%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET678+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 : n015.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 1.38s 1.74s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 99 ( 10 unt; 0 def)
% Number of atoms : 361 ( 27 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 448 ( 186 ~; 184 |; 23 &)
% ( 7 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 4 con; 0-3 aty)
% Number of variables : 195 ( 7 sgn 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p28,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',p28) ).
fof(p27,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',p27) ).
fof(p32,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',p32) ).
fof(p38,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p38) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,identity_relation_of_type(X1))
<=> ilf_type(X2,relation_type(X1,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(p22,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',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(domain(X1,X2,X3),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
fof(p34,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',p34) ).
fof(p26,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',p26) ).
fof(p35,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',p35) ).
fof(prove_relset_1_45,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,identity_relation_of_type(X1))
=> ( compose(X2,identity_relation_of(X1)) = X2
& compose(identity_relation_of(X1),X2) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_45) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( subset(domain_of(X2),X1)
=> compose(identity_relation_of(X1),X2) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p19,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( subset(range_of(X2),X1)
=> compose(X2,identity_relation_of(X1)) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(p25,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',p25) ).
fof(p15,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',p15) ).
fof(p13,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',p13) ).
fof(c_0_17,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)],[p28]) ).
fof(c_0_18,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p27]) ).
fof(c_0_19,plain,
! [X174,X175,X176] :
( ~ ilf_type(X174,set_type)
| ~ ilf_type(X175,set_type)
| ~ ilf_type(X176,relation_type(X174,X175))
| domain(X174,X175,X176) = domain_of(X176) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p32])])]) ).
fof(c_0_20,plain,
! [X196] : ilf_type(X196,set_type),
inference(variable_rename,[status(thm)],[p38]) ).
fof(c_0_21,plain,
! [X114,X115] :
( ( ~ ilf_type(X115,identity_relation_of_type(X114))
| ilf_type(X115,relation_type(X114,X114))
| ~ ilf_type(X115,set_type)
| ~ ilf_type(X114,set_type) )
& ( ~ ilf_type(X115,relation_type(X114,X114))
| ilf_type(X115,identity_relation_of_type(X114))
| ~ ilf_type(X115,set_type)
| ~ ilf_type(X114,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])]) ).
fof(c_0_22,plain,
! [X166,X167] :
( ( ~ ilf_type(X166,member_type(X167))
| member(X166,X167)
| empty(X167)
| ~ ilf_type(X167,set_type)
| ~ ilf_type(X166,set_type) )
& ( ~ member(X166,X167)
| ilf_type(X166,member_type(X167))
| empty(X167)
| ~ ilf_type(X167,set_type)
| ~ ilf_type(X166,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
fof(c_0_23,plain,
! [X147,X148] :
( ( ~ ilf_type(X148,subset_type(X147))
| ilf_type(X148,member_type(power_set(X147)))
| ~ ilf_type(X148,set_type)
| ~ ilf_type(X147,set_type) )
& ( ~ ilf_type(X148,member_type(power_set(X147)))
| ilf_type(X148,subset_type(X147))
| ~ ilf_type(X148,set_type)
| ~ ilf_type(X147,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p22])])])]) ).
fof(c_0_24,plain,
! [X165] :
( ( ~ empty(power_set(X165))
| ~ ilf_type(X165,set_type) )
& ( ilf_type(power_set(X165),set_type)
| ~ ilf_type(X165,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_25,plain,
! [X177,X178,X179] :
( ~ ilf_type(X177,set_type)
| ~ ilf_type(X178,set_type)
| ~ ilf_type(X179,relation_type(X177,X178))
| ilf_type(domain(X177,X178,X179),subset_type(X177)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p33])])]) ).
cnf(c_0_26,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_19]) ).
cnf(c_0_27,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( ilf_type(X1,relation_type(X2,X2))
| ~ ilf_type(X1,identity_relation_of_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,plain,
! [X180,X181,X182] :
( ~ ilf_type(X180,set_type)
| ~ ilf_type(X181,set_type)
| ~ ilf_type(X182,relation_type(X180,X181))
| range(X180,X181,X182) = range_of(X182) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p34])])]) ).
fof(c_0_30,plain,
! [X161,X162,X163] :
( ( ~ member(X161,power_set(X162))
| ~ ilf_type(X163,set_type)
| ~ member(X163,X161)
| member(X163,X162)
| ~ ilf_type(X162,set_type)
| ~ ilf_type(X161,set_type) )
& ( ilf_type(esk12_2(X161,X162),set_type)
| member(X161,power_set(X162))
| ~ ilf_type(X162,set_type)
| ~ ilf_type(X161,set_type) )
& ( member(esk12_2(X161,X162),X161)
| member(X161,power_set(X162))
| ~ ilf_type(X162,set_type)
| ~ ilf_type(X161,set_type) )
& ( ~ member(esk12_2(X161,X162),X162)
| member(X161,power_set(X162))
| ~ ilf_type(X162,set_type)
| ~ ilf_type(X161,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)],[p26])])])])]) ).
cnf(c_0_31,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_22]) ).
cnf(c_0_32,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_23]) ).
cnf(c_0_33,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,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_26,c_0_27]),c_0_27])]) ).
cnf(c_0_36,plain,
( ilf_type(X1,relation_type(X2,X2))
| ~ ilf_type(X1,identity_relation_of_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_27]),c_0_27])]) ).
cnf(c_0_37,plain,
( ilf_type(X1,identity_relation_of_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_38,plain,
! [X183,X184,X185] :
( ~ ilf_type(X183,set_type)
| ~ ilf_type(X184,set_type)
| ~ ilf_type(X185,relation_type(X183,X184))
| ilf_type(range(X183,X184,X185),subset_type(X184)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p35])])]) ).
cnf(c_0_39,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_29]) ).
cnf(c_0_40,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_30]) ).
cnf(c_0_41,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_31,c_0_27]),c_0_27])]) ).
cnf(c_0_42,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_32,c_0_27]),c_0_27])]) ).
cnf(c_0_43,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_27])]) ).
cnf(c_0_44,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_27]),c_0_27])]) ).
cnf(c_0_45,plain,
( domain(X1,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,identity_relation_of_type(X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,plain,
( ilf_type(X1,identity_relation_of_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_27]),c_0_27])]) ).
cnf(c_0_47,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_38]) ).
cnf(c_0_48,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_39,c_0_27]),c_0_27])]) ).
cnf(c_0_49,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_40,c_0_27]),c_0_27]),c_0_27])]) ).
cnf(c_0_50,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_51,plain,
( ilf_type(domain_of(X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
fof(c_0_52,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,identity_relation_of_type(X1))
=> ( compose(X2,identity_relation_of(X1)) = X2
& compose(identity_relation_of(X1),X2) = X2 ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_45]) ).
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_47,c_0_27]),c_0_27])]) ).
cnf(c_0_54,plain,
( range(X1,X1,X2) = range_of(X2)
| ~ ilf_type(X2,identity_relation_of_type(X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_36]) ).
fof(c_0_55,plain,
! [X98,X99] :
( ~ ilf_type(X98,set_type)
| ~ ilf_type(X99,binary_relation_type)
| ~ subset(domain_of(X99),X98)
| compose(identity_relation_of(X98),X99) = X99 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_56,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,plain,
( ilf_type(domain_of(X1),subset_type(X2))
| ~ ilf_type(X1,identity_relation_of_type(X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_36]) ).
fof(c_0_58,negated_conjecture,
( ilf_type(esk15_0,set_type)
& ilf_type(esk16_0,identity_relation_of_type(esk15_0))
& ( compose(esk16_0,identity_relation_of(esk15_0)) != esk16_0
| compose(identity_relation_of(esk15_0),esk16_0) != esk16_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
fof(c_0_59,plain,
! [X140,X141,X142] :
( ( ~ subset(X140,X141)
| ~ ilf_type(X142,set_type)
| ~ member(X142,X140)
| member(X142,X141)
| ~ ilf_type(X141,set_type)
| ~ ilf_type(X140,set_type) )
& ( ilf_type(esk7_2(X140,X141),set_type)
| subset(X140,X141)
| ~ ilf_type(X141,set_type)
| ~ ilf_type(X140,set_type) )
& ( member(esk7_2(X140,X141),X140)
| subset(X140,X141)
| ~ ilf_type(X141,set_type)
| ~ ilf_type(X140,set_type) )
& ( ~ member(esk7_2(X140,X141),X141)
| subset(X140,X141)
| ~ ilf_type(X141,set_type)
| ~ ilf_type(X140,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_60,plain,
( ilf_type(range_of(X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_46]) ).
cnf(c_0_61,plain,
( compose(identity_relation_of(X1),X2) = X2
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ subset(domain_of(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_62,plain,
! [X100,X101] :
( ~ ilf_type(X100,set_type)
| ~ ilf_type(X101,binary_relation_type)
| ~ subset(range_of(X101),X100)
| compose(X101,identity_relation_of(X100)) = X101 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])]) ).
cnf(c_0_63,plain,
( member(X1,X2)
| ~ member(X1,domain_of(X3))
| ~ ilf_type(X3,identity_relation_of_type(X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
ilf_type(esk16_0,identity_relation_of_type(esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
( member(esk7_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_66,plain,
( ilf_type(range_of(X1),subset_type(X2))
| ~ ilf_type(X1,identity_relation_of_type(X2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_36]) ).
fof(c_0_67,plain,
! [X158,X159,X160] :
( ~ ilf_type(X158,set_type)
| ~ ilf_type(X159,set_type)
| ~ ilf_type(X160,subset_type(cross_product(X158,X159)))
| relation_like(X160) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p25])])]) ).
fof(c_0_68,plain,
! [X130,X131,X132,X133] :
( ( ~ ilf_type(X132,subset_type(cross_product(X130,X131)))
| ilf_type(X132,relation_type(X130,X131))
| ~ ilf_type(X131,set_type)
| ~ ilf_type(X130,set_type) )
& ( ~ ilf_type(X133,relation_type(X130,X131))
| ilf_type(X133,subset_type(cross_product(X130,X131)))
| ~ ilf_type(X131,set_type)
| ~ ilf_type(X130,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])]) ).
cnf(c_0_69,negated_conjecture,
( compose(esk16_0,identity_relation_of(esk15_0)) != esk16_0
| compose(identity_relation_of(esk15_0),esk16_0) != esk16_0 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,plain,
( compose(identity_relation_of(X1),X2) = X2
| ~ subset(domain_of(X2),X1)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_27])]) ).
cnf(c_0_71,plain,
( compose(X2,identity_relation_of(X1)) = X2
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ subset(range_of(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_72,plain,
( subset(X1,X2)
| ~ member(esk7_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_73,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,domain_of(esk16_0)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_74,plain,
( member(esk7_2(X1,X2),X1)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_27]),c_0_27])]) ).
cnf(c_0_75,plain,
( member(X1,X2)
| ~ member(X1,range_of(X3))
| ~ ilf_type(X3,identity_relation_of_type(X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_66]) ).
cnf(c_0_76,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_67]) ).
cnf(c_0_77,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_68]) ).
cnf(c_0_78,negated_conjecture,
( compose(esk16_0,identity_relation_of(esk15_0)) != esk16_0
| ~ subset(domain_of(esk16_0),esk15_0)
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_79,plain,
( compose(X1,identity_relation_of(X2)) = X1
| ~ subset(range_of(X1),X2)
| ~ ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_27])]) ).
cnf(c_0_80,plain,
( subset(X1,X2)
| ~ member(esk7_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_27]),c_0_27])]) ).
cnf(c_0_81,negated_conjecture,
( member(esk7_2(domain_of(esk16_0),X1),esk15_0)
| subset(domain_of(esk16_0),X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,range_of(esk16_0)) ),
inference(spm,[status(thm)],[c_0_75,c_0_64]) ).
fof(c_0_83,plain,
! [X128] :
( ( relation_like(X128)
| ~ ilf_type(X128,binary_relation_type)
| ~ ilf_type(X128,set_type) )
& ( ilf_type(X128,set_type)
| ~ ilf_type(X128,binary_relation_type)
| ~ ilf_type(X128,set_type) )
& ( ~ relation_like(X128)
| ~ ilf_type(X128,set_type)
| ilf_type(X128,binary_relation_type)
| ~ ilf_type(X128,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])]) ).
cnf(c_0_84,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_76,c_0_27]),c_0_27])]) ).
cnf(c_0_85,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_77,c_0_27]),c_0_27])]) ).
cnf(c_0_86,negated_conjecture,
( ~ subset(domain_of(esk16_0),esk15_0)
| ~ subset(range_of(esk16_0),esk15_0)
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
subset(domain_of(esk16_0),esk15_0),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( member(esk7_2(range_of(esk16_0),X1),esk15_0)
| subset(range_of(esk16_0),X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_74]) ).
cnf(c_0_89,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_83]) ).
cnf(c_0_90,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,negated_conjecture,
( ~ subset(range_of(esk16_0),esk15_0)
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]) ).
cnf(c_0_92,negated_conjecture,
subset(range_of(esk16_0),esk15_0),
inference(spm,[status(thm)],[c_0_80,c_0_88]) ).
cnf(c_0_93,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_89]) ).
cnf(c_0_94,plain,
( relation_like(X1)
| ~ ilf_type(X1,identity_relation_of_type(X2)) ),
inference(spm,[status(thm)],[c_0_90,c_0_36]) ).
cnf(c_0_95,negated_conjecture,
~ ilf_type(esk16_0,binary_relation_type),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).
cnf(c_0_96,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_27])]) ).
cnf(c_0_97,negated_conjecture,
relation_like(esk16_0),
inference(spm,[status(thm)],[c_0_94,c_0_64]) ).
cnf(c_0_98,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET678+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:32:02 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.38/1.74 % Version : CSE_E---1.7
% 1.38/1.74 % Problem : theBenchmark.p
% 1.38/1.74 % SZS status Theorem for theBenchmark.p
% 1.38/1.74 % SZS output start CNFRefutation
% See solution above
% 1.38/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------