%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET652+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:08:14 PM UTC 2026
% Result : Theorem 25.62s 15.60s
% Output : CNFRefutation 25.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 17 unt; 0 def)
% Number of atoms : 315 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 388 ( 151 ~; 154 |; 26 &)
% ( 8 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 152 ( 5 sgn 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p4,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(p26,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(prove_relset_1_14,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X3,X1))
=> ( subset(range_of(X4),X2)
=> ilf_type(X4,relation_type(X3,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_14) ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(p13,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
fof(p23,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',p23) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p9,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
fof(p18,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',p18) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> subset(X1,cross_product(domain_of(X1),range_of(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(p24,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(p20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(p15,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',p15) ).
fof(c_0_14,plain,
! [X73,X74,X75,X76] :
( ( ~ ilf_type(X75,subset_type(cross_product(X73,X74)))
| ilf_type(X75,relation_type(X73,X74))
| ~ ilf_type(X74,set_type)
| ~ ilf_type(X73,set_type) )
& ( ~ ilf_type(X76,relation_type(X73,X74))
| ilf_type(X76,subset_type(cross_product(X73,X74)))
| ~ ilf_type(X74,set_type)
| ~ ilf_type(X73,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])]) ).
fof(c_0_15,plain,
! [X127] : ilf_type(X127,set_type),
inference(variable_rename,[status(thm)],[p26]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X3,X1))
=> ( subset(range_of(X4),X2)
=> ilf_type(X4,relation_type(X3,X2)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_14]) ).
fof(c_0_17,plain,
! [X69,X70,X71,X72] :
( ~ ilf_type(X69,set_type)
| ~ ilf_type(X70,set_type)
| ~ ilf_type(X71,set_type)
| ~ ilf_type(X72,set_type)
| ~ subset(X69,X70)
| ~ subset(X71,X72)
| subset(cross_product(X69,X71),cross_product(X70,X72)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])]) ).
fof(c_0_18,plain,
! [X80,X81,X82] :
( ( subset(domain_of(X82),X80)
| ~ ilf_type(X82,relation_type(X80,X81))
| ~ ilf_type(X81,set_type)
| ~ ilf_type(X80,set_type) )
& ( subset(range_of(X82),X81)
| ~ ilf_type(X82,relation_type(X80,X81))
| ~ ilf_type(X81,set_type)
| ~ ilf_type(X80,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])]) ).
fof(c_0_19,plain,
! [X97] :
( ( relation_like(X97)
| ~ ilf_type(X97,binary_relation_type)
| ~ ilf_type(X97,set_type) )
& ( ilf_type(X97,set_type)
| ~ ilf_type(X97,binary_relation_type)
| ~ ilf_type(X97,set_type) )
& ( ~ relation_like(X97)
| ~ ilf_type(X97,set_type)
| ilf_type(X97,binary_relation_type)
| ~ ilf_type(X97,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])]) ).
fof(c_0_20,plain,
! [X120,X121,X122] :
( ~ ilf_type(X120,set_type)
| ~ ilf_type(X121,set_type)
| ~ ilf_type(X122,subset_type(cross_product(X120,X121)))
| relation_like(X122) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])]) ).
cnf(c_0_21,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,relation_type(esk14_0,esk12_0))
& subset(range_of(esk15_0),esk13_0)
& ~ ilf_type(esk15_0,relation_type(esk14_0,esk13_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_24,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ subset(X1,X2)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( relation_like(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22])]) ).
cnf(c_0_29,negated_conjecture,
ilf_type(esk15_0,relation_type(esk14_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_30,plain,
! [X65,X66,X67] :
( ~ ilf_type(X65,set_type)
| ~ ilf_type(X66,set_type)
| ~ ilf_type(X67,set_type)
| ~ subset(X65,X66)
| ~ subset(X66,X67)
| subset(X65,X67) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_31,plain,
( subset(cross_product(X1,X2),cross_product(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_22]),c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_32,negated_conjecture,
subset(range_of(esk15_0),esk13_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_22]),c_0_22])]) ).
cnf(c_0_34,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_22]),c_0_22])]) ).
cnf(c_0_36,negated_conjecture,
ilf_type(esk15_0,subset_type(cross_product(esk14_0,esk12_0))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_37,plain,
! [X88,X89,X90] :
( ( ~ subset(X88,X89)
| ~ ilf_type(X90,set_type)
| ~ member(X90,X88)
| member(X90,X89)
| ~ ilf_type(X89,set_type)
| ~ ilf_type(X88,set_type) )
& ( ilf_type(esk3_2(X88,X89),set_type)
| subset(X88,X89)
| ~ ilf_type(X89,set_type)
| ~ ilf_type(X88,set_type) )
& ( member(esk3_2(X88,X89),X88)
| subset(X88,X89)
| ~ ilf_type(X89,set_type)
| ~ ilf_type(X88,set_type) )
& ( ~ member(esk3_2(X88,X89),X89)
| subset(X88,X89)
| ~ ilf_type(X89,set_type)
| ~ ilf_type(X88,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p9])])])])]) ).
fof(c_0_38,plain,
! [X104,X105,X106] :
( ( ~ member(X104,power_set(X105))
| ~ ilf_type(X106,set_type)
| ~ member(X106,X104)
| member(X106,X105)
| ~ ilf_type(X105,set_type)
| ~ ilf_type(X104,set_type) )
& ( ilf_type(esk6_2(X104,X105),set_type)
| member(X104,power_set(X105))
| ~ ilf_type(X105,set_type)
| ~ ilf_type(X104,set_type) )
& ( member(esk6_2(X104,X105),X104)
| member(X104,power_set(X105))
| ~ ilf_type(X105,set_type)
| ~ ilf_type(X104,set_type) )
& ( ~ member(esk6_2(X104,X105),X105)
| member(X104,power_set(X105))
| ~ ilf_type(X105,set_type)
| ~ ilf_type(X104,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p18])])])])]) ).
cnf(c_0_39,plain,
( subset(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,negated_conjecture,
( subset(cross_product(X1,range_of(esk15_0)),cross_product(X2,esk13_0))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
subset(domain_of(esk15_0),esk14_0),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
fof(c_0_42,plain,
! [X68] :
( ~ ilf_type(X68,binary_relation_type)
| subset(X68,cross_product(domain_of(X68),range_of(X68))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])]) ).
cnf(c_0_43,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_22])]) ).
cnf(c_0_44,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_45,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p24]) ).
cnf(c_0_46,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,plain,
( member(esk6_2(X1,X2),X1)
| member(X1,power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_49,negated_conjecture,
subset(cross_product(domain_of(esk15_0),range_of(esk15_0)),cross_product(esk14_0,esk13_0)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,plain,
( subset(X1,cross_product(domain_of(X1),range_of(X1)))
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,negated_conjecture,
ilf_type(esk15_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_52,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p20]) ).
fof(c_0_53,plain,
! [X123,X124] :
( ( ~ empty(X123)
| ~ ilf_type(X124,set_type)
| ~ member(X124,X123)
| ~ ilf_type(X123,set_type) )
& ( ilf_type(esk11_1(X123),set_type)
| empty(X123)
| ~ ilf_type(X123,set_type) )
& ( member(esk11_1(X123),X123)
| empty(X123)
| ~ ilf_type(X123,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])]) ).
cnf(c_0_54,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_55,plain,
( member(esk6_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_22]),c_0_22])]) ).
cnf(c_0_56,negated_conjecture,
( subset(X1,cross_product(esk14_0,esk13_0))
| ~ subset(X1,cross_product(domain_of(esk15_0),range_of(esk15_0))) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,negated_conjecture,
subset(esk15_0,cross_product(domain_of(esk15_0),range_of(esk15_0))),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_58,plain,
! [X109,X110] :
( ( ~ ilf_type(X109,member_type(X110))
| member(X109,X110)
| empty(X110)
| ~ ilf_type(X110,set_type)
| ~ ilf_type(X109,set_type) )
& ( ~ member(X109,X110)
| ilf_type(X109,member_type(X110))
| empty(X110)
| ~ ilf_type(X110,set_type)
| ~ ilf_type(X109,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
cnf(c_0_59,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
( member(X1,power_set(X2))
| ~ member(esk6_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_61,plain,
( member(esk6_2(X1,X2),X3)
| member(X1,power_set(X2))
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,negated_conjecture,
subset(esk15_0,cross_product(esk14_0,esk13_0)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_63,plain,
! [X99,X100] :
( ( ~ ilf_type(X100,subset_type(X99))
| ilf_type(X100,member_type(power_set(X99)))
| ~ ilf_type(X100,set_type)
| ~ ilf_type(X99,set_type) )
& ( ~ ilf_type(X100,member_type(power_set(X99)))
| ilf_type(X100,subset_type(X99))
| ~ ilf_type(X100,set_type)
| ~ ilf_type(X99,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])]) ).
cnf(c_0_64,plain,
( ilf_type(X1,member_type(X2))
| empty(X2)
| ~ member(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_22]),c_0_22])]) ).
cnf(c_0_66,plain,
( member(X1,power_set(X2))
| ~ member(esk6_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_22]),c_0_22])]) ).
cnf(c_0_67,negated_conjecture,
( member(esk6_2(esk15_0,X1),cross_product(esk14_0,esk13_0))
| member(esk15_0,power_set(X1)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_22]),c_0_22])]),c_0_65]) ).
cnf(c_0_70,negated_conjecture,
member(esk15_0,power_set(cross_product(esk14_0,esk13_0))),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_72,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_68,c_0_22]),c_0_22])]) ).
cnf(c_0_73,negated_conjecture,
ilf_type(esk15_0,member_type(power_set(cross_product(esk14_0,esk13_0)))),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,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_71,c_0_22]),c_0_22])]) ).
cnf(c_0_75,negated_conjecture,
ilf_type(esk15_0,subset_type(cross_product(esk14_0,esk13_0))),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
~ ilf_type(esk15_0,relation_type(esk14_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET652+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:31:13 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 25.62/15.60 % Version : CSE_E---1.7
% 25.62/15.60 % Problem : theBenchmark.p
% 25.62/15.60 % SZS status Theorem for theBenchmark.p
% 25.62/15.60 % SZS output start CNFRefutation
% See solution above
% 25.72/15.71 % Total time : 11.393s
%------------------------------------------------------------------------------