%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET660+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.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 05:08:15 PM UTC 2026
% Result : Theorem 1.64s 1.82s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 83 ( 12 unt; 0 def)
% Number of atoms : 349 ( 37 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 442 ( 176 ~; 184 |; 31 &)
% ( 10 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 152 ( 9 sgn 70 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p24,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/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(p23,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(p34,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34) ).
fof(p17,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',p17) ).
fof(p32,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/sandbox2/benchmark/theBenchmark.p',p32) ).
fof(prove_relset_1_23,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( ! [X4] :
( ilf_type(X4,set_type)
=> ( member(X4,X2)
=> ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X5,X4),X3) ) ) )
<=> range(X1,X2,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_23) ).
fof(p22,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',p22) ).
fof(p33,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/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(p19,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X1 = X2
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
<=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,range_of(X1))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p27,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',p27) ).
fof(p7,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/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(p15,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(c_0_13,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)],[p24]) ).
fof(c_0_14,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p23]) ).
fof(c_0_15,plain,
! [X144,X145] :
( ( ~ ilf_type(X144,member_type(X145))
| member(X144,X145)
| empty(X145)
| ~ ilf_type(X145,set_type)
| ~ ilf_type(X144,set_type) )
& ( ~ member(X144,X145)
| ilf_type(X144,member_type(X145))
| empty(X145)
| ~ ilf_type(X145,set_type)
| ~ ilf_type(X144,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_16,plain,
! [X174] : ilf_type(X174,set_type),
inference(variable_rename,[status(thm)],[p34]) ).
fof(c_0_17,plain,
! [X126,X127] :
( ( ~ ilf_type(X127,subset_type(X126))
| ilf_type(X127,member_type(power_set(X126)))
| ~ ilf_type(X127,set_type)
| ~ ilf_type(X126,set_type) )
& ( ~ ilf_type(X127,member_type(power_set(X126)))
| ilf_type(X127,subset_type(X126))
| ~ ilf_type(X127,set_type)
| ~ ilf_type(X126,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])])]) ).
fof(c_0_18,plain,
! [X143] :
( ( ~ empty(power_set(X143))
| ~ ilf_type(X143,set_type) )
& ( ilf_type(power_set(X143),set_type)
| ~ ilf_type(X143,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_19,plain,
! [X168,X169,X170] :
( ~ ilf_type(X168,set_type)
| ~ ilf_type(X169,set_type)
| ~ ilf_type(X170,relation_type(X168,X169))
| range(X168,X169,X170) = range_of(X170) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p32])])]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( ! [X4] :
( ilf_type(X4,set_type)
=> ( member(X4,X2)
=> ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X5,X4),X3) ) ) )
<=> range(X1,X2,X3) = X2 ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_23]) ).
fof(c_0_21,plain,
! [X139,X140,X141] :
( ( ~ member(X139,power_set(X140))
| ~ ilf_type(X141,set_type)
| ~ member(X141,X139)
| member(X141,X140)
| ~ ilf_type(X140,set_type)
| ~ ilf_type(X139,set_type) )
& ( ilf_type(esk8_2(X139,X140),set_type)
| member(X139,power_set(X140))
| ~ ilf_type(X140,set_type)
| ~ ilf_type(X139,set_type) )
& ( member(esk8_2(X139,X140),X139)
| member(X139,power_set(X140))
| ~ ilf_type(X140,set_type)
| ~ ilf_type(X139,set_type) )
& ( ~ member(esk8_2(X139,X140),X140)
| member(X139,power_set(X140))
| ~ ilf_type(X140,set_type)
| ~ ilf_type(X139,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)],[p22])])])])]) ).
cnf(c_0_22,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_15]) ).
cnf(c_0_23,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,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_17]) ).
cnf(c_0_25,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_26,plain,
! [X171,X172,X173] :
( ~ ilf_type(X171,set_type)
| ~ ilf_type(X172,set_type)
| ~ ilf_type(X173,relation_type(X171,X172))
| ilf_type(range(X171,X172,X173),subset_type(X172)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p33])])]) ).
cnf(c_0_27,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_19]) ).
fof(c_0_28,negated_conjecture,
! [X179,X180] :
( ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,set_type)
& ilf_type(esk16_0,relation_type(esk14_0,esk15_0))
& ( ilf_type(esk17_0,set_type)
| range(esk14_0,esk15_0,esk16_0) != esk15_0 )
& ( member(esk17_0,esk15_0)
| range(esk14_0,esk15_0,esk16_0) != esk15_0 )
& ( ~ ilf_type(X179,set_type)
| ~ member(ordered_pair(X179,esk17_0),esk16_0)
| range(esk14_0,esk15_0,esk16_0) != esk15_0 )
& ( ilf_type(esk18_1(X180),set_type)
| ~ member(X180,esk15_0)
| ~ ilf_type(X180,set_type)
| range(esk14_0,esk15_0,esk16_0) = esk15_0 )
& ( member(ordered_pair(esk18_1(X180),X180),esk16_0)
| ~ member(X180,esk15_0)
| ~ ilf_type(X180,set_type)
| range(esk14_0,esk15_0,esk16_0) = esk15_0 ) ),
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_20])])])])]) ).
cnf(c_0_29,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_21]) ).
cnf(c_0_30,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_22,c_0_23]),c_0_23])]) ).
cnf(c_0_31,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_24,c_0_23]),c_0_23])]) ).
cnf(c_0_32,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_23])]) ).
cnf(c_0_33,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_26]) ).
cnf(c_0_34,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_27,c_0_23]),c_0_23])]) ).
cnf(c_0_35,negated_conjecture,
ilf_type(esk16_0,relation_type(esk14_0,esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,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_29,c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_37,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_38,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_33,c_0_23]),c_0_23])]) ).
cnf(c_0_39,negated_conjecture,
range(esk14_0,esk15_0,esk16_0) = range_of(esk16_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_40,plain,
! [X130,X131,X132] :
( ( ~ member(X132,X130)
| member(X132,X131)
| ~ ilf_type(X132,set_type)
| X130 != X131
| ~ ilf_type(X131,set_type)
| ~ ilf_type(X130,set_type) )
& ( ~ member(X132,X131)
| member(X132,X130)
| ~ ilf_type(X132,set_type)
| X130 != X131
| ~ ilf_type(X131,set_type)
| ~ ilf_type(X130,set_type) )
& ( ilf_type(esk6_2(X130,X131),set_type)
| X130 = X131
| ~ ilf_type(X131,set_type)
| ~ ilf_type(X130,set_type) )
& ( ~ member(esk6_2(X130,X131),X130)
| ~ member(esk6_2(X130,X131),X131)
| X130 = X131
| ~ ilf_type(X131,set_type)
| ~ ilf_type(X130,set_type) )
& ( member(esk6_2(X130,X131),X130)
| member(esk6_2(X130,X131),X131)
| X130 = X131
| ~ ilf_type(X131,set_type)
| ~ ilf_type(X130,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)],[p19])])])])]) ).
cnf(c_0_41,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
ilf_type(range_of(esk16_0),subset_type(esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_35])]) ).
cnf(c_0_43,plain,
( member(esk6_2(X1,X2),X1)
| member(esk6_2(X1,X2),X2)
| X1 = X2
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,range_of(esk16_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
( X1 = X2
| member(esk6_2(X1,X2),X1)
| member(esk6_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_23]),c_0_23])]) ).
fof(c_0_46,plain,
! [X89,X90,X92] :
( ( ilf_type(esk1_2(X89,X90),set_type)
| ~ member(X90,range_of(X89))
| ~ ilf_type(X90,set_type)
| ~ ilf_type(X89,binary_relation_type) )
& ( member(ordered_pair(esk1_2(X89,X90),X90),X89)
| ~ member(X90,range_of(X89))
| ~ ilf_type(X90,set_type)
| ~ ilf_type(X89,binary_relation_type) )
& ( ~ ilf_type(X92,set_type)
| ~ member(ordered_pair(X92,X90),X89)
| member(X90,range_of(X89))
| ~ ilf_type(X90,set_type)
| ~ ilf_type(X89,binary_relation_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])])])])]) ).
cnf(c_0_47,negated_conjecture,
( member(ordered_pair(esk18_1(X1),X1),esk16_0)
| range(esk14_0,esk15_0,esk16_0) = esk15_0
| ~ member(X1,esk15_0)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_48,plain,
! [X155,X156,X157] :
( ~ ilf_type(X155,set_type)
| ~ ilf_type(X156,set_type)
| ~ ilf_type(X157,subset_type(cross_product(X155,X156)))
| relation_like(X157) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])]) ).
fof(c_0_49,plain,
! [X107,X108,X109,X110] :
( ( ~ ilf_type(X109,subset_type(cross_product(X107,X108)))
| ilf_type(X109,relation_type(X107,X108))
| ~ ilf_type(X108,set_type)
| ~ ilf_type(X107,set_type) )
& ( ~ ilf_type(X110,relation_type(X107,X108))
| ilf_type(X110,subset_type(cross_product(X107,X108)))
| ~ ilf_type(X108,set_type)
| ~ ilf_type(X107,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])]) ).
cnf(c_0_50,plain,
( X1 = X2
| ~ member(esk6_2(X1,X2),X1)
| ~ member(esk6_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,negated_conjecture,
( range_of(esk16_0) = X1
| member(esk6_2(range_of(esk16_0),X1),esk15_0)
| member(esk6_2(range_of(esk16_0),X1),X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) = esk15_0
| member(ordered_pair(esk18_1(X1),X1),esk16_0)
| ~ member(X1,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_23])]) ).
fof(c_0_54,plain,
! [X124] :
( ( relation_like(X124)
| ~ ilf_type(X124,binary_relation_type)
| ~ ilf_type(X124,set_type) )
& ( ilf_type(X124,set_type)
| ~ ilf_type(X124,binary_relation_type)
| ~ ilf_type(X124,set_type) )
& ( ~ relation_like(X124)
| ~ ilf_type(X124,set_type)
| ilf_type(X124,binary_relation_type)
| ~ ilf_type(X124,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])]) ).
cnf(c_0_55,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_48]) ).
cnf(c_0_56,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_49]) ).
cnf(c_0_57,plain,
( X1 = X2
| ~ member(esk6_2(X1,X2),X2)
| ~ member(esk6_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_23]),c_0_23])]) ).
cnf(c_0_58,negated_conjecture,
( range_of(esk16_0) = esk15_0
| member(esk6_2(range_of(esk16_0),esk15_0),esk15_0) ),
inference(ef,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
( member(X1,range_of(X2))
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_23]),c_0_23])]) ).
cnf(c_0_60,negated_conjecture,
( range_of(esk16_0) = esk15_0
| member(ordered_pair(esk18_1(X1),X1),esk16_0)
| ~ member(X1,esk15_0) ),
inference(rw,[status(thm)],[c_0_53,c_0_39]) ).
cnf(c_0_61,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_54]) ).
cnf(c_0_62,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_55,c_0_23]),c_0_23])]) ).
cnf(c_0_63,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_56,c_0_23]),c_0_23])]) ).
cnf(c_0_64,negated_conjecture,
( ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,esk17_0),esk16_0)
| range(esk14_0,esk15_0,esk16_0) != esk15_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_65,negated_conjecture,
( range_of(esk16_0) = esk15_0
| ~ member(esk6_2(range_of(esk16_0),esk15_0),range_of(esk16_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( range_of(esk16_0) = esk15_0
| member(X1,range_of(esk16_0))
| ~ member(X1,esk15_0)
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_67,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_61]) ).
cnf(c_0_68,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) != esk15_0
| ~ member(ordered_pair(X1,esk17_0),esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_23])]) ).
cnf(c_0_70,plain,
( member(ordered_pair(esk1_2(X1,X2),X2),X1)
| ~ member(X2,range_of(X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_71,negated_conjecture,
( member(esk17_0,esk15_0)
| range(esk14_0,esk15_0,esk16_0) != esk15_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_72,negated_conjecture,
( range_of(esk16_0) = esk15_0
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_58]) ).
cnf(c_0_73,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_23])]) ).
cnf(c_0_74,negated_conjecture,
relation_like(esk16_0),
inference(spm,[status(thm)],[c_0_68,c_0_35]) ).
cnf(c_0_75,negated_conjecture,
( range_of(esk16_0) != esk15_0
| ~ member(ordered_pair(X1,esk17_0),esk16_0) ),
inference(rw,[status(thm)],[c_0_69,c_0_39]) ).
cnf(c_0_76,plain,
( member(ordered_pair(esk1_2(X1,X2),X2),X1)
| ~ member(X2,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_23])]) ).
cnf(c_0_77,negated_conjecture,
( member(esk17_0,esk15_0)
| range_of(esk16_0) != esk15_0 ),
inference(rw,[status(thm)],[c_0_71,c_0_39]) ).
cnf(c_0_78,negated_conjecture,
range_of(esk16_0) = esk15_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]) ).
cnf(c_0_79,negated_conjecture,
( range_of(esk16_0) != esk15_0
| ~ member(esk17_0,range_of(esk16_0))
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,negated_conjecture,
member(esk17_0,esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_81,negated_conjecture,
~ ilf_type(esk16_0,binary_relation_type),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_78]),c_0_78])]),c_0_80])]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_73]),c_0_74])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET660+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n026.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:31:23 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.64/1.82 % Version : CSE_E---1.7
% 1.64/1.82 % Problem : theBenchmark.p
% 1.64/1.82 % SZS status Theorem for theBenchmark.p
% 1.64/1.82 % SZS output start CNFRefutation
% See solution above
% 1.64/1.82 % Total time : 1.371s
%------------------------------------------------------------------------------