%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET660+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Thu Sep 24 02:17:53 PM UTC 2026
% Result : Theorem 0.75s 0.54s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 83 ( 12 unt; 0 def)
% Number of atoms : 349 ( 37 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 442 ( 176 ~; 184 |; 31 &)
% ( 10 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 152 ( 9 sgn 70 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p24,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(p23,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(power_set(X1),set_type)
& ~ empty(power_set(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
fof(p34,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).
fof(p17,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
fof(p32,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> range(X1,X2,X3) = range_of(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p32) ).
fof(prove_relset_1_23,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( ! [X4] :
( ilf_type(X4,set_type)
=> ( member(X4,X2)
=> ? [X5] :
( member(ordered_pair(X5,X4),X3)
& ilf_type(X5,set_type) ) ) )
<=> range(X1,X2,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_23) ).
fof(p22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(p33,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ilf_type(range(X1,X2,X3),subset_type(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
fof(p19,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X1 = X2
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
<=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,range_of(X1))
<=> ? [X3] :
( member(ordered_pair(X3,X2),X1)
& ilf_type(X3,set_type) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(p15,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( ilf_type(X1,set_type)
& relation_like(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(c_0_13,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p24]) ).
fof(c_0_14,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(power_set(X1),set_type)
& ~ empty(power_set(X1)) ) ),
inference(fof_simplification,[status(thm)],[p23]) ).
fof(c_0_15,plain,
! [X61,X62] :
( ( ~ ilf_type(X61,set_type)
| ~ ilf_type(X62,set_type)
| empty(X62)
| ilf_type(X61,member_type(X62))
| ~ member(X61,X62) )
& ( ~ ilf_type(X61,set_type)
| ~ ilf_type(X62,set_type)
| empty(X62)
| member(X61,X62)
| ~ ilf_type(X61,member_type(X62)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])]) ).
fof(c_0_16,plain,
! [X91] : ilf_type(X91,set_type),
inference(variable_rename,[status(thm)],[p34]) ).
fof(c_0_17,plain,
! [X43,X44] :
( ( ~ ilf_type(X43,set_type)
| ~ ilf_type(X44,set_type)
| ilf_type(X44,subset_type(X43))
| ~ ilf_type(X44,member_type(power_set(X43))) )
& ( ~ ilf_type(X43,set_type)
| ~ ilf_type(X44,set_type)
| ilf_type(X44,member_type(power_set(X43)))
| ~ ilf_type(X44,subset_type(X43)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])])])]) ).
fof(c_0_18,plain,
! [X60] :
( ( ~ ilf_type(X60,set_type)
| ilf_type(power_set(X60),set_type) )
& ( ~ ilf_type(X60,set_type)
| ~ empty(power_set(X60)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_19,plain,
! [X85,X86,X87] :
( range(X85,X86,X87) = range_of(X87)
| ~ ilf_type(X87,relation_type(X85,X86))
| ~ ilf_type(X86,set_type)
| ~ ilf_type(X85,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p32])])])]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( ! [X4] :
( ilf_type(X4,set_type)
=> ( member(X4,X2)
=> ? [X5] :
( member(ordered_pair(X5,X4),X3)
& ilf_type(X5,set_type) ) ) )
<=> range(X1,X2,X3) = X2 ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_23]) ).
fof(c_0_21,plain,
! [X56,X57,X58] :
( ( ~ ilf_type(X56,set_type)
| ~ ilf_type(X57,set_type)
| member(X56,power_set(X57))
| ~ member(esk8_2(X56,X57),X57) )
& ( ~ ilf_type(X56,set_type)
| ~ ilf_type(X57,set_type)
| member(X56,power_set(X57))
| member(esk8_2(X56,X57),X56) )
& ( ~ ilf_type(X56,set_type)
| ~ ilf_type(X57,set_type)
| member(X56,power_set(X57))
| ilf_type(esk8_2(X56,X57),set_type) )
& ( ~ ilf_type(X56,set_type)
| ~ ilf_type(X57,set_type)
| member(X58,X57)
| ~ member(X58,X56)
| ~ ilf_type(X58,set_type)
| ~ member(X56,power_set(X57)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p22])])])])])]) ).
cnf(c_0_22,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,member_type(X2))
| empty(X2)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X2))
| ilf_type(X1,member_type(power_set(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_26,plain,
! [X88,X89,X90] :
( ilf_type(range(X88,X89,X90),subset_type(X89))
| ~ ilf_type(X90,relation_type(X88,X89))
| ~ ilf_type(X89,set_type)
| ~ ilf_type(X88,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p33])])])]) ).
cnf(c_0_27,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| range(X1,X2,X3) = range_of(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_28,negated_conjecture,
! [X96,X97] :
( ( range(esk14_0,esk15_0,esk16_0) = esk15_0
| ~ ilf_type(X97,set_type)
| ~ member(X97,esk15_0)
| member(ordered_pair(esk18_1(X97),X97),esk16_0) )
& ( range(esk14_0,esk15_0,esk16_0) = esk15_0
| ~ ilf_type(X97,set_type)
| ~ member(X97,esk15_0)
| ilf_type(esk18_1(X97),set_type) )
& ( range(esk14_0,esk15_0,esk16_0) != esk15_0
| ~ member(ordered_pair(X96,esk17_0),esk16_0)
| ~ ilf_type(X96,set_type) )
& ( range(esk14_0,esk15_0,esk16_0) != esk15_0
| member(esk17_0,esk15_0) )
& ( range(esk14_0,esk15_0,esk16_0) != esk15_0
| ilf_type(esk17_0,set_type) )
& ilf_type(esk16_0,relation_type(esk14_0,esk15_0))
& ilf_type(esk15_0,set_type)
& ilf_type(esk14_0,set_type) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])])]) ).
cnf(c_0_29,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X1,power_set(X2))
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( ~ ilf_type(X2,member_type(X1))
| member(X2,X1)
| empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23])]) ).
cnf(c_0_31,plain,
( ~ ilf_type(X1,subset_type(X2))
| ilf_type(X1,member_type(power_set(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_23]),c_0_23])]) ).
cnf(c_0_32,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_23])]) ).
cnf(c_0_33,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(range(X1,X2,X3),subset_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| range(X1,X2,X3) = range_of(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_23]),c_0_23])]) ).
cnf(c_0_35,negated_conjecture,
ilf_type(esk16_0,relation_type(esk14_0,esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( ~ member(X1,X3)
| ~ member(X3,power_set(X2))
| member(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_37,plain,
( ~ ilf_type(X1,subset_type(X2))
| member(X1,power_set(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_38,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ilf_type(range(X1,X2,X3),subset_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_23]),c_0_23])]) ).
cnf(c_0_39,negated_conjecture,
range(esk14_0,esk15_0,esk16_0) = range_of(esk16_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_40,plain,
! [X47,X48,X49] :
( ( ~ ilf_type(X47,set_type)
| ~ ilf_type(X48,set_type)
| X47 = X48
| member(esk6_2(X47,X48),X48)
| member(esk6_2(X47,X48),X47) )
& ( ~ ilf_type(X47,set_type)
| ~ ilf_type(X48,set_type)
| X47 = X48
| ~ member(esk6_2(X47,X48),X48)
| ~ member(esk6_2(X47,X48),X47) )
& ( ~ ilf_type(X47,set_type)
| ~ ilf_type(X48,set_type)
| X47 = X48
| ilf_type(esk6_2(X47,X48),set_type) )
& ( ~ ilf_type(X47,set_type)
| ~ ilf_type(X48,set_type)
| X47 != X48
| ~ ilf_type(X49,set_type)
| member(X49,X47)
| ~ member(X49,X48) )
& ( ~ ilf_type(X47,set_type)
| ~ ilf_type(X48,set_type)
| X47 != X48
| ~ ilf_type(X49,set_type)
| member(X49,X48)
| ~ member(X49,X47) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p19])])])])])]) ).
cnf(c_0_41,plain,
( ~ ilf_type(X3,subset_type(X2))
| ~ member(X1,X3)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
ilf_type(range_of(esk16_0),subset_type(esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_35])]) ).
cnf(c_0_43,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| X1 = X2
| member(esk6_2(X1,X2),X2)
| member(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( ~ member(X1,range_of(esk16_0))
| member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
( member(esk6_2(X1,X2),X2)
| member(esk6_2(X1,X2),X1)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_23]),c_0_23])]) ).
fof(c_0_46,plain,
! [X6,X7,X9] :
( ( ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X7,set_type)
| member(X7,range_of(X6))
| ~ member(ordered_pair(X9,X7),X6)
| ~ ilf_type(X9,set_type) )
& ( ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ member(X7,range_of(X6))
| member(ordered_pair(esk1_2(X6,X7),X7),X6) )
& ( ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ member(X7,range_of(X6))
| ilf_type(esk1_2(X6,X7),set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])])])]) ).
cnf(c_0_47,negated_conjecture,
( ~ ilf_type(X1,set_type)
| ~ member(X1,esk15_0)
| range(esk14_0,esk15_0,esk16_0) = esk15_0
| member(ordered_pair(esk18_1(X1),X1),esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_48,plain,
! [X72,X73,X74] :
( relation_like(X74)
| ~ ilf_type(X74,subset_type(cross_product(X72,X73)))
| ~ ilf_type(X73,set_type)
| ~ ilf_type(X72,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])])]) ).
fof(c_0_49,plain,
! [X24,X25,X26,X27] :
( ( ~ ilf_type(X24,set_type)
| ~ ilf_type(X25,set_type)
| ilf_type(X27,subset_type(cross_product(X24,X25)))
| ~ ilf_type(X27,relation_type(X24,X25)) )
& ( ~ ilf_type(X24,set_type)
| ~ ilf_type(X25,set_type)
| ilf_type(X26,relation_type(X24,X25))
| ~ ilf_type(X26,subset_type(cross_product(X24,X25))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])])]) ).
cnf(c_0_50,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk6_2(X1,X2),X2)
| ~ member(esk6_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,negated_conjecture,
( member(esk6_2(range_of(esk16_0),X1),X1)
| member(esk6_2(range_of(esk16_0),X1),esk15_0)
| range_of(esk16_0) = X1 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
( ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X1,set_type)
| member(X2,range_of(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( ~ member(X1,esk15_0)
| member(ordered_pair(esk18_1(X1),X1),esk16_0)
| range(esk14_0,esk15_0,esk16_0) = esk15_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_23])]) ).
fof(c_0_54,plain,
! [X41] :
( ( ~ ilf_type(X41,set_type)
| ilf_type(X41,binary_relation_type)
| ~ ilf_type(X41,set_type)
| ~ relation_like(X41) )
& ( ~ ilf_type(X41,set_type)
| ~ ilf_type(X41,binary_relation_type)
| ilf_type(X41,set_type) )
& ( ~ ilf_type(X41,set_type)
| ~ ilf_type(X41,binary_relation_type)
| relation_like(X41) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])]) ).
cnf(c_0_55,plain,
( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X3) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_56,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X3))
| ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,plain,
( ~ member(esk6_2(X1,X2),X1)
| ~ member(esk6_2(X1,X2),X2)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_23]),c_0_23])]) ).
cnf(c_0_58,negated_conjecture,
( member(esk6_2(range_of(esk16_0),esk15_0),esk15_0)
| range_of(esk16_0) = esk15_0 ),
inference(ef,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
( ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X3,X1),X2)
| member(X1,range_of(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_23]),c_0_23])]) ).
cnf(c_0_60,negated_conjecture,
( ~ member(X1,esk15_0)
| member(ordered_pair(esk18_1(X1),X1),esk16_0)
| range_of(esk16_0) = esk15_0 ),
inference(rw,[status(thm)],[c_0_53,c_0_39]) ).
cnf(c_0_61,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_62,plain,
( ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_23]),c_0_23])]) ).
cnf(c_0_63,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_23]),c_0_23])]) ).
cnf(c_0_64,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) != esk15_0
| ~ member(ordered_pair(X1,esk17_0),esk16_0)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_65,negated_conjecture,
( ~ member(esk6_2(range_of(esk16_0),esk15_0),range_of(esk16_0))
| range_of(esk16_0) = esk15_0 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( ~ ilf_type(esk16_0,binary_relation_type)
| ~ member(X1,esk15_0)
| member(X1,range_of(esk16_0))
| range_of(esk16_0) = esk15_0 ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_67,plain,
( ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_61]) ).
cnf(c_0_68,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| relation_like(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( ~ member(ordered_pair(X1,esk17_0),esk16_0)
| range(esk14_0,esk15_0,esk16_0) != esk15_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_23])]) ).
cnf(c_0_70,plain,
( ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ member(X2,range_of(X1))
| member(ordered_pair(esk1_2(X1,X2),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_71,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) != esk15_0
| member(esk17_0,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_72,negated_conjecture,
( ~ ilf_type(esk16_0,binary_relation_type)
| range_of(esk16_0) = esk15_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_58]) ).
cnf(c_0_73,plain,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_23])]) ).
cnf(c_0_74,negated_conjecture,
relation_like(esk16_0),
inference(spm,[status(thm)],[c_0_68,c_0_35]) ).
cnf(c_0_75,negated_conjecture,
( ~ member(ordered_pair(X1,esk17_0),esk16_0)
| range_of(esk16_0) != esk15_0 ),
inference(rw,[status(thm)],[c_0_69,c_0_39]) ).
cnf(c_0_76,plain,
( ~ ilf_type(X1,binary_relation_type)
| ~ member(X2,range_of(X1))
| member(ordered_pair(esk1_2(X1,X2),X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_23])]) ).
cnf(c_0_77,negated_conjecture,
( range_of(esk16_0) != esk15_0
| member(esk17_0,esk15_0) ),
inference(rw,[status(thm)],[c_0_71,c_0_39]) ).
cnf(c_0_78,negated_conjecture,
range_of(esk16_0) = esk15_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]) ).
cnf(c_0_79,negated_conjecture,
( ~ ilf_type(esk16_0,binary_relation_type)
| ~ member(esk17_0,range_of(esk16_0))
| range_of(esk16_0) != esk15_0 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,negated_conjecture,
member(esk17_0,esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_81,negated_conjecture,
~ ilf_type(esk16_0,binary_relation_type),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_78]),c_0_78])]),c_0_80])]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_73]),c_0_74])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET660+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:31:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.75/0.54 % Version: 3.5.1
% 0.75/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.75/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.75/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.75/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.75/0.54 % Starting sh5l with 300s (1) cores
% 0.75/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 115925 completed with status 0
% 0.75/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.75/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.75/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.75/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.75/0.54 % No SInE strategy applied
% 0.75/0.54 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.75/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.75/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.75/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.75/0.54 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S0Y with 209s (1) cores
% 0.75/0.54 % Starting new_bool_3 with 189s (1) cores
% 0.75/0.54 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.75/0.54 % G-E--_207_C01_F1_SE_CS_SP_PI_S0Y with pid 115934 completed with status 0
% 0.75/0.54 % Result found by G-E--_207_C01_F1_SE_CS_SP_PI_S0Y
% 0.75/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.75/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.75/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.75/0.54 % No SInE strategy applied
% 0.75/0.54 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.75/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.75/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.75/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.75/0.54 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S0Y with 209s (1) cores
% 0.75/0.54 % Preprocessing time : 0.002 s
% 0.75/0.54
% 0.75/0.54 % Proof found!
% 0.75/0.54 % SZS status Theorem
% 0.75/0.54 % SZS output start CNFRefutation
% See solution above
% 0.75/0.54 % Parsed axioms : 35
% 0.75/0.54 % Removed by relevancy pruning/SinE : 0
% 0.75/0.54 % Initial clauses : 73
% 0.75/0.54 % Removed in clause preprocessing : 3
% 0.75/0.54 % Initial clauses in saturation : 70
% 0.75/0.54 % Processed clauses : 1190
% 0.75/0.54 % ...of these trivial : 19
% 0.75/0.54 % ...subsumed : 670
% 0.75/0.54 % ...remaining for further processing : 501
% 0.75/0.54 % Other redundant clauses eliminated : 5
% 0.75/0.54 % Clauses deleted for lack of memory : 0
% 0.75/0.54 % Backward-subsumed : 196
% 0.75/0.54 % Backward-rewritten : 69
% 0.75/0.54 % Generated clauses : 4994
% 0.75/0.54 % ...of the previous two non-redundant : 4904
% 0.75/0.54 % ...aggressively subsumed : 0
% 0.75/0.54 % Contextual simplify-reflections : 19
% 0.75/0.54 % Paramodulations : 4957
% 0.75/0.54 % Factorizations : 32
% 0.75/0.54 % NegExts : 0
% 0.75/0.54 % Equation resolutions : 5
% 0.75/0.54 % Disequality decompositions : 0
% 0.75/0.54 % Total rewrite steps : 346
% 0.75/0.54 % ...of those cached : 280
% 0.75/0.54 % Propositional unsat checks : 0
% 0.75/0.54 % Propositional check models : 0
% 0.75/0.54 % Propositional check unsatisfiable : 0
% 0.75/0.54 % Propositional clauses : 0
% 0.75/0.54 % Propositional clauses after purity: 0
% 0.75/0.54 % Propositional unsat core size : 0
% 0.75/0.54 % Propositional preprocessing time : 0.000
% 0.75/0.54 % Propositional encoding time : 0.000
% 0.75/0.54 % Propositional solver time : 0.000
% 0.75/0.54 % Success case prop preproc time : 0.000
% 0.75/0.54 % Success case prop encoding time : 0.000
% 0.75/0.54 % Success case prop solver time : 0.000
% 0.75/0.54 % Current number of processed clauses : 232
% 0.75/0.54 % Positive orientable unit clauses : 39
% 0.75/0.54 % Positive unorientable unit clauses: 1
% 0.75/0.54 % Negative unit clauses : 5
% 0.75/0.54 % Non-unit-clauses : 187
% 0.75/0.54 % Current number of unprocessed clauses: 3758
% 0.75/0.54 % ...number of literals in the above : 14248
% 0.75/0.54 % Current number of archived formulas : 0
% 0.75/0.54 % Current number of archived clauses : 265
% 0.75/0.54 % Clause-clause subsumption calls (NU) : 24265
% 0.75/0.54 % Rec. Clause-clause subsumption calls : 16632
% 0.75/0.54 % Non-unit clause-clause subsumptions : 765
% 0.75/0.54 % Unit Clause-clause subsumption calls : 595
% 0.75/0.54 % Rewrite failures with RHS unbound : 0
% 0.75/0.54 % BW rewrite match attempts : 28
% 0.75/0.54 % BW rewrite match successes : 7
% 0.75/0.54 % Condensation attempts : 0
% 0.75/0.54 % Condensation successes : 0
% 0.75/0.54 % Termbank termtop insertions : 72939
% 0.75/0.54 % Search garbage collected termcells : 1633
% 0.75/0.54
% 0.75/0.54 % -------------------------------------------------
% 0.75/0.54 % User time : 0.084 s
% 0.75/0.54 % System time : 0.010 s
% 0.75/0.54 % Total time : 0.094 s
% 0.75/0.54 % Maximum resident set size: 3680 pages
% 0.75/0.54
% 0.75/0.54 % -------------------------------------------------
% 0.75/0.54 % User time : 0.372 s
% 0.75/0.54 % System time : 0.039 s
% 0.75/0.54 % Total time : 0.411 s
% 0.75/0.54 % Maximum resident set size: 4864 pages
% 0.75/0.54 % E exiting
%------------------------------------------------------------------------------