%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET682+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 : n024.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 05:08:18 PM UTC 2026
% Result : Theorem 1.10s 1.72s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 82 ( 12 unt; 0 def)
% Number of atoms : 313 ( 8 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 390 ( 159 ~; 146 |; 32 &)
% ( 7 <=>; 46 =>; 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 : 161 ( 9 sgn 74 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p4,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',p4) ).
fof(p15,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(p24,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
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(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(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(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(p2,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',p2) ).
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(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,domain_of(X2))
=> ? [X3] :
( ilf_type(X3,set_type)
& member(X3,range_of(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(prove_relset_1_49,conjecture,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(X5,range(X1,X2,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_49) ).
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)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
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(c_0_14,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)],[p4]) ).
fof(c_0_15,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p15]) ).
fof(c_0_16,plain,
! [X74,X75] :
( ( ~ ilf_type(X74,member_type(X75))
| member(X74,X75)
| empty(X75)
| ~ ilf_type(X75,set_type)
| ~ ilf_type(X74,set_type) )
& ( ~ member(X74,X75)
| ilf_type(X74,member_type(X75))
| empty(X75)
| ~ ilf_type(X75,set_type)
| ~ ilf_type(X74,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_17,plain,
! [X121] : ilf_type(X121,set_type),
inference(variable_rename,[status(thm)],[p24]) ).
fof(c_0_18,plain,
! [X87,X88] :
( ( ~ ilf_type(X88,subset_type(X87))
| ilf_type(X88,member_type(power_set(X87)))
| ~ ilf_type(X88,set_type)
| ~ ilf_type(X87,set_type) )
& ( ~ ilf_type(X88,member_type(power_set(X87)))
| ilf_type(X88,subset_type(X87))
| ~ ilf_type(X88,set_type)
| ~ ilf_type(X87,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p12])])])]) ).
fof(c_0_19,plain,
! [X95] :
( ( ~ empty(power_set(X95))
| ~ ilf_type(X95,set_type) )
& ( ilf_type(power_set(X95),set_type)
| ~ ilf_type(X95,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_20,plain,
! [X91,X92,X93] :
( ( ~ member(X91,power_set(X92))
| ~ ilf_type(X93,set_type)
| ~ member(X93,X91)
| member(X93,X92)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( ilf_type(esk7_2(X91,X92),set_type)
| member(X91,power_set(X92))
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( member(esk7_2(X91,X92),X91)
| member(X91,power_set(X92))
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( ~ member(esk7_2(X91,X92),X92)
| member(X91,power_set(X92))
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,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)],[p14])])])])]) ).
cnf(c_0_21,plain,
( member(X1,X2)
| empty(X2)
| ~ ilf_type(X1,member_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,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_26,plain,
! [X104,X105,X106] :
( ~ ilf_type(X104,set_type)
| ~ ilf_type(X105,set_type)
| ~ ilf_type(X106,subset_type(cross_product(X104,X105)))
| relation_like(X106) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p18])])]) ).
fof(c_0_27,plain,
! [X67,X68,X69,X70] :
( ( ~ ilf_type(X69,subset_type(cross_product(X67,X68)))
| ilf_type(X69,relation_type(X67,X68))
| ~ ilf_type(X68,set_type)
| ~ ilf_type(X67,set_type) )
& ( ~ ilf_type(X70,relation_type(X67,X68))
| ilf_type(X70,subset_type(cross_product(X67,X68)))
| ~ ilf_type(X68,set_type)
| ~ ilf_type(X67,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
cnf(c_0_28,plain,
( member(X3,X2)
| ~ member(X1,power_set(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_20]) ).
cnf(c_0_29,plain,
( empty(X1)
| member(X2,X1)
| ~ ilf_type(X2,member_type(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22])]) ).
cnf(c_0_30,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_23,c_0_22]),c_0_22])]) ).
cnf(c_0_31,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_22])]) ).
fof(c_0_32,plain,
! [X118,X119,X120] :
( ~ ilf_type(X118,set_type)
| ~ ilf_type(X119,set_type)
| ~ ilf_type(X120,relation_type(X118,X119))
| ilf_type(range(X118,X119,X120),subset_type(X119)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])]) ).
fof(c_0_33,plain,
! [X78,X79] :
( ( ~ empty(X78)
| ~ ilf_type(X79,set_type)
| ~ member(X79,X78)
| ~ ilf_type(X78,set_type) )
& ( ilf_type(esk4_1(X78),set_type)
| empty(X78)
| ~ ilf_type(X78,set_type) )
& ( member(esk4_1(X78),X78)
| empty(X78)
| ~ ilf_type(X78,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_25])])])])]) ).
fof(c_0_34,plain,
! [X64,X65] :
( ( ilf_type(esk1_2(X64,X65),set_type)
| ~ member(X64,domain_of(X65))
| ~ ilf_type(X65,binary_relation_type)
| ~ ilf_type(X64,set_type) )
& ( member(esk1_2(X64,X65),range_of(X65))
| ~ member(X64,domain_of(X65))
| ~ ilf_type(X65,binary_relation_type)
| ~ ilf_type(X64,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)],[p1])])])])]) ).
fof(c_0_35,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(X5,range(X1,X2,X3)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_relset_1_49])]) ).
fof(c_0_36,plain,
! [X109,X110,X111] :
( ~ ilf_type(X109,set_type)
| ~ ilf_type(X110,set_type)
| ~ ilf_type(X111,relation_type(X109,X110))
| domain(X109,X110,X111) = domain_of(X111) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p20])])]) ).
fof(c_0_37,plain,
! [X85] :
( ( relation_like(X85)
| ~ ilf_type(X85,binary_relation_type)
| ~ ilf_type(X85,set_type) )
& ( ilf_type(X85,set_type)
| ~ ilf_type(X85,binary_relation_type)
| ~ ilf_type(X85,set_type) )
& ( ~ relation_like(X85)
| ~ ilf_type(X85,set_type)
| ilf_type(X85,binary_relation_type)
| ~ ilf_type(X85,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])]) ).
cnf(c_0_38,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_26]) ).
cnf(c_0_39,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_27]) ).
cnf(c_0_40,plain,
( member(X1,X2)
| ~ member(X3,power_set(X2))
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_41,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_42,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_43,plain,
! [X115,X116,X117] :
( ~ ilf_type(X115,set_type)
| ~ ilf_type(X116,set_type)
| ~ ilf_type(X117,relation_type(X115,X116))
| range(X115,X116,X117) = range_of(X117) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p22])])]) ).
cnf(c_0_44,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,plain,
( member(esk1_2(X1,X2),range_of(X2))
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_46,negated_conjecture,
! [X126] :
( ~ empty(esk11_0)
& ilf_type(esk11_0,set_type)
& ~ empty(esk12_0)
& ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,relation_type(esk11_0,esk12_0))
& ilf_type(esk14_0,member_type(esk11_0))
& member(esk14_0,domain(esk11_0,esk12_0,esk13_0))
& ( ~ ilf_type(X126,member_type(esk12_0))
| ~ member(X126,range(esk11_0,esk12_0,esk13_0)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])]) ).
cnf(c_0_47,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,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_37]) ).
cnf(c_0_49,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_38,c_0_22]),c_0_22])]) ).
cnf(c_0_50,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_39,c_0_22]),c_0_22])]) ).
cnf(c_0_51,plain,
( member(esk4_1(X1),X1)
| empty(X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_52,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_53,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_22]),c_0_22])]) ).
cnf(c_0_54,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_22]),c_0_22])]) ).
cnf(c_0_56,plain,
( member(esk1_2(X1,X2),range_of(X2))
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_22])]) ).
cnf(c_0_57,negated_conjecture,
member(esk14_0,domain(esk11_0,esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X3,relation_type(X1,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_59,negated_conjecture,
ilf_type(esk13_0,relation_type(esk11_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_60,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_48]) ).
cnf(c_0_61,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_62,negated_conjecture,
( ~ ilf_type(X1,member_type(esk12_0))
| ~ member(X1,range(esk11_0,esk12_0,esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_63,plain,
( empty(X1)
| member(esk4_1(X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_22])]) ).
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_16]) ).
cnf(c_0_65,plain,
( member(X1,X2)
| ~ member(X1,range(X3,X2,X4))
| ~ ilf_type(X4,relation_type(X3,X2)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_66,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_22]),c_0_22])]) ).
cnf(c_0_67,plain,
( ~ empty(range_of(X1))
| ~ member(X2,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_68,negated_conjecture,
member(esk14_0,domain_of(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
cnf(c_0_69,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_22])]) ).
cnf(c_0_70,negated_conjecture,
relation_like(esk13_0),
inference(spm,[status(thm)],[c_0_61,c_0_59]) ).
cnf(c_0_71,negated_conjecture,
( empty(range(esk11_0,esk12_0,esk13_0))
| ~ ilf_type(esk4_1(range(esk11_0,esk12_0,esk13_0)),member_type(esk12_0)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,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_55]) ).
cnf(c_0_73,plain,
( member(X1,X2)
| ~ member(X1,range_of(X3))
| ~ ilf_type(X3,relation_type(X4,X2)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_74,negated_conjecture,
( ~ empty(range_of(esk13_0))
| ~ ilf_type(esk13_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_75,negated_conjecture,
ilf_type(esk13_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( empty(range(esk11_0,esk12_0,esk13_0))
| ~ member(esk4_1(range(esk11_0,esk12_0,esk13_0)),esk12_0) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( member(X1,esk12_0)
| ~ member(X1,range_of(esk13_0)) ),
inference(spm,[status(thm)],[c_0_73,c_0_59]) ).
cnf(c_0_78,negated_conjecture,
~ empty(range_of(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_79,negated_conjecture,
( empty(range_of(esk13_0))
| ~ member(esk4_1(range_of(esk13_0)),esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_66]),c_0_59])]) ).
cnf(c_0_80,negated_conjecture,
member(esk4_1(range_of(esk13_0)),esk12_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_63]),c_0_78]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]),c_0_78]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET682+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.07/0.34 % Computer : n024.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8042.1875MB
% 0.07/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon May 4 21:31:27 EDT 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % start to proof: theBenchmark
% 1.10/1.72 % Version : CSE_E---1.7
% 1.10/1.72 % Problem : theBenchmark.p
% 1.10/1.72 % SZS status Theorem for theBenchmark.p
% 1.10/1.72 % SZS output start CNFRefutation
% See solution above
% 1.10/1.72 % Total time : 1.361s
%------------------------------------------------------------------------------