%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET684+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 : n003.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 02:14:59 PM UTC 2026
% Result : Theorem 6.92s 1.59s
% Output : CNFRefutation 6.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 86 ( 17 unt; 0 def)
% Number of atoms : 367 ( 6 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 456 ( 175 ~; 175 |; 45 &)
% ( 9 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-5 aty)
% Number of variables : 167 ( 9 sgn 81 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_relset_1_51,conjecture,
! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ( ilf_type(X3,set_type)
& ~ empty(X3) )
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,relation_type(X2,X3))
=> ! [X6] :
( ilf_type(X6,member_type(X1))
=> ! [X7] :
( ilf_type(X7,member_type(X3))
=> ( member(ordered_pair(X6,X7),compose5(X1,X2,X3,X4,X5))
<=> ? [X8] :
( member(ordered_pair(X8,X7),X5)
& member(ordered_pair(X6,X8),X4)
& ilf_type(X8,member_type(X2)) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_51) ).
fof(p27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,relation_type(X2,X3))
=> compose5(X1,X2,X3,X4,X5) = compose(X4,X5) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(p29,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).
fof(p5,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',p5) ).
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(p26,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',p26) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ! [X4] :
( ilf_type(X4,binary_relation_type)
=> ( member(ordered_pair(X1,X2),compose(X3,X4))
<=> ? [X5] :
( member(ordered_pair(X5,X2),X4)
& member(ordered_pair(X1,X5),X3)
& ilf_type(X5,set_type) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p9,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',p9) ).
fof(p2,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)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X4,X2)
& member(X3,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(p7,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',p7) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ( ilf_type(X3,set_type)
& ~ empty(X3) )
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,relation_type(X2,X3))
=> ! [X6] :
( ilf_type(X6,member_type(X1))
=> ! [X7] :
( ilf_type(X7,member_type(X3))
=> ( member(ordered_pair(X6,X7),compose5(X1,X2,X3,X4,X5))
<=> ? [X8] :
( member(ordered_pair(X8,X7),X5)
& member(ordered_pair(X6,X8),X4)
& ilf_type(X8,member_type(X2)) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_51]) ).
fof(c_0_11,plain,
! [X79,X80,X81,X82,X83] :
( compose5(X79,X80,X81,X82,X83) = compose(X82,X83)
| ~ ilf_type(X83,relation_type(X80,X81))
| ~ ilf_type(X82,relation_type(X79,X80))
| ~ ilf_type(X81,set_type)
| ~ ilf_type(X80,set_type)
| ~ ilf_type(X79,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_12,plain,
! [X89] : ilf_type(X89,set_type),
inference(variable_rename,[status(thm)],[p29]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ( ilf_type(X3,set_type)
& ~ empty(X3) )
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,relation_type(X2,X3))
=> ! [X6] :
( ilf_type(X6,member_type(X1))
=> ! [X7] :
( ilf_type(X7,member_type(X3))
=> ( member(ordered_pair(X6,X7),compose5(X1,X2,X3,X4,X5))
<=> ? [X8] :
( member(ordered_pair(X8,X7),X5)
& member(ordered_pair(X6,X8),X4)
& ilf_type(X8,member_type(X2)) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X27,X28,X29,X30] :
( ( ~ ilf_type(X27,set_type)
| ~ ilf_type(X28,set_type)
| ilf_type(X30,subset_type(cross_product(X27,X28)))
| ~ ilf_type(X30,relation_type(X27,X28)) )
& ( ~ ilf_type(X27,set_type)
| ~ ilf_type(X28,set_type)
| ilf_type(X29,relation_type(X27,X28))
| ~ ilf_type(X29,subset_type(cross_product(X27,X28))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])])]) ).
cnf(c_0_15,plain,
( ~ ilf_type(X5,relation_type(X2,X3))
| ~ ilf_type(X4,relation_type(X1,X2))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| compose5(X1,X2,X3,X4,X5) = compose(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,negated_conjecture,
! [X97] :
( ( member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0))
| member(ordered_pair(esk19_0,esk18_0),esk16_0) )
& ( member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0))
| member(ordered_pair(esk17_0,esk19_0),esk15_0) )
& ( member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0))
| ilf_type(esk19_0,member_type(esk13_0)) )
& ( ~ member(ordered_pair(X97,esk18_0),esk16_0)
| ~ member(ordered_pair(esk17_0,X97),esk15_0)
| ~ ilf_type(X97,member_type(esk13_0))
| ~ member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0)) )
& ilf_type(esk18_0,member_type(esk14_0))
& ilf_type(esk17_0,member_type(esk12_0))
& ilf_type(esk16_0,relation_type(esk13_0,esk14_0))
& ilf_type(esk15_0,relation_type(esk12_0,esk13_0))
& ilf_type(esk14_0,set_type)
& ~ empty(esk14_0)
& ilf_type(esk13_0,set_type)
& ~ empty(esk13_0)
& ilf_type(esk12_0,set_type)
& ~ empty(esk12_0) ),
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_13])])])])])]) ).
fof(c_0_18,plain,
! [X50] :
( ( ~ ilf_type(X50,set_type)
| ilf_type(X50,binary_relation_type)
| ~ ilf_type(X50,set_type)
| ~ relation_like(X50) )
& ( ~ ilf_type(X50,set_type)
| ~ ilf_type(X50,binary_relation_type)
| ilf_type(X50,set_type) )
& ( ~ ilf_type(X50,set_type)
| ~ ilf_type(X50,binary_relation_type)
| relation_like(X50) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])]) ).
fof(c_0_19,plain,
! [X76,X77,X78] :
( relation_like(X78)
| ~ ilf_type(X78,subset_type(cross_product(X76,X77)))
| ~ ilf_type(X77,set_type)
| ~ ilf_type(X76,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p26])])])]) ).
cnf(c_0_20,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_21,plain,
( ~ ilf_type(X4,relation_type(X1,X2))
| ~ ilf_type(X5,relation_type(X2,X3))
| compose5(X1,X2,X3,X4,X5) = compose(X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]),c_0_16])]) ).
cnf(c_0_22,negated_conjecture,
ilf_type(esk16_0,relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,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_18]) ).
cnf(c_0_24,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_19]) ).
cnf(c_0_25,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_20,c_0_16]),c_0_16])]) ).
cnf(c_0_26,negated_conjecture,
ilf_type(esk15_0,relation_type(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_27,plain,
! [X9,X10,X11,X12,X14] :
( ( ~ ilf_type(X9,set_type)
| ~ ilf_type(X10,set_type)
| ~ ilf_type(X11,binary_relation_type)
| ~ ilf_type(X12,binary_relation_type)
| member(ordered_pair(X9,X10),compose(X11,X12))
| ~ member(ordered_pair(X14,X10),X12)
| ~ member(ordered_pair(X9,X14),X11)
| ~ ilf_type(X14,set_type) )
& ( ~ ilf_type(X9,set_type)
| ~ ilf_type(X10,set_type)
| ~ ilf_type(X11,binary_relation_type)
| ~ ilf_type(X12,binary_relation_type)
| ~ member(ordered_pair(X9,X10),compose(X11,X12))
| member(ordered_pair(esk1_4(X9,X10,X11,X12),X10),X12) )
& ( ~ ilf_type(X9,set_type)
| ~ ilf_type(X10,set_type)
| ~ ilf_type(X11,binary_relation_type)
| ~ ilf_type(X12,binary_relation_type)
| ~ member(ordered_pair(X9,X10),compose(X11,X12))
| member(ordered_pair(X9,esk1_4(X9,X10,X11,X12)),X11) )
& ( ~ ilf_type(X9,set_type)
| ~ ilf_type(X10,set_type)
| ~ ilf_type(X11,binary_relation_type)
| ~ ilf_type(X12,binary_relation_type)
| ~ member(ordered_pair(X9,X10),compose(X11,X12))
| ilf_type(esk1_4(X9,X10,X11,X12),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_28,negated_conjecture,
( ~ ilf_type(X2,relation_type(X1,esk13_0))
| compose5(X1,esk13_0,esk14_0,X2,esk16_0) = compose(X2,esk16_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_23]) ).
cnf(c_0_30,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_24,c_0_16]),c_0_16])]) ).
cnf(c_0_31,negated_conjecture,
ilf_type(esk16_0,subset_type(cross_product(esk13_0,esk14_0))),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_32,negated_conjecture,
ilf_type(esk15_0,subset_type(cross_product(esk12_0,esk13_0))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_33,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p9]) ).
fof(c_0_34,plain,
! [X15,X16,X17,X18,X19] :
( ( ~ ilf_type(X15,set_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X19,relation_type(X15,X16))
| ~ member(ordered_pair(X17,X18),X19)
| member(X18,X16) )
& ( ~ ilf_type(X15,set_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X19,relation_type(X15,X16))
| ~ member(ordered_pair(X17,X18),X19)
| member(X17,X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])])]) ).
cnf(c_0_35,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X1,X2),compose(X3,X4))
| member(ordered_pair(X1,esk1_4(X1,X2,X3,X4)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,negated_conjecture,
( member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0))
| member(ordered_pair(esk19_0,esk18_0),esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_37,negated_conjecture,
compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0) = compose(esk15_0,esk16_0),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_38,plain,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_16])]) ).
cnf(c_0_39,negated_conjecture,
relation_like(esk16_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
( member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0))
| ilf_type(esk19_0,member_type(esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_42,negated_conjecture,
( member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0))
| member(ordered_pair(esk17_0,esk19_0),esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_43,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)],[p7]) ).
fof(c_0_44,plain,
! [X38,X39] :
( ( ~ ilf_type(X38,set_type)
| empty(X38)
| member(esk4_1(X38),X38) )
& ( ~ ilf_type(X38,set_type)
| empty(X38)
| ilf_type(esk4_1(X38),set_type) )
& ( ~ ilf_type(X38,set_type)
| ~ member(X39,X38)
| ~ ilf_type(X39,set_type)
| ~ empty(X38) ) ),
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_33])])])])])]) ).
cnf(c_0_45,plain,
( ~ ilf_type(X5,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X4,relation_type(X5,X2))
| ~ member(ordered_pair(X3,X1),X4)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,plain,
( ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X1,X2),compose(X3,X4))
| member(ordered_pair(X1,esk1_4(X1,X2,X3,X4)),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_16]),c_0_16])]) ).
cnf(c_0_47,negated_conjecture,
( member(ordered_pair(esk19_0,esk18_0),esk16_0)
| member(ordered_pair(esk17_0,esk18_0),compose(esk15_0,esk16_0)) ),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_48,negated_conjecture,
ilf_type(esk16_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_49,negated_conjecture,
ilf_type(esk15_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_50,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X1,X2),compose(X3,X4))
| member(ordered_pair(esk1_4(X1,X2,X3,X4),X2),X4) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_51,negated_conjecture,
( ilf_type(esk19_0,member_type(esk13_0))
| member(ordered_pair(esk17_0,esk18_0),compose(esk15_0,esk16_0)) ),
inference(rw,[status(thm)],[c_0_41,c_0_37]) ).
cnf(c_0_52,negated_conjecture,
( member(ordered_pair(esk17_0,esk19_0),esk15_0)
| member(ordered_pair(esk17_0,esk18_0),compose(esk15_0,esk16_0)) ),
inference(rw,[status(thm)],[c_0_42,c_0_37]) ).
fof(c_0_53,plain,
! [X34,X35] :
( ( ~ ilf_type(X34,set_type)
| ~ ilf_type(X35,set_type)
| empty(X35)
| ilf_type(X34,member_type(X35))
| ~ member(X34,X35) )
& ( ~ ilf_type(X34,set_type)
| ~ ilf_type(X35,set_type)
| empty(X35)
| member(X34,X35)
| ~ ilf_type(X34,member_type(X35)) ) ),
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_43])])])])]) ).
cnf(c_0_54,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
( ~ ilf_type(X4,relation_type(X5,X2))
| ~ member(ordered_pair(X3,X1),X4)
| member(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_16]),c_0_16]),c_0_16]),c_0_16])]) ).
cnf(c_0_56,negated_conjecture,
( member(ordered_pair(esk19_0,esk18_0),esk16_0)
| member(ordered_pair(esk17_0,esk1_4(esk17_0,esk18_0,esk15_0,esk16_0)),esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_57,negated_conjecture,
( ~ member(ordered_pair(X1,esk18_0),esk16_0)
| ~ member(ordered_pair(esk17_0,X1),esk15_0)
| ~ ilf_type(X1,member_type(esk13_0))
| ~ member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_58,plain,
( ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X1,X2),compose(X3,X4))
| member(ordered_pair(esk1_4(X1,X2,X3,X4),X2),X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_16]),c_0_16])]) ).
cnf(c_0_59,negated_conjecture,
( ilf_type(esk19_0,member_type(esk13_0))
| member(ordered_pair(esk17_0,esk1_4(esk17_0,esk18_0,esk15_0,esk16_0)),esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_51]),c_0_48]),c_0_49])]) ).
cnf(c_0_60,negated_conjecture,
( member(ordered_pair(esk17_0,esk19_0),esk15_0)
| member(ordered_pair(esk17_0,esk1_4(esk17_0,esk18_0,esk15_0,esk16_0)),esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_52]),c_0_48]),c_0_49])]) ).
cnf(c_0_61,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_53]) ).
cnf(c_0_62,plain,
( ~ member(X2,X1)
| ~ empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_16]),c_0_16])]) ).
cnf(c_0_63,negated_conjecture,
( ~ ilf_type(esk15_0,relation_type(X2,X1))
| member(ordered_pair(esk19_0,esk18_0),esk16_0)
| member(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_64,negated_conjecture,
( ~ ilf_type(X1,member_type(esk13_0))
| ~ member(ordered_pair(esk17_0,X1),esk15_0)
| ~ member(ordered_pair(X1,esk18_0),esk16_0)
| ~ member(ordered_pair(esk17_0,esk18_0),compose(esk15_0,esk16_0)) ),
inference(rw,[status(thm)],[c_0_57,c_0_37]) ).
cnf(c_0_65,negated_conjecture,
( member(ordered_pair(esk19_0,esk18_0),esk16_0)
| member(ordered_pair(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),esk18_0),esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_66,negated_conjecture,
( ~ ilf_type(esk15_0,relation_type(X2,X1))
| ilf_type(esk19_0,member_type(esk13_0))
| member(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( ilf_type(esk19_0,member_type(esk13_0))
| member(ordered_pair(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),esk18_0),esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_51]),c_0_48]),c_0_49])]) ).
cnf(c_0_68,negated_conjecture,
( ~ ilf_type(esk15_0,relation_type(X2,X1))
| member(ordered_pair(esk17_0,esk19_0),esk15_0)
| member(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_60]) ).
cnf(c_0_69,negated_conjecture,
( member(ordered_pair(esk17_0,esk19_0),esk15_0)
| member(ordered_pair(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),esk18_0),esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_52]),c_0_48]),c_0_49])]) ).
cnf(c_0_70,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_61,c_0_16]),c_0_16])]),c_0_62]) ).
cnf(c_0_71,negated_conjecture,
( member(ordered_pair(esk19_0,esk18_0),esk16_0)
| member(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_26]) ).
cnf(c_0_72,negated_conjecture,
( ~ ilf_type(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),member_type(esk13_0))
| member(ordered_pair(esk19_0,esk18_0),esk16_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_47]),c_0_56]) ).
cnf(c_0_73,negated_conjecture,
( ilf_type(esk19_0,member_type(esk13_0))
| member(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_66,c_0_26]) ).
cnf(c_0_74,negated_conjecture,
( ~ ilf_type(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),member_type(esk13_0))
| ilf_type(esk19_0,member_type(esk13_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_67]),c_0_51]),c_0_59]) ).
cnf(c_0_75,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type)
| ~ member(ordered_pair(X1,X4),X5)
| ~ member(ordered_pair(X2,X1),X3)
| ~ ilf_type(X1,set_type)
| member(ordered_pair(X2,X4),compose(X3,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_76,negated_conjecture,
( member(ordered_pair(esk17_0,esk19_0),esk15_0)
| member(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_26]) ).
cnf(c_0_77,negated_conjecture,
( ~ ilf_type(esk1_4(esk17_0,esk18_0,esk15_0,esk16_0),member_type(esk13_0))
| member(ordered_pair(esk17_0,esk19_0),esk15_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_69]),c_0_52]),c_0_60]) ).
cnf(c_0_78,negated_conjecture,
member(ordered_pair(esk19_0,esk18_0),esk16_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_79,negated_conjecture,
ilf_type(esk19_0,member_type(esk13_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_73]),c_0_74]) ).
cnf(c_0_80,plain,
( ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X5,X2),X4)
| ~ member(ordered_pair(X1,X5),X3)
| member(ordered_pair(X1,X2),compose(X3,X4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_16]),c_0_16]),c_0_16])]) ).
cnf(c_0_81,negated_conjecture,
member(ordered_pair(esk17_0,esk19_0),esk15_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_76]),c_0_77]) ).
cnf(c_0_82,negated_conjecture,
( ~ member(ordered_pair(esk17_0,esk19_0),esk15_0)
| ~ member(ordered_pair(esk17_0,esk18_0),compose(esk15_0,esk16_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_78]),c_0_79])]) ).
cnf(c_0_83,negated_conjecture,
( ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(esk19_0,X1),X2)
| member(ordered_pair(esk17_0,X1),compose(esk15_0,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_49])]) ).
cnf(c_0_84,negated_conjecture,
~ member(ordered_pair(esk17_0,esk18_0),compose(esk15_0,esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_81])]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_78]),c_0_48])]),c_0_84]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET684+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.59 % Computer : n003.cluster.edu
% 0.11/0.59 % Model : x86_64 x86_64
% 0.11/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.59 % Memory : 8046.5625MB
% 0.11/0.59 % OS : Linux 6.8.0-71-generic
% 0.11/0.59 % CPULimit : 300
% 0.11/0.59 % WCLimit : 300
% 0.11/0.59 % DateTime : Mon Sep 21 05:34:16 UTC 2026
% 0.11/0.59 % CPUTime :
% 0.11/0.59 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.63 Running first-order theorem proving
% 0.16/0.63 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
% 6.92/1.59 % Version: 3.5.1
% 6.92/1.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.92/1.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.92/1.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.92/1.59 % Starting new_bool_3 with 300s (1) cores
% 6.92/1.59 % Starting new_bool_1 with 300s (1) cores
% 6.92/1.59 % Starting sh5l with 300s (1) cores
% 6.92/1.59 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3509007 completed with status 0
% 6.92/1.59 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 6.92/1.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.92/1.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.92/1.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.92/1.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.92/1.59 % No SInE strategy applied
% 6.92/1.59 % Search class: FGHSF-FFMM31-SFFFFFNN
% 6.92/1.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.92/1.59 % Starting SubtermCWHack with 136s (1) cores
% 6.92/1.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.92/1.59 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 6.92/1.59 % Starting new_bool_3 with 136s (1) cores
% 6.92/1.59 % Starting new_bool_1 with 136s (1) cores
% 6.92/1.59 % new_bool_1 with pid 3509020 completed with status 0
% 6.92/1.59 % Result found by new_bool_1
% 6.92/1.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.92/1.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.92/1.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.92/1.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.92/1.59 % No SInE strategy applied
% 6.92/1.59 % Search class: FGHSF-FFMM31-SFFFFFNN
% 6.92/1.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.92/1.59 % Starting SubtermCWHack with 136s (1) cores
% 6.92/1.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.92/1.59 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 6.92/1.59 % Starting new_bool_3 with 136s (1) cores
% 6.92/1.59 % Starting new_bool_1 with 136s (1) cores
% 6.92/1.59 % Preprocessing time : 0.002 s
% 6.92/1.59 % Presaturation interreduction done
% 6.92/1.59
% 6.92/1.59 % Proof found!
% 6.92/1.59 % SZS status Theorem
% 6.92/1.59 % SZS output start CNFRefutation
% See solution above
% 6.92/1.59 % Parsed axioms : 30
% 6.92/1.59 % Removed by relevancy pruning/SinE : 0
% 6.92/1.59 % Initial clauses : 68
% 6.92/1.59 % Removed in clause preprocessing : 5
% 6.92/1.59 % Initial clauses in saturation : 63
% 6.92/1.59 % Processed clauses : 7031
% 6.92/1.59 % ...of these trivial : 31
% 6.92/1.59 % ...subsumed : 4684
% 6.92/1.59 % ...remaining for further processing : 2316
% 6.92/1.59 % Other redundant clauses eliminated : 19
% 6.92/1.59 % Clauses deleted for lack of memory : 0
% 6.92/1.59 % Backward-subsumed : 116
% 6.92/1.59 % Backward-rewritten : 168
% 6.92/1.59 % Generated clauses : 48977
% 6.92/1.59 % ...of the previous two non-redundant : 48451
% 6.92/1.59 % ...aggressively subsumed : 0
% 6.92/1.59 % Contextual simplify-reflections : 20
% 6.92/1.59 % Paramodulations : 48948
% 6.92/1.59 % Factorizations : 2
% 6.92/1.59 % NegExts : 0
% 6.92/1.59 % Equation resolutions : 19
% 6.92/1.59 % Disequality decompositions : 0
% 6.92/1.59 % Total rewrite steps : 900
% 6.92/1.59 % ...of those cached : 428
% 6.92/1.59 % Propositional unsat checks : 0
% 6.92/1.59 % Propositional check models : 0
% 6.92/1.59 % Propositional check unsatisfiable : 0
% 6.92/1.59 % Propositional clauses : 0
% 6.92/1.59 % Propositional clauses after purity: 0
% 6.92/1.59 % Propositional unsat core size : 0
% 6.92/1.59 % Propositional preprocessing time : 0.000
% 6.92/1.59 % Propositional encoding time : 0.000
% 6.92/1.59 % Propositional solver time : 0.000
% 6.92/1.59 % Success case prop preproc time : 0.000
% 6.92/1.59 % Success case prop encoding time : 0.000
% 6.92/1.59 % Success case prop solver time : 0.000
% 6.92/1.59 % Current number of processed clauses : 1976
% 6.92/1.59 % Positive orientable unit clauses : 1008
% 6.92/1.59 % Positive unorientable unit clauses: 1
% 6.92/1.59 % Negative unit clauses : 9
% 6.92/1.59 % Non-unit-clauses : 958
% 6.92/1.59 % Current number of unprocessed clauses: 40984
% 6.92/1.59 % ...number of literals in the above : 65133
% 6.92/1.59 % Current number of archived formulas : 0
% 6.92/1.59 % Current number of archived clauses : 339
% 6.92/1.59 % Clause-clause subsumption calls (NU) : 217584
% 6.92/1.59 % Rec. Clause-clause subsumption calls : 141874
% 6.92/1.59 % Non-unit clause-clause subsumptions : 4342
% 6.92/1.59 % Unit Clause-clause subsumption calls : 8080
% 6.92/1.59 % Rewrite failures with RHS unbound : 0
% 6.92/1.59 % BW rewrite match attempts : 20357
% 6.92/1.59 % BW rewrite match successes : 12
% 6.92/1.59 % Condensation attempts : 0
% 6.92/1.59 % Condensation successes : 0
% 6.92/1.59 % Termbank termtop insertions : 760516
% 6.92/1.59 % Search garbage collected termcells : 1570
% 6.92/1.59
% 6.92/1.59 % -------------------------------------------------
% 6.92/1.59 % User time : 0.857 s
% 6.92/1.59 % System time : 0.052 s
% 6.92/1.59 % Total time : 0.909 s
% 6.92/1.59 % Maximum resident set size: 3932 pages
% 6.92/1.59
% 6.92/1.59 % -------------------------------------------------
% 6.92/1.59 % User time : 4.260 s
% 6.92/1.59 % System time : 0.277 s
% 6.92/1.59 % Total time : 4.537 s
% 6.92/1.59 % Maximum resident set size: 4864 pages
% 6.92/1.59 % E exiting
%------------------------------------------------------------------------------