%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET652+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 : Thu Sep 24 02:14:53 PM UTC 2026
% Result : Theorem 65.22s 10.13s
% Output : CNFRefutation 65.22s
% 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)
=> ( ! [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/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(p26,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/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/sandbox2/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(X3,X4)
& subset(X1,X2) )
=> subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ) ),
file('/export/starexec/sandbox2/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(range_of(X3),X2)
& subset(domain_of(X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(p13,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( ilf_type(X1,set_type)
& relation_like(X1) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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(X2,X3)
& subset(X1,X2) )
=> subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(p20,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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(c_0_14,plain,
! [X13,X14,X15,X16] :
( ( ~ ilf_type(X13,set_type)
| ~ ilf_type(X14,set_type)
| ilf_type(X16,subset_type(cross_product(X13,X14)))
| ~ ilf_type(X16,relation_type(X13,X14)) )
& ( ~ ilf_type(X13,set_type)
| ~ ilf_type(X14,set_type)
| ilf_type(X15,relation_type(X13,X14))
| ~ ilf_type(X15,subset_type(cross_product(X13,X14))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])])]) ).
fof(c_0_15,plain,
! [X67] : ilf_type(X67,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,
! [X9,X10,X11,X12] :
( subset(cross_product(X9,X11),cross_product(X10,X12))
| ~ subset(X11,X12)
| ~ subset(X9,X10)
| ~ ilf_type(X12,set_type)
| ~ ilf_type(X11,set_type)
| ~ ilf_type(X10,set_type)
| ~ ilf_type(X9,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])]) ).
fof(c_0_18,plain,
! [X20,X21,X22] :
( ( ~ ilf_type(X20,set_type)
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X22,relation_type(X20,X21))
| subset(range_of(X22),X21) )
& ( ~ ilf_type(X20,set_type)
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X22,relation_type(X20,X21))
| subset(domain_of(X22),X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])])]) ).
fof(c_0_19,plain,
! [X37] :
( ( ~ ilf_type(X37,set_type)
| ilf_type(X37,binary_relation_type)
| ~ ilf_type(X37,set_type)
| ~ relation_like(X37) )
& ( ~ ilf_type(X37,set_type)
| ~ ilf_type(X37,binary_relation_type)
| ilf_type(X37,set_type) )
& ( ~ ilf_type(X37,set_type)
| ~ ilf_type(X37,binary_relation_type)
| relation_like(X37) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])])]) ).
fof(c_0_20,plain,
! [X60,X61,X62] :
( relation_like(X62)
| ~ ilf_type(X62,subset_type(cross_product(X60,X61)))
| ~ ilf_type(X61,set_type)
| ~ ilf_type(X60,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])])]) ).
cnf(c_0_21,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_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(esk15_0,relation_type(esk14_0,esk13_0))
& subset(range_of(esk15_0),esk13_0)
& ilf_type(esk15_0,relation_type(esk14_0,esk12_0))
& ilf_type(esk14_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk12_0,set_type) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_24,plain,
( ~ subset(X3,X4)
| ~ subset(X1,X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| subset(cross_product(X1,X3),cross_product(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X3))
| subset(domain_of(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,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_19]) ).
cnf(c_0_27,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_20]) ).
cnf(c_0_28,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_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,
! [X5,X6,X7] :
( subset(X5,X7)
| ~ subset(X6,X7)
| ~ subset(X5,X6)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
cnf(c_0_31,plain,
( ~ subset(X1,X3)
| ~ subset(X2,X4)
| subset(cross_product(X1,X2),cross_product(X3,X4)) ),
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,
( ~ ilf_type(X1,relation_type(X2,X3))
| subset(domain_of(X1),X2) ),
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,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_26]) ).
cnf(c_0_35,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_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,
! [X28,X29,X30] :
( ( ~ ilf_type(X28,set_type)
| ~ ilf_type(X29,set_type)
| subset(X28,X29)
| ~ member(esk3_2(X28,X29),X29) )
& ( ~ ilf_type(X28,set_type)
| ~ ilf_type(X29,set_type)
| subset(X28,X29)
| member(esk3_2(X28,X29),X28) )
& ( ~ ilf_type(X28,set_type)
| ~ ilf_type(X29,set_type)
| subset(X28,X29)
| ilf_type(esk3_2(X28,X29),set_type) )
& ( ~ ilf_type(X28,set_type)
| ~ ilf_type(X29,set_type)
| member(X30,X29)
| ~ member(X30,X28)
| ~ ilf_type(X30,set_type)
| ~ subset(X28,X29) ) ),
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)],[p9])])])])])]) ).
fof(c_0_38,plain,
! [X44,X45,X46] :
( ( ~ ilf_type(X44,set_type)
| ~ ilf_type(X45,set_type)
| member(X44,power_set(X45))
| ~ member(esk6_2(X44,X45),X45) )
& ( ~ ilf_type(X44,set_type)
| ~ ilf_type(X45,set_type)
| member(X44,power_set(X45))
| member(esk6_2(X44,X45),X44) )
& ( ~ ilf_type(X44,set_type)
| ~ ilf_type(X45,set_type)
| member(X44,power_set(X45))
| ilf_type(esk6_2(X44,X45),set_type) )
& ( ~ ilf_type(X44,set_type)
| ~ ilf_type(X45,set_type)
| member(X46,X45)
| ~ member(X46,X44)
| ~ ilf_type(X46,set_type)
| ~ member(X44,power_set(X45)) ) ),
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)],[p18])])])])])]) ).
cnf(c_0_39,plain,
( ~ subset(X2,X3)
| ~ subset(X1,X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,negated_conjecture,
( ~ subset(X1,X2)
| subset(cross_product(X1,range_of(esk15_0)),cross_product(X2,esk13_0)) ),
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,
! [X8] :
( subset(X8,cross_product(domain_of(X8),range_of(X8)))
| ~ ilf_type(X8,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])]) ).
cnf(c_0_43,plain,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
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,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X1,power_set(X2))
| member(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,plain,
( ~ subset(X1,X3)
| ~ subset(X3,X2)
| subset(X1,X2) ),
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,
( ~ ilf_type(X1,binary_relation_type)
| subset(X1,cross_product(domain_of(X1),range_of(X1))) ),
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] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p20]) ).
fof(c_0_53,plain,
! [X63,X64] :
( ( ~ ilf_type(X63,set_type)
| empty(X63)
| member(esk11_1(X63),X63) )
& ( ~ ilf_type(X63,set_type)
| empty(X63)
| ilf_type(esk11_1(X63),set_type) )
& ( ~ ilf_type(X63,set_type)
| ~ member(X64,X63)
| ~ ilf_type(X64,set_type)
| ~ empty(X63) ) ),
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_45])])])])])]) ).
cnf(c_0_54,plain,
( ~ subset(X3,X2)
| ~ member(X1,X3)
| member(X1,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(X1,power_set(X2))
| member(esk6_2(X1,X2),X1) ),
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(domain_of(esk15_0),range_of(esk15_0)))
| subset(X1,cross_product(esk14_0,esk13_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,
! [X49,X50] :
( ( ~ ilf_type(X49,set_type)
| ~ ilf_type(X50,set_type)
| empty(X50)
| ilf_type(X49,member_type(X50))
| ~ member(X49,X50) )
& ( ~ ilf_type(X49,set_type)
| ~ ilf_type(X50,set_type)
| empty(X50)
| member(X49,X50)
| ~ ilf_type(X49,member_type(X50)) ) ),
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_52])])])])]) ).
cnf(c_0_59,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk6_2(X1,X2),X2)
| member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_61,plain,
( ~ subset(X1,X3)
| member(X1,power_set(X2))
| member(esk6_2(X1,X2),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,
! [X39,X40] :
( ( ~ ilf_type(X39,set_type)
| ~ ilf_type(X40,set_type)
| ilf_type(X40,subset_type(X39))
| ~ ilf_type(X40,member_type(power_set(X39))) )
& ( ~ ilf_type(X39,set_type)
| ~ ilf_type(X40,set_type)
| ilf_type(X40,member_type(power_set(X39)))
| ~ ilf_type(X40,subset_type(X39)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,X2)
| empty(X2)
| ilf_type(X1,member_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
( ~ member(X2,X1)
| ~ empty(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(esk6_2(X1,X2),X2)
| member(X1,power_set(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(esk15_0,power_set(X1))
| member(esk6_2(esk15_0,X1),cross_product(esk14_0,esk13_0)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(power_set(X2)))
| ilf_type(X1,subset_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,plain,
( ~ member(X1,X2)
| ilf_type(X1,member_type(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(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ilf_type(X1,relation_type(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_72,plain,
( ~ ilf_type(X1,member_type(power_set(X2)))
| ilf_type(X1,subset_type(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,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_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
% 0.00/0.02 % Problem : SET652+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:31:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 65.22/10.13 % Version: 3.5.1
% 65.22/10.13 % Preprocessing class: FSMSSMSSSSSNFFN.
% 65.22/10.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 65.22/10.13 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 65.22/10.13 % Starting new_bool_3 with 300s (1) cores
% 65.22/10.13 % Starting new_bool_1 with 300s (1) cores
% 65.22/10.13 % Starting sh5l with 300s (1) cores
% 65.22/10.13 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3234054 completed with status 0
% 65.22/10.13 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 65.22/10.13 % Preprocessing class: FSMSSMSSSSSNFFN.
% 65.22/10.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 65.22/10.13 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 65.22/10.13 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 65.22/10.13 % No SInE strategy applied
% 65.22/10.13 % Search class: FGHSF-FFMM21-SFFFFFNN
% 65.22/10.13 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 65.22/10.13 % Starting SubtermCWHack with 136s (1) cores
% 65.22/10.13 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 65.22/10.13 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 65.22/10.13 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 65.22/10.13 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 65.22/10.13 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 3234060 completed with status 0
% 65.22/10.13 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 65.22/10.13 % Preprocessing class: FSMSSMSSSSSNFFN.
% 65.22/10.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 65.22/10.13 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 65.22/10.13 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 65.22/10.13 % No SInE strategy applied
% 65.22/10.13 % Search class: FGHSF-FFMM21-SFFFFFNN
% 65.22/10.13 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 65.22/10.13 % Starting SubtermCWHack with 136s (1) cores
% 65.22/10.13 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 65.22/10.13 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 65.22/10.13 % Preprocessing time : 0.003 s
% 65.22/10.13 % Presaturation interreduction done
% 65.22/10.13
% 65.22/10.13 % Proof found!
% 65.22/10.13 % SZS status Theorem
% 65.22/10.13 % SZS output start CNFRefutation
% See solution above
% 65.22/10.13 % Parsed axioms : 27
% 65.22/10.13 % Removed by relevancy pruning/SinE : 0
% 65.22/10.13 % Initial clauses : 54
% 65.22/10.13 % Removed in clause preprocessing : 1
% 65.22/10.13 % Initial clauses in saturation : 53
% 65.22/10.13 % Processed clauses : 20891
% 65.22/10.13 % ...of these trivial : 294
% 65.22/10.13 % ...subsumed : 15873
% 65.22/10.13 % ...remaining for further processing : 4724
% 65.22/10.13 % Other redundant clauses eliminated : 0
% 65.22/10.13 % Clauses deleted for lack of memory : 0
% 65.22/10.13 % Backward-subsumed : 948
% 65.22/10.13 % Backward-rewritten : 11
% 65.22/10.13 % Generated clauses : 363895
% 65.22/10.13 % ...of the previous two non-redundant : 360869
% 65.22/10.13 % ...aggressively subsumed : 0
% 65.22/10.13 % Contextual simplify-reflections : 3
% 65.22/10.13 % Paramodulations : 363887
% 65.22/10.13 % Factorizations : 0
% 65.22/10.13 % NegExts : 0
% 65.22/10.13 % Equation resolutions : 0
% 65.22/10.13 % Disequality decompositions : 0
% 65.22/10.13 % Total rewrite steps : 3524
% 65.22/10.13 % ...of those cached : 2079
% 65.22/10.13 % Propositional unsat checks : 0
% 65.22/10.13 % Propositional check models : 0
% 65.22/10.13 % Propositional check unsatisfiable : 0
% 65.22/10.13 % Propositional clauses : 0
% 65.22/10.13 % Propositional clauses after purity: 0
% 65.22/10.13 % Propositional unsat core size : 0
% 65.22/10.13 % Propositional preprocessing time : 0.000
% 65.22/10.13 % Propositional encoding time : 0.000
% 65.22/10.13 % Propositional solver time : 0.000
% 65.22/10.13 % Success case prop preproc time : 0.000
% 65.22/10.13 % Success case prop encoding time : 0.000
% 65.22/10.13 % Success case prop solver time : 0.000
% 65.22/10.13 % Current number of processed clauses : 3719
% 65.22/10.13 % Positive orientable unit clauses : 1190
% 65.22/10.13 % Positive unorientable unit clauses: 0
% 65.22/10.13 % Negative unit clauses : 12
% 65.22/10.13 % Non-unit-clauses : 2517
% 65.22/10.13 % Current number of unprocessed clauses: 339934
% 65.22/10.13 % ...number of literals in the above : 583694
% 65.22/10.13 % Current number of archived formulas : 0
% 65.22/10.13 % Current number of archived clauses : 1005
% 65.22/10.13 % Clause-clause subsumption calls (NU) : 991962
% 65.22/10.13 % Rec. Clause-clause subsumption calls : 811935
% 65.22/10.13 % Non-unit clause-clause subsumptions : 15378
% 65.22/10.13 % Unit Clause-clause subsumption calls : 45167
% 65.22/10.13 % Rewrite failures with RHS unbound : 0
% 65.22/10.13 % BW rewrite match attempts : 8326
% 65.22/10.13 % BW rewrite match successes : 11
% 65.22/10.13 % Condensation attempts : 0
% 65.22/10.13 % Condensation successes : 0
% 65.22/10.13 % Termbank termtop insertions : 6401376
% 65.22/10.13 % Search garbage collected termcells : 1110
% 65.22/10.13
% 65.22/10.13 % -------------------------------------------------
% 65.22/10.13 % User time : 8.873 s
% 65.22/10.13 % System time : 0.416 s
% 65.22/10.13 % Total time : 9.289 s
% 65.22/10.13 % Maximum resident set size: 3868 pages
% 65.22/10.13
% 65.22/10.13 % -------------------------------------------------
% 65.22/10.13 % User time : 43.980 s
% 65.22/10.13 % System time : 1.958 s
% 65.22/10.13 % Total time : 45.938 s
% 65.22/10.13 % Maximum resident set size: 4608 pages
% 65.22/10.13 % E exiting
%------------------------------------------------------------------------------