%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP201^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:05:49 AM UTC 2026
% Result : Theorem 17.28s 2.87s
% Output : CNFRefutation 17.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 12 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 682 ( 31 ~; 25 |; 3 &; 616 @)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 77 ( 23 ^; 54 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
variable: $tType ).
thf(decl_sort2,type,
real: $tType ).
thf(decl_sort3,type,
set_variable: $tType ).
thf(decl_sort4,type,
denotational_interp: $tType ).
thf(decl_sort5,type,
game: $tType ).
thf(decl_sort6,type,
set_variable_real: $tType ).
thf(decl_sort7,type,
produc1078154247n_game: $tType ).
thf(decl_sort8,type,
option_game: $tType ).
thf(decl_sort9,type,
produc735959047riable: $tType ).
thf(decl_sort10,type,
produc1418842292n_game: $tType ).
thf(decl_24,type,
denota1245701238me_sem: denotational_interp > game > set_variable_real > set_variable_real ).
thf(decl_25,type,
uminus970116630real_o: ( ( variable > real ) > $o ) > ( variable > real ) > $o ).
thf(decl_33,type,
uminus430703407e_real: set_variable_real > set_variable_real ).
thf(decl_39,type,
the_game: option_game > game ).
thf(decl_52,type,
produc884810027riable: produc735959047riable > option_game ).
thf(decl_61,type,
produc293487213n_game: produc1078154247n_game > option_game ).
thf(decl_65,type,
produc354409183n_game: produc1078154247n_game > produc735959047riable ).
thf(decl_66,type,
collec633296133e_real: ( ( variable > real ) > $o ) > set_variable_real ).
thf(decl_71,type,
dual: game > game ).
thf(decl_76,type,
uSubst1599435252djoint: produc1418842292n_game > denotational_interp > ( variable > real ) > denotational_interp ).
thf(decl_77,type,
uSubst516392814stappp: produc1418842292n_game > set_variable > game > produc1078154247n_game ).
thf(decl_78,type,
member_variable_real: ( variable > real ) > set_variable_real > $o ).
thf(decl_81,type,
i: denotational_interp ).
thf(decl_83,type,
ua: set_variable ).
thf(decl_84,type,
xa: set_variable_real ).
thf(decl_85,type,
alpha: game ).
thf(decl_87,type,
nu2: variable > real ).
thf(decl_89,type,
omega2: variable > real ).
thf(decl_90,type,
sigma: produc1418842292n_game ).
thf(fact_13_Compl__iff,axiom,
! [X14: variable > real,X15: set_variable_real] :
( ( member_variable_real @ X14 @ ( uminus430703407e_real @ X15 ) )
<=> ~ ( member_variable_real @ X14 @ X15 ) ),
file('/export/starexec/sandbox/tmp/tmp.bjf7f90hRw/E---3.1_3157191.p',fact_13_Compl__iff) ).
thf(fact_55_uminus__set__def,axiom,
( uminus430703407e_real
= ( ^ [X77: set_variable_real] :
( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [X78: variable > real] : ( member_variable_real @ X78 @ X77 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bjf7f90hRw/E---3.1_3157191.p',fact_55_uminus__set__def) ).
thf(fact_35_game__sem_Osimps_I7_J,axiom,
! [X48: denotational_interp,X38: game] :
( ( denota1245701238me_sem @ X48 @ ( dual @ X38 ) )
= ( ^ [X49: set_variable_real] : ( uminus430703407e_real @ ( denota1245701238me_sem @ X48 @ X38 @ ( uminus430703407e_real @ X49 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bjf7f90hRw/E---3.1_3157191.p',fact_35_game__sem_Osimps_I7_J) ).
thf(conj_0,conjecture,
( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
<=> ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bjf7f90hRw/E---3.1_3157191.p',conj_0) ).
thf(fact_10_ComplI,axiom,
! [X10: variable > real,X11: set_variable_real] :
( ~ ( member_variable_real @ X10 @ X11 )
=> ( member_variable_real @ X10 @ ( uminus430703407e_real @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bjf7f90hRw/E---3.1_3157191.p',fact_10_ComplI) ).
thf(fact_244_fst__swap,axiom,
! [X501: produc1078154247n_game] :
( ( produc884810027riable @ ( produc354409183n_game @ X501 ) )
= ( produc293487213n_game @ X501 ) ),
file('/export/starexec/sandbox/tmp/tmp.bjf7f90hRw/E---3.1_3157191.p',fact_244_fst__swap) ).
thf(fact_0__092_060open_062_092_060And_062X_O_A_I_092_060nu_062_A_092_060in_062_Agame__sem_AI_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_AX_J_A_061_A_I_092_060nu_062_A_092_060in_062_Agame__sem_A_IUSubst__Mirabelle__vidvnmlwwz_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062,axiom,
! [X1: set_variable_real] :
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X1 ) )
<=> ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bjf7f90hRw/E---3.1_3157191.p',fact_0__092_060open_062_092_060And_062X_O_A_I_092_060nu_062_A_092_060in_062_Agame__sem_AI_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_AX_J_A_061_A_I_092_060nu_062_A_092_060in_062_Agame__sem_A_IUSubst__Mirabelle__vidvnmlwwz_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062) ).
thf(c_0_7,plain,
! [X14: variable > real,X15: set_variable_real] :
( ( member_variable_real @ X14 @ ( uminus430703407e_real @ X15 ) )
<=> ~ ( member_variable_real @ X14 @ X15 ) ),
inference(fof_simplification,[status(thm)],[fact_13_Compl__iff]) ).
thf(c_0_8,plain,
! [X1573: set_variable_real] :
( ( uminus430703407e_real @ X1573 )
= ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] : ( member_variable_real @ Z0 @ X1573 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_55_uminus__set__def])]) ).
thf(c_0_9,plain,
! [X48: denotational_interp,X38: game,X1566: set_variable_real] :
( ( denota1245701238me_sem @ X48 @ ( dual @ X38 ) @ X1566 )
= ( uminus430703407e_real @ ( denota1245701238me_sem @ X48 @ X38 @ ( uminus430703407e_real @ X1566 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_35_game__sem_Osimps_I7_J])]) ).
thf(c_0_10,negated_conjecture,
~ ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
<=> ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_11,plain,
! [X10: variable > real,X11: set_variable_real] :
( ~ ( member_variable_real @ X10 @ X11 )
=> ( member_variable_real @ X10 @ ( uminus430703407e_real @ X11 ) ) ),
inference(fof_simplification,[status(thm)],[fact_10_ComplI]) ).
thf(c_0_12,plain,
! [X1658: variable > real,X1659: set_variable_real] :
( ( ~ ( member_variable_real @ X1658 @ ( uminus430703407e_real @ X1659 ) )
| ~ ( member_variable_real @ X1658 @ X1659 ) )
& ( ( member_variable_real @ X1658 @ X1659 )
| ( member_variable_real @ X1658 @ ( uminus430703407e_real @ X1659 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
thf(c_0_13,plain,
! [X1752: set_variable_real] :
( ( uminus430703407e_real @ X1752 )
= ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] : ( member_variable_real @ Z0 @ X1752 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
! [X1696: denotational_interp,X1697: game,X1698: set_variable_real] :
( ( denota1245701238me_sem @ X1696 @ ( dual @ X1697 ) @ X1698 )
= ( uminus430703407e_real @ ( denota1245701238me_sem @ X1696 @ X1697 @ ( uminus430703407e_real @ X1698 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
( ( ~ ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
| ~ ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) )
& ( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
| ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
thf(c_0_16,plain,
! [X2296: produc1078154247n_game] :
( ( produc884810027riable @ ( produc354409183n_game @ X2296 ) )
= ( produc293487213n_game @ X2296 ) ),
inference(variable_rename,[status(thm)],[fact_244_fst__swap]) ).
thf(c_0_17,plain,
! [X1652: variable > real,X1653: set_variable_real] :
( ( member_variable_real @ X1652 @ X1653 )
| ( member_variable_real @ X1652 @ ( uminus430703407e_real @ X1653 ) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
thf(c_0_18,plain,
! [X10: variable > real,X1: set_variable_real] :
( ~ ( member_variable_real @ X10 @ ( uminus430703407e_real @ X1 ) )
| ~ ( member_variable_real @ X10 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,plain,
! [X1: set_variable_real] :
( ( uminus430703407e_real @ X1 )
= ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] : ( member_variable_real @ Z0 @ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_20,plain,
! [X48: denotational_interp,X38: game,X1: set_variable_real] :
( ( denota1245701238me_sem @ X48 @ ( dual @ X38 ) @ X1 )
= ( uminus430703407e_real @ ( denota1245701238me_sem @ X48 @ X38 @ ( uminus430703407e_real @ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_21,negated_conjecture,
( ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
| ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_22,plain,
! [X6: produc1078154247n_game] :
( ( produc884810027riable @ ( produc354409183n_game @ X6 ) )
= ( produc293487213n_game @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_23,negated_conjecture,
( ~ ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ ( uminus430703407e_real @ xa ) ) ) )
| ~ ( member_variable_real @ nu2 @ ( uminus430703407e_real @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ ( uminus430703407e_real @ xa ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_24,plain,
! [X10: variable > real,X1: set_variable_real] :
( ( member_variable_real @ X10 @ X1 )
| ( member_variable_real @ X10 @ ( uminus430703407e_real @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,plain,
! [X10: variable > real,X1: set_variable_real] :
( ~ ( member_variable_real @ X10 @ X1 )
| ~ ( member_variable_real @ X10
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] : ( member_variable_real @ Z0 @ X1 ) ) ) ) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_26,plain,
! [X48: denotational_interp,X38: game,X1: set_variable_real] :
( ( denota1245701238me_sem @ X48 @ ( dual @ X38 ) @ X1 )
= ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] :
( member_variable_real @ Z0
@ ( denota1245701238me_sem @ X48 @ X38
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z1: variable > real] : ( member_variable_real @ Z1 @ X1 ) ) ) ) ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_19]),c_0_19]) ).
thf(c_0_27,negated_conjecture,
( ( member_variable_real @ nu2
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] :
( member_variable_real @ Z0
@ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z1: variable > real] : ( member_variable_real @ Z1 @ xa ) ) ) ) ) ) ) )
| ( member_variable_real @ nu2
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] :
( member_variable_real @ Z0
@ ( denota1245701238me_sem @ i @ ( the_game @ ( produc884810027riable @ ( produc354409183n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) )
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z1: variable > real] : ( member_variable_real @ Z1 @ xa ) ) ) ) ) ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
thf(c_0_28,plain,
! [X1642: set_variable_real] :
( ( ~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X1642 ) )
| ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X1642 ) ) )
& ( ~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X1642 ) )
| ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X1642 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0__092_060open_062_092_060And_062X_O_A_I_092_060nu_062_A_092_060in_062_Agame__sem_AI_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_AX_J_A_061_A_I_092_060nu_062_A_092_060in_062_Agame__sem_A_IUSubst__Mirabelle__vidvnmlwwz_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062])])]) ).
thf(c_0_29,negated_conjecture,
( ~ ( member_variable_real @ nu2
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] :
( member_variable_real @ Z0
@ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z1: variable > real] : ( member_variable_real @ Z1 @ xa ) ) ) ) ) ) ) )
| ~ ( member_variable_real @ nu2
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] :
( member_variable_real @ Z0
@ ( denota1245701238me_sem @ i @ ( the_game @ ( produc884810027riable @ ( produc354409183n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) )
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z1: variable > real] : ( member_variable_real @ Z1 @ xa ) ) ) ) ) ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_22]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
thf(c_0_30,plain,
! [X10: variable > real,X1: set_variable_real] :
( ( member_variable_real @ X10 @ X1 )
| ( member_variable_real @ X10
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] : ( member_variable_real @ Z0 @ X1 ) ) ) ) ),
inference(rw,[status(thm)],[c_0_24,c_0_19]) ).
thf(c_0_31,plain,
! [X48: denotational_interp,X38: game,X10: variable > real,X1: set_variable_real] :
( ~ ( member_variable_real @ X10
@ ( denota1245701238me_sem @ X48 @ X38
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] : ( member_variable_real @ Z0 @ X1 ) ) ) ) )
| ~ ( member_variable_real @ X10 @ ( denota1245701238me_sem @ X48 @ ( dual @ X38 ) @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_32,negated_conjecture,
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( dual @ ( the_game @ ( produc884810027riable @ ( produc354409183n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ xa ) )
| ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ ( dual @ alpha ) @ xa ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_26]),c_0_26]) ).
thf(c_0_33,plain,
! [X1: set_variable_real] :
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X1 ) )
| ~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_34,plain,
! [X1: set_variable_real] :
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc293487213n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) @ X1 ) )
| ~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_35,negated_conjecture,
( ~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( dual @ ( the_game @ ( produc884810027riable @ ( produc354409183n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ xa ) )
| ~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ ( dual @ alpha ) @ xa ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_26]),c_0_26]) ).
thf(c_0_36,plain,
! [X48: denotational_interp,X38: game,X10: variable > real,X1: set_variable_real] :
( ( member_variable_real @ X10
@ ( denota1245701238me_sem @ X48 @ X38
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] : ( member_variable_real @ Z0 @ X1 ) ) ) ) )
| ( member_variable_real @ X10 @ ( denota1245701238me_sem @ X48 @ ( dual @ X38 ) @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
thf(c_0_37,negated_conjecture,
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( dual @ ( the_game @ ( produc884810027riable @ ( produc354409183n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ xa ) )
| ~ ( member_variable_real @ nu2
@ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] : ( member_variable_real @ Z0 @ xa ) ) ) ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_38,plain,
! [X1: set_variable_real] :
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X1 ) )
| ~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc884810027riable @ ( produc354409183n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ X1 ) ) ),
inference(rw,[status(thm)],[c_0_33,c_0_22]) ).
thf(c_0_39,plain,
! [X1: set_variable_real] :
( ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( the_game @ ( produc884810027riable @ ( produc354409183n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) @ X1 ) )
| ~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha @ X1 ) ) ),
inference(rw,[status(thm)],[c_0_34,c_0_22]) ).
thf(c_0_40,negated_conjecture,
( ( member_variable_real @ nu2
@ ( denota1245701238me_sem @ ( uSubst1599435252djoint @ sigma @ i @ omega2 ) @ alpha
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] : ( member_variable_real @ Z0 @ xa ) ) ) ) )
| ~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( dual @ ( the_game @ ( produc884810027riable @ ( produc354409183n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ xa ) ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_41,negated_conjecture,
~ ( member_variable_real @ nu2
@ ( denota1245701238me_sem @ i @ ( the_game @ ( produc884810027riable @ ( produc354409183n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) )
@ ( collec633296133e_real
@ ( uminus970116630real_o
@ ^ [Z0: variable > real] : ( member_variable_real @ Z0 @ xa ) ) ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31]) ).
thf(c_0_42,negated_conjecture,
~ ( member_variable_real @ nu2 @ ( denota1245701238me_sem @ i @ ( dual @ ( the_game @ ( produc884810027riable @ ( produc354409183n_game @ ( uSubst516392814stappp @ sigma @ ua @ alpha ) ) ) ) ) @ xa ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
thf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_36]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP201^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n014.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 20:10:44 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.27 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.bjf7f90hRw/E---3.1_3157191.p
% 17.28/2.87 % Version: 3.5.1-ho
% 17.28/2.87 % Preprocessing class: HSLSSMSMSSLNHSA.
% 17.28/2.87 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 17.28/2.87 % Starting ho_unfolding_8 with 900s (3) cores
% 17.28/2.87 % Starting new_bool_8 with 300s (1) cores
% 17.28/2.87 % Starting post_as_ho6 with 300s (1) cores
% 17.28/2.87 % Starting ho_unfolding_1 with 300s (1) cores
% 17.28/2.87 % Starting full_lambda_4 with 300s (1) cores
% 17.28/2.87 % Starting pre_casc_5 with 300s (1) cores
% 17.28/2.87 % ho_unfolding_8 with pid 3157204 completed with status 0
% 17.28/2.87 % Result found by ho_unfolding_8
% 17.28/2.87 % Preprocessing class: HSLSSMSMSSLNHSA.
% 17.28/2.87 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 17.28/2.87 % Starting ho_unfolding_8 with 900s (3) cores
% 17.28/2.87 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.28/2.87 % No SInE strategy applied
% 17.28/2.87 % Search class: HGHSM-FSLM32-DHSFFSBN
% 17.28/2.87 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 17.28/2.87 % Starting SubtermCWHack with 82s (1) cores
% 17.28/2.87 % Starting ho_unfolding_8 with 91s (1) cores
% 17.28/2.87 % Starting sh4l with 129s (1) cores
% 17.28/2.87 % ho_unfolding_8 with pid 3157215 completed with status 0
% 17.28/2.87 % Result found by ho_unfolding_8
% 17.28/2.87 % Preprocessing class: HSLSSMSMSSLNHSA.
% 17.28/2.87 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 17.28/2.87 % Starting ho_unfolding_8 with 900s (3) cores
% 17.28/2.87 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.28/2.87 % No SInE strategy applied
% 17.28/2.87 % Search class: HGHSM-FSLM32-DHSFFSBN
% 17.28/2.87 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 17.28/2.87 % Starting SubtermCWHack with 82s (1) cores
% 17.28/2.87 % Starting ho_unfolding_8 with 91s (1) cores
% 17.28/2.87 % Preprocessing time : 0.319 s
% 17.28/2.87 % Presaturation interreduction done
% 17.28/2.87
% 17.28/2.87 % Proof found!
% 17.28/2.87 % SZS status Theorem
% 17.28/2.87 % SZS output start CNFRefutation
% See solution above
% 17.28/2.87 % Parsed axioms : 438
% 17.28/2.87 % Removed by relevancy pruning/SinE : 0
% 17.28/2.87 % Initial clauses : 637
% 17.28/2.87 % Removed in clause preprocessing : 120
% 17.28/2.87 % Initial clauses in saturation : 517
% 17.28/2.87 % Processed clauses : 3700
% 17.28/2.87 % ...of these trivial : 231
% 17.28/2.87 % ...subsumed : 1315
% 17.28/2.87 % ...remaining for further processing : 2154
% 17.28/2.87 % Other redundant clauses eliminated : 468
% 17.28/2.87 % Clauses deleted for lack of memory : 0
% 17.28/2.87 % Backward-subsumed : 90
% 17.28/2.87 % Backward-rewritten : 69
% 17.28/2.87 % Generated clauses : 35116
% 17.28/2.87 % ...of the previous two non-redundant : 32640
% 17.28/2.87 % ...aggressively subsumed : 0
% 17.28/2.87 % Contextual simplify-reflections : 5
% 17.28/2.87 % Paramodulations : 32902
% 17.28/2.87 % Factorizations : 13
% 17.28/2.87 % NegExts : 403
% 17.28/2.87 % Equation resolutions : 637
% 17.28/2.87 % Disequality decompositions : 0
% 17.28/2.87 % Total rewrite steps : 7305
% 17.28/2.87 % ...of those cached : 5702
% 17.28/2.87 % Propositional unsat checks : 0
% 17.28/2.87 % Propositional check models : 0
% 17.28/2.87 % Propositional check unsatisfiable : 0
% 17.28/2.87 % Propositional clauses : 0
% 17.28/2.87 % Propositional clauses after purity: 0
% 17.28/2.87 % Propositional unsat core size : 0
% 17.28/2.87 % Propositional preprocessing time : 0.000
% 17.28/2.87 % Propositional encoding time : 0.000
% 17.28/2.87 % Propositional solver time : 0.000
% 17.28/2.87 % Success case prop preproc time : 0.000
% 17.28/2.87 % Success case prop encoding time : 0.000
% 17.28/2.87 % Success case prop solver time : 0.000
% 17.28/2.87 % Current number of processed clauses : 1591
% 17.28/2.87 % Positive orientable unit clauses : 292
% 17.28/2.87 % Positive unorientable unit clauses: 4
% 17.28/2.87 % Negative unit clauses : 15
% 17.28/2.87 % Non-unit-clauses : 1280
% 17.28/2.87 % Current number of unprocessed clauses: 29683
% 17.28/2.87 % ...number of literals in the above : 81371
% 17.28/2.87 % Current number of archived formulas : 0
% 17.28/2.87 % Current number of archived clauses : 514
% 17.28/2.87 % Clause-clause subsumption calls (NU) : 340972
% 17.28/2.87 % Rec. Clause-clause subsumption calls : 268552
% 17.28/2.87 % Non-unit clause-clause subsumptions : 1358
% 17.28/2.87 % Unit Clause-clause subsumption calls : 14327
% 17.28/2.87 % Rewrite failures with RHS unbound : 0
% 17.28/2.87 % BW rewrite match attempts : 4611
% 17.28/2.87 % BW rewrite match successes : 105
% 17.28/2.87 % Condensation attempts : 0
% 17.28/2.87 % Condensation successes : 0
% 17.28/2.87 % Termbank termtop insertions : 2377961
% 17.28/2.87 % Search garbage collected termcells : 11991
% 17.28/2.87
% 17.28/2.87 % -------------------------------------------------
% 17.28/2.87 % User time : 2.377 s
% 17.28/2.87 % System time : 0.099 s
% 17.28/2.87 % Total time : 2.477 s
% 17.28/2.87 % Maximum resident set size: 6892 pages
% 17.28/2.87
% 17.28/2.87 % -------------------------------------------------
% 17.28/2.87 % User time : 7.031 s
% 17.28/2.87 % System time : 0.240 s
% 17.28/2.87 % Total time : 7.271 s
% 17.28/2.87 % Maximum resident set size: 5632 pages
% 17.28/2.87 % E exiting
%------------------------------------------------------------------------------