%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP111^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:44 AM UTC 2026
% Result : Theorem 5.56s 1.13s
% Output : Refutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 33
% Syntax : Number of formulae : 336 ( 31 unt; 0 typ; 26 def)
% Number of atoms : 2757 ( 695 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 4116 ( 487 ~; 895 |; 123 &;2342 @)
% ( 26 <=>; 129 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 109 ( 104 usr; 39 con; 0-4 aty)
% ( 76 !!; 38 ??; 0 @@+; 0 @@-)
% Number of variables : 320 ( 0 sgn 178 !; 7 ?; 320 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
extended_ereal: $tType ).
thf(type_def_6,type,
set_a: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(type_def_8,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
extend1289208545_ereal: extended_ereal ).
thf(func_def_1,type,
extended_MInfty: extended_ereal ).
thf(func_def_2,type,
extended_PInfty: extended_ereal ).
thf(func_def_3,type,
times_1966848393_ereal: extended_ereal > extended_ereal > extended_ereal ).
thf(func_def_4,type,
uminus1208298309_ereal: extended_ereal > extended_ereal ).
thf(func_def_5,type,
zero_z163181189_ereal: extended_ereal ).
thf(func_def_6,type,
lower_191460856_ereal: a > ( a > extended_ereal ) > $o ).
thf(func_def_7,type,
ord_le2001149050_ereal: extended_ereal > extended_ereal > $o ).
thf(func_def_8,type,
divide595620860_ereal: extended_ereal > extended_ereal > extended_ereal ).
thf(func_def_9,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_10,type,
topolo1276428101open_a: set_a > $o ).
thf(func_def_11,type,
member_a: a > set_a > $o ).
thf(func_def_12,type,
f: a > extended_ereal ).
thf(func_def_13,type,
x0: a ).
thf(func_def_15,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_16,type,
vIMP: $o > $o > $o ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_19,type,
vAND: $o > $o > $o ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_25,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(func_def_27,type,
vOR: $o > $o > $o ).
thf(func_def_28,type,
sK0: a > a > set_a ).
thf(func_def_29,type,
sK1: a > a > set_a ).
thf(func_def_30,type,
sK2: extended_ereal > extended_ereal ).
thf(func_def_31,type,
sK3: extended_ereal > extended_ereal ).
thf(func_def_32,type,
sK4: extended_ereal > extended_ereal ).
thf(func_def_33,type,
sK5: extended_ereal > extended_ereal ).
thf(func_def_34,type,
sK6: ( extended_ereal > $o ) > ( extended_ereal > $o ) > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_35,type,
sK7: extended_ereal > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_36,type,
sK8: extended_ereal > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_37,type,
sK9: ( extended_ereal > $o ) > ( extended_ereal > $o ) > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_38,type,
sK10: extended_ereal > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_39,type,
sK11: extended_ereal > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_40,type,
sK12: ( extended_ereal > $o ) > ( extended_ereal > $o ) > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_41,type,
sK13: extended_ereal > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_42,type,
sK14: extended_ereal > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_43,type,
sK15: extended_ereal > extended_ereal ).
thf(func_def_44,type,
sK16: extended_ereal > extended_ereal ).
thf(func_def_45,type,
sK17: extended_ereal > extended_ereal ).
thf(func_def_46,type,
sK18: extended_ereal > extended_ereal ).
thf(func_def_47,type,
sK19: ( extended_ereal > $o ) > ( extended_ereal > $o ) > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_48,type,
sK20: extended_ereal > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_49,type,
sK21: extended_ereal > ( extended_ereal > $o ) > ( extended_ereal > $o ) > extended_ereal ).
thf(func_def_50,type,
sK22: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_51,type,
sK23: extended_ereal > extended_ereal ).
thf(func_def_52,type,
sK24: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_53,type,
sK25: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_54,type,
sK26: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_55,type,
sK27: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_56,type,
sK28: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_57,type,
sK29: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_58,type,
sK30: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_59,type,
sK31: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_60,type,
sK32: extended_ereal > extended_ereal > extended_ereal ).
thf(func_def_61,type,
sK33: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_62,type,
sK34: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_63,type,
sK35: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_64,type,
sK36: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_65,type,
sK37: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_66,type,
sK38: extended_ereal ).
thf(func_def_67,type,
sK39: set_a > a ).
thf(func_def_68,type,
sK40: extended_ereal > set_a ).
thf(func_def_69,type,
sK41: a > a > set_a ).
thf(func_def_70,type,
sK42: a > a > set_a ).
thf(func_def_71,type,
sK43: extended_ereal > set_a ).
thf(func_def_72,type,
sK44: extended_ereal ).
thf(func_def_73,type,
sK45: set_a > a ).
thf(func_def_74,type,
sK46: extended_ereal > set_a ).
thf(func_def_75,type,
sK47: extended_ereal ).
thf(func_def_76,type,
sK48: set_a > a ).
thf(func_def_77,type,
sK49: extended_ereal > set_a ).
thf(func_def_78,type,
sK50: extended_ereal ).
thf(func_def_79,type,
sK51: set_a > a ).
thf(f1,axiom,
( ( ( f @ x0 )
= extend1289208545_ereal )
=> ( ( lower_191460856_ereal @ x0 @ f )
= ( ! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062) ).
thf(f3,axiom,
( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ( ( ( f @ x0 )
!= extend1289208545_ereal )
=> ( ( lower_191460856_ereal @ x0 @ f )
= ( ! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062) ).
thf(f4,axiom,
! [X0: a > extended_ereal,X1: a] :
( ( ( X0 @ X1 )
= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ( lower_191460856_ereal @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_lsc__at__MInfty) ).
thf(f26,axiom,
! [X0: extended_ereal] :
~ ( ord_le2001149050_ereal @ X0 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_less__ereal_Osimps_I3_J) ).
thf(f40,axiom,
( ( uminus1208298309_ereal @ extended_PInfty )
= extended_MInfty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_uminus__ereal_Osimps_I2_J) ).
thf(f50,axiom,
extend1289208545_ereal = extended_PInfty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_infinity__ereal__def) ).
thf(f121,conjecture,
( ( lower_191460856_ereal @ x0 @ f )
!= ( ~ ! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f122,negated_conjecture,
~ ( ( ( lower_191460856_ereal @ x0 @ f )
!= ( ~ ! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f121]) ).
thf(f123,plain,
( ( ( f @ x0 )
= extend1289208545_ereal )
=> ( ( lower_191460856_ereal @ x0 @ f )
= ( ! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f124,plain,
( ( ( f @ x0 )
= extend1289208545_ereal )
=> ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f123]) ).
thf(f127,plain,
( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ( ( ( f @ x0 )
!= extend1289208545_ereal )
=> ( ( lower_191460856_ereal @ x0 @ f )
= ( ! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f128,plain,
( ( ( f @ x0 )
!= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ( ( ( f @ x0 )
!= extend1289208545_ereal )
=> ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f127]) ).
thf(f129,plain,
! [X0: a > extended_ereal,X1: a] :
( ( ( X0 @ X1 )
= ( uminus1208298309_ereal @ extend1289208545_ereal ) )
=> ( lower_191460856_ereal @ X1 @ X0 ) ),
inference(rectify,[],[f4]) ).
thf(f130,plain,
! [X0: a > extended_ereal,X1: a] :
( ( ( uminus1208298309_ereal @ extend1289208545_ereal )
= ( X0 @ X1 ) )
=> ( ( lower_191460856_ereal @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f129]) ).
thf(f169,plain,
! [X0: extended_ereal] :
~ ( ord_le2001149050_ereal @ X0 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) ),
inference(rectify,[],[f26]) ).
thf(f170,plain,
! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
!= $true ),
inference(fool_elimination,[],[f169]) ).
thf(f285,plain,
~ ( ( ( lower_191460856_ereal @ x0 @ f )
!= ( ~ ! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( f @ x0 ) )
=> ? [X1: set_a] :
( ! [X2: a] :
( ( member_a @ X2 @ X1 )
=> ( ord_le2001149050_ereal @ X0 @ ( f @ X2 ) ) )
& ( member_a @ x0 @ X1 )
& ( topolo1276428101open_a @ X1 ) ) ) ) ) ),
inference(rectify,[],[f122]) ).
thf(f286,plain,
~ ( ( ( lower_191460856_ereal @ x0 @ f )
!= ( ~ ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f285]) ).
thf(f290,plain,
! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
!= $true ),
inference(flattening,[],[f170]) ).
thf(f306,plain,
( ( lower_191460856_ereal @ x0 @ f )
= ( ~ ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f286]) ).
thf(f307,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
| ( ( f @ x0 )
!= extend1289208545_ereal ) ),
inference(ennf_transformation,[],[f124]) ).
thf(f309,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
| ( ( f @ x0 )
= extend1289208545_ereal )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ),
inference(ennf_transformation,[],[f128]) ).
thf(f310,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
| ( ( f @ x0 )
= extend1289208545_ereal )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ),
inference(flattening,[],[f309]) ).
thf(f311,plain,
! [X0: a > extended_ereal,X1: a] :
( ( ( lower_191460856_ereal @ X1 @ X0 )
= $true )
| ( ( uminus1208298309_ereal @ extend1289208545_ereal )
!= ( X0 @ X1 ) ) ),
inference(ennf_transformation,[],[f130]) ).
thf(f425,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
| ( ( f @ x0 )
!= extend1289208545_ereal ) ),
inference(cnf_transformation,[],[f307]) ).
thf(f427,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
| ( ( f @ x0 )
= extend1289208545_ereal )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ),
inference(cnf_transformation,[],[f310]) ).
thf(f428,plain,
! [X0: a > extended_ereal,X1: a] :
( ( ( lower_191460856_ereal @ X1 @ X0 )
= $true )
| ( ( uminus1208298309_ereal @ extend1289208545_ereal )
!= ( X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f311]) ).
thf(f465,plain,
! [X0: extended_ereal] :
( ( ord_le2001149050_ereal @ X0 @ ( uminus1208298309_ereal @ extend1289208545_ereal ) )
!= $true ),
inference(cnf_transformation,[],[f290]) ).
thf(f479,plain,
( extended_MInfty
= ( uminus1208298309_ereal @ extended_PInfty ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f489,plain,
extend1289208545_ereal = extended_PInfty,
inference(cnf_transformation,[],[f50]) ).
thf(f574,plain,
( ( lower_191460856_ereal @ x0 @ f )
= ( ~ ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f306]) ).
thf(f577,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
| ( ( f @ x0 )
!= extended_PInfty ) ),
inference(definition_unfolding,[],[f425,f489]) ).
thf(f579,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) ) ),
inference(definition_unfolding,[],[f427,f489,f489]) ).
thf(f580,plain,
! [X0: a > extended_ereal,X1: a] :
( ( ( lower_191460856_ereal @ X1 @ X0 )
= $true )
| ( ( X0 @ X1 )
!= ( uminus1208298309_ereal @ extended_PInfty ) ) ),
inference(definition_unfolding,[],[f428,f489]) ).
thf(f585,plain,
! [X0: extended_ereal] :
( $true
!= ( ord_le2001149050_ereal @ X0 @ ( uminus1208298309_ereal @ extended_PInfty ) ) ),
inference(definition_unfolding,[],[f465,f489]) ).
thf(f641,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( ~ ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f574]) ).
thf(f642,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $true
= ( ~ ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f574]) ).
thf(f643,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f642]) ).
thf(f644,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $false
= ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) )
@ sK38 ) ) ),
inference(sigma_proxy_clausification,[],[f643]) ).
thf(f645,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $false
= ( ( ord_le2001149050_ereal @ sK38 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK38 @ ( f @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f644]) ).
thf(f646,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $false
= ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK38 @ ( f @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f645]) ).
thf(f647,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $true
= ( ord_le2001149050_ereal @ sK38 @ ( f @ x0 ) ) ) ),
inference(imp_proxy_clausification,[],[f645]) ).
thf(f648,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $false
= ( ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK38 @ ( f @ Y1 ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f646]) ).
thf(f649,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $false
= ( ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK38 @ ( f @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f648]) ).
thf(f650,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK38 @ ( f @ Y0 ) ) ) ) )
| ( $false
= ( ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f649]) ).
thf(f651,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $false
= ( ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK38 @ ( f @ Y0 ) ) )
@ ( sK39 @ X1 ) ) )
| ( $false
= ( ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f650]) ).
thf(f652,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $false
= ( ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK38 @ ( f @ Y0 ) ) )
@ ( sK39 @ X1 ) ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f651]) ).
thf(f653,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $false
= ( ( member_a @ ( sK39 @ X1 ) @ X1 )
=> ( ord_le2001149050_ereal @ sK38 @ ( f @ ( sK39 @ X1 ) ) ) ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f652]) ).
thf(f654,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $false
= ( ord_le2001149050_ereal @ sK38 @ ( f @ ( sK39 @ X1 ) ) ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f653]) ).
thf(f655,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( $true
= ( member_a @ ( sK39 @ X1 ) @ X1 ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f653]) ).
thf(f656,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f641]) ).
thf(f657,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $true
= ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f656]) ).
thf(f658,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $true
= ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f657]) ).
thf(f659,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f658]) ).
thf(f660,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) )
@ ( sK40 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f659]) ).
thf(f661,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ( topolo1276428101open_a @ ( sK40 @ X1 ) )
& ( member_a @ x0 @ ( sK40 @ X1 ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK40 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f660]) ).
thf(f662,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK40 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f661]) ).
thf(f663,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ( topolo1276428101open_a @ ( sK40 @ X1 ) )
& ( member_a @ x0 @ ( sK40 @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f661]) ).
thf(f664,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( member_a @ x0 @ ( sK40 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f663]) ).
thf(f665,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( topolo1276428101open_a @ ( sK40 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f663]) ).
thf(f666,plain,
! [X2: a,X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK40 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f662]) ).
thf(f667,plain,
! [X2: a,X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ( member_a @ X2 @ ( sK40 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f666]) ).
thf(f668,plain,
! [X2: a,X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $false
= ( member_a @ X2 @ ( sK40 @ X1 ) ) )
| ( $true
= ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f667]) ).
thf(f1311,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f579]) ).
thf(f1312,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f579]) ).
thf(f1313,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $true
= ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1312]) ).
thf(f1314,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $true
= ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1313]) ).
thf(f1315,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1314]) ).
thf(f1316,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) )
@ ( sK43 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1315]) ).
thf(f1317,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ( topolo1276428101open_a @ ( sK43 @ X1 ) )
& ( member_a @ x0 @ ( sK43 @ X1 ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK43 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1316]) ).
thf(f1318,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK43 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1317]) ).
thf(f1319,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ( topolo1276428101open_a @ ( sK43 @ X1 ) )
& ( member_a @ x0 @ ( sK43 @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1317]) ).
thf(f1320,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( member_a @ x0 @ ( sK43 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1319]) ).
thf(f1321,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( topolo1276428101open_a @ ( sK43 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1319]) ).
thf(f1322,plain,
! [X2: a,X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK43 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1318]) ).
thf(f1323,plain,
! [X2: a,X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ( member_a @ X2 @ ( sK43 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1322]) ).
thf(f1324,plain,
! [X2: a,X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $false
= ( member_a @ X2 @ ( sK43 @ X1 ) ) )
| ( $true
= ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f1323]) ).
thf(f1325,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) )
@ sK44 ) ) ),
inference(sigma_proxy_clausification,[],[f1311]) ).
thf(f1326,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ( ord_le2001149050_ereal @ sK44 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK44 @ ( f @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1325]) ).
thf(f1327,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK44 @ ( f @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1326]) ).
thf(f1328,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $true
= ( ord_le2001149050_ereal @ sK44 @ ( f @ x0 ) ) ) ),
inference(imp_proxy_clausification,[],[f1326]) ).
thf(f1329,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK44 @ ( f @ Y1 ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1327]) ).
thf(f1330,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK44 @ ( f @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1329]) ).
thf(f1331,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK44 @ ( f @ Y0 ) ) ) ) )
| ( $false
= ( ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1330]) ).
thf(f1332,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK44 @ ( f @ Y0 ) ) )
@ ( sK45 @ X1 ) ) )
| ( $false
= ( ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1331]) ).
thf(f1333,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK44 @ ( f @ Y0 ) ) )
@ ( sK45 @ X1 ) ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f1332]) ).
thf(f1334,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ( member_a @ ( sK45 @ X1 ) @ X1 )
=> ( ord_le2001149050_ereal @ sK44 @ ( f @ ( sK45 @ X1 ) ) ) ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f1333]) ).
thf(f1335,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $false
= ( ord_le2001149050_ereal @ sK44 @ ( f @ ( sK45 @ X1 ) ) ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1334]) ).
thf(f1336,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( ( f @ x0 )
= ( uminus1208298309_ereal @ extended_PInfty ) )
| ( $true
= ( member_a @ ( sK45 @ X1 ) @ X1 ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1334]) ).
thf(f1363,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f577]) ).
thf(f1364,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( ( !! @ extended_ereal
@ ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f577]) ).
thf(f1365,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $true
= ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1364]) ).
thf(f1366,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $true
= ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1365]) ).
thf(f1367,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1366]) ).
thf(f1368,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y1 ) ) ) ) )
@ ( sK49 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1367]) ).
thf(f1369,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ( topolo1276428101open_a @ ( sK49 @ X1 ) )
& ( member_a @ x0 @ ( sK49 @ X1 ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK49 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1368]) ).
thf(f1370,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK49 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1369]) ).
thf(f1371,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ( topolo1276428101open_a @ ( sK49 @ X1 ) )
& ( member_a @ x0 @ ( sK49 @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1369]) ).
thf(f1372,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( member_a @ x0 @ ( sK49 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1371]) ).
thf(f1373,plain,
! [X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( topolo1276428101open_a @ ( sK49 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1371]) ).
thf(f1374,plain,
! [X2: a,X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ^ [Y0: a] :
( ( member_a @ Y0 @ ( sK49 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1370]) ).
thf(f1375,plain,
! [X2: a,X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ( member_a @ X2 @ ( sK49 @ X1 ) )
=> ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1374]) ).
thf(f1376,plain,
! [X2: a,X1: extended_ereal] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $false
= ( member_a @ X2 @ ( sK49 @ X1 ) ) )
| ( $true
= ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f1375]) ).
thf(f1377,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ^ [Y0: extended_ereal] :
( ( ord_le2001149050_ereal @ Y0 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y1: set_a] :
( ( topolo1276428101open_a @ Y1 )
& ( member_a @ x0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( member_a @ Y2 @ Y1 )
=> ( ord_le2001149050_ereal @ Y0 @ ( f @ Y2 ) ) ) ) ) ) )
@ sK50 ) ) ),
inference(sigma_proxy_clausification,[],[f1363]) ).
thf(f1378,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ( ord_le2001149050_ereal @ sK50 @ ( f @ x0 ) )
=> ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK50 @ ( f @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1377]) ).
thf(f1379,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ?? @ set_a
@ ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK50 @ ( f @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1378]) ).
thf(f1380,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $true
= ( ord_le2001149050_ereal @ sK50 @ ( f @ x0 ) ) ) ),
inference(imp_proxy_clausification,[],[f1378]) ).
thf(f1381,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ^ [Y0: set_a] :
( ( topolo1276428101open_a @ Y0 )
& ( member_a @ x0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( member_a @ Y1 @ Y0 )
=> ( ord_le2001149050_ereal @ sK50 @ ( f @ Y1 ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1379]) ).
thf(f1382,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK50 @ ( f @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1381]) ).
thf(f1383,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK50 @ ( f @ Y0 ) ) ) ) )
| ( $false
= ( ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1382]) ).
thf(f1384,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK50 @ ( f @ Y0 ) ) )
@ ( sK51 @ X1 ) ) )
| ( $false
= ( ( topolo1276428101open_a @ X1 )
& ( member_a @ x0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1383]) ).
thf(f1385,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ^ [Y0: a] :
( ( member_a @ Y0 @ X1 )
=> ( ord_le2001149050_ereal @ sK50 @ ( f @ Y0 ) ) )
@ ( sK51 @ X1 ) ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f1384]) ).
thf(f1386,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ( member_a @ ( sK51 @ X1 ) @ X1 )
=> ( ord_le2001149050_ereal @ sK50 @ ( f @ ( sK51 @ X1 ) ) ) ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f1385]) ).
thf(f1387,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ sK50 @ ( f @ ( sK51 @ X1 ) ) ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1386]) ).
thf(f1388,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
!= extended_PInfty )
| ( $true
= ( member_a @ ( sK51 @ X1 ) @ X1 ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1386]) ).
thf(f1390,definition,
( spl52_1
<=> ( $true
= ( ord_le2001149050_ereal @ sK38 @ ( f @ x0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_1])],[avatar_definition]) ).
thf(f1392,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK38 @ ( f @ x0 ) ) )
| ~ spl52_1 ),
inference(avatar_component_clause,[],[f1390]) ).
thf(f1394,definition,
( spl52_2
<=> ( ( lower_191460856_ereal @ x0 @ f )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl52_2])],[avatar_definition]) ).
thf(f1396,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ~ spl52_2 ),
inference(avatar_component_clause,[],[f1394]) ).
thf(f1397,plain,
( spl52_1
| spl52_2 ),
inference(avatar_split_clause,[],[f647,f1394,f1390]) ).
thf(f1399,definition,
( spl52_3
<=> ! [X1: set_a] :
( ( $true
= ( member_a @ ( sK39 @ X1 ) @ X1 ) )
| ( ( topolo1276428101open_a @ X1 )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl52_3])],[avatar_definition]) ).
thf(f1400,plain,
( ! [X1: set_a] :
( ( $true
= ( member_a @ ( sK39 @ X1 ) @ X1 ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) )
| ~ spl52_3 ),
inference(avatar_component_clause,[],[f1399]) ).
thf(f1401,plain,
( spl52_3
| spl52_2 ),
inference(avatar_split_clause,[],[f655,f1394,f1399]) ).
thf(f1403,definition,
( spl52_4
<=> ! [X1: set_a] :
( ( $false
= ( ord_le2001149050_ereal @ sK38 @ ( f @ ( sK39 @ X1 ) ) ) )
| ( ( topolo1276428101open_a @ X1 )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl52_4])],[avatar_definition]) ).
thf(f1404,plain,
( ! [X1: set_a] :
( ( $false
= ( ord_le2001149050_ereal @ sK38 @ ( f @ ( sK39 @ X1 ) ) ) )
| ( ( topolo1276428101open_a @ X1 )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false ) )
| ~ spl52_4 ),
inference(avatar_component_clause,[],[f1403]) ).
thf(f1405,plain,
( spl52_4
| spl52_2 ),
inference(avatar_split_clause,[],[f654,f1394,f1403]) ).
thf(f1407,definition,
( spl52_5
<=> ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( topolo1276428101open_a @ ( sK40 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_5])],[avatar_definition]) ).
thf(f1408,plain,
( ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( topolo1276428101open_a @ ( sK40 @ X1 ) ) ) )
| ~ spl52_5 ),
inference(avatar_component_clause,[],[f1407]) ).
thf(f1410,definition,
( spl52_6
<=> ( ( lower_191460856_ereal @ x0 @ f )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl52_6])],[avatar_definition]) ).
thf(f1412,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ~ spl52_6 ),
inference(avatar_component_clause,[],[f1410]) ).
thf(f1413,plain,
( spl52_5
| spl52_6 ),
inference(avatar_split_clause,[],[f665,f1410,f1407]) ).
thf(f1415,definition,
( spl52_7
<=> ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( member_a @ x0 @ ( sK40 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_7])],[avatar_definition]) ).
thf(f1416,plain,
( ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( member_a @ x0 @ ( sK40 @ X1 ) ) ) )
| ~ spl52_7 ),
inference(avatar_component_clause,[],[f1415]) ).
thf(f1417,plain,
( spl52_7
| spl52_6 ),
inference(avatar_split_clause,[],[f664,f1410,f1415]) ).
thf(f1419,definition,
( spl52_8
<=> ! [X2: a,X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) )
| ( $false
= ( member_a @ X2 @ ( sK40 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_8])],[avatar_definition]) ).
thf(f1420,plain,
( ! [X2: a,X1: extended_ereal] :
( ( $true
= ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $false
= ( member_a @ X2 @ ( sK40 @ X1 ) ) ) )
| ~ spl52_8 ),
inference(avatar_component_clause,[],[f1419]) ).
thf(f1421,plain,
( spl52_8
| spl52_6 ),
inference(avatar_split_clause,[],[f668,f1410,f1419]) ).
thf(f1425,plain,
! [X0: extended_ereal] :
( $true
!= ( ord_le2001149050_ereal @ X0 @ extended_MInfty ) ),
inference(forward_demodulation,[],[f585,f479]) ).
thf(f1428,plain,
! [X0: a > extended_ereal,X1: a] :
( ( ( X0 @ X1 )
!= extended_MInfty )
| ( ( lower_191460856_ereal @ X1 @ X0 )
= $true ) ),
inference(forward_demodulation,[],[f580,f479]) ).
thf(f1429,plain,
! [X1: extended_ereal] :
( ( ( f @ x0 )
= extended_MInfty )
| ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( topolo1276428101open_a @ ( sK43 @ X1 ) ) ) ),
inference(forward_demodulation,[],[f1321,f479]) ).
thf(f1430,plain,
! [X1: extended_ereal] :
( ( ( f @ x0 )
= extended_MInfty )
| ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( member_a @ x0 @ ( sK43 @ X1 ) ) ) ),
inference(forward_demodulation,[],[f1320,f479]) ).
thf(f1431,plain,
! [X2: a,X1: extended_ereal] :
( ( ( f @ x0 )
= extended_MInfty )
| ( ( lower_191460856_ereal @ x0 @ f )
= $false )
| ( ( f @ x0 )
= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $false
= ( member_a @ X2 @ ( sK43 @ X1 ) ) )
| ( $true
= ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) ) ),
inference(forward_demodulation,[],[f1324,f479]) ).
thf(f1432,plain,
( ( ( f @ x0 )
= extended_MInfty )
| ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( $true
= ( ord_le2001149050_ereal @ sK44 @ ( f @ x0 ) ) ) ),
inference(forward_demodulation,[],[f1328,f479]) ).
thf(f1433,plain,
! [X1: set_a] :
( ( ( f @ x0 )
= extended_MInfty )
| ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( $true
= ( member_a @ ( sK45 @ X1 ) @ X1 ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(forward_demodulation,[],[f1336,f479]) ).
thf(f1434,plain,
! [X1: set_a] :
( ( ( f @ x0 )
= extended_MInfty )
| ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ sK44 @ ( f @ ( sK45 @ X1 ) ) ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(forward_demodulation,[],[f1335,f479]) ).
thf(f1442,definition,
( spl52_9
<=> ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( topolo1276428101open_a @ ( sK49 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_9])],[avatar_definition]) ).
thf(f1443,plain,
( ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( topolo1276428101open_a @ ( sK49 @ X1 ) ) ) )
| ~ spl52_9 ),
inference(avatar_component_clause,[],[f1442]) ).
thf(f1445,definition,
( spl52_10
<=> ( ( f @ x0 )
= extended_PInfty ) ),
introduced(definition,[new_symbols(definition,[spl52_10])],[avatar_definition]) ).
thf(f1446,plain,
( ( ( f @ x0 )
= extended_PInfty )
| ~ spl52_10 ),
inference(avatar_component_clause,[],[f1445]) ).
thf(f1448,plain,
( spl52_9
| ~ spl52_10
| spl52_2 ),
inference(avatar_split_clause,[],[f1373,f1394,f1445,f1442]) ).
thf(f1450,definition,
( spl52_11
<=> ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( member_a @ x0 @ ( sK49 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_11])],[avatar_definition]) ).
thf(f1451,plain,
( ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( member_a @ x0 @ ( sK49 @ X1 ) ) ) )
| ~ spl52_11 ),
inference(avatar_component_clause,[],[f1450]) ).
thf(f1452,plain,
( spl52_11
| ~ spl52_10
| spl52_2 ),
inference(avatar_split_clause,[],[f1372,f1394,f1445,f1450]) ).
thf(f1454,definition,
( spl52_12
<=> ! [X2: a,X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) )
| ( $false
= ( member_a @ X2 @ ( sK49 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_12])],[avatar_definition]) ).
thf(f1455,plain,
( ! [X2: a,X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) )
| ( $false
= ( member_a @ X2 @ ( sK49 @ X1 ) ) ) )
| ~ spl52_12 ),
inference(avatar_component_clause,[],[f1454]) ).
thf(f1456,plain,
( spl52_12
| ~ spl52_10
| spl52_2 ),
inference(avatar_split_clause,[],[f1376,f1394,f1445,f1454]) ).
thf(f1458,definition,
( spl52_13
<=> ( $true
= ( ord_le2001149050_ereal @ sK50 @ ( f @ x0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_13])],[avatar_definition]) ).
thf(f1460,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK50 @ ( f @ x0 ) ) )
| ~ spl52_13 ),
inference(avatar_component_clause,[],[f1458]) ).
thf(f1461,plain,
( spl52_13
| ~ spl52_10
| spl52_6 ),
inference(avatar_split_clause,[],[f1380,f1410,f1445,f1458]) ).
thf(f1463,definition,
( spl52_14
<=> ! [X1: set_a] :
( ( $true
= ( member_a @ ( sK51 @ X1 ) @ X1 ) )
| ( ( topolo1276428101open_a @ X1 )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl52_14])],[avatar_definition]) ).
thf(f1464,plain,
( ! [X1: set_a] :
( ( $true
= ( member_a @ ( sK51 @ X1 ) @ X1 ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) )
| ~ spl52_14 ),
inference(avatar_component_clause,[],[f1463]) ).
thf(f1465,plain,
( spl52_14
| ~ spl52_10
| spl52_6 ),
inference(avatar_split_clause,[],[f1388,f1410,f1445,f1463]) ).
thf(f1467,definition,
( spl52_15
<=> ! [X1: set_a] :
( ( $false
= ( ord_le2001149050_ereal @ sK50 @ ( f @ ( sK51 @ X1 ) ) ) )
| ( ( topolo1276428101open_a @ X1 )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl52_15])],[avatar_definition]) ).
thf(f1468,plain,
( ! [X1: set_a] :
( ( $false
= ( ord_le2001149050_ereal @ sK50 @ ( f @ ( sK51 @ X1 ) ) ) )
| ( ( topolo1276428101open_a @ X1 )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false ) )
| ~ spl52_15 ),
inference(avatar_component_clause,[],[f1467]) ).
thf(f1469,plain,
( spl52_15
| ~ spl52_10
| spl52_6 ),
inference(avatar_split_clause,[],[f1387,f1410,f1445,f1467]) ).
thf(f1473,definition,
( spl52_16
<=> ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( topolo1276428101open_a @ ( sK43 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_16])],[avatar_definition]) ).
thf(f1474,plain,
( ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( topolo1276428101open_a @ ( sK43 @ X1 ) ) ) )
| ~ spl52_16 ),
inference(avatar_component_clause,[],[f1473]) ).
thf(f1476,definition,
( spl52_17
<=> ( ( f @ x0 )
= extended_MInfty ) ),
introduced(definition,[new_symbols(definition,[spl52_17])],[avatar_definition]) ).
thf(f1478,plain,
( ( ( f @ x0 )
= extended_MInfty )
| ~ spl52_17 ),
inference(avatar_component_clause,[],[f1476]) ).
thf(f1479,plain,
( spl52_16
| spl52_10
| spl52_2
| spl52_17 ),
inference(avatar_split_clause,[],[f1429,f1476,f1394,f1445,f1473]) ).
thf(f1481,definition,
( spl52_18
<=> ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( member_a @ x0 @ ( sK43 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_18])],[avatar_definition]) ).
thf(f1482,plain,
( ! [X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( member_a @ x0 @ ( sK43 @ X1 ) ) ) )
| ~ spl52_18 ),
inference(avatar_component_clause,[],[f1481]) ).
thf(f1483,plain,
( spl52_18
| spl52_10
| spl52_2
| spl52_17 ),
inference(avatar_split_clause,[],[f1430,f1476,f1394,f1445,f1481]) ).
thf(f1485,definition,
( spl52_19
<=> ! [X2: a,X1: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $true
= ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) )
| ( $false
= ( member_a @ X2 @ ( sK43 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_19])],[avatar_definition]) ).
thf(f1486,plain,
( ! [X2: a,X1: extended_ereal] :
( ( $true
= ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) ) )
| ( $false
= ( member_a @ X2 @ ( sK43 @ X1 ) ) ) )
| ~ spl52_19 ),
inference(avatar_component_clause,[],[f1485]) ).
thf(f1487,plain,
( spl52_19
| spl52_10
| spl52_2
| spl52_17 ),
inference(avatar_split_clause,[],[f1431,f1476,f1394,f1445,f1485]) ).
thf(f1488,plain,
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( $true
= ( ord_le2001149050_ereal @ sK44 @ ( f @ x0 ) ) ) ),
inference(forward_subsumption_resolution,[],[f1432,f1428]) ).
thf(f1489,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( $true
= ( member_a @ ( sK45 @ X1 ) @ X1 ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(forward_subsumption_resolution,[],[f1433,f1428]) ).
thf(f1490,plain,
! [X1: set_a] :
( ( ( lower_191460856_ereal @ x0 @ f )
= $true )
| ( ( f @ x0 )
= extended_PInfty )
| ( $false
= ( ord_le2001149050_ereal @ sK44 @ ( f @ ( sK45 @ X1 ) ) ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) ),
inference(forward_subsumption_resolution,[],[f1434,f1428]) ).
thf(f1504,definition,
( spl52_23
<=> ( $true
= ( ord_le2001149050_ereal @ sK44 @ ( f @ x0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_23])],[avatar_definition]) ).
thf(f1506,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK44 @ ( f @ x0 ) ) )
| ~ spl52_23 ),
inference(avatar_component_clause,[],[f1504]) ).
thf(f1507,plain,
( spl52_23
| spl52_10
| spl52_6 ),
inference(avatar_split_clause,[],[f1488,f1410,f1445,f1504]) ).
thf(f1509,definition,
( spl52_24
<=> ! [X1: set_a] :
( ( $true
= ( member_a @ ( sK45 @ X1 ) @ X1 ) )
| ( ( topolo1276428101open_a @ X1 )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl52_24])],[avatar_definition]) ).
thf(f1510,plain,
( ! [X1: set_a] :
( ( $true
= ( member_a @ ( sK45 @ X1 ) @ X1 ) )
| ( ( member_a @ x0 @ X1 )
= $false )
| ( ( topolo1276428101open_a @ X1 )
= $false ) )
| ~ spl52_24 ),
inference(avatar_component_clause,[],[f1509]) ).
thf(f1511,plain,
( spl52_24
| spl52_10
| spl52_6 ),
inference(avatar_split_clause,[],[f1489,f1410,f1445,f1509]) ).
thf(f1513,definition,
( spl52_25
<=> ! [X1: set_a] :
( ( $false
= ( ord_le2001149050_ereal @ sK44 @ ( f @ ( sK45 @ X1 ) ) ) )
| ( ( topolo1276428101open_a @ X1 )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl52_25])],[avatar_definition]) ).
thf(f1514,plain,
( ! [X1: set_a] :
( ( $false
= ( ord_le2001149050_ereal @ sK44 @ ( f @ ( sK45 @ X1 ) ) ) )
| ( ( topolo1276428101open_a @ X1 )
= $false )
| ( ( member_a @ x0 @ X1 )
= $false ) )
| ~ spl52_25 ),
inference(avatar_component_clause,[],[f1513]) ).
thf(f1515,plain,
( spl52_25
| spl52_10
| spl52_6 ),
inference(avatar_split_clause,[],[f1490,f1410,f1445,f1513]) ).
thf(f1516,plain,
( ( $true = $false )
| ~ spl52_2
| ~ spl52_6 ),
inference(forward_demodulation,[],[f1412,f1396]) ).
thf(f1517,plain,
( $false
| ~ spl52_2
| ~ spl52_6 ),
inference(trivial_inequality_removal,[],[f1516]) ).
thf(f1518,plain,
( ~ spl52_2
| ~ spl52_6 ),
inference(avatar_contradiction_clause,[],[f1517]) ).
thf(f1520,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK50 @ extended_PInfty ) )
| ~ spl52_10
| ~ spl52_13 ),
inference(forward_demodulation,[],[f1460,f1446]) ).
thf(f1529,plain,
( ! [X0: extended_ereal] :
( ( $true
= ( member_a @ x0 @ ( sK40 @ X0 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X0 @ extended_PInfty ) ) )
| ~ spl52_7
| ~ spl52_10 ),
inference(constrained_superposition,[],[f1416,f1446]) ).
thf(f1530,plain,
( ! [X0: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X0 @ extended_PInfty ) )
| ( $true
= ( topolo1276428101open_a @ ( sK40 @ X0 ) ) ) )
| ~ spl52_5
| ~ spl52_10 ),
inference(constrained_superposition,[],[f1408,f1446]) ).
thf(f1533,plain,
( ( $true = $false )
| ( $true
= ( topolo1276428101open_a @ ( sK40 @ sK50 ) ) )
| ~ spl52_5
| ~ spl52_10
| ~ spl52_13 ),
inference(constrained_superposition,[],[f1520,f1530]) ).
thf(f1534,plain,
( ( $true
= ( topolo1276428101open_a @ ( sK40 @ sK50 ) ) )
| ~ spl52_5
| ~ spl52_10
| ~ spl52_13 ),
inference(trivial_inequality_removal,[],[f1533]) ).
thf(f1537,plain,
( ! [X0: set_a] :
( ( $true = $false )
| ( $false
= ( ord_le2001149050_ereal @ sK50 @ ( f @ x0 ) ) )
| ( $false
= ( member_a @ ( sK51 @ X0 ) @ ( sK40 @ sK50 ) ) )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ x0 @ X0 ) ) )
| ~ spl52_8
| ~ spl52_15 ),
inference(constrained_superposition,[],[f1420,f1468]) ).
thf(f1538,plain,
( ! [X0: set_a] :
( ( $false
= ( ord_le2001149050_ereal @ sK50 @ ( f @ x0 ) ) )
| ( $false
= ( member_a @ ( sK51 @ X0 ) @ ( sK40 @ sK50 ) ) )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ x0 @ X0 ) ) )
| ~ spl52_8
| ~ spl52_15 ),
inference(trivial_inequality_removal,[],[f1537]) ).
thf(f1540,plain,
( ! [X0: set_a] :
( ( $false
= ( ord_le2001149050_ereal @ sK50 @ extended_PInfty ) )
| ( $false
= ( member_a @ ( sK51 @ X0 ) @ ( sK40 @ sK50 ) ) )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ x0 @ X0 ) ) )
| ~ spl52_8
| ~ spl52_10
| ~ spl52_15 ),
inference(forward_demodulation,[],[f1538,f1446]) ).
thf(f1542,plain,
( ! [X0: set_a] :
( ( $true = $false )
| ( $false
= ( member_a @ ( sK51 @ X0 ) @ ( sK40 @ sK50 ) ) )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ x0 @ X0 ) ) )
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_15 ),
inference(forward_demodulation,[],[f1540,f1520]) ).
thf(f1543,plain,
( ! [X0: set_a] :
( ( $false
= ( member_a @ x0 @ X0 ) )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ ( sK51 @ X0 ) @ ( sK40 @ sK50 ) ) ) )
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_15 ),
inference(trivial_inequality_removal,[],[f1542]) ).
thf(f1547,plain,
( ! [X0: extended_ereal] :
( ( $true = $false )
| ( $true
= ( member_a @ ( sK51 @ ( sK40 @ X0 ) ) @ ( sK40 @ X0 ) ) )
| ( $false
= ( topolo1276428101open_a @ ( sK40 @ X0 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X0 @ extended_PInfty ) ) )
| ~ spl52_7
| ~ spl52_10
| ~ spl52_14 ),
inference(constrained_superposition,[],[f1464,f1529]) ).
thf(f1548,plain,
( ! [X0: extended_ereal] :
( ( $true
= ( member_a @ ( sK51 @ ( sK40 @ X0 ) ) @ ( sK40 @ X0 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X0 @ extended_PInfty ) )
| ( $false
= ( topolo1276428101open_a @ ( sK40 @ X0 ) ) ) )
| ~ spl52_7
| ~ spl52_10
| ~ spl52_14 ),
inference(trivial_inequality_removal,[],[f1547]) ).
thf(f1551,plain,
( ! [X0: extended_ereal] :
( ( $true = $false )
| ( $false
= ( ord_le2001149050_ereal @ X0 @ extended_PInfty ) )
| ( $false
= ( topolo1276428101open_a @ ( sK40 @ X0 ) ) )
| ( $false
= ( member_a @ ( sK51 @ ( sK40 @ X0 ) ) @ ( sK40 @ sK50 ) ) ) )
| ~ spl52_7
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_15 ),
inference(constrained_superposition,[],[f1529,f1543]) ).
thf(f1552,plain,
( ! [X0: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X0 @ extended_PInfty ) )
| ( $false
= ( topolo1276428101open_a @ ( sK40 @ X0 ) ) )
| ( $false
= ( member_a @ ( sK51 @ ( sK40 @ X0 ) ) @ ( sK40 @ sK50 ) ) ) )
| ~ spl52_7
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_15 ),
inference(trivial_inequality_removal,[],[f1551]) ).
thf(f1572,plain,
( ( $true = $false )
| ( $true
= ( member_a @ ( sK51 @ ( sK40 @ sK50 ) ) @ ( sK40 @ sK50 ) ) )
| ( $false
= ( topolo1276428101open_a @ ( sK40 @ sK50 ) ) )
| ~ spl52_7
| ~ spl52_10
| ~ spl52_13
| ~ spl52_14 ),
inference(constrained_superposition,[],[f1520,f1548]) ).
thf(f1573,plain,
( ( $true
= ( member_a @ ( sK51 @ ( sK40 @ sK50 ) ) @ ( sK40 @ sK50 ) ) )
| ( $false
= ( topolo1276428101open_a @ ( sK40 @ sK50 ) ) )
| ~ spl52_7
| ~ spl52_10
| ~ spl52_13
| ~ spl52_14 ),
inference(trivial_inequality_removal,[],[f1572]) ).
thf(f1575,plain,
( ( $true = $false )
| ( $true
= ( member_a @ ( sK51 @ ( sK40 @ sK50 ) ) @ ( sK40 @ sK50 ) ) )
| ~ spl52_5
| ~ spl52_7
| ~ spl52_10
| ~ spl52_13
| ~ spl52_14 ),
inference(forward_demodulation,[],[f1573,f1534]) ).
thf(f1576,plain,
( ( $true
= ( member_a @ ( sK51 @ ( sK40 @ sK50 ) ) @ ( sK40 @ sK50 ) ) )
| ~ spl52_5
| ~ spl52_7
| ~ spl52_10
| ~ spl52_13
| ~ spl52_14 ),
inference(trivial_inequality_removal,[],[f1575]) ).
thf(f1580,plain,
( ( $true = $false )
| ( $false
= ( topolo1276428101open_a @ ( sK40 @ sK50 ) ) )
| ( $false
= ( member_a @ ( sK51 @ ( sK40 @ sK50 ) ) @ ( sK40 @ sK50 ) ) )
| ~ spl52_7
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_15 ),
inference(constrained_superposition,[],[f1520,f1552]) ).
thf(f1581,plain,
( ( $false
= ( topolo1276428101open_a @ ( sK40 @ sK50 ) ) )
| ( $false
= ( member_a @ ( sK51 @ ( sK40 @ sK50 ) ) @ ( sK40 @ sK50 ) ) )
| ~ spl52_7
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_15 ),
inference(trivial_inequality_removal,[],[f1580]) ).
thf(f1583,plain,
( ( $true = $false )
| ( $false
= ( member_a @ ( sK51 @ ( sK40 @ sK50 ) ) @ ( sK40 @ sK50 ) ) )
| ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_15 ),
inference(forward_demodulation,[],[f1581,f1534]) ).
thf(f1584,plain,
( ( $false
= ( member_a @ ( sK51 @ ( sK40 @ sK50 ) ) @ ( sK40 @ sK50 ) ) )
| ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_15 ),
inference(trivial_inequality_removal,[],[f1583]) ).
thf(f1587,plain,
( ( $true = $false )
| ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_14
| ~ spl52_15 ),
inference(constrained_superposition,[],[f1584,f1576]) ).
thf(f1591,plain,
( $false
| ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_14
| ~ spl52_15 ),
inference(trivial_inequality_removal,[],[f1587]) ).
thf(f1592,plain,
( ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_14
| ~ spl52_15 ),
inference(avatar_contradiction_clause,[],[f1591]) ).
thf(f1612,plain,
( ( $true = $false )
| ( $true
= ( member_a @ x0 @ ( sK40 @ sK44 ) ) )
| ~ spl52_7
| ~ spl52_23 ),
inference(constrained_superposition,[],[f1416,f1506]) ).
thf(f1613,plain,
( ( $true = $false )
| ( $true
= ( topolo1276428101open_a @ ( sK40 @ sK44 ) ) )
| ~ spl52_5
| ~ spl52_23 ),
inference(constrained_superposition,[],[f1408,f1506]) ).
thf(f1614,plain,
( ! [X0: a] :
( ( $true = $false )
| ( $true
= ( ord_le2001149050_ereal @ sK44 @ ( f @ X0 ) ) )
| ( $false
= ( member_a @ X0 @ ( sK40 @ sK44 ) ) ) )
| ~ spl52_8
| ~ spl52_23 ),
inference(constrained_superposition,[],[f1420,f1506]) ).
thf(f1615,plain,
( ! [X0: a] :
( ( $true
= ( ord_le2001149050_ereal @ sK44 @ ( f @ X0 ) ) )
| ( $false
= ( member_a @ X0 @ ( sK40 @ sK44 ) ) ) )
| ~ spl52_8
| ~ spl52_23 ),
inference(trivial_inequality_removal,[],[f1614]) ).
thf(f1616,plain,
( ( $true
= ( topolo1276428101open_a @ ( sK40 @ sK44 ) ) )
| ~ spl52_5
| ~ spl52_23 ),
inference(trivial_inequality_removal,[],[f1613]) ).
thf(f1617,plain,
( ( $true
= ( member_a @ x0 @ ( sK40 @ sK44 ) ) )
| ~ spl52_7
| ~ spl52_23 ),
inference(trivial_inequality_removal,[],[f1612]) ).
thf(f1668,plain,
( ( $true = $false )
| ( $true
= ( member_a @ ( sK45 @ ( sK40 @ sK44 ) ) @ ( sK40 @ sK44 ) ) )
| ( $false
= ( topolo1276428101open_a @ ( sK40 @ sK44 ) ) )
| ~ spl52_7
| ~ spl52_23
| ~ spl52_24 ),
inference(constrained_superposition,[],[f1617,f1510]) ).
thf(f1669,plain,
( ( $true
= ( member_a @ ( sK45 @ ( sK40 @ sK44 ) ) @ ( sK40 @ sK44 ) ) )
| ( $false
= ( topolo1276428101open_a @ ( sK40 @ sK44 ) ) )
| ~ spl52_7
| ~ spl52_23
| ~ spl52_24 ),
inference(trivial_inequality_removal,[],[f1668]) ).
thf(f1673,plain,
( ( $true = $false )
| ( $true
= ( member_a @ ( sK45 @ ( sK40 @ sK44 ) ) @ ( sK40 @ sK44 ) ) )
| ~ spl52_5
| ~ spl52_7
| ~ spl52_23
| ~ spl52_24 ),
inference(forward_demodulation,[],[f1669,f1616]) ).
thf(f1674,plain,
( ( $true
= ( member_a @ ( sK45 @ ( sK40 @ sK44 ) ) @ ( sK40 @ sK44 ) ) )
| ~ spl52_5
| ~ spl52_7
| ~ spl52_23
| ~ spl52_24 ),
inference(trivial_inequality_removal,[],[f1673]) ).
thf(f1684,plain,
( ! [X0: set_a] :
( ( $true = $false )
| ( $false
= ( member_a @ ( sK45 @ X0 ) @ ( sK40 @ sK44 ) ) )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ x0 @ X0 ) ) )
| ~ spl52_8
| ~ spl52_23
| ~ spl52_25 ),
inference(constrained_superposition,[],[f1615,f1514]) ).
thf(f1685,plain,
( ! [X0: set_a] :
( ( $false
= ( member_a @ x0 @ X0 ) )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ ( sK45 @ X0 ) @ ( sK40 @ sK44 ) ) ) )
| ~ spl52_8
| ~ spl52_23
| ~ spl52_25 ),
inference(trivial_inequality_removal,[],[f1684]) ).
thf(f1708,plain,
( ( $true = $false )
| ( $false
= ( topolo1276428101open_a @ ( sK40 @ sK44 ) ) )
| ( $false
= ( member_a @ ( sK45 @ ( sK40 @ sK44 ) ) @ ( sK40 @ sK44 ) ) )
| ~ spl52_7
| ~ spl52_8
| ~ spl52_23
| ~ spl52_25 ),
inference(constrained_superposition,[],[f1617,f1685]) ).
thf(f1709,plain,
( ( $false
= ( topolo1276428101open_a @ ( sK40 @ sK44 ) ) )
| ( $false
= ( member_a @ ( sK45 @ ( sK40 @ sK44 ) ) @ ( sK40 @ sK44 ) ) )
| ~ spl52_7
| ~ spl52_8
| ~ spl52_23
| ~ spl52_25 ),
inference(trivial_inequality_removal,[],[f1708]) ).
thf(f1713,plain,
( ( $true = $false )
| ( $false
= ( member_a @ ( sK45 @ ( sK40 @ sK44 ) ) @ ( sK40 @ sK44 ) ) )
| ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_23
| ~ spl52_25 ),
inference(forward_demodulation,[],[f1709,f1616]) ).
thf(f1714,plain,
( ( $false
= ( member_a @ ( sK45 @ ( sK40 @ sK44 ) ) @ ( sK40 @ sK44 ) ) )
| ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_23
| ~ spl52_25 ),
inference(trivial_inequality_removal,[],[f1713]) ).
thf(f1736,plain,
( ( $true = $false )
| ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_23
| ~ spl52_24
| ~ spl52_25 ),
inference(constrained_superposition,[],[f1714,f1674]) ).
thf(f1740,plain,
( $false
| ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_23
| ~ spl52_24
| ~ spl52_25 ),
inference(trivial_inequality_removal,[],[f1736]) ).
thf(f1741,plain,
( ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_23
| ~ spl52_24
| ~ spl52_25 ),
inference(avatar_contradiction_clause,[],[f1740]) ).
thf(f1946,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK38 @ extended_MInfty ) )
| ~ spl52_1
| ~ spl52_17 ),
inference(constrained_superposition,[],[f1392,f1478]) ).
thf(f1952,plain,
( $false
| ~ spl52_1
| ~ spl52_17 ),
inference(forward_subsumption_resolution,[],[f1946,f1425]) ).
thf(f1953,plain,
( ~ spl52_1
| ~ spl52_17 ),
inference(avatar_contradiction_clause,[],[f1952]) ).
thf(f1979,plain,
( ! [X0: set_a] :
( ( $true = $false )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ x0 @ X0 ) )
| ( $false
= ( ord_le2001149050_ereal @ sK38 @ ( f @ x0 ) ) )
| ( $false
= ( member_a @ ( sK39 @ X0 ) @ ( sK43 @ sK38 ) ) ) )
| ~ spl52_4
| ~ spl52_19 ),
inference(constrained_superposition,[],[f1404,f1486]) ).
thf(f1997,plain,
( ! [X0: set_a] :
( ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ x0 @ X0 ) )
| ( $false
= ( ord_le2001149050_ereal @ sK38 @ ( f @ x0 ) ) )
| ( $false
= ( member_a @ ( sK39 @ X0 ) @ ( sK43 @ sK38 ) ) ) )
| ~ spl52_4
| ~ spl52_19 ),
inference(trivial_inequality_removal,[],[f1979]) ).
thf(f2011,plain,
( ! [X0: set_a] :
( ( $true = $false )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ x0 @ X0 ) )
| ( $false
= ( member_a @ ( sK39 @ X0 ) @ ( sK43 @ sK38 ) ) ) )
| ~ spl52_1
| ~ spl52_4
| ~ spl52_19 ),
inference(forward_demodulation,[],[f1997,f1392]) ).
thf(f2012,plain,
( ! [X0: set_a] :
( ( $false
= ( member_a @ x0 @ X0 ) )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ ( sK39 @ X0 ) @ ( sK43 @ sK38 ) ) ) )
| ~ spl52_1
| ~ spl52_4
| ~ spl52_19 ),
inference(trivial_inequality_removal,[],[f2011]) ).
thf(f2157,plain,
( ( $true = $false )
| ( $true
= ( topolo1276428101open_a @ ( sK43 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_16 ),
inference(constrained_superposition,[],[f1392,f1474]) ).
thf(f2166,plain,
( ( $true
= ( topolo1276428101open_a @ ( sK43 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_16 ),
inference(trivial_inequality_removal,[],[f2157]) ).
thf(f2178,definition,
( spl52_39
<=> ( $true
= ( topolo1276428101open_a @ ( sK43 @ sK38 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_39])],[avatar_definition]) ).
thf(f2180,plain,
( ( $true
= ( topolo1276428101open_a @ ( sK43 @ sK38 ) ) )
| ~ spl52_39 ),
inference(avatar_component_clause,[],[f2178]) ).
thf(f2187,plain,
( spl52_39
| ~ spl52_1
| ~ spl52_16 ),
inference(avatar_split_clause,[],[f2166,f1473,f1390,f2178]) ).
thf(f2241,plain,
( ( $true = $false )
| ( $true
= ( member_a @ x0 @ ( sK43 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_18 ),
inference(constrained_superposition,[],[f1392,f1482]) ).
thf(f2250,plain,
( ( $true
= ( member_a @ x0 @ ( sK43 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_18 ),
inference(trivial_inequality_removal,[],[f2241]) ).
thf(f2262,definition,
( spl52_42
<=> ( $true
= ( member_a @ x0 @ ( sK43 @ sK38 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_42])],[avatar_definition]) ).
thf(f2264,plain,
( ( $true
= ( member_a @ x0 @ ( sK43 @ sK38 ) ) )
| ~ spl52_42 ),
inference(avatar_component_clause,[],[f2262]) ).
thf(f2266,plain,
( spl52_42
| ~ spl52_1
| ~ spl52_18 ),
inference(avatar_split_clause,[],[f2250,f1481,f1390,f2262]) ).
thf(f2276,plain,
( ( $true = $false )
| ( $true
= ( member_a @ ( sK39 @ ( sK43 @ sK38 ) ) @ ( sK43 @ sK38 ) ) )
| ( $false
= ( topolo1276428101open_a @ ( sK43 @ sK38 ) ) )
| ~ spl52_3
| ~ spl52_42 ),
inference(constrained_superposition,[],[f1400,f2264]) ).
thf(f2281,plain,
( ( $true
= ( member_a @ ( sK39 @ ( sK43 @ sK38 ) ) @ ( sK43 @ sK38 ) ) )
| ( $false
= ( topolo1276428101open_a @ ( sK43 @ sK38 ) ) )
| ~ spl52_3
| ~ spl52_42 ),
inference(trivial_inequality_removal,[],[f2276]) ).
thf(f2291,plain,
( ( $true = $false )
| ( $true
= ( member_a @ ( sK39 @ ( sK43 @ sK38 ) ) @ ( sK43 @ sK38 ) ) )
| ~ spl52_3
| ~ spl52_39
| ~ spl52_42 ),
inference(forward_demodulation,[],[f2281,f2180]) ).
thf(f2292,plain,
( ( $true
= ( member_a @ ( sK39 @ ( sK43 @ sK38 ) ) @ ( sK43 @ sK38 ) ) )
| ~ spl52_3
| ~ spl52_39
| ~ spl52_42 ),
inference(trivial_inequality_removal,[],[f2291]) ).
thf(f2457,plain,
( ( $true = $false )
| ( $false
= ( topolo1276428101open_a @ ( sK43 @ sK38 ) ) )
| ( $false
= ( member_a @ ( sK39 @ ( sK43 @ sK38 ) ) @ ( sK43 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_4
| ~ spl52_19
| ~ spl52_42 ),
inference(constrained_superposition,[],[f2264,f2012]) ).
thf(f2460,plain,
( ( $false
= ( topolo1276428101open_a @ ( sK43 @ sK38 ) ) )
| ( $false
= ( member_a @ ( sK39 @ ( sK43 @ sK38 ) ) @ ( sK43 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_4
| ~ spl52_19
| ~ spl52_42 ),
inference(trivial_inequality_removal,[],[f2457]) ).
thf(f2468,plain,
( ( $true = $false )
| ( $false
= ( member_a @ ( sK39 @ ( sK43 @ sK38 ) ) @ ( sK43 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_4
| ~ spl52_19
| ~ spl52_39
| ~ spl52_42 ),
inference(forward_demodulation,[],[f2460,f2180]) ).
thf(f2469,plain,
( ( $false
= ( member_a @ ( sK39 @ ( sK43 @ sK38 ) ) @ ( sK43 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_4
| ~ spl52_19
| ~ spl52_39
| ~ spl52_42 ),
inference(trivial_inequality_removal,[],[f2468]) ).
thf(f2584,plain,
( ( $true = $false )
| ~ spl52_1
| ~ spl52_3
| ~ spl52_4
| ~ spl52_19
| ~ spl52_39
| ~ spl52_42 ),
inference(constrained_superposition,[],[f2469,f2292]) ).
thf(f2590,plain,
( $false
| ~ spl52_1
| ~ spl52_3
| ~ spl52_4
| ~ spl52_19
| ~ spl52_39
| ~ spl52_42 ),
inference(trivial_inequality_removal,[],[f2584]) ).
thf(f2591,plain,
( ~ spl52_1
| ~ spl52_3
| ~ spl52_4
| ~ spl52_19
| ~ spl52_39
| ~ spl52_42 ),
inference(avatar_contradiction_clause,[],[f2590]) ).
thf(f2594,plain,
( ! [X1: extended_ereal] :
( ( $true
= ( member_a @ x0 @ ( sK49 @ X1 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ extended_PInfty ) ) )
| ~ spl52_10
| ~ spl52_11 ),
inference(forward_demodulation,[],[f1451,f1446]) ).
thf(f2595,plain,
( ! [X2: a,X1: extended_ereal] :
( ( $true
= ( ord_le2001149050_ereal @ X1 @ ( f @ X2 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X1 @ extended_PInfty ) )
| ( $false
= ( member_a @ X2 @ ( sK49 @ X1 ) ) ) )
| ~ spl52_10
| ~ spl52_12 ),
inference(forward_demodulation,[],[f1455,f1446]) ).
thf(f2602,plain,
( ! [X0: set_a] :
( ( $true = $false )
| ( $false
= ( ord_le2001149050_ereal @ sK38 @ extended_PInfty ) )
| ( $false
= ( member_a @ ( sK39 @ X0 ) @ ( sK49 @ sK38 ) ) )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ x0 @ X0 ) ) )
| ~ spl52_4
| ~ spl52_10
| ~ spl52_12 ),
inference(constrained_superposition,[],[f2595,f1404]) ).
thf(f2631,plain,
( ! [X0: set_a] :
( ( $false
= ( ord_le2001149050_ereal @ sK38 @ extended_PInfty ) )
| ( $false
= ( member_a @ ( sK39 @ X0 ) @ ( sK49 @ sK38 ) ) )
| ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ x0 @ X0 ) ) )
| ~ spl52_4
| ~ spl52_10
| ~ spl52_12 ),
inference(trivial_inequality_removal,[],[f2602]) ).
thf(f2661,definition,
( spl52_57
<=> ( $false
= ( ord_le2001149050_ereal @ sK38 @ extended_PInfty ) ) ),
introduced(definition,[new_symbols(definition,[spl52_57])],[avatar_definition]) ).
thf(f2663,plain,
( ( $false
= ( ord_le2001149050_ereal @ sK38 @ extended_PInfty ) )
| ~ spl52_57 ),
inference(avatar_component_clause,[],[f2661]) ).
thf(f2665,definition,
( spl52_58
<=> ! [X0: set_a] :
( ( $false
= ( topolo1276428101open_a @ X0 ) )
| ( $false
= ( member_a @ ( sK39 @ X0 ) @ ( sK49 @ sK38 ) ) )
| ( $false
= ( member_a @ x0 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl52_58])],[avatar_definition]) ).
thf(f2666,plain,
( ! [X0: set_a] :
( ( $false
= ( member_a @ x0 @ X0 ) )
| ( $false
= ( member_a @ ( sK39 @ X0 ) @ ( sK49 @ sK38 ) ) )
| ( $false
= ( topolo1276428101open_a @ X0 ) ) )
| ~ spl52_58 ),
inference(avatar_component_clause,[],[f2665]) ).
thf(f2671,plain,
( spl52_58
| spl52_57
| ~ spl52_4
| ~ spl52_10
| ~ spl52_12 ),
inference(avatar_split_clause,[],[f2631,f1454,f1445,f1403,f2661,f2665]) ).
thf(f2677,plain,
( ( $true
= ( ord_le2001149050_ereal @ sK38 @ extended_PInfty ) )
| ~ spl52_1
| ~ spl52_10 ),
inference(constrained_superposition,[],[f1392,f1446]) ).
thf(f2757,plain,
( ( $true = $false )
| ( $true
= ( topolo1276428101open_a @ ( sK49 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_9 ),
inference(constrained_superposition,[],[f1392,f1443]) ).
thf(f2761,plain,
( ( $true
= ( topolo1276428101open_a @ ( sK49 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_9 ),
inference(trivial_inequality_removal,[],[f2757]) ).
thf(f2779,plain,
( ! [X0: extended_ereal] :
( ( $true = $false )
| ( $true
= ( member_a @ ( sK39 @ ( sK49 @ X0 ) ) @ ( sK49 @ X0 ) ) )
| ( $false
= ( topolo1276428101open_a @ ( sK49 @ X0 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X0 @ extended_PInfty ) ) )
| ~ spl52_3
| ~ spl52_10
| ~ spl52_11 ),
inference(constrained_superposition,[],[f1400,f2594]) ).
thf(f2786,plain,
( ! [X0: extended_ereal] :
( ( $true = $false )
| ( $false
= ( member_a @ ( sK39 @ ( sK49 @ X0 ) ) @ ( sK49 @ sK38 ) ) )
| ( $false
= ( topolo1276428101open_a @ ( sK49 @ X0 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X0 @ extended_PInfty ) ) )
| ~ spl52_10
| ~ spl52_11
| ~ spl52_58 ),
inference(constrained_superposition,[],[f2666,f2594]) ).
thf(f2789,plain,
( ! [X0: extended_ereal] :
( ( $false
= ( ord_le2001149050_ereal @ X0 @ extended_PInfty ) )
| ( $false
= ( topolo1276428101open_a @ ( sK49 @ X0 ) ) )
| ( $false
= ( member_a @ ( sK39 @ ( sK49 @ X0 ) ) @ ( sK49 @ sK38 ) ) ) )
| ~ spl52_10
| ~ spl52_11
| ~ spl52_58 ),
inference(trivial_inequality_removal,[],[f2786]) ).
thf(f2796,plain,
( ! [X0: extended_ereal] :
( ( $true
= ( member_a @ ( sK39 @ ( sK49 @ X0 ) ) @ ( sK49 @ X0 ) ) )
| ( $false
= ( ord_le2001149050_ereal @ X0 @ extended_PInfty ) )
| ( $false
= ( topolo1276428101open_a @ ( sK49 @ X0 ) ) ) )
| ~ spl52_3
| ~ spl52_10
| ~ spl52_11 ),
inference(trivial_inequality_removal,[],[f2779]) ).
thf(f2859,plain,
( ( $true = $false )
| ( $true
= ( member_a @ ( sK39 @ ( sK49 @ sK38 ) ) @ ( sK49 @ sK38 ) ) )
| ( $false
= ( topolo1276428101open_a @ ( sK49 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_3
| ~ spl52_10
| ~ spl52_11 ),
inference(constrained_superposition,[],[f2677,f2796]) ).
thf(f2860,plain,
( ( $true
= ( member_a @ ( sK39 @ ( sK49 @ sK38 ) ) @ ( sK49 @ sK38 ) ) )
| ( $false
= ( topolo1276428101open_a @ ( sK49 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_3
| ~ spl52_10
| ~ spl52_11 ),
inference(trivial_inequality_removal,[],[f2859]) ).
thf(f2863,plain,
( ( $true = $false )
| ( $true
= ( member_a @ ( sK39 @ ( sK49 @ sK38 ) ) @ ( sK49 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_3
| ~ spl52_9
| ~ spl52_10
| ~ spl52_11 ),
inference(forward_demodulation,[],[f2860,f2761]) ).
thf(f2864,plain,
( ( $true
= ( member_a @ ( sK39 @ ( sK49 @ sK38 ) ) @ ( sK49 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_3
| ~ spl52_9
| ~ spl52_10
| ~ spl52_11 ),
inference(trivial_inequality_removal,[],[f2863]) ).
thf(f3033,plain,
( ( $true = $false )
| ( $false
= ( topolo1276428101open_a @ ( sK49 @ sK38 ) ) )
| ( $false
= ( member_a @ ( sK39 @ ( sK49 @ sK38 ) ) @ ( sK49 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_10
| ~ spl52_11
| ~ spl52_58 ),
inference(constrained_superposition,[],[f2677,f2789]) ).
thf(f3035,plain,
( ( $false
= ( topolo1276428101open_a @ ( sK49 @ sK38 ) ) )
| ( $false
= ( member_a @ ( sK39 @ ( sK49 @ sK38 ) ) @ ( sK49 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_10
| ~ spl52_11
| ~ spl52_58 ),
inference(trivial_inequality_removal,[],[f3033]) ).
thf(f3038,plain,
( ( $true = $false )
| ( $false
= ( member_a @ ( sK39 @ ( sK49 @ sK38 ) ) @ ( sK49 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_9
| ~ spl52_10
| ~ spl52_11
| ~ spl52_58 ),
inference(forward_demodulation,[],[f3035,f2761]) ).
thf(f3039,plain,
( ( $false
= ( member_a @ ( sK39 @ ( sK49 @ sK38 ) ) @ ( sK49 @ sK38 ) ) )
| ~ spl52_1
| ~ spl52_9
| ~ spl52_10
| ~ spl52_11
| ~ spl52_58 ),
inference(trivial_inequality_removal,[],[f3038]) ).
thf(f3090,plain,
( ( $true = $false )
| ~ spl52_1
| ~ spl52_3
| ~ spl52_9
| ~ spl52_10
| ~ spl52_11
| ~ spl52_58 ),
inference(constrained_superposition,[],[f3039,f2864]) ).
thf(f3096,plain,
( $false
| ~ spl52_1
| ~ spl52_3
| ~ spl52_9
| ~ spl52_10
| ~ spl52_11
| ~ spl52_58 ),
inference(trivial_inequality_removal,[],[f3090]) ).
thf(f3097,plain,
( ~ spl52_1
| ~ spl52_3
| ~ spl52_9
| ~ spl52_10
| ~ spl52_11
| ~ spl52_58 ),
inference(avatar_contradiction_clause,[],[f3096]) ).
thf(f3098,plain,
( ( $true = $false )
| ~ spl52_1
| ~ spl52_10
| ~ spl52_57 ),
inference(constrained_superposition,[],[f2663,f2677]) ).
thf(f3104,plain,
( $false
| ~ spl52_1
| ~ spl52_10
| ~ spl52_57 ),
inference(trivial_inequality_removal,[],[f3098]) ).
thf(f3105,plain,
( ~ spl52_1
| ~ spl52_10
| ~ spl52_57 ),
inference(avatar_contradiction_clause,[],[f3104]) ).
cnf(s1,plain,
( spl52_1
| spl52_2 ),
inference(sat_conversion,[],[f1397]) ).
cnf(s2,plain,
( spl52_2
| spl52_3 ),
inference(sat_conversion,[],[f1401]) ).
cnf(s3,plain,
( spl52_2
| spl52_4 ),
inference(sat_conversion,[],[f1405]) ).
cnf(s4,plain,
( spl52_5
| spl52_6 ),
inference(sat_conversion,[],[f1413]) ).
cnf(s5,plain,
( spl52_6
| spl52_7 ),
inference(sat_conversion,[],[f1417]) ).
cnf(s6,plain,
( spl52_6
| spl52_8 ),
inference(sat_conversion,[],[f1421]) ).
cnf(s7,plain,
( spl52_2
| spl52_9
| ~ spl52_10 ),
inference(sat_conversion,[],[f1448]) ).
cnf(s8,plain,
( spl52_2
| ~ spl52_10
| spl52_11 ),
inference(sat_conversion,[],[f1452]) ).
cnf(s9,plain,
( spl52_2
| ~ spl52_10
| spl52_12 ),
inference(sat_conversion,[],[f1456]) ).
cnf(s10,plain,
( spl52_6
| ~ spl52_10
| spl52_13 ),
inference(sat_conversion,[],[f1461]) ).
cnf(s11,plain,
( spl52_6
| ~ spl52_10
| spl52_14 ),
inference(sat_conversion,[],[f1465]) ).
cnf(s12,plain,
( spl52_6
| ~ spl52_10
| spl52_15 ),
inference(sat_conversion,[],[f1469]) ).
cnf(s13,plain,
( spl52_2
| spl52_10
| spl52_16
| spl52_17 ),
inference(sat_conversion,[],[f1479]) ).
cnf(s14,plain,
( spl52_2
| spl52_10
| spl52_17
| spl52_18 ),
inference(sat_conversion,[],[f1483]) ).
cnf(s15,plain,
( spl52_2
| spl52_10
| spl52_17
| spl52_19 ),
inference(sat_conversion,[],[f1487]) ).
cnf(s19,plain,
( spl52_6
| spl52_10
| spl52_23 ),
inference(sat_conversion,[],[f1507]) ).
cnf(s20,plain,
( spl52_6
| spl52_10
| spl52_24 ),
inference(sat_conversion,[],[f1511]) ).
cnf(s21,plain,
( spl52_6
| spl52_10
| spl52_25 ),
inference(sat_conversion,[],[f1515]) ).
cnf(s22,plain,
( ~ spl52_2
| ~ spl52_6 ),
inference(sat_conversion,[],[f1518]) ).
cnf(s24,plain,
( ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_10
| ~ spl52_13
| ~ spl52_14
| ~ spl52_15 ),
inference(sat_conversion,[],[f1592]) ).
cnf(s30,plain,
( ~ spl52_5
| ~ spl52_7
| ~ spl52_8
| ~ spl52_23
| ~ spl52_24
| ~ spl52_25 ),
inference(sat_conversion,[],[f1741]) ).
cnf(s41,plain,
( ~ spl52_1
| ~ spl52_17 ),
inference(sat_conversion,[],[f1953]) ).
cnf(s53,plain,
( ~ spl52_1
| ~ spl52_16
| spl52_39 ),
inference(sat_conversion,[],[f2187]) ).
cnf(s68,plain,
( ~ spl52_1
| ~ spl52_18
| spl52_42 ),
inference(sat_conversion,[],[f2266]) ).
cnf(s96,plain,
( ~ spl52_1
| ~ spl52_3
| ~ spl52_4
| ~ spl52_19
| ~ spl52_39
| ~ spl52_42 ),
inference(sat_conversion,[],[f2591]) ).
cnf(s105,plain,
( ~ spl52_4
| ~ spl52_10
| ~ spl52_12
| spl52_57
| spl52_58 ),
inference(sat_conversion,[],[f2671]) ).
cnf(s108,plain,
( ~ spl52_1
| ~ spl52_3
| ~ spl52_9
| ~ spl52_10
| ~ spl52_11
| ~ spl52_58 ),
inference(sat_conversion,[],[f3097]) ).
cnf(s110,plain,
( ~ spl52_1
| ~ spl52_10
| ~ spl52_57 ),
inference(sat_conversion,[],[f3105]) ).
cnf(s111,plain,
( spl52_10
| spl52_6 ),
inference(rat,[],[s30,s19,s20,s21,s6,s5,s4]) ).
cnf(s112,plain,
spl52_6,
inference(rat,[],[s24,s10,s11,s12,s111,s4,s5,s6]) ).
cnf(s113,plain,
~ spl52_2,
inference(rat,[],[s22,s112]) ).
cnf(s114,plain,
spl52_4,
inference(rat,[],[s3,s113]) ).
cnf(s115,plain,
spl52_3,
inference(rat,[],[s2,s113]) ).
cnf(s116,plain,
spl52_1,
inference(rat,[],[s1,s113]) ).
cnf(s117,plain,
~ spl52_17,
inference(rat,[],[s41,s116]) ).
cnf(s118,plain,
spl52_10,
inference(rat,[],[s96,s53,s68,s13,s14,s15,s116,s114,s115,s113,s117]) ).
cnf(s119,plain,
~ spl52_57,
inference(rat,[],[s110,s116,s118]) ).
cnf(s120,plain,
spl52_12,
inference(rat,[],[s9,s113,s118]) ).
cnf(s121,plain,
spl52_11,
inference(rat,[],[s8,s113,s118]) ).
cnf(s122,plain,
spl52_9,
inference(rat,[],[s7,s113,s118]) ).
cnf(s123,plain,
spl52_58,
inference(rat,[],[s105,s118,s119,s114,s120]) ).
cnf(s124,plain,
$false,
inference(rat,[],[s108,s123,s118,s115,s116,s122,s121]) ).
thf(f3106,plain,
$false,
inference(avatar_sat_refutation,[],[s124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP111^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 19:55:16 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.56/1.13 % (563892)Will run a generic schedule for satisfiability detection.
% 5.56/1.13 % (563898)% WARNING: option uhcvi not known.
% 5.56/1.13 % (563898)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2869770540:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.56/1.13 % (563900)dis+10_1_sil=32000:sp=arity:random_seed=1727429429:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.56/1.13 % (563899)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3995410134:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.56/1.13 % (563897)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=36774867_2999 on theBenchmark for (2999ds/0Mi)
% 5.56/1.13 % (563898)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.56/1.13 % (563903)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1937251816:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.56/1.13 % (563898)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.56/1.13 % Exception at run slice level
% 5.56/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.56/1.13 % (563902)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1563218139:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.56/1.13 % (563901)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1217268177:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.56/1.13 % (563901)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.56/1.13 % (563909)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=329778996:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.56/1.13 % Exception at run slice level
% 5.56/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.56/1.13 % (563900)Instruction limit reached!
% 5.56/1.13 % (563900)------------------------------
% 5.56/1.13 % (563900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.56/1.13 % (563900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.13 % (563900)CaDiCaL version: 2.1.3
% 5.56/1.13 % (563900)Termination reason: Instruction limit
% 5.56/1.13 % (563900)Termination phase: Saturation
% 5.56/1.13 % (563900)Time elapsed: 0.051 s
% 5.56/1.13 % (563900)Peak memory usage: 12 MB
% 5.56/1.13 % (563900)Instructions burned: 103 (million)
% 5.56/1.13 % (563913)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=676475790:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.56/1.13 % (563914)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3921550562:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.56/1.13 % (563901)Instruction limit reached!
% 5.56/1.13 % (563901)------------------------------
% 5.56/1.13 % (563901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.56/1.13 % (563901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.13 % (563901)CaDiCaL version: 2.1.3
% 5.56/1.13 % (563901)Termination reason: Instruction limit
% 5.56/1.13 % (563901)Termination phase: Saturation
% 5.56/1.13 % (563901)Time elapsed: 0.051 s
% 5.56/1.13 % (563901)Peak memory usage: 13 MB
% 5.56/1.13 % (563901)Instructions burned: 116 (million)
% 5.56/1.13 % (563914)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.56/1.13 % (563902)Instruction limit reached!
% 5.56/1.13 % (563902)------------------------------
% 5.56/1.13 % (563902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.56/1.13 % (563902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.13 % (563902)CaDiCaL version: 2.1.3
% 5.56/1.13 % (563902)Termination reason: Instruction limit
% 5.56/1.13 % (563902)Termination phase: Saturation
% 5.56/1.13 % (563902)Time elapsed: 0.064 s
% 5.56/1.13 % (563902)Peak memory usage: 13 MB
% 5.56/1.13 % (563902)Instructions burned: 132 (million)
% 5.56/1.13 % (563914)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.56/1.13 % (563917)ott-21_1_sil=16000:fs=off:random_seed=3426383276:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 5.56/1.13 % (563903)Instruction limit reached!
% 5.56/1.13 % (563903)------------------------------
% 5.56/1.13 % (563903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.56/1.13 % (563903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.13 % (563903)CaDiCaL version: 2.1.3
% 5.56/1.13 % (563903)Termination reason: Instruction limit
% 5.56/1.13 % (563903)Termination phase: Saturation
% 5.56/1.13 % (563903)Time elapsed: 0.107 s
% 5.56/1.13 % (563903)Peak memory usage: 13 MB
% 5.56/1.13 % (563903)Instructions burned: 159 (million)
% 5.56/1.13 % (563918)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2034075723:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.56/1.13 % (563913)Instruction limit reached!
% 5.56/1.13 % (563913)------------------------------
% 5.56/1.13 % (563913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.56/1.13 % (563913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.13 % (563913)CaDiCaL version: 2.1.3
% 5.56/1.13 % (563913)Termination reason: Instruction limit
% 5.56/1.13 % (563913)Termination phase: Saturation
% 5.56/1.13 % (563913)Time elapsed: 0.069 s
% 5.56/1.13 % (563913)Peak memory usage: 12 MB
% 5.56/1.13 % (563913)Instructions burned: 133 (million)
% 5.56/1.13 % (563920)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4240310671:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.56/1.13 % (563922)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1610300080:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.56/1.13 % Exception at run slice level
% 5.56/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.56/1.13 % (563925)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2352478055:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 5.56/1.13 % Exception at run slice level
% 5.56/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.56/1.13 % (563927)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2680804912:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 5.56/1.13 % (563917)Instruction limit reached!
% 5.56/1.13 % (563917)------------------------------
% 5.56/1.13 % (563917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.56/1.13 % (563917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.13 % (563917)CaDiCaL version: 2.1.3
% 5.56/1.13 % (563917)Termination reason: Instruction limit
% 5.56/1.13 % (563917)Termination phase: Saturation
% 5.56/1.13 % (563917)Time elapsed: 0.112 s
% 5.56/1.13 % (563917)Peak memory usage: 12 MB
% 5.56/1.13 % (563917)Instructions burned: 182 (million)
% 5.56/1.13 % (563927)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.56/1.13 % (563929)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4076102295:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 5.56/1.13 % (563929)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.56/1.13 % (563918)Instruction limit reached!
% 5.56/1.13 % (563918)------------------------------
% 5.56/1.13 % (563918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.56/1.13 % (563918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.13 % (563918)CaDiCaL version: 2.1.3
% 5.56/1.13 % (563918)Termination reason: Instruction limit
% 5.56/1.13 % (563918)Termination phase: Saturation
% 5.56/1.13 % (563918)Time elapsed: 0.263 s
% 5.56/1.13 % (563918)Peak memory usage: 13 MB
% 5.56/1.13 % (563918)Instructions burned: 477 (million)
% 5.56/1.13 % (563931)fmb+10_1_sil=64000:random_seed=1345155147:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 5.56/1.13 % (563931)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.56/1.13 % Exception at run slice level
% 5.56/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.56/1.13 % (563934)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3343128401:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 5.56/1.13 % Exception at run slice level
% 5.56/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.56/1.13 % (563936)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2876776309:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 5.56/1.13 % Exception at run slice level
% 5.56/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.56/1.13 % (563938)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1793095161:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 5.56/1.13 % (563938)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.56/1.13 % (563927)Instruction limit reached!
% 5.56/1.13 % (563927)------------------------------
% 5.56/1.13 % (563927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.56/1.13 % (563927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.13 % (563927)CaDiCaL version: 2.1.3
% 5.56/1.13 % (563927)Termination reason: Instruction limit
% 5.56/1.13 % (563927)Termination phase: Saturation
% 5.56/1.13 % (563927)Time elapsed: 0.338 s
% 5.56/1.13 % (563927)Peak memory usage: 15 MB
% 5.56/1.13 % (563927)Instructions burned: 694 (million)
% 5.56/1.13 % (563914)Instruction limit reached!
% 5.56/1.13 % (563914)------------------------------
% 5.56/1.13 % (563914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.56/1.13 % (563914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.13 % (563914)CaDiCaL version: 2.1.3
% 5.56/1.13 % (563914)Termination reason: Instruction limit
% 5.56/1.13 % (563914)Termination phase: Saturation
% 5.56/1.13 % (563914)Time elapsed: 0.483 s
% 5.56/1.13 % (563914)Peak memory usage: 14 MB
% 5.56/1.13 % (563914)Instructions burned: 685 (million)
% 5.56/1.13 % (563940)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=914377932:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 5.56/1.13 % (563941)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=655971684:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 5.56/1.13 % (563940)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.56/1.13 % (563940)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.56/1.13 % Exception at run slice level
% 5.56/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.56/1.13 % (563944)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3413268154:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 5.56/1.13 % Exception at run slice level
% 5.56/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.56/1.13 % (563946)ott-2_1_sil=16000:newcnf=on:random_seed=2261996352:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 5.56/1.13 % (563946)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.56/1.13 % (563929)Instruction limit reached!
% 5.56/1.13 % (563929)------------------------------
% 5.56/1.13 % (563929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.56/1.13 % (563929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.13 % (563929)CaDiCaL version: 2.1.3
% 5.56/1.13 % (563929)Termination reason: Instruction limit
% 5.56/1.13 % (563929)Termination phase: Saturation
% 5.56/1.13 % (563929)Time elapsed: 0.533 s
% 5.56/1.13 % (563929)Peak memory usage: 17 MB
% 5.56/1.13 % (563929)Instructions burned: 879 (million)
% 5.56/1.13 % (563948)ott+10_1_sil=32000:tgt=ground:random_seed=2504234347:i=5114:av=off_2991 on theBenchmark for (2991ds/5114Mi)
% 5.56/1.13 % (563946) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-563892-563946"...
% 5.56/1.13 % (563946)...printing done.
% 5.56/1.13 % (563946)Refutation found. Thanks to Tanya!
% 5.56/1.13 % SZS status Theorem for theBenchmark
% 5.56/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 5.56/1.13 % (563946)------------------------------
% 5.56/1.13 % (563946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.56/1.13 % (563946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.13 % (563946)CaDiCaL version: 2.1.3
% 5.56/1.13 % (563946)Termination reason: Refutation
% 5.56/1.13 % (563946)Time elapsed: 0.224 s
% 5.56/1.13 % (563946)Peak memory usage: 14 MB
% 5.56/1.13 % (563946)Instructions burned: 261 (million)
% 5.56/1.13 % (563892)Success in time 0.91 s
% 5.56/1.13 % Vampire exiting
%------------------------------------------------------------------------------