%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET682+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 : n004.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 0.11s 0.47s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 82 ( 14 unt; 0 def)
% Number of atoms : 316 ( 8 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 394 ( 160 ~; 141 |; 35 &)
% ( 7 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 162 ( 9 sgn 78 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p6,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',p6) ).
fof(prove_relset_1_49,conjecture,
! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
=> ? [X5] :
( member(X5,range(X1,X2,X3))
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_49) ).
fof(p18,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',p18) ).
fof(p24,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(p2,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',p2) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,domain_of(X2))
=> ? [X3] :
( member(X3,range_of(X2))
& ilf_type(X3,set_type) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> domain(X1,X2,X3) = domain_of(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(p10,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',p10) ).
fof(p4,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',p4) ).
fof(p15,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',p15) ).
fof(p12,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',p12) ).
fof(p23,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',p23) ).
fof(p22,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',p22) ).
fof(p14,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',p14) ).
fof(c_0_14,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p6]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
=> ? [X5] :
( member(X5,range(X1,X2,X3))
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_49]) ).
fof(c_0_16,plain,
! [X46,X47,X48] :
( relation_like(X48)
| ~ ilf_type(X48,subset_type(cross_product(X46,X47)))
| ~ ilf_type(X47,set_type)
| ~ ilf_type(X46,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p18])])])]) ).
fof(c_0_17,plain,
! [X63] : ilf_type(X63,set_type),
inference(variable_rename,[status(thm)],[p24]) ).
fof(c_0_18,plain,
! [X9,X10,X11,X12] :
( ( ~ ilf_type(X9,set_type)
| ~ ilf_type(X10,set_type)
| ilf_type(X12,subset_type(cross_product(X9,X10)))
| ~ ilf_type(X12,relation_type(X9,X10)) )
& ( ~ ilf_type(X9,set_type)
| ~ ilf_type(X10,set_type)
| ilf_type(X11,relation_type(X9,X10))
| ~ ilf_type(X11,subset_type(cross_product(X9,X10))) ) ),
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])])])])]) ).
fof(c_0_19,plain,
! [X20,X21] :
( ( ~ ilf_type(X20,set_type)
| empty(X20)
| member(esk4_1(X20),X20) )
& ( ~ ilf_type(X20,set_type)
| empty(X20)
| ilf_type(esk4_1(X20),set_type) )
& ( ~ ilf_type(X20,set_type)
| ~ member(X21,X20)
| ~ ilf_type(X21,set_type)
| ~ empty(X20) ) ),
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_14])])])])])]) ).
fof(c_0_20,plain,
! [X6,X7] :
( ( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,binary_relation_type)
| ~ member(X6,domain_of(X7))
| member(esk1_2(X6,X7),range_of(X7)) )
& ( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,binary_relation_type)
| ~ member(X6,domain_of(X7))
| 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])])])])])]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
=> ? [X5] :
( member(X5,range(X1,X2,X3))
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X51,X52,X53] :
( domain(X51,X52,X53) = domain_of(X53)
| ~ ilf_type(X53,relation_type(X51,X52))
| ~ ilf_type(X52,set_type)
| ~ ilf_type(X51,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p20])])])]) ).
fof(c_0_23,plain,
! [X27] :
( ( ~ ilf_type(X27,set_type)
| ilf_type(X27,binary_relation_type)
| ~ ilf_type(X27,set_type)
| ~ relation_like(X27) )
& ( ~ ilf_type(X27,set_type)
| ~ ilf_type(X27,binary_relation_type)
| ilf_type(X27,set_type) )
& ( ~ ilf_type(X27,set_type)
| ~ ilf_type(X27,binary_relation_type)
| relation_like(X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])])]) ).
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_16]) ).
cnf(c_0_25,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,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_18]) ).
fof(c_0_27,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)],[p4]) ).
fof(c_0_28,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(power_set(X1),set_type)
& ~ empty(power_set(X1)) ) ),
inference(fof_simplification,[status(thm)],[p15]) ).
cnf(c_0_29,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,domain_of(X2))
| member(esk1_2(X1,X2),range_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_31,negated_conjecture,
! [X68] :
( ( ~ member(X68,range(esk11_0,esk12_0,esk13_0))
| ~ ilf_type(X68,member_type(esk12_0)) )
& member(esk14_0,domain(esk11_0,esk12_0,esk13_0))
& ilf_type(esk14_0,member_type(esk11_0))
& ilf_type(esk13_0,relation_type(esk11_0,esk12_0))
& ilf_type(esk12_0,set_type)
& ~ empty(esk12_0)
& ilf_type(esk11_0,set_type)
& ~ empty(esk11_0) ),
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_21])])])])]) ).
cnf(c_0_32,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| domain(X1,X2,X3) = domain_of(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,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_23]) ).
cnf(c_0_34,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_25]),c_0_25])]) ).
cnf(c_0_35,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_26,c_0_25]),c_0_25])]) ).
fof(c_0_36,plain,
! [X16,X17] :
( ( ~ ilf_type(X16,set_type)
| ~ ilf_type(X17,set_type)
| empty(X17)
| ilf_type(X16,member_type(X17))
| ~ member(X16,X17) )
& ( ~ ilf_type(X16,set_type)
| ~ ilf_type(X17,set_type)
| empty(X17)
| member(X16,X17)
| ~ ilf_type(X16,member_type(X17)) ) ),
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_27])])])])]) ).
fof(c_0_37,plain,
! [X29,X30] :
( ( ~ ilf_type(X29,set_type)
| ~ ilf_type(X30,set_type)
| ilf_type(X30,subset_type(X29))
| ~ ilf_type(X30,member_type(power_set(X29))) )
& ( ~ ilf_type(X29,set_type)
| ~ ilf_type(X30,set_type)
| ilf_type(X30,member_type(power_set(X29)))
| ~ ilf_type(X30,subset_type(X29)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p12])])])])]) ).
fof(c_0_38,plain,
! [X37] :
( ( ~ ilf_type(X37,set_type)
| ilf_type(power_set(X37),set_type) )
& ( ~ ilf_type(X37,set_type)
| ~ empty(power_set(X37)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
fof(c_0_39,plain,
! [X60,X61,X62] :
( ilf_type(range(X60,X61,X62),subset_type(X61))
| ~ ilf_type(X62,relation_type(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])])])]) ).
fof(c_0_40,plain,
! [X57,X58,X59] :
( range(X57,X58,X59) = range_of(X59)
| ~ ilf_type(X59,relation_type(X57,X58))
| ~ ilf_type(X58,set_type)
| ~ ilf_type(X57,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p22])])])]) ).
cnf(c_0_41,plain,
( ~ member(X2,X1)
| ~ empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_25]),c_0_25])]) ).
cnf(c_0_42,plain,
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,domain_of(X2))
| member(esk1_2(X1,X2),range_of(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_25])]) ).
cnf(c_0_43,negated_conjecture,
member(esk14_0,domain(esk11_0,esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| domain(X1,X2,X3) = domain_of(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_25]),c_0_25])]) ).
cnf(c_0_45,negated_conjecture,
ilf_type(esk13_0,relation_type(esk11_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_46,plain,
( ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_33]) ).
cnf(c_0_47,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| relation_like(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_48,plain,
! [X33,X34,X35] :
( ( ~ ilf_type(X33,set_type)
| ~ ilf_type(X34,set_type)
| member(X33,power_set(X34))
| ~ member(esk7_2(X33,X34),X34) )
& ( ~ ilf_type(X33,set_type)
| ~ ilf_type(X34,set_type)
| member(X33,power_set(X34))
| member(esk7_2(X33,X34),X33) )
& ( ~ ilf_type(X33,set_type)
| ~ ilf_type(X34,set_type)
| member(X33,power_set(X34))
| ilf_type(esk7_2(X33,X34),set_type) )
& ( ~ ilf_type(X33,set_type)
| ~ ilf_type(X34,set_type)
| member(X35,X34)
| ~ member(X35,X33)
| ~ ilf_type(X35,set_type)
| ~ member(X33,power_set(X34)) ) ),
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)],[p14])])])])])]) ).
cnf(c_0_49,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_36]) ).
cnf(c_0_50,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_37]) ).
cnf(c_0_51,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_52,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_39]) ).
cnf(c_0_53,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_40]) ).
cnf(c_0_54,plain,
( ~ ilf_type(X1,binary_relation_type)
| ~ member(X2,domain_of(X1))
| ~ empty(range_of(X1)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_55,negated_conjecture,
member(esk14_0,domain_of(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_56,plain,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_25])]) ).
cnf(c_0_57,negated_conjecture,
relation_like(esk13_0),
inference(spm,[status(thm)],[c_0_47,c_0_45]) ).
cnf(c_0_58,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_48]) ).
cnf(c_0_59,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_49,c_0_25]),c_0_25])]) ).
cnf(c_0_60,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_50,c_0_25]),c_0_25])]) ).
cnf(c_0_61,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_25])]) ).
cnf(c_0_62,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_52,c_0_25]),c_0_25])]) ).
cnf(c_0_63,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_53,c_0_25]),c_0_25])]) ).
cnf(c_0_64,negated_conjecture,
( ~ member(X1,range(esk11_0,esk12_0,esk13_0))
| ~ ilf_type(X1,member_type(esk12_0)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_65,plain,
( ~ ilf_type(X1,set_type)
| empty(X1)
| member(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_66,negated_conjecture,
( ~ ilf_type(esk13_0,binary_relation_type)
| ~ empty(range_of(esk13_0)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_67,negated_conjecture,
ilf_type(esk13_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_68,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_58,c_0_25]),c_0_25]),c_0_25])]) ).
cnf(c_0_69,plain,
( ~ ilf_type(X1,subset_type(X2))
| member(X1,power_set(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_70,plain,
( ~ ilf_type(X1,relation_type(X3,X2))
| ilf_type(range_of(X1),subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
( ~ ilf_type(X1,member_type(esk12_0))
| ~ member(X1,range_of(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_63]),c_0_45])]) ).
cnf(c_0_72,plain,
( member(esk4_1(X1),X1)
| empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_25])]) ).
cnf(c_0_73,negated_conjecture,
~ empty(range_of(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]) ).
cnf(c_0_74,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_36]) ).
cnf(c_0_75,plain,
( ~ ilf_type(X3,subset_type(X2))
| ~ member(X1,X3)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,negated_conjecture,
ilf_type(range_of(esk13_0),subset_type(esk12_0)),
inference(spm,[status(thm)],[c_0_70,c_0_45]) ).
cnf(c_0_77,negated_conjecture,
~ ilf_type(esk4_1(range_of(esk13_0)),member_type(esk12_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_78,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_74,c_0_25]),c_0_25])]),c_0_41]) ).
cnf(c_0_79,negated_conjecture,
( ~ member(X1,range_of(esk13_0))
| member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,negated_conjecture,
~ member(esk4_1(range_of(esk13_0)),esk12_0),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_72]),c_0_80]),c_0_73]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET682+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 05:32:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.47 % Version: 3.5.1
% 0.11/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.47 % Starting sh5l with 300s (1) cores
% 0.11/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2344583 completed with status 0
% 0.11/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.47 % No SInE strategy applied
% 0.11/0.47 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.11/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 0.11/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.47 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.47 % SubtermCWHack with pid 2344590 completed with status 0
% 0.11/0.47 % Result found by SubtermCWHack
% 0.11/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.47 % No SInE strategy applied
% 0.11/0.47 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.11/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.47 % Preprocessing time : 0.001 s
% 0.11/0.47
% 0.11/0.47 % Proof found!
% 0.11/0.47 % SZS status Theorem
% 0.11/0.47 % SZS output start CNFRefutation
% See solution above
% 0.11/0.47 % Parsed axioms : 25
% 0.11/0.47 % Removed by relevancy pruning/SinE : 0
% 0.11/0.47 % Initial clauses : 49
% 0.11/0.47 % Removed in clause preprocessing : 1
% 0.11/0.47 % Initial clauses in saturation : 48
% 0.11/0.47 % Processed clauses : 267
% 0.11/0.47 % ...of these trivial : 11
% 0.11/0.47 % ...subsumed : 50
% 0.11/0.47 % ...remaining for further processing : 206
% 0.11/0.47 % Other redundant clauses eliminated : 1
% 0.11/0.47 % Clauses deleted for lack of memory : 0
% 0.11/0.47 % Backward-subsumed : 3
% 0.11/0.47 % Backward-rewritten : 3
% 0.11/0.47 % Generated clauses : 525
% 0.11/0.47 % ...of the previous two non-redundant : 498
% 0.11/0.47 % ...aggressively subsumed : 0
% 0.11/0.47 % Contextual simplify-reflections : 1
% 0.11/0.47 % Paramodulations : 524
% 0.11/0.47 % Factorizations : 0
% 0.11/0.47 % NegExts : 0
% 0.11/0.47 % Equation resolutions : 1
% 0.11/0.47 % Disequality decompositions : 0
% 0.11/0.47 % Total rewrite steps : 94
% 0.11/0.47 % ...of those cached : 68
% 0.11/0.47 % Propositional unsat checks : 0
% 0.11/0.47 % Propositional check models : 0
% 0.11/0.47 % Propositional check unsatisfiable : 0
% 0.11/0.47 % Propositional clauses : 0
% 0.11/0.47 % Propositional clauses after purity: 0
% 0.11/0.47 % Propositional unsat core size : 0
% 0.11/0.47 % Propositional preprocessing time : 0.000
% 0.11/0.47 % Propositional encoding time : 0.000
% 0.11/0.47 % Propositional solver time : 0.000
% 0.11/0.47 % Success case prop preproc time : 0.000
% 0.11/0.47 % Success case prop encoding time : 0.000
% 0.11/0.47 % Success case prop solver time : 0.000
% 0.11/0.47 % Current number of processed clauses : 200
% 0.11/0.47 % Positive orientable unit clauses : 50
% 0.11/0.47 % Positive unorientable unit clauses: 0
% 0.11/0.47 % Negative unit clauses : 10
% 0.11/0.47 % Non-unit-clauses : 140
% 0.11/0.47 % Current number of unprocessed clauses: 267
% 0.11/0.47 % ...number of literals in the above : 618
% 0.11/0.47 % Current number of archived formulas : 0
% 0.11/0.47 % Current number of archived clauses : 6
% 0.11/0.47 % Clause-clause subsumption calls (NU) : 1258
% 0.11/0.47 % Rec. Clause-clause subsumption calls : 1052
% 0.11/0.47 % Non-unit clause-clause subsumptions : 36
% 0.11/0.47 % Unit Clause-clause subsumption calls : 355
% 0.11/0.47 % Rewrite failures with RHS unbound : 0
% 0.11/0.47 % BW rewrite match attempts : 15
% 0.11/0.47 % BW rewrite match successes : 3
% 0.11/0.47 % Condensation attempts : 0
% 0.11/0.47 % Condensation successes : 0
% 0.11/0.47 % Termbank termtop insertions : 11575
% 0.11/0.47 % Search garbage collected termcells : 963
% 0.11/0.47
% 0.11/0.47 % -------------------------------------------------
% 0.11/0.47 % User time : 0.017 s
% 0.11/0.47 % System time : 0.003 s
% 0.11/0.47 % Total time : 0.020 s
% 0.11/0.47 % Maximum resident set size: 3664 pages
% 0.11/0.47
% 0.11/0.47 % -------------------------------------------------
% 0.11/0.47 % User time : 0.061 s
% 0.11/0.47 % System time : 0.017 s
% 0.11/0.47 % Total time : 0.077 s
% 0.11/0.47 % Maximum resident set size: 4864 pages
% 0.11/0.47 % E exiting
%------------------------------------------------------------------------------