf(f2269,plain,(
% 0.23/0.70 (uminus($o) = $true) | ~spl40_12),
% 0.23/0.70 inference(avatar_component_clause,[],[f2267])).
% 0.23/0.70 thf(f2433,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : ((uminus(X1) != $true) | ($true = uminus(sTfun(X0,X1)))) ) | ~spl40_41),
% 0.23/0.70 inference(avatar_component_clause,[],[f2432])).
% 0.23/0.70 thf(f2885,plain,(
% 0.23/0.70 spl40_99),
% 0.23/0.70 inference(avatar_split_clause,[],[f1281,f2883])).
% 0.23/0.70 thf(f2883,plain,(
% 0.23/0.70 spl40_99 <=> ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((none(trm) = X0) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X2),X1),X0)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_99])])).
% 0.23/0.70 thf(f1281,plain,(
% 0.23/0.70 ( ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((none(trm) = X0) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X2),X1),X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1051])).
% 0.23/0.70 thf(f2881,plain,(
% 0.23/0.70 spl40_98),
% 0.23/0.70 inference(avatar_split_clause,[],[f1280,f2879])).
% 0.23/0.70 thf(f2879,plain,(
% 0.23/0.70 spl40_98 <=> ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((none(trm) = X1) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X2),X1),X0)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_98])])).
% 0.23/0.70 thf(f1280,plain,(
% 0.23/0.70 ( ! [X2 : option(trm),X0 : option(trm),X1 : option(trm)] : ((none(trm) = X1) | ($true != vAPP(option(trm),$o,vAPP(option(trm),sTfun(option(trm),$o),vAPP(option(trm),sTfun(option(trm),sTfun(option(trm),$o)),sP1,X2),X1),X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1051])).
% 0.23/0.70 thf(f2877,plain,(
% 0.23/0.70 spl40_97),
% 0.23/0.70 inference(avatar_split_clause,[],[f1235,f2875])).
% 0.23/0.70 thf(f2875,plain,(
% 0.23/0.70 spl40_97 <=> ! [X1 : $tType,X0 : $tType] : ((uminus_uminus(sTfun(X1,X0)) = vAPP(sTfun(X0,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)),bCOMB,uminus_uminus(X0))) | ($true != uminus(X0)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_97])])).
% 0.23/0.70 thf(f1235,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : ((uminus_uminus(sTfun(X1,X0)) = vAPP(sTfun(X0,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)),bCOMB,uminus_uminus(X0))) | ($true != uminus(X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f928])).
% 0.23/0.70 thf(f928,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : ((uminus_uminus(sTfun(X1,X0)) = vAPP(sTfun(X0,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)),bCOMB,uminus_uminus(X0))) | ($true != uminus(X0)))),
% 0.23/0.70 inference(ennf_transformation,[],[f521])).
% 0.23/0.70 thf(f521,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : (($true = uminus(X0)) => (uminus_uminus(sTfun(X1,X0)) = vAPP(sTfun(X0,X0),sTfun(sTfun(X1,X0),sTfun(X1,X0)),bCOMB,uminus_uminus(X0))))),
% 0.23/0.70 inference(fool_elimination,[],[f520])).
% 0.23/0.70 thf(f520,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : (uminus(X0) => (uminus_uminus(sTfun(X1,X0)) = (^[X2 : X1 > X0, X3 : X1] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X1,X0,X2,X3))))))),
% 0.23/0.70 inference(rectify,[],[f195])).
% 0.23/0.70 thf(f195,axiom,(
% 0.23/0.70 ! [X1 : $tType,X0 : $tType] : (uminus(X1) => (uminus_uminus(sTfun(X0,X1)) = (^[X28 : X0 > X1, X12 : X0] : (vAPP(X1,X1,uminus_uminus(X1),vAPP(X0,X1,X28,X12))))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_uminus__apply)).
% 0.23/0.70 thf(f2873,plain,(
% 0.23/0.70 spl40_96),
% 0.23/0.70 inference(avatar_split_clause,[],[f1314,f2871])).
% 0.23/0.70 thf(f2871,plain,(
% 0.23/0.70 spl40_96 <=> ! [X0 : $tType,X2 : set(X0),X1 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_96])])).
% 0.23/0.70 thf(f1314,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f629])).
% 0.23/0.70 thf(f629,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2)))),
% 0.23/0.70 inference(fool_elimination,[],[f628])).
% 0.23/0.70 thf(f628,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2))),
% 0.23/0.70 inference(rectify,[],[f41])).
% 0.23/0.70 thf(f41,axiom,(
% 0.23/0.70 ! [X0 : $tType,X4 : X0,X5 : set(X0)] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X4),X5))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_insertI1)).
% 0.23/0.70 thf(f2866,plain,(
% 0.23/0.70 spl40_95),
% 0.23/0.70 inference(avatar_split_clause,[],[f1254,f2864])).
% 0.23/0.70 thf(f2864,plain,(
% 0.23/0.70 spl40_95 <=> ! [X0 : $tType,X1 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1))))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_95])])).
% 0.23/0.70 thf(f1254,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1))))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f559])).
% 0.23/0.70 thf(f559,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1))))),
% 0.23/0.70 inference(fool_elimination,[],[f558])).
% 0.23/0.70 thf(f558,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1)))),
% 0.23/0.70 inference(rectify,[],[f174])).
% 0.23/0.70 thf(f174,axiom,(
% 0.23/0.70 ! [X0 : $tType,X54 : X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X54),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X54)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_option_Oset__intros)).
% 0.23/0.70 thf(f2840,plain,(
% 0.23/0.70 spl40_94 | ~spl40_14 | ~spl40_41),
% 0.23/0.70 inference(avatar_split_clause,[],[f2488,f2432,f2277,f2838])).
% 0.23/0.70 thf(f2838,plain,(
% 0.23/0.70 spl40_94 <=> ! [X0 : $tType] : ($true = uminus(sTfun(X0,real)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_94])])).
% 0.23/0.70 thf(f2277,plain,(
% 0.23/0.70 spl40_14 <=> (uminus(real) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_14])])).
% 0.23/0.70 thf(f2488,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = uminus(sTfun(X0,real)))) ) | (~spl40_14 | ~spl40_41)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2483])).
% 0.23/0.70 thf(f2483,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = uminus(sTfun(X0,real)))) ) | (~spl40_14 | ~spl40_41)),
% 0.23/0.70 inference(superposition,[],[f2433,f2279])).
% 0.23/0.70 thf(f2279,plain,(
% 0.23/0.70 (uminus(real) = $true) | ~spl40_14),
% 0.23/0.70 inference(avatar_component_clause,[],[f2277])).
% 0.23/0.70 thf(f2826,plain,(
% 0.23/0.70 spl40_93),
% 0.23/0.70 inference(avatar_split_clause,[],[f1230,f2824])).
% 0.23/0.70 thf(f2824,plain,(
% 0.23/0.70 spl40_93 <=> ! [X0 : $tType,X1 : set(X0)] : ((bot_bot(set(X0)) = X1) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK10(X0),X1)),X1)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_93])])).
% 0.23/0.70 thf(f1230,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : ((bot_bot(set(X0)) = X1) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK10(X0),X1)),X1))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1039])).
% 0.23/0.70 thf(f1039,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : ((bot_bot(set(X0)) = X1) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK10(X0),X1)),X1)))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f921,f1038])).
% 0.23/0.70 thf(f1038,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (? [X2 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK10(X0),X1)),X1)))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f921,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : ((bot_bot(set(X0)) = X1) | ? [X2 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)))),
% 0.23/0.70 inference(ennf_transformation,[],[f811])).
% 0.23/0.70 thf(f811,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (! [X2 : X0] : ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => (bot_bot(set(X0)) = X1))),
% 0.23/0.70 inference(flattening,[],[f511])).
% 0.23/0.70 thf(f511,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (! [X2 : X0] : ~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => (bot_bot(set(X0)) = X1))),
% 0.23/0.70 inference(fool_elimination,[],[f510])).
% 0.23/0.70 thf(f510,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (! [X2 : X0] : ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1) => (bot_bot(set(X0)) = X1))),
% 0.23/0.70 inference(rectify,[],[f31])).
% 0.23/0.70 thf(f31,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0)] : (! [X16 : X0] : ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X16),X7) => (bot_bot(set(X0)) = X7))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_equals0I)).
% 0.23/0.70 thf(f2822,plain,(
% 0.23/0.70 spl40_92),
% 0.23/0.70 inference(avatar_split_clause,[],[f1166,f2820])).
% 0.23/0.70 thf(f2820,plain,(
% 0.23/0.70 spl40_92 <=> ! [X0 : $tType] : ((sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0))) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_92])])).
% 0.23/0.70 thf(f1166,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : ((sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0))) | (semilattice_sup(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f899])).
% 0.23/0.70 thf(f899,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0))) | (semilattice_sup(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f423])).
% 0.23/0.70 thf(f423,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((semilattice_sup(X0) = $true) => (sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0))))),
% 0.23/0.70 inference(fool_elimination,[],[f422])).
% 0.23/0.70 thf(f422,plain,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_sup(X0) => (sup_sup(X0) = (^[X1 : X0, X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X1)))))),
% 0.23/0.70 inference(rectify,[],[f50])).
% 0.23/0.70 thf(f50,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (semilattice_sup(X0) => (sup_sup(X0) = (^[X25 : X0, X26 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X26),X25)))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_sup_Ocommute)).
% 0.23/0.70 thf(f2818,plain,(
% 0.23/0.70 spl40_91),
% 0.23/0.70 inference(avatar_split_clause,[],[f1146,f2816])).
% 0.23/0.70 thf(f2816,plain,(
% 0.23/0.70 spl40_91 <=> ! [X0 : $tType] : ((sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0))) | (lattice(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_91])])).
% 0.23/0.70 thf(f1146,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : ((sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0))) | (lattice(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f879])).
% 0.23/0.70 thf(f879,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0))) | (lattice(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f383])).
% 0.23/0.70 thf(f383,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((lattice(X0) = $true) => (sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0))))),
% 0.23/0.70 inference(fool_elimination,[],[f382])).
% 0.23/0.70 thf(f382,plain,(
% 0.23/0.70 ! [X0 : $tType] : (lattice(X0) => (sup_sup(X0) = (^[X1 : X0, X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X1)))))),
% 0.23/0.70 inference(rectify,[],[f56])).
% 0.23/0.70 thf(f56,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (lattice(X0) => (sup_sup(X0) = (^[X12 : X0, X20 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X20),X12)))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_inf__sup__aci_I5_J)).
% 0.23/0.70 thf(f2814,plain,(
% 0.23/0.70 spl40_90),
% 0.23/0.70 inference(avatar_split_clause,[],[f1132,f2812])).
% 0.23/0.70 thf(f2812,plain,(
% 0.23/0.70 spl40_90 <=> ! [X0 : $tType] : ((zero_zero(set(X0)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),zero_zero(X0)),bot_bot(set(X0)))) | (zero(X0) != $true))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_90])])).
% 0.23/0.70 thf(f1132,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : ((zero_zero(set(X0)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),zero_zero(X0)),bot_bot(set(X0)))) | (zero(X0) != $true)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f865])).
% 0.23/0.70 thf(f865,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((zero_zero(set(X0)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),zero_zero(X0)),bot_bot(set(X0)))) | (zero(X0) != $true))),
% 0.23/0.70 inference(ennf_transformation,[],[f355])).
% 0.23/0.70 thf(f355,plain,(
% 0.23/0.70 ! [X0 : $tType] : ((zero(X0) = $true) => (zero_zero(set(X0)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),zero_zero(X0)),bot_bot(set(X0)))))),
% 0.23/0.70 inference(fool_elimination,[],[f354])).
% 0.23/0.70 thf(f354,plain,(
% 0.23/0.70 ! [X0 : $tType] : (zero(X0) => (zero_zero(set(X0)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),zero_zero(X0)),bot_bot(set(X0)))))),
% 0.23/0.70 inference(rectify,[],[f89])).
% 0.23/0.70 thf(f89,axiom,(
% 0.23/0.70 ! [X0 : $tType] : (zero(X0) => (zero_zero(set(X0)) = vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),zero_zero(X0)),bot_bot(set(X0)))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_set__zero)).
% 0.23/0.70 thf(f2807,plain,(
% 0.23/0.70 spl40_89),
% 0.23/0.70 inference(avatar_split_clause,[],[f1115,f2805])).
% 0.23/0.70 thf(f2805,plain,(
% 0.23/0.70 spl40_89 <=> ! [X0 : trm] : (none(trm) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),some(trm),X0)),none(trm)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_89])])).
% 0.23/0.70 thf(f1115,plain,(
% 0.23/0.70 ( ! [X0 : trm] : ((none(trm) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),some(trm),X0)),none(trm)))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f790])).
% 0.23/0.70 thf(f790,plain,(
% 0.23/0.70 ! [X0 : trm] : (none(trm) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),some(trm),X0)),none(trm)))),
% 0.23/0.70 inference(rectify,[],[f190])).
% 0.23/0.70 thf(f190,axiom,(
% 0.23/0.70 ! [X97 : trm] : (none(trm) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,vAPP(trm,option(trm),some(trm),X97)),none(trm)))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_Timeso_Osimps_I3_J)).
% 0.23/0.70 thf(f2799,plain,(
% 0.23/0.70 spl40_88 | ~spl40_87),
% 0.23/0.70 inference(avatar_split_clause,[],[f2795,f2792,f2797])).
% 0.23/0.70 thf(f2797,plain,(
% 0.23/0.70 spl40_88 <=> ! [X0 : $tType,X1 : X0] : (vAPP(set(X0),X0,the_elem(X0),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1))) = X1)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_88])])).
% 0.23/0.70 thf(f2792,plain,(
% 0.23/0.70 spl40_87 <=> ! [X0 : $tType,X1 : X0] : (vAPP(set(X0),X0,the_elem(X0),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0)))) = X1)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_87])])).
% 0.23/0.70 thf(f2795,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : X0] : ((vAPP(set(X0),X0,the_elem(X0),vAPP(option(X0),set(X0),set_option(X0),vAPP(X0,option(X0),some(X0),X1))) = X1)) ) | ~spl40_87),
% 0.23/0.70 inference(forward_demodulation,[],[f2793,f1199])).
% 0.23/0.70 thf(f2793,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : X0] : ((vAPP(set(X0),X0,the_elem(X0),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0)))) = X1)) ) | ~spl40_87),
% 0.23/0.70 inference(avatar_component_clause,[],[f2792])).
% 0.23/0.70 thf(f2794,plain,(
% 0.23/0.70 spl40_87),
% 0.23/0.70 inference(avatar_split_clause,[],[f1198,f2792])).
% 0.23/0.70 thf(f1198,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : X0] : ((vAPP(set(X0),X0,the_elem(X0),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0)))) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f800])).
% 0.23/0.70 thf(f800,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0] : (vAPP(set(X0),X0,the_elem(X0),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),bot_bot(set(X0)))) = X1)),
% 0.23/0.70 inference(rectify,[],[f93])).
% 0.23/0.70 thf(f93,axiom,(
% 0.23/0.70 ! [X0 : $tType,X8 : X0] : (vAPP(set(X0),X0,the_elem(X0),vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X8),bot_bot(set(X0)))) = X8)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_the__elem__eq)).
% 0.23/0.70 thf(f2790,plain,(
% 0.23/0.70 spl40_86 | ~spl40_13 | ~spl40_40),
% 0.23/0.70 inference(avatar_split_clause,[],[f2481,f2428,f2272,f2788])).
% 0.23/0.70 thf(f2788,plain,(
% 0.23/0.70 spl40_86 <=> ! [X0 : $tType] : ($true = preorder(sTfun(X0,$o)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_86])])).
% 0.23/0.70 thf(f2272,plain,(
% 0.23/0.70 spl40_13 <=> (preorder($o) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_13])])).
% 0.23/0.70 thf(f2428,plain,(
% 0.23/0.70 spl40_40 <=> ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_40])])).
% 0.23/0.70 thf(f2481,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,$o)))) ) | (~spl40_13 | ~spl40_40)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2472])).
% 0.23/0.70 thf(f2472,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X0,$o)))) ) | (~spl40_13 | ~spl40_40)),
% 0.23/0.70 inference(superposition,[],[f2429,f2274])).
% 0.23/0.70 thf(f2274,plain,(
% 0.23/0.70 (preorder($o) = $true) | ~spl40_13),
% 0.23/0.70 inference(avatar_component_clause,[],[f2272])).
% 0.23/0.70 thf(f2429,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : (($true != preorder(X1)) | ($true = preorder(sTfun(X0,X1)))) ) | ~spl40_40),
% 0.23/0.70 inference(avatar_component_clause,[],[f2428])).
% 0.23/0.70 thf(f2786,plain,(
% 0.23/0.70 spl40_85),
% 0.23/0.70 inference(avatar_split_clause,[],[f1197,f2784])).
% 0.23/0.70 thf(f2784,plain,(
% 0.23/0.70 spl40_85 <=> ! [X0 : $tType,X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),bot_bot(set(X0))),X1) = X1)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_85])])).
% 0.23/0.70 thf(f1197,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),bot_bot(set(X0))),X1) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f799])).
% 0.23/0.70 thf(f799,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),bot_bot(set(X0))),X1) = X1)),
% 0.23/0.70 inference(rectify,[],[f80])).
% 0.23/0.70 thf(f80,axiom,(
% 0.23/0.70 ! [X0 : $tType,X5 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),bot_bot(set(X0))),X5) = X5)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Un__empty__left)).
% 0.23/0.70 thf(f2782,plain,(
% 0.23/0.70 spl40_84),
% 0.23/0.70 inference(avatar_split_clause,[],[f1196,f2780])).
% 0.23/0.70 thf(f1196,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),bot_bot(set(X0))) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f798])).
% 0.23/0.70 thf(f798,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),bot_bot(set(X0))) = X1)),
% 0.23/0.70 inference(rectify,[],[f79])).
% 0.23/0.70 thf(f79,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),bot_bot(set(X0))) = X7)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Un__empty__right)).
% 0.23/0.70 thf(f2770,plain,(
% 0.23/0.70 spl40_83),
% 0.23/0.70 inference(avatar_split_clause,[],[f1276,f2768])).
% 0.23/0.70 thf(f2768,plain,(
% 0.23/0.70 spl40_83 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_83])])).
% 0.23/0.70 thf(f1276,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f585])).
% 0.23/0.70 thf(f585,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)),
% 0.23/0.70 inference(fool_elimination,[],[f584])).
% 0.23/0.70 thf(f584,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)),
% 0.23/0.70 inference(rectify,[],[f301])).
% 0.23/0.70 thf(f301,axiom,(
% 0.23/0.70 ! [X0 : $tType,X8 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X8),X9) = X8)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T)).
% 0.23/0.70 thf(f2766,plain,(
% 0.23/0.70 spl40_82),
% 0.23/0.70 inference(avatar_split_clause,[],[f1275,f2764])).
% 0.23/0.70 thf(f2764,plain,(
% 0.23/0.70 spl40_82 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_82])])).
% 0.23/0.70 thf(f1275,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f583])).
% 0.23/0.70 thf(f583,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)),
% 0.23/0.70 inference(fool_elimination,[],[f582])).
% 0.23/0.70 thf(f582,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)),
% 0.23/0.70 inference(rectify,[],[f300])).
% 0.23/0.70 thf(f300,axiom,(
% 0.23/0.70 ! [X0 : $tType,X8 : X0,X9 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X8),X9) = X9)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T)).
% 0.23/0.70 thf(f2762,plain,(
% 0.23/0.70 spl40_81),
% 0.23/0.70 inference(avatar_split_clause,[],[f1126,f2760])).
% 0.23/0.70 thf(f2760,plain,(
% 0.23/0.70 spl40_81 <=> ! [X0 : variable] : ((vAPP(char,variable,dVar,vAPP(variable,char,sK4,X0)) = X0) | (vAPP(char,variable,rVar,vAPP(variable,char,sK5,X0)) = X0))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_81])])).
% 0.23/0.70 thf(f1126,plain,(
% 0.23/0.70 ( ! [X0 : variable] : ((vAPP(char,variable,dVar,vAPP(variable,char,sK4,X0)) = X0) | (vAPP(char,variable,rVar,vAPP(variable,char,sK5,X0)) = X0)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1031])).
% 0.23/0.70 thf(f1031,plain,(
% 0.23/0.70 ! [X0 : variable] : ((vAPP(char,variable,dVar,vAPP(variable,char,sK4,X0)) = X0) | (vAPP(char,variable,rVar,vAPP(variable,char,sK5,X0)) = X0))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f1028,f1030,f1029])).
% 0.23/0.70 thf(f1029,plain,(
% 0.23/0.70 ! [X0 : variable] : (? [X1 : char] : (vAPP(char,variable,dVar,X1) = X0) => (vAPP(char,variable,dVar,vAPP(variable,char,sK4,X0)) = X0))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1030,plain,(
% 0.23/0.70 ! [X0 : variable] : (? [X2 : char] : (vAPP(char,variable,rVar,X2) = X0) => (vAPP(char,variable,rVar,vAPP(variable,char,sK5,X0)) = X0))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f1028,plain,(
% 0.23/0.70 ! [X0 : variable] : (? [X1 : char] : (vAPP(char,variable,dVar,X1) = X0) | ? [X2 : char] : (vAPP(char,variable,rVar,X2) = X0))),
% 0.23/0.70 inference(rectify,[],[f859])).
% 0.23/0.70 thf(f859,plain,(
% 0.23/0.70 ! [X0 : variable] : (? [X2 : char] : (vAPP(char,variable,dVar,X2) = X0) | ? [X1 : char] : (vAPP(char,variable,rVar,X1) = X0))),
% 0.23/0.70 inference(ennf_transformation,[],[f791])).
% 0.23/0.70 thf(f791,plain,(
% 0.23/0.70 ! [X0 : variable] : (! [X1 : char] : (vAPP(char,variable,rVar,X1) != X0) => ~! [X2 : char] : (vAPP(char,variable,dVar,X2) != X0))),
% 0.23/0.70 inference(rectify,[],[f102])).
% 0.23/0.70 thf(f102,axiom,(
% 0.23/0.70 ! [X9 : variable] : (! [X68 : char] : (vAPP(char,variable,rVar,X68) != X9) => ~! [X69 : char] : (vAPP(char,variable,dVar,X69) != X9))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_variable_Oexhaust)).
% 0.23/0.70 thf(f2758,plain,(
% 0.23/0.70 spl40_80 | ~spl40_15 | ~spl40_40),
% 0.23/0.70 inference(avatar_split_clause,[],[f2480,f2428,f2282,f2756])).
% 0.23/0.70 thf(f2756,plain,(
% 0.23/0.70 spl40_80 <=> ! [X0 : $tType] : ($true = preorder(sTfun(X0,real)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_80])])).
% 0.23/0.70 thf(f2282,plain,(
% 0.23/0.70 spl40_15 <=> (preorder(real) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_15])])).
% 0.23/0.70 thf(f2480,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,real)))) ) | (~spl40_15 | ~spl40_40)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2473])).
% 0.23/0.70 thf(f2473,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X0,real)))) ) | (~spl40_15 | ~spl40_40)),
% 0.23/0.70 inference(superposition,[],[f2429,f2284])).
% 0.23/0.70 thf(f2284,plain,(
% 0.23/0.70 (preorder(real) = $true) | ~spl40_15),
% 0.23/0.70 inference(avatar_component_clause,[],[f2282])).
% 0.23/0.70 thf(f2737,plain,(
% 0.23/0.70 spl40_79),
% 0.23/0.70 inference(avatar_split_clause,[],[f1259,f2735])).
% 0.23/0.70 thf(f2735,plain,(
% 0.23/0.70 spl40_79 <=> ! [X0 : $tType,X2 : set(X0),X1 : X0] : (bot_bot(set(X0)) != vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_79])])).
% 0.23/0.70 thf(f1259,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X2 : set(X0),X1 : X0] : ((bot_bot(set(X0)) != vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f814])).
% 0.23/0.70 thf(f814,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : X0,X2 : set(X0)] : (bot_bot(set(X0)) != vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X1),X2))),
% 0.23/0.70 inference(rectify,[],[f75])).
% 0.23/0.70 thf(f75,axiom,(
% 0.23/0.70 ! [X0 : $tType,X4 : X0,X7 : set(X0)] : (bot_bot(set(X0)) != vAPP(set(X0),set(X0),vAPP(X0,sTfun(set(X0),set(X0)),insert(X0),X4),X7))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_insert__not__empty)).
% 0.23/0.70 thf(f2733,plain,(
% 0.23/0.70 spl40_78),
% 0.23/0.70 inference(avatar_split_clause,[],[f1237,f2731])).
% 0.23/0.70 thf(f2731,plain,(
% 0.23/0.70 spl40_78 <=> ! [X1 : $tType,X0 : $tType] : ((bot_bot(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,bot_bot(X0))) | ($true != bot(X0)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_78])])).
% 0.23/0.70 thf(f1237,plain,(
% 0.23/0.70 ( ! [X1 : $tType,X0 : $tType] : ((bot_bot(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,bot_bot(X0))) | ($true != bot(X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f930])).
% 0.23/0.70 thf(f930,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : ((bot_bot(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,bot_bot(X0))) | ($true != bot(X0)))),
% 0.23/0.70 inference(ennf_transformation,[],[f525])).
% 0.23/0.70 thf(f525,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : (($true = bot(X0)) => (bot_bot(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,bot_bot(X0))))),
% 0.23/0.70 inference(fool_elimination,[],[f524])).
% 0.23/0.70 thf(f524,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : $tType] : (bot(X0) => (bot_bot(sTfun(X1,X0)) = (^[X2 : X1] : (bot_bot(X0)))))),
% 0.23/0.70 inference(rectify,[],[f97])).
% 0.23/0.70 thf(f97,axiom,(
% 0.23/0.70 ! [X1 : $tType,X0 : $tType] : (bot(X1) => (bot_bot(sTfun(X0,X1)) = (^[X12 : X0] : (bot_bot(X1)))))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_bot__fun__def)).
% 0.23/0.70 thf(f2729,plain,(
% 0.23/0.70 spl40_77),
% 0.23/0.70 inference(avatar_split_clause,[],[f1225,f2727])).
% 0.23/0.70 thf(f2727,plain,(
% 0.23/0.70 spl40_77 <=> ! [X0 : $tType,X1 : option(X0)] : ((vAPP(X0,option(X0),some(X0),vAPP(option(X0),X0,sK7(X0),X1)) = X1) | (none(X0) = X1))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_77])])).
% 0.23/0.70 thf(f1225,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : option(X0)] : ((vAPP(X0,option(X0),some(X0),vAPP(option(X0),X0,sK7(X0),X1)) = X1) | (none(X0) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f1035])).
% 0.23/0.70 thf(f1035,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0)] : ((vAPP(X0,option(X0),some(X0),vAPP(option(X0),X0,sK7(X0),X1)) = X1) | (none(X0) = X1))),
% 0.23/0.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f917,f1034])).
% 0.23/0.70 thf(f1034,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0)] : (? [X2 : X0] : (vAPP(X0,option(X0),some(X0),X2) = X1) => (vAPP(X0,option(X0),some(X0),vAPP(option(X0),X0,sK7(X0),X1)) = X1))),
% 0.23/0.70 introduced(choice_axiom,[])).
% 0.23/0.70 thf(f917,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0)] : (? [X2 : X0] : (vAPP(X0,option(X0),some(X0),X2) = X1) | (none(X0) = X1))),
% 0.23/0.70 inference(ennf_transformation,[],[f810])).
% 0.23/0.70 thf(f810,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0)] : ((none(X0) != X1) => ~! [X2 : X0] : (vAPP(X0,option(X0),some(X0),X2) != X1))),
% 0.23/0.70 inference(rectify,[],[f152])).
% 0.23/0.70 thf(f152,axiom,(
% 0.23/0.70 ! [X0 : $tType,X9 : option(X0)] : ((none(X0) != X9) => ~! [X69 : X0] : (vAPP(X0,option(X0),some(X0),X69) != X9))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_option_Oexhaust)).
% 0.23/0.70 thf(f2725,plain,(
% 0.23/0.70 spl40_76),
% 0.23/0.70 inference(avatar_split_clause,[],[f1223,f2723])).
% 0.23/0.70 thf(f2723,plain,(
% 0.23/0.70 spl40_76 <=> ! [X0 : $tType,X1 : option(X0)] : ((vAPP(X0,option(X0),some(X0),vAPP(option(X0),X0,the(X0),X1)) = X1) | (none(X0) = X1))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_76])])).
% 0.23/0.70 thf(f1223,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : option(X0)] : ((vAPP(X0,option(X0),some(X0),vAPP(option(X0),X0,the(X0),X1)) = X1) | (none(X0) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f915])).
% 0.23/0.70 thf(f915,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0)] : ((vAPP(X0,option(X0),some(X0),vAPP(option(X0),X0,the(X0),X1)) = X1) | (none(X0) = X1))),
% 0.23/0.70 inference(ennf_transformation,[],[f808])).
% 0.23/0.70 thf(f808,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : option(X0)] : ((none(X0) != X1) => (vAPP(X0,option(X0),some(X0),vAPP(option(X0),X0,the(X0),X1)) = X1))),
% 0.23/0.70 inference(rectify,[],[f163])).
% 0.23/0.70 thf(f163,axiom,(
% 0.23/0.70 ! [X0 : $tType,X71 : option(X0)] : ((none(X0) != X71) => (vAPP(X0,option(X0),some(X0),vAPP(option(X0),X0,the(X0),X71)) = X71))),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_option_Oexhaust__sel)).
% 0.23/0.70 thf(f2721,plain,(
% 0.23/0.70 spl40_75 | ~spl40_9 | ~spl40_40),
% 0.23/0.70 inference(avatar_split_clause,[],[f2478,f2428,f2252,f2719])).
% 0.23/0.70 thf(f2719,plain,(
% 0.23/0.70 spl40_75 <=> ! [X0 : $tType] : ($true = preorder(sTfun(X0,nat)))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_75])])).
% 0.23/0.70 thf(f2252,plain,(
% 0.23/0.70 spl40_9 <=> (preorder(nat) = $true)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_9])])).
% 0.23/0.70 thf(f2478,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,nat)))) ) | (~spl40_9 | ~spl40_40)),
% 0.23/0.70 inference(trivial_inequality_removal,[],[f2475])).
% 0.23/0.70 thf(f2475,plain,(
% 0.23/0.70 ( ! [X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X0,nat)))) ) | (~spl40_9 | ~spl40_40)),
% 0.23/0.70 inference(superposition,[],[f2429,f2254])).
% 0.23/0.70 thf(f2254,plain,(
% 0.23/0.70 (preorder(nat) = $true) | ~spl40_9),
% 0.23/0.70 inference(avatar_component_clause,[],[f2252])).
% 0.23/0.70 thf(f2717,plain,(
% 0.23/0.70 spl40_74),
% 0.23/0.70 inference(avatar_split_clause,[],[f1195,f2715])).
% 0.23/0.70 thf(f2715,plain,(
% 0.23/0.70 spl40_74 <=> ! [X0 : $tType,X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X1) = X1)),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_74])])).
% 0.23/0.70 thf(f1195,plain,(
% 0.23/0.70 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X1) = X1)) )),
% 0.23/0.70 inference(cnf_transformation,[],[f797])).
% 0.23/0.70 thf(f797,plain,(
% 0.23/0.70 ! [X0 : $tType,X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X1) = X1)),
% 0.23/0.70 inference(rectify,[],[f63])).
% 0.23/0.70 thf(f63,axiom,(
% 0.23/0.70 ! [X0 : $tType,X7 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X7),X7) = X7)),
% 0.23/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Un__absorb)).
% 0.23/0.70 thf(f2713,plain,(
% 0.23/0.70 spl40_73),
% 0.23/0.70 inference(avatar_split_clause,[],[f1114,f2711])).
% 0.23/0.70 thf(f2711,plain,(
% 0.23/0.70 spl40_73 <=> ! [X0 : option(trm)] : (none(trm) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,none(trm)),X0))),
% 0.23/0.70 introduced(avatar_definition,[new_symbols(naming,[spl40_73])])).
% 0.23/0.70 thf(f1114,plain,(
% 0.23/0.70 ( ! [X0 : option(trm)] : ((none(trm) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,none(trm)),X0))) )),
% 0.23/0.70 inference(cnf_transformation,[],[f789])).
% 0.23/0.70 thf(f789,plain,(
% 0.23/0.70 ! [X0 : option(trm)] : (none(trm) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,none(trm)),X0))),
% 0.23/0.71 inference(rectify,[],[f210])).
% 0.23/0.71 thf(f210,axiom,(
% 0.23/0.71 ! [X65 : option(trm)] : (none(trm) = vAPP(option(trm),option(trm),vAPP(option(trm),sTfun(option(trm),option(trm)),uSubst277968634Timeso,none(trm)),X65))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Timeso_Osimps_I2_J)).
% 0.23/0.71 thf(f2707,plain,(
% 0.23/0.71 spl40_72),
% 0.23/0.71 inference(avatar_split_clause,[],[f1252,f2705])).
% 0.23/0.71 thf(f2705,plain,(
% 0.23/0.71 spl40_72 <=> ! [X0 : $tType,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),bot_bot(set(X0))),X1))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_72])])).
% 0.23/0.71 thf(f1252,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),bot_bot(set(X0))),X1))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f555])).
% 0.23/0.71 thf(f555,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),bot_bot(set(X0))),X1))),
% 0.23/0.71 inference(fool_elimination,[],[f554])).
% 0.23/0.71 thf(f554,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : set(X0)] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),bot_bot(set(X0))),X1)),
% 0.23/0.71 inference(rectify,[],[f253])).
% 0.23/0.71 thf(f253,axiom,(
% 0.23/0.71 ! [X0 : $tType,X7 : set(X0)] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),bot_bot(set(X0))),X7)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_empty__subsetI)).
% 0.23/0.71 thf(f2703,plain,(
% 0.23/0.71 spl40_71),
% 0.23/0.71 inference(avatar_split_clause,[],[f1194,f2701])).
% 0.23/0.71 thf(f2701,plain,(
% 0.23/0.71 spl40_71 <=> ! [X0 : $tType,X1 : set(X0)] : (vAPP(set(X0),set(X0),uminus_uminus(set(X0)),vAPP(set(X0),set(X0),uminus_uminus(set(X0)),X1)) = X1)),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_71])])).
% 0.23/0.71 thf(f1194,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(set(X0),set(X0),uminus_uminus(set(X0)),vAPP(set(X0),set(X0),uminus_uminus(set(X0)),X1)) = X1)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f796])).
% 0.23/0.71 thf(f796,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : set(X0)] : (vAPP(set(X0),set(X0),uminus_uminus(set(X0)),vAPP(set(X0),set(X0),uminus_uminus(set(X0)),X1)) = X1)),
% 0.23/0.71 inference(rectify,[],[f208])).
% 0.23/0.71 thf(f208,axiom,(
% 0.23/0.71 ! [X0 : $tType,X7 : set(X0)] : (vAPP(set(X0),set(X0),uminus_uminus(set(X0)),vAPP(set(X0),set(X0),uminus_uminus(set(X0)),X7)) = X7)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_double__complement)).
% 0.23/0.71 thf(f2699,plain,(
% 0.23/0.71 spl40_70),
% 0.23/0.71 inference(avatar_split_clause,[],[f1127,f2697])).
% 0.23/0.71 thf(f2697,plain,(
% 0.23/0.71 spl40_70 <=> ! [X0 : option(trm)] : ((none(trm) = X0) | (vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,sK6,X0)) = X0))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_70])])).
% 0.23/0.71 thf(f1127,plain,(
% 0.23/0.71 ( ! [X0 : option(trm)] : ((none(trm) = X0) | (vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,sK6,X0)) = X0)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f1033])).
% 0.23/0.71 thf(f1033,plain,(
% 0.23/0.71 ! [X0 : option(trm)] : ((none(trm) = X0) | (vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,sK6,X0)) = X0))),
% 0.23/0.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f860,f1032])).
% 0.23/0.71 thf(f1032,plain,(
% 0.23/0.71 ! [X0 : option(trm)] : (? [X1 : trm] : (vAPP(trm,option(trm),some(trm),X1) = X0) => (vAPP(trm,option(trm),some(trm),vAPP(option(trm),trm,sK6,X0)) = X0))),
% 0.23/0.71 introduced(choice_axiom,[])).
% 0.23/0.71 thf(f860,plain,(
% 0.23/0.71 ! [X0 : option(trm)] : ((none(trm) = X0) | ? [X1 : trm] : (vAPP(trm,option(trm),some(trm),X1) = X0))),
% 0.23/0.71 inference(ennf_transformation,[],[f792])).
% 0.23/0.71 thf(f792,plain,(
% 0.23/0.71 ! [X0 : option(trm)] : (! [X1 : trm] : (vAPP(trm,option(trm),some(trm),X1) != X0) => (none(trm) = X0))),
% 0.23/0.71 inference(rectify,[],[f161])).
% 0.23/0.71 thf(f161,axiom,(
% 0.23/0.71 ! [X8 : option(trm)] : (! [X86 : trm] : (vAPP(trm,option(trm),some(trm),X86) != X8) => (none(trm) = X8))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Differentialo_Ocases)).
% 0.23/0.71 thf(f2679,plain,(
% 0.23/0.71 spl40_69 | ~spl40_5 | ~spl40_39),
% 0.23/0.71 inference(avatar_split_clause,[],[f2471,f2424,f2232,f2677])).
% 0.23/0.71 thf(f2677,plain,(
% 0.23/0.71 spl40_69 <=> ! [X0 : $tType] : ($true = bounde1808546759up_bot(sTfun(X0,$o)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_69])])).
% 0.23/0.71 thf(f2232,plain,(
% 0.23/0.71 spl40_5 <=> (bounded_lattice($o) = $true)),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_5])])).
% 0.23/0.71 thf(f2424,plain,(
% 0.23/0.71 spl40_39 <=> ! [X1 : $tType,X0 : $tType] : (($true = bounde1808546759up_bot(sTfun(X0,X1))) | ($true != bounded_lattice(X1)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_39])])).
% 0.23/0.71 thf(f2471,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = bounde1808546759up_bot(sTfun(X0,$o)))) ) | (~spl40_5 | ~spl40_39)),
% 0.23/0.71 inference(trivial_inequality_removal,[],[f2466])).
% 0.23/0.71 thf(f2466,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true != $true) | ($true = bounde1808546759up_bot(sTfun(X0,$o)))) ) | (~spl40_5 | ~spl40_39)),
% 0.23/0.71 inference(superposition,[],[f2425,f2234])).
% 0.23/0.71 thf(f2234,plain,(
% 0.23/0.71 (bounded_lattice($o) = $true) | ~spl40_5),
% 0.23/0.71 inference(avatar_component_clause,[],[f2232])).
% 0.23/0.71 thf(f2425,plain,(
% 0.23/0.71 ( ! [X1 : $tType,X0 : $tType] : (($true != bounded_lattice(X1)) | ($true = bounde1808546759up_bot(sTfun(X0,X1)))) ) | ~spl40_39),
% 0.23/0.71 inference(avatar_component_clause,[],[f2424])).
% 0.23/0.71 thf(f2675,plain,(
% 0.23/0.71 spl40_68),
% 0.23/0.71 inference(avatar_split_clause,[],[f1152,f2673])).
% 0.23/0.71 thf(f2673,plain,(
% 0.23/0.71 spl40_68 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),bot_bot(X0)),X1) = X1) | (bounde1808546759up_bot(X0) != $true))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_68])])).
% 0.23/0.71 thf(f1152,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),bot_bot(X0)),X1) = X1) | (bounde1808546759up_bot(X0) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f885])).
% 0.23/0.71 thf(f885,plain,(
% 0.23/0.71 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),bot_bot(X0)),X1) = X1) | (bounde1808546759up_bot(X0) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f395])).
% 0.23/0.71 thf(f395,plain,(
% 0.23/0.71 ! [X0 : $tType] : ((bounde1808546759up_bot(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),bot_bot(X0)),X1) = X1))),
% 0.23/0.71 inference(fool_elimination,[],[f394])).
% 0.23/0.71 thf(f394,plain,(
% 0.23/0.71 ! [X0 : $tType] : (bounde1808546759up_bot(X0) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),bot_bot(X0)),X1) = X1))),
% 0.23/0.71 inference(rectify,[],[f11])).
% 0.23/0.71 thf(f11,axiom,(
% 0.23/0.71 ! [X0 : $tType] : (bounde1808546759up_bot(X0) => ! [X4 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),bot_bot(X0)),X4) = X4))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_sup__bot_Oleft__neutral)).
% 0.23/0.71 thf(f2671,plain,(
% 0.23/0.71 spl40_67),
% 0.23/0.71 inference(avatar_split_clause,[],[f1150,f2669])).
% 0.23/0.71 thf(f2669,plain,(
% 0.23/0.71 spl40_67 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),bot_bot(X0)) = X1) | (bounde1808546759up_bot(X0) != $true))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_67])])).
% 0.23/0.71 thf(f1150,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),bot_bot(X0)) = X1) | (bounde1808546759up_bot(X0) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f883])).
% 0.23/0.71 thf(f883,plain,(
% 0.23/0.71 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),bot_bot(X0)) = X1) | (bounde1808546759up_bot(X0) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f391])).
% 0.23/0.71 thf(f391,plain,(
% 0.23/0.71 ! [X0 : $tType] : ((bounde1808546759up_bot(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),bot_bot(X0)) = X1))),
% 0.23/0.71 inference(fool_elimination,[],[f390])).
% 0.23/0.71 thf(f390,plain,(
% 0.23/0.71 ! [X0 : $tType] : (bounde1808546759up_bot(X0) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),bot_bot(X0)) = X1))),
% 0.23/0.71 inference(rectify,[],[f7])).
% 0.23/0.71 thf(f7,axiom,(
% 0.23/0.71 ! [X0 : $tType] : (bounde1808546759up_bot(X0) => ! [X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),bot_bot(X0)) = X8))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_sup__bot__right)).
% 0.23/0.71 thf(f2631,plain,(
% 0.23/0.71 spl40_66),
% 0.23/0.71 inference(avatar_split_clause,[],[f1250,f2629])).
% 0.23/0.71 thf(f2629,plain,(
% 0.23/0.71 spl40_66 <=> ! [X0 : $tType,X1 : X0] : ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0))))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_66])])).
% 0.23/0.71 thf(f1250,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0))))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f812])).
% 0.23/0.71 thf(f812,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : X0] : ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0))))),
% 0.23/0.71 inference(flattening,[],[f551])).
% 0.23/0.71 thf(f551,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : X0] : ~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0))))),
% 0.23/0.71 inference(fool_elimination,[],[f550])).
% 0.23/0.71 thf(f550,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : X0] : ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0)))),
% 0.23/0.71 inference(rectify,[],[f17])).
% 0.23/0.71 thf(f17,axiom,(
% 0.23/0.71 ! [X0 : $tType,X13 : X0] : ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),bot_bot(set(X0)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_empty__iff)).
% 0.23/0.71 thf(f2627,plain,(
% 0.23/0.71 spl40_65),
% 0.23/0.71 inference(avatar_split_clause,[],[f1168,f2625])).
% 0.23/0.71 thf(f2625,plain,(
% 0.23/0.71 spl40_65 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X1) = X1) | (semilattice_sup(X0) != $true))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_65])])).
% 0.23/0.71 thf(f1168,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X1) = X1) | (semilattice_sup(X0) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f901])).
% 0.23/0.71 thf(f901,plain,(
% 0.23/0.71 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X1) = X1) | (semilattice_sup(X0) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f427])).
% 0.23/0.71 thf(f427,plain,(
% 0.23/0.71 ! [X0 : $tType] : ((semilattice_sup(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X1) = X1))),
% 0.23/0.71 inference(fool_elimination,[],[f426])).
% 0.23/0.71 thf(f426,plain,(
% 0.23/0.71 ! [X0 : $tType] : (semilattice_sup(X0) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X1) = X1))),
% 0.23/0.71 inference(rectify,[],[f24])).
% 0.23/0.71 thf(f24,axiom,(
% 0.23/0.71 ! [X0 : $tType] : (semilattice_sup(X0) => ! [X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X8),X8) = X8))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_sup__idem)).
% 0.23/0.71 thf(f2623,plain,(
% 0.23/0.71 spl40_64),
% 0.23/0.71 inference(avatar_split_clause,[],[f1158,f2621])).
% 0.23/0.71 thf(f2621,plain,(
% 0.23/0.71 spl40_64 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1) | (semilattice_inf(X0) != $true))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_64])])).
% 0.23/0.71 thf(f1158,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1) | (semilattice_inf(X0) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f891])).
% 0.23/0.71 thf(f891,plain,(
% 0.23/0.71 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1) | (semilattice_inf(X0) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f407])).
% 0.23/0.71 thf(f407,plain,(
% 0.23/0.71 ! [X0 : $tType] : ((semilattice_inf(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1))),
% 0.23/0.71 inference(fool_elimination,[],[f406])).
% 0.23/0.71 thf(f406,plain,(
% 0.23/0.71 ! [X0 : $tType] : (semilattice_inf(X0) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1))),
% 0.23/0.71 inference(rectify,[],[f238])).
% 0.23/0.71 thf(f238,axiom,(
% 0.23/0.71 ! [X0 : $tType] : (semilattice_inf(X0) => ! [X4 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X4),X4) = X4))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_inf_Oidem)).
% 0.23/0.71 thf(f2619,plain,(
% 0.23/0.71 spl40_63),
% 0.23/0.71 inference(avatar_split_clause,[],[f1136,f2617])).
% 0.23/0.71 thf(f2617,plain,(
% 0.23/0.71 spl40_63 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_63])])).
% 0.23/0.71 thf(f1136,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f869])).
% 0.23/0.71 thf(f869,plain,(
% 0.23/0.71 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f363])).
% 0.23/0.71 thf(f363,plain,(
% 0.23/0.71 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)))),
% 0.23/0.71 inference(fool_elimination,[],[f362])).
% 0.23/0.71 thf(f362,plain,(
% 0.23/0.71 ! [X0 : $tType] : (preorder(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1))),
% 0.23/0.71 inference(rectify,[],[f234])).
% 0.23/0.71 thf(f234,axiom,(
% 0.23/0.71 ! [X0 : $tType] : (preorder(X0) => ! [X8 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X8),X8))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_order__refl)).
% 0.23/0.71 thf(f2615,plain,(
% 0.23/0.71 spl40_62 | ~spl40_5 | ~spl40_38),
% 0.23/0.71 inference(avatar_split_clause,[],[f2465,f2420,f2232,f2613])).
% 0.23/0.71 thf(f2613,plain,(
% 0.23/0.71 spl40_62 <=> ! [X0 : $tType] : ($true = bounded_lattice(sTfun(X0,$o)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_62])])).
% 0.23/0.71 thf(f2420,plain,(
% 0.23/0.71 spl40_38 <=> ! [X1 : $tType,X0 : $tType] : (($true = bounded_lattice(sTfun(X0,X1))) | ($true != bounded_lattice(X1)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_38])])).
% 0.23/0.71 thf(f2465,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = bounded_lattice(sTfun(X0,$o)))) ) | (~spl40_5 | ~spl40_38)),
% 0.23/0.71 inference(trivial_inequality_removal,[],[f2460])).
% 0.23/0.71 thf(f2460,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true != $true) | ($true = bounded_lattice(sTfun(X0,$o)))) ) | (~spl40_5 | ~spl40_38)),
% 0.23/0.71 inference(superposition,[],[f2421,f2234])).
% 0.23/0.71 thf(f2421,plain,(
% 0.23/0.71 ( ! [X1 : $tType,X0 : $tType] : (($true != bounded_lattice(X1)) | ($true = bounded_lattice(sTfun(X0,X1)))) ) | ~spl40_38),
% 0.23/0.71 inference(avatar_component_clause,[],[f2420])).
% 0.23/0.71 thf(f2599,plain,(
% 0.23/0.71 spl40_61),
% 0.23/0.71 inference(avatar_split_clause,[],[f1140,f2597])).
% 0.23/0.71 thf(f2597,plain,(
% 0.23/0.71 spl40_61 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1) | (group_add(X0) != $true))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_61])])).
% 0.23/0.71 thf(f1140,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1) | (group_add(X0) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f873])).
% 0.23/0.71 thf(f873,plain,(
% 0.23/0.71 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1) | (group_add(X0) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f371])).
% 0.23/0.71 thf(f371,plain,(
% 0.23/0.71 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1))),
% 0.23/0.71 inference(fool_elimination,[],[f370])).
% 0.23/0.71 thf(f370,plain,(
% 0.23/0.71 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1))),
% 0.23/0.71 inference(rectify,[],[f192])).
% 0.23/0.71 thf(f192,axiom,(
% 0.23/0.71 ! [X0 : $tType] : (group_add(X0) => ! [X4 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X4)) = X4))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_add_Oinverse__inverse)).
% 0.23/0.71 thf(f2595,plain,(
% 0.23/0.71 spl40_60),
% 0.23/0.71 inference(avatar_split_clause,[],[f1135,f2593])).
% 0.23/0.71 thf(f2593,plain,(
% 0.23/0.71 spl40_60 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1) | (boolean_algebra(X0) != $true))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_60])])).
% 0.23/0.71 thf(f1135,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1) | (boolean_algebra(X0) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f868])).
% 0.23/0.71 thf(f868,plain,(
% 0.23/0.71 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1) | (boolean_algebra(X0) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f361])).
% 0.23/0.71 thf(f361,plain,(
% 0.23/0.71 ! [X0 : $tType] : ((boolean_algebra(X0) = $true) => ! [X1 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1))),
% 0.23/0.71 inference(fool_elimination,[],[f360])).
% 0.23/0.71 thf(f360,plain,(
% 0.23/0.71 ! [X0 : $tType] : (boolean_algebra(X0) => ! [X1 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1))),
% 0.23/0.71 inference(rectify,[],[f194])).
% 0.23/0.71 thf(f194,axiom,(
% 0.23/0.71 ! [X0 : $tType] : (boolean_algebra(X0) => ! [X8 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X8)) = X8))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_double__compl)).
% 0.23/0.71 thf(f2591,plain,(
% 0.23/0.71 spl40_59),
% 0.23/0.71 inference(avatar_split_clause,[],[f1113,f2589])).
% 0.23/0.71 thf(f2589,plain,(
% 0.23/0.71 spl40_59 <=> ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),bot_bot(sTfun(X0,$o))))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_59])])).
% 0.23/0.71 thf(f1113,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : ((bot_bot(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),bot_bot(sTfun(X0,$o))))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f29])).
% 0.23/0.71 thf(f29,axiom,(
% 0.23/0.71 ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),bot_bot(sTfun(X0,$o))))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_bot__set__def)).
% 0.23/0.71 thf(f2587,plain,(
% 0.23/0.71 spl40_58),
% 0.23/0.71 inference(avatar_split_clause,[],[f1112,f2585])).
% 0.23/0.71 thf(f2585,plain,(
% 0.23/0.71 spl40_58 <=> ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(set(option(X0)),set(X0),these(X0),bot_bot(set(option(X0)))))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_58])])).
% 0.23/0.71 thf(f1112,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : ((bot_bot(set(X0)) = vAPP(set(option(X0)),set(X0),these(X0),bot_bot(set(option(X0)))))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f132])).
% 0.23/0.71 thf(f132,axiom,(
% 0.23/0.71 ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(set(option(X0)),set(X0),these(X0),bot_bot(set(option(X0)))))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_these__empty)).
% 0.23/0.71 thf(f2582,plain,(
% 0.23/0.71 spl40_57),
% 0.23/0.71 inference(avatar_split_clause,[],[f1193,f2580])).
% 0.23/0.71 thf(f2580,plain,(
% 0.23/0.71 spl40_57 <=> ! [X0 : $tType,X1 : X0] : (vAPP(option(X0),X0,the(X0),vAPP(X0,option(X0),some(X0),X1)) = X1)),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_57])])).
% 0.23/0.71 thf(f1193,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : X0] : ((vAPP(option(X0),X0,the(X0),vAPP(X0,option(X0),some(X0),X1)) = X1)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f795])).
% 0.23/0.71 thf(f795,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : X0] : (vAPP(option(X0),X0,the(X0),vAPP(X0,option(X0),some(X0),X1)) = X1)),
% 0.23/0.71 inference(rectify,[],[f150])).
% 0.23/0.71 thf(f150,axiom,(
% 0.23/0.71 ! [X0 : $tType,X54 : X0] : (vAPP(option(X0),X0,the(X0),vAPP(X0,option(X0),some(X0),X54)) = X54)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_option_Osel)).
% 0.23/0.71 thf(f2572,plain,(
% 0.23/0.71 spl40_56),
% 0.23/0.71 inference(avatar_split_clause,[],[f1139,f2570])).
% 0.23/0.71 thf(f2570,plain,(
% 0.23/0.71 spl40_56 <=> ! [X0 : $tType] : ((zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0))) | (group_add(X0) != $true))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_56])])).
% 0.23/0.71 thf(f1139,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : ((zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0))) | (group_add(X0) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f872])).
% 0.23/0.71 thf(f872,plain,(
% 0.23/0.71 ! [X0 : $tType] : ((zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0))) | (group_add(X0) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f369])).
% 0.23/0.71 thf(f369,plain,(
% 0.23/0.71 ! [X0 : $tType] : ((group_add(X0) = $true) => (zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0))))),
% 0.23/0.71 inference(fool_elimination,[],[f368])).
% 0.23/0.71 thf(f368,plain,(
% 0.23/0.71 ! [X0 : $tType] : (group_add(X0) => (zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0))))),
% 0.23/0.71 inference(rectify,[],[f199])).
% 0.23/0.71 thf(f199,axiom,(
% 0.23/0.71 ! [X0 : $tType] : (group_add(X0) => (zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0))))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_add_Oinverse__neutral)).
% 0.23/0.71 thf(f2568,plain,(
% 0.23/0.71 spl40_55),
% 0.23/0.71 inference(avatar_split_clause,[],[f1111,f2566])).
% 0.23/0.71 thf(f2566,plain,(
% 0.23/0.71 spl40_55 <=> ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(option(X0),set(X0),set_option(X0),none(X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_55])])).
% 0.23/0.71 thf(f1111,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : ((bot_bot(set(X0)) = vAPP(option(X0),set(X0),set_option(X0),none(X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f185])).
% 0.23/0.71 thf(f185,axiom,(
% 0.23/0.71 ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(option(X0),set(X0),set_option(X0),none(X0)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_option_Osimps_I14_J)).
% 0.23/0.71 thf(f2564,plain,(
% 0.23/0.71 spl40_54),
% 0.23/0.71 inference(avatar_split_clause,[],[f1110,f2562])).
% 0.23/0.71 thf(f2562,plain,(
% 0.23/0.71 spl40_54 <=> ! [X0 : char] : (zero_zero(nat) = vAPP(variable,nat,size_size(variable),vAPP(char,variable,rVar,X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_54])])).
% 0.23/0.71 thf(f1110,plain,(
% 0.23/0.71 ( ! [X0 : char] : ((zero_zero(nat) = vAPP(variable,nat,size_size(variable),vAPP(char,variable,rVar,X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f788])).
% 0.23/0.71 thf(f788,plain,(
% 0.23/0.71 ! [X0 : char] : (zero_zero(nat) = vAPP(variable,nat,size_size(variable),vAPP(char,variable,rVar,X0)))),
% 0.23/0.71 inference(rectify,[],[f123])).
% 0.23/0.71 thf(f123,axiom,(
% 0.23/0.71 ! [X52 : char] : (zero_zero(nat) = vAPP(variable,nat,size_size(variable),vAPP(char,variable,rVar,X52)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_variable_Osize_I3_J)).
% 0.23/0.71 thf(f2560,plain,(
% 0.23/0.71 spl40_53),
% 0.23/0.71 inference(avatar_split_clause,[],[f1109,f2558])).
% 0.23/0.71 thf(f2558,plain,(
% 0.23/0.71 spl40_53 <=> ! [X0 : char] : (zero_zero(nat) = vAPP(variable,nat,size_size(variable),vAPP(char,variable,dVar,X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_53])])).
% 0.23/0.71 thf(f1109,plain,(
% 0.23/0.71 ( ! [X0 : char] : ((zero_zero(nat) = vAPP(variable,nat,size_size(variable),vAPP(char,variable,dVar,X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f787])).
% 0.23/0.71 thf(f787,plain,(
% 0.23/0.71 ! [X0 : char] : (zero_zero(nat) = vAPP(variable,nat,size_size(variable),vAPP(char,variable,dVar,X0)))),
% 0.23/0.71 inference(rectify,[],[f124])).
% 0.23/0.71 thf(f124,axiom,(
% 0.23/0.71 ! [X54 : char] : (zero_zero(nat) = vAPP(variable,nat,size_size(variable),vAPP(char,variable,dVar,X54)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_variable_Osize_I4_J)).
% 0.23/0.71 thf(f2554,plain,(
% 0.23/0.71 spl40_52),
% 0.23/0.71 inference(avatar_split_clause,[],[f1108,f2552])).
% 0.23/0.71 thf(f2552,plain,(
% 0.23/0.71 spl40_52 <=> ! [X0 : char] : (zero_zero(nat) = vAPP(variable,nat,size_variable,vAPP(char,variable,rVar,X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_52])])).
% 0.23/0.71 thf(f1108,plain,(
% 0.23/0.71 ( ! [X0 : char] : ((zero_zero(nat) = vAPP(variable,nat,size_variable,vAPP(char,variable,rVar,X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f786])).
% 0.23/0.71 thf(f786,plain,(
% 0.23/0.71 ! [X0 : char] : (zero_zero(nat) = vAPP(variable,nat,size_variable,vAPP(char,variable,rVar,X0)))),
% 0.23/0.71 inference(rectify,[],[f116])).
% 0.23/0.71 thf(f116,axiom,(
% 0.23/0.71 ! [X52 : char] : (vAPP(variable,nat,size_variable,vAPP(char,variable,rVar,X52)) = zero_zero(nat))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_variable_Osize__gen_I1_J)).
% 0.23/0.71 thf(f2550,plain,(
% 0.23/0.71 spl40_51),
% 0.23/0.71 inference(avatar_split_clause,[],[f1107,f2548])).
% 0.23/0.71 thf(f2548,plain,(
% 0.23/0.71 spl40_51 <=> ! [X0 : char] : (zero_zero(nat) = vAPP(variable,nat,size_variable,vAPP(char,variable,dVar,X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_51])])).
% 0.23/0.71 thf(f1107,plain,(
% 0.23/0.71 ( ! [X0 : char] : ((zero_zero(nat) = vAPP(variable,nat,size_variable,vAPP(char,variable,dVar,X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f785])).
% 0.23/0.71 thf(f785,plain,(
% 0.23/0.71 ! [X0 : char] : (zero_zero(nat) = vAPP(variable,nat,size_variable,vAPP(char,variable,dVar,X0)))),
% 0.23/0.71 inference(rectify,[],[f121])).
% 0.23/0.71 thf(f121,axiom,(
% 0.23/0.71 ! [X54 : char] : (zero_zero(nat) = vAPP(variable,nat,size_variable,vAPP(char,variable,dVar,X54)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_variable_Osize__gen_I2_J)).
% 0.23/0.71 thf(f2546,plain,(
% 0.23/0.71 spl40_50),
% 0.23/0.71 inference(avatar_split_clause,[],[f1192,f2544])).
% 0.23/0.71 thf(f2544,plain,(
% 0.23/0.71 spl40_50 <=> ! [X0 : char,X1 : char] : (vAPP(char,variable,dVar,X1) != vAPP(char,variable,rVar,X0))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_50])])).
% 0.23/0.71 thf(f1192,plain,(
% 0.23/0.71 ( ! [X0 : char,X1 : char] : ((vAPP(char,variable,dVar,X1) != vAPP(char,variable,rVar,X0))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f794])).
% 0.23/0.71 thf(f794,plain,(
% 0.23/0.71 ! [X0 : char,X1 : char] : (vAPP(char,variable,dVar,X1) != vAPP(char,variable,rVar,X0))),
% 0.23/0.71 inference(rectify,[],[f100])).
% 0.23/0.71 thf(f100,axiom,(
% 0.23/0.71 ! [X52 : char,X54 : char] : (vAPP(char,variable,rVar,X52) != vAPP(char,variable,dVar,X54))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_variable_Odistinct_I1_J)).
% 0.23/0.71 thf(f2542,plain,(
% 0.23/0.71 spl40_49),
% 0.23/0.71 inference(avatar_split_clause,[],[f1191,f2540])).
% 0.23/0.71 thf(f2540,plain,(
% 0.23/0.71 spl40_49 <=> ! [X0 : $tType,X1 : X0] : (none(X0) != vAPP(X0,option(X0),some(X0),X1))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_49])])).
% 0.23/0.71 thf(f1191,plain,(
% 0.23/0.71 ( ! [X0 : $tType,X1 : X0] : ((none(X0) != vAPP(X0,option(X0),some(X0),X1))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f793])).
% 0.23/0.71 thf(f793,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : X0] : (none(X0) != vAPP(X0,option(X0),some(X0),X1))),
% 0.23/0.71 inference(rectify,[],[f149])).
% 0.23/0.71 thf(f149,axiom,(
% 0.23/0.71 ! [X0 : $tType,X54 : X0] : (none(X0) != vAPP(X0,option(X0),some(X0),X54))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_option_Odistinct_I1_J)).
% 0.23/0.71 thf(f2500,plain,(
% 0.23/0.71 spl40_48 | ~spl40_6 | ~spl40_37),
% 0.23/0.71 inference(avatar_split_clause,[],[f2418,f2410,f2237,f2497])).
% 0.23/0.71 thf(f2497,plain,(
% 0.23/0.71 spl40_48 <=> ($true = zero(set(nat)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_48])])).
% 0.23/0.71 thf(f2237,plain,(
% 0.23/0.71 spl40_6 <=> (zero(nat) = $true)),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_6])])).
% 0.23/0.71 thf(f2410,plain,(
% 0.23/0.71 spl40_37 <=> ! [X0 : $tType] : (($true = zero(set(X0))) | (zero(X0) != $true))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_37])])).
% 0.23/0.71 thf(f2418,plain,(
% 0.23/0.71 ($true = zero(set(nat))) | (~spl40_6 | ~spl40_37)),
% 0.23/0.71 inference(trivial_inequality_removal,[],[f2413])).
% 0.23/0.71 thf(f2413,plain,(
% 0.23/0.71 ($true != $true) | ($true = zero(set(nat))) | (~spl40_6 | ~spl40_37)),
% 0.23/0.71 inference(superposition,[],[f2411,f2239])).
% 0.23/0.71 thf(f2239,plain,(
% 0.23/0.71 (zero(nat) = $true) | ~spl40_6),
% 0.23/0.71 inference(avatar_component_clause,[],[f2237])).
% 0.23/0.71 thf(f2411,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : ((zero(X0) != $true) | ($true = zero(set(X0)))) ) | ~spl40_37),
% 0.23/0.71 inference(avatar_component_clause,[],[f2410])).
% 0.23/0.71 thf(f2459,plain,(
% 0.23/0.71 spl40_47),
% 0.23/0.71 inference(avatar_split_clause,[],[f1248,f2457])).
% 0.23/0.71 thf(f1248,plain,(
% 0.23/0.71 ( ! [X1 : $tType,X0 : $tType] : (($true = semilattice_sup(sTfun(X0,X1))) | (semilattice_sup(X1) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f941])).
% 0.23/0.71 thf(f941,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = semilattice_sup(sTfun(X0,X1))) | (semilattice_sup(X1) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f547])).
% 0.23/0.71 thf(f547,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : ((semilattice_sup(X1) = $true) => ($true = semilattice_sup(sTfun(X0,X1))))),
% 0.23/0.71 inference(fool_elimination,[],[f546])).
% 0.23/0.71 thf(f546,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (semilattice_sup(X1) => semilattice_sup(sTfun(X0,X1)))),
% 0.23/0.71 inference(rectify,[],[f259])).
% 0.23/0.71 thf(f259,axiom,(
% 0.23/0.71 ! [X111 : $tType,X112 : $tType] : (semilattice_sup(X112) => semilattice_sup(sTfun(X111,X112)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__sup)).
% 0.23/0.71 thf(f2455,plain,(
% 0.23/0.71 spl40_46),
% 0.23/0.71 inference(avatar_split_clause,[],[f1245,f2453])).
% 0.23/0.71 thf(f1245,plain,(
% 0.23/0.71 ( ! [X1 : $tType,X0 : $tType] : (($true = semilattice_inf(sTfun(X0,X1))) | (semilattice_inf(X1) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f938])).
% 0.23/0.71 thf(f938,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = semilattice_inf(sTfun(X0,X1))) | (semilattice_inf(X1) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f541])).
% 0.23/0.71 thf(f541,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : ((semilattice_inf(X1) = $true) => ($true = semilattice_inf(sTfun(X0,X1))))),
% 0.23/0.71 inference(fool_elimination,[],[f540])).
% 0.23/0.71 thf(f540,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (semilattice_inf(X1) => semilattice_inf(sTfun(X0,X1)))),
% 0.23/0.71 inference(rectify,[],[f260])).
% 0.23/0.71 thf(f260,axiom,(
% 0.23/0.71 ! [X111 : $tType,X112 : $tType] : (semilattice_inf(X112) => semilattice_inf(sTfun(X111,X112)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf)).
% 0.23/0.71 thf(f2451,plain,(
% 0.23/0.71 spl40_45),
% 0.23/0.71 inference(avatar_split_clause,[],[f1243,f2449])).
% 0.23/0.71 thf(f1243,plain,(
% 0.23/0.71 ( ! [X1 : $tType,X0 : $tType] : (($true = lattice(sTfun(X0,X1))) | ($true != lattice(X1))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f936])).
% 0.23/0.71 thf(f936,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = lattice(sTfun(X0,X1))) | ($true != lattice(X1)))),
% 0.23/0.71 inference(ennf_transformation,[],[f537])).
% 0.23/0.71 thf(f537,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = lattice(X1)) => ($true = lattice(sTfun(X0,X1))))),
% 0.23/0.71 inference(fool_elimination,[],[f536])).
% 0.23/0.71 thf(f536,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (lattice(X1) => lattice(sTfun(X0,X1)))),
% 0.23/0.71 inference(rectify,[],[f263])).
% 0.23/0.71 thf(f263,axiom,(
% 0.23/0.71 ! [X111 : $tType,X112 : $tType] : (lattice(X112) => lattice(sTfun(X111,X112)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice)).
% 0.23/0.71 thf(f2447,plain,(
% 0.23/0.71 spl40_44),
% 0.23/0.71 inference(avatar_split_clause,[],[f1242,f2445])).
% 0.23/0.71 thf(f1242,plain,(
% 0.23/0.71 ( ! [X1 : $tType,X0 : $tType] : (($true = bot(sTfun(X0,X1))) | (bot(X1) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f935])).
% 0.23/0.71 thf(f935,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = bot(sTfun(X0,X1))) | (bot(X1) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f535])).
% 0.23/0.71 thf(f535,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : ((bot(X1) = $true) => ($true = bot(sTfun(X0,X1))))),
% 0.23/0.71 inference(fool_elimination,[],[f534])).
% 0.23/0.71 thf(f534,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (bot(X1) => bot(sTfun(X0,X1)))),
% 0.23/0.71 inference(rectify,[],[f264])).
% 0.23/0.71 thf(f264,axiom,(
% 0.23/0.71 ! [X111 : $tType,X112 : $tType] : (bot(X112) => bot(sTfun(X111,X112)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot)).
% 0.23/0.71 thf(f2443,plain,(
% 0.23/0.71 spl40_43),
% 0.23/0.71 inference(avatar_split_clause,[],[f1241,f2441])).
% 0.23/0.71 thf(f1241,plain,(
% 0.23/0.71 ( ! [X1 : $tType,X0 : $tType] : (($true = boolean_algebra(sTfun(X0,X1))) | ($true != boolean_algebra(X1))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f934])).
% 0.23/0.71 thf(f934,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = boolean_algebra(sTfun(X0,X1))) | ($true != boolean_algebra(X1)))),
% 0.23/0.71 inference(ennf_transformation,[],[f533])).
% 0.23/0.71 thf(f533,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = boolean_algebra(X1)) => ($true = boolean_algebra(sTfun(X0,X1))))),
% 0.23/0.71 inference(fool_elimination,[],[f532])).
% 0.23/0.71 thf(f532,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (boolean_algebra(X1) => boolean_algebra(sTfun(X0,X1)))),
% 0.23/0.71 inference(rectify,[],[f261])).
% 0.23/0.71 thf(f261,axiom,(
% 0.23/0.71 ! [X111 : $tType,X112 : $tType] : (boolean_algebra(X112) => boolean_algebra(sTfun(X111,X112)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra)).
% 0.23/0.71 thf(f2439,plain,(
% 0.23/0.71 spl40_42 | ~spl40_7 | ~spl40_37),
% 0.23/0.71 inference(avatar_split_clause,[],[f2417,f2410,f2242,f2436])).
% 0.23/0.71 thf(f2436,plain,(
% 0.23/0.71 spl40_42 <=> ($true = zero(set(real)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_42])])).
% 0.23/0.71 thf(f2242,plain,(
% 0.23/0.71 spl40_7 <=> (zero(real) = $true)),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_7])])).
% 0.23/0.71 thf(f2417,plain,(
% 0.23/0.71 ($true = zero(set(real))) | (~spl40_7 | ~spl40_37)),
% 0.23/0.71 inference(trivial_inequality_removal,[],[f2414])).
% 0.23/0.71 thf(f2414,plain,(
% 0.23/0.71 ($true != $true) | ($true = zero(set(real))) | (~spl40_7 | ~spl40_37)),
% 0.23/0.71 inference(superposition,[],[f2411,f2244])).
% 0.23/0.71 thf(f2244,plain,(
% 0.23/0.71 (zero(real) = $true) | ~spl40_7),
% 0.23/0.71 inference(avatar_component_clause,[],[f2242])).
% 0.23/0.71 thf(f2434,plain,(
% 0.23/0.71 spl40_41),
% 0.23/0.71 inference(avatar_split_clause,[],[f1240,f2432])).
% 0.23/0.71 thf(f1240,plain,(
% 0.23/0.71 ( ! [X1 : $tType,X0 : $tType] : (($true = uminus(sTfun(X0,X1))) | (uminus(X1) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f933])).
% 0.23/0.71 thf(f933,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = uminus(sTfun(X0,X1))) | (uminus(X1) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f531])).
% 0.23/0.71 thf(f531,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : ((uminus(X1) = $true) => ($true = uminus(sTfun(X0,X1))))),
% 0.23/0.71 inference(fool_elimination,[],[f530])).
% 0.23/0.71 thf(f530,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (uminus(X1) => uminus(sTfun(X0,X1)))),
% 0.23/0.71 inference(rectify,[],[f265])).
% 0.23/0.71 thf(f265,axiom,(
% 0.23/0.71 ! [X111 : $tType,X112 : $tType] : (uminus(X112) => uminus(sTfun(X111,X112)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus)).
% 0.23/0.71 thf(f2430,plain,(
% 0.23/0.71 spl40_40),
% 0.23/0.71 inference(avatar_split_clause,[],[f1239,f2428])).
% 0.23/0.71 thf(f1239,plain,(
% 0.23/0.71 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f932])).
% 0.23/0.71 thf(f932,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1)))),
% 0.23/0.71 inference(ennf_transformation,[],[f529])).
% 0.23/0.71 thf(f529,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = preorder(X1)) => ($true = preorder(sTfun(X0,X1))))),
% 0.23/0.71 inference(fool_elimination,[],[f528])).
% 0.23/0.71 thf(f528,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (preorder(X1) => preorder(sTfun(X0,X1)))),
% 0.23/0.71 inference(rectify,[],[f262])).
% 0.23/0.71 thf(f262,axiom,(
% 0.23/0.71 ! [X111 : $tType,X112 : $tType] : (preorder(X112) => preorder(sTfun(X111,X112)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder)).
% 0.23/0.71 thf(f2426,plain,(
% 0.23/0.71 spl40_39),
% 0.23/0.71 inference(avatar_split_clause,[],[f1234,f2424])).
% 0.23/0.71 thf(f1234,plain,(
% 0.23/0.71 ( ! [X1 : $tType,X0 : $tType] : (($true = bounde1808546759up_bot(sTfun(X0,X1))) | ($true != bounded_lattice(X1))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f927])).
% 0.23/0.71 thf(f927,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = bounde1808546759up_bot(sTfun(X0,X1))) | ($true != bounded_lattice(X1)))),
% 0.23/0.71 inference(ennf_transformation,[],[f519])).
% 0.23/0.71 thf(f519,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = bounded_lattice(X1)) => ($true = bounde1808546759up_bot(sTfun(X0,X1))))),
% 0.23/0.71 inference(fool_elimination,[],[f518])).
% 0.23/0.71 thf(f518,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (bounded_lattice(X1) => bounde1808546759up_bot(sTfun(X0,X1)))),
% 0.23/0.71 inference(rectify,[],[f258])).
% 0.23/0.71 thf(f258,axiom,(
% 0.23/0.71 ! [X111 : $tType,X112 : $tType] : (bounded_lattice(X112) => bounde1808546759up_bot(sTfun(X111,X112)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__semilattice__sup__bot)).
% 0.23/0.71 thf(f2422,plain,(
% 0.23/0.71 spl40_38),
% 0.23/0.71 inference(avatar_split_clause,[],[f1233,f2420])).
% 0.23/0.71 thf(f1233,plain,(
% 0.23/0.71 ( ! [X1 : $tType,X0 : $tType] : (($true = bounded_lattice(sTfun(X0,X1))) | ($true != bounded_lattice(X1))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f926])).
% 0.23/0.71 thf(f926,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = bounded_lattice(sTfun(X0,X1))) | ($true != bounded_lattice(X1)))),
% 0.23/0.71 inference(ennf_transformation,[],[f517])).
% 0.23/0.71 thf(f517,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (($true = bounded_lattice(X1)) => ($true = bounded_lattice(sTfun(X0,X1))))),
% 0.23/0.71 inference(fool_elimination,[],[f516])).
% 0.23/0.71 thf(f516,plain,(
% 0.23/0.71 ! [X0 : $tType,X1 : $tType] : (bounded_lattice(X1) => bounded_lattice(sTfun(X0,X1)))),
% 0.23/0.71 inference(rectify,[],[f257])).
% 0.23/0.71 thf(f257,axiom,(
% 0.23/0.71 ! [X111 : $tType,X112 : $tType] : (bounded_lattice(X112) => bounded_lattice(sTfun(X111,X112)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_2)).
% 0.23/0.71 thf(f2412,plain,(
% 0.23/0.71 spl40_37),
% 0.23/0.71 inference(avatar_split_clause,[],[f1134,f2410])).
% 0.23/0.71 thf(f1134,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = zero(set(X0))) | (zero(X0) != $true)) )),
% 0.23/0.71 inference(cnf_transformation,[],[f867])).
% 0.23/0.71 thf(f867,plain,(
% 0.23/0.71 ! [X0 : $tType] : (($true = zero(set(X0))) | (zero(X0) != $true))),
% 0.23/0.71 inference(ennf_transformation,[],[f359])).
% 0.23/0.71 thf(f359,plain,(
% 0.23/0.71 ! [X0 : $tType] : ((zero(X0) = $true) => ($true = zero(set(X0))))),
% 0.23/0.71 inference(fool_elimination,[],[f358])).
% 0.23/0.71 thf(f358,plain,(
% 0.23/0.71 ! [X0 : $tType] : (zero(X0) => zero(set(X0)))),
% 0.23/0.71 inference(rectify,[],[f281])).
% 0.23/0.71 thf(f281,axiom,(
% 0.23/0.71 ! [X111 : $tType] : (zero(X111) => zero(set(X111)))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ozero_16)).
% 0.23/0.71 thf(f2380,plain,(
% 0.23/0.71 spl40_36),
% 0.23/0.71 inference(avatar_split_clause,[],[f305,f2378])).
% 0.23/0.71 thf(f2378,plain,(
% 0.23/0.71 spl40_36 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_36])])).
% 0.23/0.71 thf(f305,plain,(
% 0.23/0.71 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.23/0.71 introduced(fool_axiom,[])).
% 0.23/0.71 thf(f2376,plain,(
% 0.23/0.71 spl40_35),
% 0.23/0.71 inference(avatar_split_clause,[],[f1190,f2374])).
% 0.23/0.71 thf(f2374,plain,(
% 0.23/0.71 spl40_35 <=> ! [X0 : $tType] : ($true = semilattice_sup(set(X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_35])])).
% 0.23/0.71 thf(f1190,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = semilattice_sup(set(X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f471])).
% 0.23/0.71 thf(f471,plain,(
% 0.23/0.71 ! [X0 : $tType] : ($true = semilattice_sup(set(X0)))),
% 0.23/0.71 inference(fool_elimination,[],[f470])).
% 0.23/0.71 thf(f470,plain,(
% 0.23/0.71 ! [X0 : $tType] : semilattice_sup(set(X0))),
% 0.23/0.71 inference(rectify,[],[f274])).
% 0.23/0.71 thf(f274,axiom,(
% 0.23/0.71 ! [X111 : $tType] : semilattice_sup(set(X111))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__sup_9)).
% 0.23/0.71 thf(f2372,plain,(
% 0.23/0.71 spl40_34),
% 0.23/0.71 inference(avatar_split_clause,[],[f1189,f2370])).
% 0.23/0.71 thf(f2370,plain,(
% 0.23/0.71 spl40_34 <=> ! [X0 : $tType] : ($true = semilattice_inf(set(X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_34])])).
% 0.23/0.71 thf(f1189,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = semilattice_inf(set(X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f469])).
% 0.23/0.71 thf(f469,plain,(
% 0.23/0.71 ! [X0 : $tType] : ($true = semilattice_inf(set(X0)))),
% 0.23/0.71 inference(fool_elimination,[],[f468])).
% 0.23/0.71 thf(f468,plain,(
% 0.23/0.71 ! [X0 : $tType] : semilattice_inf(set(X0))),
% 0.23/0.71 inference(rectify,[],[f275])).
% 0.23/0.71 thf(f275,axiom,(
% 0.23/0.71 ! [X111 : $tType] : semilattice_inf(set(X111))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_10)).
% 0.23/0.71 thf(f2368,plain,(
% 0.23/0.71 spl40_33),
% 0.23/0.71 inference(avatar_split_clause,[],[f1188,f2366])).
% 0.23/0.71 thf(f2366,plain,(
% 0.23/0.71 spl40_33 <=> ! [X0 : $tType] : ($true = bounde1808546759up_bot(set(X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_33])])).
% 0.23/0.71 thf(f1188,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = bounde1808546759up_bot(set(X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f467])).
% 0.23/0.71 thf(f467,plain,(
% 0.23/0.71 ! [X0 : $tType] : ($true = bounde1808546759up_bot(set(X0)))),
% 0.23/0.71 inference(fool_elimination,[],[f466])).
% 0.23/0.71 thf(f466,plain,(
% 0.23/0.71 ! [X0 : $tType] : bounde1808546759up_bot(set(X0))),
% 0.23/0.71 inference(rectify,[],[f273])).
% 0.23/0.71 thf(f273,axiom,(
% 0.23/0.71 ! [X111 : $tType] : bounde1808546759up_bot(set(X111))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_8)).
% 0.23/0.71 thf(f2364,plain,(
% 0.23/0.71 spl40_32),
% 0.23/0.71 inference(avatar_split_clause,[],[f1187,f2362])).
% 0.23/0.71 thf(f2362,plain,(
% 0.23/0.71 spl40_32 <=> ! [X0 : $tType] : ($true = lattice(set(X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_32])])).
% 0.23/0.71 thf(f1187,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = lattice(set(X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f465])).
% 0.23/0.71 thf(f465,plain,(
% 0.23/0.71 ! [X0 : $tType] : ($true = lattice(set(X0)))),
% 0.23/0.71 inference(fool_elimination,[],[f464])).
% 0.23/0.71 thf(f464,plain,(
% 0.23/0.71 ! [X0 : $tType] : lattice(set(X0))),
% 0.23/0.71 inference(rectify,[],[f278])).
% 0.23/0.71 thf(f278,axiom,(
% 0.23/0.71 ! [X111 : $tType] : lattice(set(X111))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_13)).
% 0.23/0.71 thf(f2360,plain,(
% 0.23/0.71 spl40_31),
% 0.23/0.71 inference(avatar_split_clause,[],[f1186,f2358])).
% 0.23/0.71 thf(f2358,plain,(
% 0.23/0.71 spl40_31 <=> ! [X0 : $tType] : ($true = bot(set(X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_31])])).
% 0.23/0.71 thf(f1186,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = bot(set(X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f463])).
% 0.23/0.71 thf(f463,plain,(
% 0.23/0.71 ! [X0 : $tType] : ($true = bot(set(X0)))),
% 0.23/0.71 inference(fool_elimination,[],[f462])).
% 0.23/0.71 thf(f462,plain,(
% 0.23/0.71 ! [X0 : $tType] : bot(set(X0))),
% 0.23/0.71 inference(rectify,[],[f279])).
% 0.23/0.71 thf(f279,axiom,(
% 0.23/0.71 ! [X111 : $tType] : bot(set(X111))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_14)).
% 0.23/0.71 thf(f2356,plain,(
% 0.23/0.71 spl40_30),
% 0.23/0.71 inference(avatar_split_clause,[],[f1185,f2354])).
% 0.23/0.71 thf(f2354,plain,(
% 0.23/0.71 spl40_30 <=> ! [X0 : $tType] : ($true = preorder(set(X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_30])])).
% 0.23/0.71 thf(f1185,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = preorder(set(X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f461])).
% 0.23/0.71 thf(f461,plain,(
% 0.23/0.71 ! [X0 : $tType] : ($true = preorder(set(X0)))),
% 0.23/0.71 inference(fool_elimination,[],[f460])).
% 0.23/0.71 thf(f460,plain,(
% 0.23/0.71 ! [X0 : $tType] : preorder(set(X0))),
% 0.23/0.71 inference(rectify,[],[f277])).
% 0.23/0.71 thf(f277,axiom,(
% 0.23/0.71 ! [X111 : $tType] : preorder(set(X111))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_12)).
% 0.23/0.71 thf(f2352,plain,(
% 0.23/0.71 spl40_29),
% 0.23/0.71 inference(avatar_split_clause,[],[f1184,f2350])).
% 0.23/0.71 thf(f2350,plain,(
% 0.23/0.71 spl40_29 <=> ! [X0 : $tType] : ($true = boolean_algebra(set(X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_29])])).
% 0.23/0.71 thf(f1184,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = boolean_algebra(set(X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f459])).
% 0.23/0.71 thf(f459,plain,(
% 0.23/0.71 ! [X0 : $tType] : ($true = boolean_algebra(set(X0)))),
% 0.23/0.71 inference(fool_elimination,[],[f458])).
% 0.23/0.71 thf(f458,plain,(
% 0.23/0.71 ! [X0 : $tType] : boolean_algebra(set(X0))),
% 0.23/0.71 inference(rectify,[],[f276])).
% 0.23/0.71 thf(f276,axiom,(
% 0.23/0.71 ! [X111 : $tType] : boolean_algebra(set(X111))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Oboolean__algebra_11)).
% 0.23/0.71 thf(f2348,plain,(
% 0.23/0.71 spl40_28),
% 0.23/0.71 inference(avatar_split_clause,[],[f1183,f2346])).
% 0.23/0.71 thf(f2346,plain,(
% 0.23/0.71 spl40_28 <=> ! [X0 : $tType] : ($true = uminus(set(X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_28])])).
% 0.23/0.71 thf(f1183,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = uminus(set(X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f457])).
% 0.23/0.71 thf(f457,plain,(
% 0.23/0.71 ! [X0 : $tType] : ($true = uminus(set(X0)))),
% 0.23/0.71 inference(fool_elimination,[],[f456])).
% 0.23/0.71 thf(f456,plain,(
% 0.23/0.71 ! [X0 : $tType] : uminus(set(X0))),
% 0.23/0.71 inference(rectify,[],[f280])).
% 0.23/0.71 thf(f280,axiom,(
% 0.23/0.71 ! [X111 : $tType] : uminus(set(X111))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ouminus_15)).
% 0.23/0.71 thf(f2344,plain,(
% 0.23/0.71 spl40_27),
% 0.23/0.71 inference(avatar_split_clause,[],[f1182,f2342])).
% 0.23/0.71 thf(f2342,plain,(
% 0.23/0.71 spl40_27 <=> ! [X0 : $tType] : ($true = bounded_lattice(set(X0)))),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_27])])).
% 0.23/0.71 thf(f1182,plain,(
% 0.23/0.71 ( ! [X0 : $tType] : (($true = bounded_lattice(set(X0)))) )),
% 0.23/0.71 inference(cnf_transformation,[],[f455])).
% 0.23/0.71 thf(f455,plain,(
% 0.23/0.71 ! [X0 : $tType] : ($true = bounded_lattice(set(X0)))),
% 0.23/0.71 inference(fool_elimination,[],[f454])).
% 0.23/0.71 thf(f454,plain,(
% 0.23/0.71 ! [X0 : $tType] : bounded_lattice(set(X0))),
% 0.23/0.71 inference(rectify,[],[f256])).
% 0.23/0.71 thf(f256,axiom,(
% 0.23/0.71 ! [X111 : $tType] : bounded_lattice(set(X111))),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_1)).
% 0.23/0.71 thf(f2340,plain,(
% 0.23/0.71 spl40_26),
% 0.23/0.71 inference(avatar_split_clause,[],[f1421,f2337])).
% 0.23/0.71 thf(f1421,plain,(
% 0.23/0.71 (semilattice_sup(real) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f779])).
% 0.23/0.71 thf(f779,plain,(
% 0.23/0.71 (semilattice_sup(real) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f778])).
% 0.23/0.71 thf(f778,plain,(
% 0.23/0.71 semilattice_sup(real)),
% 0.23/0.71 inference(rectify,[],[f292])).
% 0.23/0.71 thf(f292,axiom,(
% 0.23/0.71 semilattice_sup(real)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Osemilattice__sup_25)).
% 0.23/0.71 thf(f2335,plain,(
% 0.23/0.71 spl40_25),
% 0.23/0.71 inference(avatar_split_clause,[],[f1420,f2332])).
% 0.23/0.71 thf(f1420,plain,(
% 0.23/0.71 (semilattice_sup($o) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f777])).
% 0.23/0.71 thf(f777,plain,(
% 0.23/0.71 (semilattice_sup($o) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f776])).
% 0.23/0.71 thf(f776,plain,(
% 0.23/0.71 semilattice_sup($o)),
% 0.23/0.71 inference(rectify,[],[f283])).
% 0.23/0.71 thf(f283,axiom,(
% 0.23/0.71 semilattice_sup($o)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__sup_18)).
% 0.23/0.71 thf(f2330,plain,(
% 0.23/0.71 spl40_24),
% 0.23/0.71 inference(avatar_split_clause,[],[f1419,f2327])).
% 0.23/0.71 thf(f1419,plain,(
% 0.23/0.71 (semilattice_sup(nat) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f775])).
% 0.23/0.71 thf(f775,plain,(
% 0.23/0.71 (semilattice_sup(nat) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f774])).
% 0.23/0.71 thf(f774,plain,(
% 0.23/0.71 semilattice_sup(nat)),
% 0.23/0.71 inference(rectify,[],[f267])).
% 0.23/0.71 thf(f267,axiom,(
% 0.23/0.71 semilattice_sup(nat)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__sup_3)).
% 0.23/0.71 thf(f2325,plain,(
% 0.23/0.71 spl40_23),
% 0.23/0.71 inference(avatar_split_clause,[],[f1418,f2322])).
% 0.23/0.71 thf(f1418,plain,(
% 0.23/0.71 (semilattice_inf(real) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f773])).
% 0.23/0.71 thf(f773,plain,(
% 0.23/0.71 (semilattice_inf(real) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f772])).
% 0.23/0.71 thf(f772,plain,(
% 0.23/0.71 semilattice_inf(real)),
% 0.23/0.71 inference(rectify,[],[f293])).
% 0.23/0.71 thf(f293,axiom,(
% 0.23/0.71 semilattice_inf(real)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Osemilattice__inf_26)).
% 0.23/0.71 thf(f2320,plain,(
% 0.23/0.71 spl40_22),
% 0.23/0.71 inference(avatar_split_clause,[],[f1417,f2317])).
% 0.23/0.71 thf(f1417,plain,(
% 0.23/0.71 (semilattice_inf($o) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f771])).
% 0.23/0.71 thf(f771,plain,(
% 0.23/0.71 (semilattice_inf($o) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f770])).
% 0.23/0.71 thf(f770,plain,(
% 0.23/0.71 semilattice_inf($o)),
% 0.23/0.71 inference(rectify,[],[f284])).
% 0.23/0.71 thf(f284,axiom,(
% 0.23/0.71 semilattice_inf($o)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_19)).
% 0.23/0.71 thf(f2315,plain,(
% 0.23/0.71 spl40_21),
% 0.23/0.71 inference(avatar_split_clause,[],[f1416,f2312])).
% 0.23/0.71 thf(f1416,plain,(
% 0.23/0.71 (semilattice_inf(nat) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f769])).
% 0.23/0.71 thf(f769,plain,(
% 0.23/0.71 (semilattice_inf(nat) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f768])).
% 0.23/0.71 thf(f768,plain,(
% 0.23/0.71 semilattice_inf(nat)),
% 0.23/0.71 inference(rectify,[],[f268])).
% 0.23/0.71 thf(f268,axiom,(
% 0.23/0.71 semilattice_inf(nat)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__inf_4)).
% 0.23/0.71 thf(f2310,plain,(
% 0.23/0.71 spl40_20),
% 0.23/0.71 inference(avatar_split_clause,[],[f1415,f2307])).
% 0.23/0.71 thf(f2307,plain,(
% 0.23/0.71 spl40_20 <=> (bounde1808546759up_bot($o) = $true)),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_20])])).
% 0.23/0.71 thf(f1415,plain,(
% 0.23/0.71 (bounde1808546759up_bot($o) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f767])).
% 0.23/0.71 thf(f767,plain,(
% 0.23/0.71 (bounde1808546759up_bot($o) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f766])).
% 0.23/0.71 thf(f766,plain,(
% 0.23/0.71 bounde1808546759up_bot($o)),
% 0.23/0.71 inference(rectify,[],[f282])).
% 0.23/0.71 thf(f282,axiom,(
% 0.23/0.71 bounde1808546759up_bot($o)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_17)).
% 0.23/0.71 thf(f2305,plain,(
% 0.23/0.71 spl40_19),
% 0.23/0.71 inference(avatar_split_clause,[],[f1414,f2302])).
% 0.23/0.71 thf(f1414,plain,(
% 0.23/0.71 (lattice(real) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f765])).
% 0.23/0.71 thf(f765,plain,(
% 0.23/0.71 (lattice(real) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f764])).
% 0.23/0.71 thf(f764,plain,(
% 0.23/0.71 lattice(real)),
% 0.23/0.71 inference(rectify,[],[f295])).
% 0.23/0.71 thf(f295,axiom,(
% 0.23/0.71 lattice(real)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Olattice_28)).
% 0.23/0.71 thf(f2300,plain,(
% 0.23/0.71 spl40_18),
% 0.23/0.71 inference(avatar_split_clause,[],[f1413,f2297])).
% 0.23/0.71 thf(f1413,plain,(
% 0.23/0.71 (lattice($o) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f763])).
% 0.23/0.71 thf(f763,plain,(
% 0.23/0.71 (lattice($o) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f762])).
% 0.23/0.71 thf(f762,plain,(
% 0.23/0.71 lattice($o)),
% 0.23/0.71 inference(rectify,[],[f287])).
% 0.23/0.71 thf(f287,axiom,(
% 0.23/0.71 lattice($o)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_22)).
% 0.23/0.71 thf(f2295,plain,(
% 0.23/0.71 spl40_17),
% 0.23/0.71 inference(avatar_split_clause,[],[f1412,f2292])).
% 0.23/0.71 thf(f1412,plain,(
% 0.23/0.71 (lattice(nat) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f761])).
% 0.23/0.71 thf(f761,plain,(
% 0.23/0.71 (lattice(nat) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f760])).
% 0.23/0.71 thf(f760,plain,(
% 0.23/0.71 lattice(nat)),
% 0.23/0.71 inference(rectify,[],[f270])).
% 0.23/0.71 thf(f270,axiom,(
% 0.23/0.71 lattice(nat)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Olattice_6)).
% 0.23/0.71 thf(f2290,plain,(
% 0.23/0.71 spl40_16),
% 0.23/0.71 inference(avatar_split_clause,[],[f1411,f2287])).
% 0.23/0.71 thf(f2287,plain,(
% 0.23/0.71 spl40_16 <=> (group_add(real) = $true)),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_16])])).
% 0.23/0.71 thf(f1411,plain,(
% 0.23/0.71 (group_add(real) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f759])).
% 0.23/0.71 thf(f759,plain,(
% 0.23/0.71 (group_add(real) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f758])).
% 0.23/0.71 thf(f758,plain,(
% 0.23/0.71 group_add(real)),
% 0.23/0.71 inference(rectify,[],[f296])).
% 0.23/0.71 thf(f296,axiom,(
% 0.23/0.71 group_add(real)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add)).
% 0.23/0.71 thf(f2285,plain,(
% 0.23/0.71 spl40_15),
% 0.23/0.71 inference(avatar_split_clause,[],[f1410,f2282])).
% 0.23/0.71 thf(f1410,plain,(
% 0.23/0.71 (preorder(real) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f757])).
% 0.23/0.71 thf(f757,plain,(
% 0.23/0.71 (preorder(real) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f756])).
% 0.23/0.71 thf(f756,plain,(
% 0.23/0.71 preorder(real)),
% 0.23/0.71 inference(rectify,[],[f294])).
% 0.23/0.71 thf(f294,axiom,(
% 0.23/0.71 preorder(real)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_27)).
% 0.23/0.71 thf(f2280,plain,(
% 0.23/0.71 spl40_14),
% 0.23/0.71 inference(avatar_split_clause,[],[f1409,f2277])).
% 0.23/0.71 thf(f1409,plain,(
% 0.23/0.71 (uminus(real) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f755])).
% 0.23/0.71 thf(f755,plain,(
% 0.23/0.71 (uminus(real) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f754])).
% 0.23/0.71 thf(f754,plain,(
% 0.23/0.71 uminus(real)),
% 0.23/0.71 inference(rectify,[],[f297])).
% 0.23/0.71 thf(f297,axiom,(
% 0.23/0.71 uminus(real)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ouminus_29)).
% 0.23/0.71 thf(f2275,plain,(
% 0.23/0.71 spl40_13),
% 0.23/0.71 inference(avatar_split_clause,[],[f1408,f2272])).
% 0.23/0.71 thf(f1408,plain,(
% 0.23/0.71 (preorder($o) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f753])).
% 0.23/0.71 thf(f753,plain,(
% 0.23/0.71 (preorder($o) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f752])).
% 0.23/0.71 thf(f752,plain,(
% 0.23/0.71 preorder($o)),
% 0.23/0.71 inference(rectify,[],[f286])).
% 0.23/0.71 thf(f286,axiom,(
% 0.23/0.71 preorder($o)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_21)).
% 0.23/0.71 thf(f2270,plain,(
% 0.23/0.71 spl40_12),
% 0.23/0.71 inference(avatar_split_clause,[],[f1407,f2267])).
% 0.23/0.71 thf(f1407,plain,(
% 0.23/0.71 (uminus($o) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f751])).
% 0.23/0.71 thf(f751,plain,(
% 0.23/0.71 (uminus($o) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f750])).
% 0.23/0.71 thf(f750,plain,(
% 0.23/0.71 uminus($o)),
% 0.23/0.71 inference(rectify,[],[f289])).
% 0.23/0.71 thf(f289,axiom,(
% 0.23/0.71 uminus($o)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_24)).
% 0.23/0.71 thf(f2265,plain,(
% 0.23/0.71 spl40_11),
% 0.23/0.71 inference(avatar_split_clause,[],[f1406,f2262])).
% 0.23/0.71 thf(f1406,plain,(
% 0.23/0.71 (bot($o) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f749])).
% 0.23/0.71 thf(f749,plain,(
% 0.23/0.71 (bot($o) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f748])).
% 0.23/0.71 thf(f748,plain,(
% 0.23/0.71 bot($o)),
% 0.23/0.71 inference(rectify,[],[f288])).
% 0.23/0.71 thf(f288,axiom,(
% 0.23/0.71 bot($o)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_23)).
% 0.23/0.71 thf(f2260,plain,(
% 0.23/0.71 spl40_10),
% 0.23/0.71 inference(avatar_split_clause,[],[f1405,f2257])).
% 0.23/0.71 thf(f1405,plain,(
% 0.23/0.71 (boolean_algebra($o) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f747])).
% 0.23/0.71 thf(f747,plain,(
% 0.23/0.71 (boolean_algebra($o) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f746])).
% 0.23/0.71 thf(f746,plain,(
% 0.23/0.71 boolean_algebra($o)),
% 0.23/0.71 inference(rectify,[],[f285])).
% 0.23/0.71 thf(f285,axiom,(
% 0.23/0.71 boolean_algebra($o)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_20)).
% 0.23/0.71 thf(f2255,plain,(
% 0.23/0.71 spl40_9),
% 0.23/0.71 inference(avatar_split_clause,[],[f1404,f2252])).
% 0.23/0.71 thf(f1404,plain,(
% 0.23/0.71 (preorder(nat) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f745])).
% 0.23/0.71 thf(f745,plain,(
% 0.23/0.71 (preorder(nat) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f744])).
% 0.23/0.71 thf(f744,plain,(
% 0.23/0.71 preorder(nat)),
% 0.23/0.71 inference(rectify,[],[f269])).
% 0.23/0.71 thf(f269,axiom,(
% 0.23/0.71 preorder(nat)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_5)).
% 0.23/0.71 thf(f2250,plain,(
% 0.23/0.71 spl40_8),
% 0.23/0.71 inference(avatar_split_clause,[],[f1403,f2247])).
% 0.23/0.71 thf(f1403,plain,(
% 0.23/0.71 (bot(nat) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f743])).
% 0.23/0.71 thf(f743,plain,(
% 0.23/0.71 (bot(nat) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f742])).
% 0.23/0.71 thf(f742,plain,(
% 0.23/0.71 bot(nat)),
% 0.23/0.71 inference(rectify,[],[f271])).
% 0.23/0.71 thf(f271,axiom,(
% 0.23/0.71 bot(nat)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Obot_7)).
% 0.23/0.71 thf(f2245,plain,(
% 0.23/0.71 spl40_7),
% 0.23/0.71 inference(avatar_split_clause,[],[f1402,f2242])).
% 0.23/0.71 thf(f1402,plain,(
% 0.23/0.71 (zero(real) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f741])).
% 0.23/0.71 thf(f741,plain,(
% 0.23/0.71 (zero(real) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f740])).
% 0.23/0.71 thf(f740,plain,(
% 0.23/0.71 zero(real)),
% 0.23/0.71 inference(rectify,[],[f298])).
% 0.23/0.71 thf(f298,axiom,(
% 0.23/0.71 zero(real)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_30)).
% 0.23/0.71 thf(f2240,plain,(
% 0.23/0.71 spl40_6),
% 0.23/0.71 inference(avatar_split_clause,[],[f1401,f2237])).
% 0.23/0.71 thf(f1401,plain,(
% 0.23/0.71 (zero(nat) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f739])).
% 0.23/0.71 thf(f739,plain,(
% 0.23/0.71 (zero(nat) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f738])).
% 0.23/0.71 thf(f738,plain,(
% 0.23/0.71 zero(nat)),
% 0.23/0.71 inference(rectify,[],[f272])).
% 0.23/0.71 thf(f272,axiom,(
% 0.23/0.71 zero(nat)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero)).
% 0.23/0.71 thf(f2235,plain,(
% 0.23/0.71 spl40_5),
% 0.23/0.71 inference(avatar_split_clause,[],[f1400,f2232])).
% 0.23/0.71 thf(f1400,plain,(
% 0.23/0.71 (bounded_lattice($o) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f737])).
% 0.23/0.71 thf(f737,plain,(
% 0.23/0.71 (bounded_lattice($o) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f736])).
% 0.23/0.71 thf(f736,plain,(
% 0.23/0.71 bounded_lattice($o)),
% 0.23/0.71 inference(rectify,[],[f255])).
% 0.23/0.71 thf(f255,axiom,(
% 0.23/0.71 bounded_lattice($o)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice)).
% 0.23/0.71 thf(f2230,plain,(
% 0.23/0.71 spl40_4),
% 0.23/0.71 inference(avatar_split_clause,[],[f1399,f2227])).
% 0.23/0.71 thf(f2227,plain,(
% 0.23/0.71 spl40_4 <=> (linord219039673up_add(real) = $true)),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_4])])).
% 0.23/0.71 thf(f1399,plain,(
% 0.23/0.71 (linord219039673up_add(real) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f735])).
% 0.23/0.71 thf(f735,plain,(
% 0.23/0.71 (linord219039673up_add(real) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f734])).
% 0.23/0.71 thf(f734,plain,(
% 0.23/0.71 linord219039673up_add(real)),
% 0.23/0.71 inference(rectify,[],[f290])).
% 0.23/0.71 thf(f290,axiom,(
% 0.23/0.71 linord219039673up_add(real)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Olinordered__ab__group__add)).
% 0.23/0.71 thf(f2225,plain,(
% 0.23/0.71 spl40_3),
% 0.23/0.71 inference(avatar_split_clause,[],[f1398,f2222])).
% 0.23/0.71 thf(f2222,plain,(
% 0.23/0.71 spl40_3 <=> (ordered_ab_group_add(real) = $true)),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_3])])).
% 0.23/0.71 thf(f1398,plain,(
% 0.23/0.71 (ordered_ab_group_add(real) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f733])).
% 0.23/0.71 thf(f733,plain,(
% 0.23/0.71 (ordered_ab_group_add(real) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f732])).
% 0.23/0.71 thf(f732,plain,(
% 0.23/0.71 ordered_ab_group_add(real)),
% 0.23/0.71 inference(rectify,[],[f291])).
% 0.23/0.71 thf(f291,axiom,(
% 0.23/0.71 ordered_ab_group_add(real)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add)).
% 0.23/0.71 thf(f2220,plain,(
% 0.23/0.71 spl40_2),
% 0.23/0.71 inference(avatar_split_clause,[],[f1397,f2217])).
% 0.23/0.71 thf(f2217,plain,(
% 0.23/0.71 spl40_2 <=> (canoni770627133id_add(nat) = $true)),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_2])])).
% 0.23/0.71 thf(f1397,plain,(
% 0.23/0.71 (canoni770627133id_add(nat) = $true)),
% 0.23/0.71 inference(cnf_transformation,[],[f731])).
% 0.23/0.71 thf(f731,plain,(
% 0.23/0.71 (canoni770627133id_add(nat) = $true)),
% 0.23/0.71 inference(fool_elimination,[],[f730])).
% 0.23/0.71 thf(f730,plain,(
% 0.23/0.71 canoni770627133id_add(nat)),
% 0.23/0.71 inference(rectify,[],[f266])).
% 0.23/0.71 thf(f266,axiom,(
% 0.23/0.71 canoni770627133id_add(nat)),
% 0.23/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add)).
% 0.23/0.71 thf(f2215,plain,(
% 0.23/0.71 ~spl40_1),
% 0.23/0.71 inference(avatar_split_clause,[],[f304,f2212])).
% 0.23/0.71 thf(f2212,plain,(
% 0.23/0.71 spl40_1 <=> ($true = $false)),
% 0.23/0.71 introduced(avatar_definition,[new_symbols(naming,[spl40_1])])).
% 0.23/0.71 thf(f304,plain,(
% 0.23/0.71 ($true != $false)),
% 0.23/0.71 introduced(fool_axiom,[])).
% 0.23/0.71 % SZS output end Proof for theBenchmark
% 0.23/0.71 % (5590)------------------------------
% 0.23/0.71 % (5590)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.23/0.71 % (5590)Termination reason: Refutation
% 0.23/0.71
% 0.23/0.71 % (5590)Memory used [KB]: 3586
% 0.23/0.71 % (5590)Time elapsed: 0.289 s
% 0.23/0.71 % (5590)Instructions burned: 804 (million)
% 0.23/0.71 % (5585)Success in time 0.318 s
%------------------------------------------------------------------------------