%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET678+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 : n001.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 02:14:58 PM UTC 2026
% Result : Theorem 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 99 ( 10 unt; 0 def)
% Number of atoms : 362 ( 27 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 450 ( 187 ~; 185 |; 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 : 196 ( 7 sgn 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p28,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',p28) ).
fof(p27,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',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(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(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(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(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(identity_relation_of(X1),X2) = X2
& compose(X2,identity_relation_of(X1)) = 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)
=> ( ! [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',p15) ).
fof(p13,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',p13) ).
fof(c_0_17,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)],[p28]) ).
fof(c_0_18,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(power_set(X1),set_type)
& ~ empty(power_set(X1)) ) ),
inference(fof_simplification,[status(thm)],[p27]) ).
fof(c_0_19,plain,
! [X82,X83,X84] :
( domain(X82,X83,X84) = domain_of(X84)
| ~ ilf_type(X84,relation_type(X82,X83))
| ~ ilf_type(X83,set_type)
| ~ ilf_type(X82,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p32])])])]) ).
fof(c_0_20,plain,
! [X104] : ilf_type(X104,set_type),
inference(variable_rename,[status(thm)],[p38]) ).
fof(c_0_21,plain,
! [X22,X23] :
( ( ~ ilf_type(X22,set_type)
| ~ ilf_type(X23,set_type)
| ilf_type(X23,identity_relation_of_type(X22))
| ~ ilf_type(X23,relation_type(X22,X22)) )
& ( ~ ilf_type(X22,set_type)
| ~ ilf_type(X23,set_type)
| ilf_type(X23,relation_type(X22,X22))
| ~ ilf_type(X23,identity_relation_of_type(X22)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])])]) ).
fof(c_0_22,plain,
! [X69,X70,X71] :
( ( ~ ilf_type(X69,set_type)
| ~ ilf_type(X70,set_type)
| member(X69,power_set(X70))
| ~ member(esk12_2(X69,X70),X70) )
& ( ~ ilf_type(X69,set_type)
| ~ ilf_type(X70,set_type)
| member(X69,power_set(X70))
| member(esk12_2(X69,X70),X69) )
& ( ~ ilf_type(X69,set_type)
| ~ ilf_type(X70,set_type)
| member(X69,power_set(X70))
| ilf_type(esk12_2(X69,X70),set_type) )
& ( ~ ilf_type(X69,set_type)
| ~ ilf_type(X70,set_type)
| member(X71,X70)
| ~ member(X71,X69)
| ~ ilf_type(X71,set_type)
| ~ member(X69,power_set(X70)) ) ),
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)],[p26])])])])])]) ).
fof(c_0_23,plain,
! [X74,X75] :
( ( ~ ilf_type(X74,set_type)
| ~ ilf_type(X75,set_type)
| empty(X75)
| ilf_type(X74,member_type(X75))
| ~ member(X74,X75) )
& ( ~ ilf_type(X74,set_type)
| ~ ilf_type(X75,set_type)
| empty(X75)
| member(X74,X75)
| ~ ilf_type(X74,member_type(X75)) ) ),
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_17])])])])]) ).
fof(c_0_24,plain,
! [X73] :
( ( ~ ilf_type(X73,set_type)
| ilf_type(power_set(X73),set_type) )
& ( ~ ilf_type(X73,set_type)
| ~ empty(power_set(X73)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_25,plain,
! [X85,X86,X87] :
( ilf_type(domain(X85,X86,X87),subset_type(X85))
| ~ ilf_type(X87,relation_type(X85,X86))
| ~ ilf_type(X86,set_type)
| ~ ilf_type(X85,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p33])])])]) ).
cnf(c_0_26,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_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(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,identity_relation_of_type(X2))
| ilf_type(X1,relation_type(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,plain,
! [X88,X89,X90] :
( range(X88,X89,X90) = range_of(X90)
| ~ ilf_type(X90,relation_type(X88,X89))
| ~ ilf_type(X89,set_type)
| ~ ilf_type(X88,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p34])])])]) ).
cnf(c_0_30,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_22]) ).
cnf(c_0_31,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_23]) ).
cnf(c_0_32,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_33,plain,
! [X55,X56] :
( ( ~ ilf_type(X55,set_type)
| ~ ilf_type(X56,set_type)
| ilf_type(X56,subset_type(X55))
| ~ ilf_type(X56,member_type(power_set(X55))) )
& ( ~ ilf_type(X55,set_type)
| ~ ilf_type(X56,set_type)
| ilf_type(X56,member_type(power_set(X55)))
| ~ ilf_type(X56,subset_type(X55)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p22])])])])]) ).
cnf(c_0_34,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(domain(X1,X2,X3),subset_type(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,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_26,c_0_27]),c_0_27])]) ).
cnf(c_0_36,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_28,c_0_27]),c_0_27])]) ).
cnf(c_0_37,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,relation_type(X2,X2))
| ilf_type(X1,identity_relation_of_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_38,plain,
! [X91,X92,X93] :
( ilf_type(range(X91,X92,X93),subset_type(X92))
| ~ ilf_type(X93,relation_type(X91,X92))
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p35])])])]) ).
cnf(c_0_39,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_29]) ).
cnf(c_0_40,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_30,c_0_27]),c_0_27]),c_0_27])]) ).
cnf(c_0_41,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_31,c_0_27]),c_0_27])]) ).
cnf(c_0_42,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_27])]) ).
cnf(c_0_43,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_33]) ).
cnf(c_0_44,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X3),subset_type(X1)) ),
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,
( ~ ilf_type(X2,identity_relation_of_type(X1))
| domain(X1,X1,X2) = domain_of(X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,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_37,c_0_27]),c_0_27])]) ).
cnf(c_0_47,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_38]) ).
cnf(c_0_48,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_39,c_0_27]),c_0_27])]) ).
cnf(c_0_49,plain,
( ~ ilf_type(X3,member_type(power_set(X2)))
| ~ member(X1,X3)
| member(X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_50,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_43,c_0_27]),c_0_27])]) ).
cnf(c_0_51,plain,
( ~ ilf_type(X1,relation_type(X2,X2))
| ilf_type(domain_of(X1),subset_type(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(identity_relation_of(X1),X2) = X2
& compose(X2,identity_relation_of(X1)) = X2 ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_45]) ).
cnf(c_0_53,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_47,c_0_27]),c_0_27])]) ).
cnf(c_0_54,plain,
( ~ ilf_type(X2,identity_relation_of_type(X1))
| range(X1,X1,X2) = range_of(X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_36]) ).
fof(c_0_55,plain,
! [X6,X7] :
( compose(identity_relation_of(X6),X7) = X7
| ~ subset(domain_of(X7),X6)
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
cnf(c_0_56,plain,
( ~ ilf_type(X3,subset_type(X2))
| ~ member(X1,X3)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,plain,
( ~ ilf_type(X1,identity_relation_of_type(X2))
| ilf_type(domain_of(X1),subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_36]) ).
fof(c_0_58,negated_conjecture,
( ( compose(identity_relation_of(esk15_0),esk16_0) != esk16_0
| compose(esk16_0,identity_relation_of(esk15_0)) != esk16_0 )
& ilf_type(esk16_0,identity_relation_of_type(esk15_0))
& ilf_type(esk15_0,set_type) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
fof(c_0_59,plain,
! [X48,X49,X50] :
( ( ~ ilf_type(X48,set_type)
| ~ ilf_type(X49,set_type)
| subset(X48,X49)
| ~ member(esk7_2(X48,X49),X49) )
& ( ~ ilf_type(X48,set_type)
| ~ ilf_type(X49,set_type)
| subset(X48,X49)
| member(esk7_2(X48,X49),X48) )
& ( ~ ilf_type(X48,set_type)
| ~ ilf_type(X49,set_type)
| subset(X48,X49)
| ilf_type(esk7_2(X48,X49),set_type) )
& ( ~ ilf_type(X48,set_type)
| ~ ilf_type(X49,set_type)
| member(X50,X49)
| ~ member(X50,X48)
| ~ ilf_type(X50,set_type)
| ~ subset(X48,X49) ) ),
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)],[p19])])])])])]) ).
cnf(c_0_60,plain,
( ~ ilf_type(X1,relation_type(X2,X2))
| ilf_type(range_of(X1),subset_type(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_46]) ).
cnf(c_0_61,plain,
( ~ subset(domain_of(X2),X1)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| compose(identity_relation_of(X1),X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_62,plain,
! [X8,X9] :
( compose(X9,identity_relation_of(X8)) = X9
| ~ subset(range_of(X9),X8)
| ~ ilf_type(X9,binary_relation_type)
| ~ ilf_type(X8,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
cnf(c_0_63,plain,
( ~ ilf_type(X3,identity_relation_of_type(X2))
| ~ member(X1,domain_of(X3))
| member(X1,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,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(X1,X2)
| member(esk7_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_66,plain,
( ~ ilf_type(X1,identity_relation_of_type(X2))
| ilf_type(range_of(X1),subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_36]) ).
fof(c_0_67,plain,
! [X66,X67,X68] :
( relation_like(X68)
| ~ ilf_type(X68,subset_type(cross_product(X66,X67)))
| ~ ilf_type(X67,set_type)
| ~ ilf_type(X66,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p25])])])]) ).
fof(c_0_68,plain,
! [X38,X39,X40,X41] :
( ( ~ ilf_type(X38,set_type)
| ~ ilf_type(X39,set_type)
| ilf_type(X41,subset_type(cross_product(X38,X39)))
| ~ ilf_type(X41,relation_type(X38,X39)) )
& ( ~ ilf_type(X38,set_type)
| ~ ilf_type(X39,set_type)
| ilf_type(X40,relation_type(X38,X39))
| ~ ilf_type(X40,subset_type(cross_product(X38,X39))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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(identity_relation_of(esk15_0),esk16_0) != esk16_0
| compose(esk16_0,identity_relation_of(esk15_0)) != esk16_0 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,plain,
( ~ ilf_type(X2,binary_relation_type)
| ~ subset(domain_of(X2),X1)
| compose(identity_relation_of(X1),X2) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_27])]) ).
cnf(c_0_71,plain,
( ~ subset(range_of(X2),X1)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| compose(X2,identity_relation_of(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_72,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk7_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_73,negated_conjecture,
( ~ member(X1,domain_of(esk16_0))
| member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_74,plain,
( subset(X1,X2)
| member(esk7_2(X1,X2),X1) ),
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,
( ~ ilf_type(X3,identity_relation_of_type(X2))
| ~ member(X1,range_of(X3))
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_66]) ).
cnf(c_0_76,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_67]) ).
cnf(c_0_77,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_68]) ).
cnf(c_0_78,negated_conjecture,
( ~ ilf_type(esk16_0,binary_relation_type)
| ~ subset(domain_of(esk16_0),esk15_0)
| compose(esk16_0,identity_relation_of(esk15_0)) != esk16_0 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_79,plain,
( ~ ilf_type(X1,binary_relation_type)
| ~ subset(range_of(X1),X2)
| compose(X1,identity_relation_of(X2)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_27])]) ).
cnf(c_0_80,plain,
( ~ member(esk7_2(X1,X2),X2)
| subset(X1,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,
( subset(domain_of(esk16_0),X1)
| member(esk7_2(domain_of(esk16_0),X1),esk15_0) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
( ~ member(X1,range_of(esk16_0))
| member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_75,c_0_64]) ).
fof(c_0_83,plain,
! [X36] :
( ( ~ ilf_type(X36,set_type)
| ilf_type(X36,binary_relation_type)
| ~ ilf_type(X36,set_type)
| ~ relation_like(X36) )
& ( ~ ilf_type(X36,set_type)
| ~ ilf_type(X36,binary_relation_type)
| ilf_type(X36,set_type) )
& ( ~ ilf_type(X36,set_type)
| ~ ilf_type(X36,binary_relation_type)
| relation_like(X36) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])])]) ).
cnf(c_0_84,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_76,c_0_27]),c_0_27])]) ).
cnf(c_0_85,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_77,c_0_27]),c_0_27])]) ).
cnf(c_0_86,negated_conjecture,
( ~ ilf_type(esk16_0,binary_relation_type)
| ~ subset(range_of(esk16_0),esk15_0)
| ~ subset(domain_of(esk16_0),esk15_0) ),
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,
( subset(range_of(esk16_0),X1)
| member(esk7_2(range_of(esk16_0),X1),esk15_0) ),
inference(spm,[status(thm)],[c_0_82,c_0_74]) ).
cnf(c_0_89,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_83]) ).
cnf(c_0_90,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| relation_like(X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,negated_conjecture,
( ~ ilf_type(esk16_0,binary_relation_type)
| ~ subset(range_of(esk16_0),esk15_0) ),
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,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_89]) ).
cnf(c_0_94,plain,
( ~ ilf_type(X1,identity_relation_of_type(X2))
| relation_like(X1) ),
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,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
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
% 0.00/0.03 % Problem : SET678+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:37:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.17/0.49 % Version: 3.5.1
% 0.17/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.49 % Starting sh5l with 300s (1) cores
% 0.17/0.49 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2296737 completed with status 0
% 0.17/0.49 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.17/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.49 % No SInE strategy applied
% 0.17/0.49 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.17/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.17/0.49 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S0Y with 209s (1) cores
% 0.17/0.49 % Starting new_bool_3 with 189s (1) cores
% 0.17/0.49 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.17/0.49 % G-E--_207_C01_F1_SE_CS_SP_PI_S0Y with pid 2296745 completed with status 0
% 0.17/0.49 % Result found by G-E--_207_C01_F1_SE_CS_SP_PI_S0Y
% 0.17/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.49 % No SInE strategy applied
% 0.17/0.49 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.17/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.17/0.49 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S0Y with 209s (1) cores
% 0.17/0.49 % Preprocessing time : 0.003 s
% 0.17/0.49
% 0.17/0.49 % Proof found!
% 0.17/0.49 % SZS status Theorem
% 0.17/0.49 % SZS output start CNFRefutation
% See solution above
% 0.17/0.49 % Parsed axioms : 39
% 0.17/0.49 % Removed by relevancy pruning/SinE : 0
% 0.17/0.49 % Initial clauses : 71
% 0.17/0.49 % Removed in clause preprocessing : 5
% 0.17/0.49 % Initial clauses in saturation : 66
% 0.17/0.49 % Processed clauses : 413
% 0.17/0.49 % ...of these trivial : 15
% 0.17/0.49 % ...subsumed : 97
% 0.17/0.49 % ...remaining for further processing : 301
% 0.17/0.49 % Other redundant clauses eliminated : 2
% 0.17/0.49 % Clauses deleted for lack of memory : 0
% 0.17/0.49 % Backward-subsumed : 21
% 0.17/0.49 % Backward-rewritten : 5
% 0.17/0.49 % Generated clauses : 914
% 0.17/0.49 % ...of the previous two non-redundant : 881
% 0.17/0.49 % ...aggressively subsumed : 0
% 0.17/0.49 % Contextual simplify-reflections : 5
% 0.17/0.49 % Paramodulations : 912
% 0.17/0.49 % Factorizations : 0
% 0.17/0.49 % NegExts : 0
% 0.17/0.49 % Equation resolutions : 2
% 0.17/0.49 % Disequality decompositions : 0
% 0.17/0.49 % Total rewrite steps : 183
% 0.17/0.49 % ...of those cached : 136
% 0.17/0.49 % Propositional unsat checks : 0
% 0.17/0.49 % Propositional check models : 0
% 0.17/0.49 % Propositional check unsatisfiable : 0
% 0.17/0.49 % Propositional clauses : 0
% 0.17/0.49 % Propositional clauses after purity: 0
% 0.17/0.49 % Propositional unsat core size : 0
% 0.17/0.49 % Propositional preprocessing time : 0.000
% 0.17/0.49 % Propositional encoding time : 0.000
% 0.17/0.49 % Propositional solver time : 0.000
% 0.17/0.49 % Success case prop preproc time : 0.000
% 0.17/0.49 % Success case prop encoding time : 0.000
% 0.17/0.49 % Success case prop solver time : 0.000
% 0.17/0.49 % Current number of processed clauses : 274
% 0.17/0.49 % Positive orientable unit clauses : 41
% 0.17/0.49 % Positive unorientable unit clauses: 0
% 0.17/0.49 % Negative unit clauses : 3
% 0.17/0.49 % Non-unit-clauses : 230
% 0.17/0.49 % Current number of unprocessed clauses: 531
% 0.17/0.49 % ...number of literals in the above : 1863
% 0.17/0.49 % Current number of archived formulas : 0
% 0.17/0.49 % Current number of archived clauses : 26
% 0.17/0.49 % Clause-clause subsumption calls (NU) : 9232
% 0.17/0.49 % Rec. Clause-clause subsumption calls : 4321
% 0.17/0.49 % Non-unit clause-clause subsumptions : 104
% 0.17/0.49 % Unit Clause-clause subsumption calls : 716
% 0.17/0.49 % Rewrite failures with RHS unbound : 0
% 0.17/0.49 % BW rewrite match attempts : 15
% 0.17/0.49 % BW rewrite match successes : 3
% 0.17/0.49 % Condensation attempts : 0
% 0.17/0.49 % Condensation successes : 0
% 0.17/0.49 % Termbank termtop insertions : 21194
% 0.17/0.49 % Search garbage collected termcells : 1632
% 0.17/0.49
% 0.17/0.49 % -------------------------------------------------
% 0.17/0.49 % User time : 0.046 s
% 0.17/0.49 % System time : 0.006 s
% 0.17/0.49 % Total time : 0.053 s
% 0.17/0.49 % Maximum resident set size: 3684 pages
% 0.17/0.49
% 0.17/0.49 % -------------------------------------------------
% 0.17/0.49 % User time : 0.169 s
% 0.17/0.49 % System time : 0.025 s
% 0.17/0.49 % Total time : 0.194 s
% 0.17/0.49 % Maximum resident set size: 4608 pages
% 0.17/0.49 % E exiting
%------------------------------------------------------------------------------