%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET678+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:17:56 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 92 ( 15 unt; 0 def)
% Number of atoms : 336 ( 26 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 409 ( 165 ~; 166 |; 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 : 177 ( 8 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(p38,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p38) ).
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/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(domain(X1,X2,X3),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
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/sandbox2/benchmark/theBenchmark.p',p32) ).
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/sandbox2/benchmark/theBenchmark.p',p7) ).
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/sandbox2/benchmark/theBenchmark.p',prove_relset_1_45) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p35) ).
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/sandbox2/benchmark/theBenchmark.p',p34) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p15) ).
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/sandbox2/benchmark/theBenchmark.p',p19) ).
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/sandbox2/benchmark/theBenchmark.p',p13) ).
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/sandbox2/benchmark/theBenchmark.p',p1) ).
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/sandbox2/benchmark/theBenchmark.p',p2) ).
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,
! [X72,X73] :
( ( ~ ilf_type(X72,set_type)
| ~ ilf_type(X73,set_type)
| empty(X73)
| ilf_type(X72,member_type(X73))
| ~ member(X72,X73) )
& ( ~ ilf_type(X72,set_type)
| ~ ilf_type(X73,set_type)
| empty(X73)
| member(X72,X73)
| ~ ilf_type(X72,member_type(X73)) ) ),
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_20,plain,
! [X36] : ilf_type(X36,set_type),
inference(variable_rename,[status(thm)],[p38]) ).
fof(c_0_21,plain,
! [X98,X99] :
( ( ~ ilf_type(X98,set_type)
| ~ ilf_type(X99,set_type)
| ilf_type(X99,subset_type(X98))
| ~ ilf_type(X99,member_type(power_set(X98))) )
& ( ~ ilf_type(X98,set_type)
| ~ ilf_type(X99,set_type)
| ilf_type(X99,member_type(power_set(X98)))
| ~ ilf_type(X99,subset_type(X98)) ) ),
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])])])])]) ).
fof(c_0_22,plain,
! [X100] :
( ( ~ ilf_type(X100,set_type)
| ilf_type(power_set(X100),set_type) )
& ( ~ ilf_type(X100,set_type)
| ~ empty(power_set(X100)) ) ),
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_23,plain,
! [X88,X89,X90] :
( ilf_type(domain(X88,X89,X90),subset_type(X88))
| ~ 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)],[p33])])])]) ).
fof(c_0_24,plain,
! [X47,X48,X49] :
( domain(X47,X48,X49) = domain_of(X49)
| ~ ilf_type(X49,relation_type(X47,X48))
| ~ ilf_type(X48,set_type)
| ~ ilf_type(X47,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_25,plain,
! [X37,X38] :
( ( ~ ilf_type(X37,set_type)
| ~ ilf_type(X38,set_type)
| ilf_type(X38,identity_relation_of_type(X37))
| ~ ilf_type(X38,relation_type(X37,X37)) )
& ( ~ ilf_type(X37,set_type)
| ~ ilf_type(X38,set_type)
| ilf_type(X38,relation_type(X37,X37))
| ~ ilf_type(X38,identity_relation_of_type(X37)) ) ),
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_26,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]) ).
fof(c_0_27,plain,
! [X68,X69,X70] :
( ( ~ ilf_type(X68,set_type)
| ~ ilf_type(X69,set_type)
| member(X68,power_set(X69))
| ~ member(esk13_2(X68,X69),X69) )
& ( ~ ilf_type(X68,set_type)
| ~ ilf_type(X69,set_type)
| member(X68,power_set(X69))
| member(esk13_2(X68,X69),X68) )
& ( ~ ilf_type(X68,set_type)
| ~ ilf_type(X69,set_type)
| member(X68,power_set(X69))
| ilf_type(esk13_2(X68,X69),set_type) )
& ( ~ ilf_type(X68,set_type)
| ~ ilf_type(X69,set_type)
| member(X70,X69)
| ~ member(X70,X68)
| ~ ilf_type(X70,set_type)
| ~ member(X68,power_set(X69)) ) ),
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])])])])])]) ).
cnf(c_0_28,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_19]) ).
cnf(c_0_29,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,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_21]) ).
cnf(c_0_31,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,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_23]) ).
cnf(c_0_33,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_24]) ).
cnf(c_0_34,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_25]) ).
fof(c_0_35,negated_conjecture,
( ( compose(identity_relation_of(esk1_0),esk2_0) != esk2_0
| compose(esk2_0,identity_relation_of(esk1_0)) != esk2_0 )
& ilf_type(esk2_0,identity_relation_of_type(esk1_0))
& ilf_type(esk1_0,set_type) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
fof(c_0_36,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])])])]) ).
fof(c_0_37,plain,
! [X58,X59,X60] :
( range(X58,X59,X60) = range_of(X60)
| ~ ilf_type(X60,relation_type(X58,X59))
| ~ ilf_type(X59,set_type)
| ~ ilf_type(X58,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_38,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_27]) ).
cnf(c_0_39,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_28,c_0_29]),c_0_29])]) ).
cnf(c_0_40,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_30,c_0_29]),c_0_29])]) ).
cnf(c_0_41,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_29])]) ).
cnf(c_0_42,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_32,c_0_29]),c_0_29])]) ).
cnf(c_0_43,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_33,c_0_29]),c_0_29])]) ).
cnf(c_0_44,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_34,c_0_29]),c_0_29])]) ).
cnf(c_0_45,negated_conjecture,
ilf_type(esk2_0,identity_relation_of_type(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_46,plain,
! [X94,X95,X96] :
( relation_like(X96)
| ~ ilf_type(X96,subset_type(cross_product(X94,X95)))
| ~ ilf_type(X95,set_type)
| ~ ilf_type(X94,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_47,plain,
! [X84,X85,X86,X87] :
( ( ~ ilf_type(X84,set_type)
| ~ ilf_type(X85,set_type)
| ilf_type(X87,subset_type(cross_product(X84,X85)))
| ~ ilf_type(X87,relation_type(X84,X85)) )
& ( ~ ilf_type(X84,set_type)
| ~ ilf_type(X85,set_type)
| ilf_type(X86,relation_type(X84,X85))
| ~ ilf_type(X86,subset_type(cross_product(X84,X85))) ) ),
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_48,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_36]) ).
cnf(c_0_49,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_37]) ).
cnf(c_0_50,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_38,c_0_29]),c_0_29]),c_0_29])]) ).
cnf(c_0_51,plain,
( ~ ilf_type(X1,subset_type(X2))
| member(X1,power_set(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_52,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| ilf_type(domain_of(X1),subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_53,negated_conjecture,
ilf_type(esk2_0,relation_type(esk1_0,esk1_0)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_54,plain,
! [X41,X42,X43] :
( ( ~ ilf_type(X41,set_type)
| ~ ilf_type(X42,set_type)
| subset(X41,X42)
| ~ member(esk7_2(X41,X42),X42) )
& ( ~ ilf_type(X41,set_type)
| ~ ilf_type(X42,set_type)
| subset(X41,X42)
| member(esk7_2(X41,X42),X41) )
& ( ~ ilf_type(X41,set_type)
| ~ ilf_type(X42,set_type)
| subset(X41,X42)
| ilf_type(esk7_2(X41,X42),set_type) )
& ( ~ ilf_type(X41,set_type)
| ~ ilf_type(X42,set_type)
| member(X43,X42)
| ~ member(X43,X41)
| ~ ilf_type(X43,set_type)
| ~ subset(X41,X42) ) ),
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])])])])])]) ).
fof(c_0_55,plain,
! [X57] :
( ( ~ ilf_type(X57,set_type)
| ilf_type(X57,binary_relation_type)
| ~ ilf_type(X57,set_type)
| ~ relation_like(X57) )
& ( ~ ilf_type(X57,set_type)
| ~ ilf_type(X57,binary_relation_type)
| ilf_type(X57,set_type) )
& ( ~ ilf_type(X57,set_type)
| ~ ilf_type(X57,binary_relation_type)
| relation_like(X57) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])])]) ).
cnf(c_0_56,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_46]) ).
cnf(c_0_57,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_47]) ).
cnf(c_0_58,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_48,c_0_29]),c_0_29])]) ).
cnf(c_0_59,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_49,c_0_29]),c_0_29])]) ).
cnf(c_0_60,plain,
( ~ ilf_type(X3,subset_type(X2))
| ~ member(X1,X3)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_61,negated_conjecture,
ilf_type(domain_of(esk2_0),subset_type(esk1_0)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,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_54]) ).
cnf(c_0_63,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_55]) ).
cnf(c_0_64,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_56,c_0_29]),c_0_29])]) ).
cnf(c_0_65,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_57,c_0_29]),c_0_29])]) ).
cnf(c_0_66,plain,
( ~ ilf_type(X1,relation_type(X3,X2))
| ilf_type(range_of(X1),subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_67,plain,
! [X8,X9] :
( compose(identity_relation_of(X8),X9) = X9
| ~ subset(domain_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)],[p1])])])]) ).
cnf(c_0_68,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_54]) ).
cnf(c_0_69,negated_conjecture,
( ~ member(X1,domain_of(esk2_0))
| member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,plain,
( subset(X1,X2)
| member(esk7_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_29]),c_0_29])]) ).
cnf(c_0_71,plain,
( ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_63]) ).
cnf(c_0_72,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| relation_like(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_73,negated_conjecture,
ilf_type(range_of(esk2_0),subset_type(esk1_0)),
inference(spm,[status(thm)],[c_0_66,c_0_53]) ).
cnf(c_0_74,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_67]) ).
cnf(c_0_75,plain,
( ~ member(esk7_2(X1,X2),X2)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_29]),c_0_29])]) ).
cnf(c_0_76,negated_conjecture,
( subset(domain_of(esk2_0),X1)
| member(esk7_2(domain_of(esk2_0),X1),esk1_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,plain,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_29])]) ).
cnf(c_0_78,negated_conjecture,
relation_like(esk2_0),
inference(spm,[status(thm)],[c_0_72,c_0_53]) ).
fof(c_0_79,plain,
! [X10,X11] :
( compose(X11,identity_relation_of(X10)) = X11
| ~ subset(range_of(X11),X10)
| ~ ilf_type(X11,binary_relation_type)
| ~ ilf_type(X10,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_80,negated_conjecture,
( ~ member(X1,range_of(esk2_0))
| member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_73]) ).
cnf(c_0_81,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_74,c_0_29])]) ).
cnf(c_0_82,negated_conjecture,
subset(domain_of(esk2_0),esk1_0),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,negated_conjecture,
ilf_type(esk2_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,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_79]) ).
cnf(c_0_85,negated_conjecture,
( subset(range_of(esk2_0),X1)
| member(esk7_2(range_of(esk2_0),X1),esk1_0) ),
inference(spm,[status(thm)],[c_0_80,c_0_70]) ).
cnf(c_0_86,negated_conjecture,
( compose(identity_relation_of(esk1_0),esk2_0) != esk2_0
| compose(esk2_0,identity_relation_of(esk1_0)) != esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_87,negated_conjecture,
compose(identity_relation_of(esk1_0),esk2_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
cnf(c_0_88,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_84,c_0_29])]) ).
cnf(c_0_89,negated_conjecture,
subset(range_of(esk2_0),esk1_0),
inference(spm,[status(thm)],[c_0_75,c_0_85]) ).
cnf(c_0_90,negated_conjecture,
compose(esk2_0,identity_relation_of(esk1_0)) != esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]) ).
cnf(c_0_91,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_83])]),c_0_90]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET678+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.34 % Computer : n004.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 05:32:19 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.14/0.45 % Version: 3.5.1
% 0.14/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % sh5l with pid 2345403 completed with status 0
% 0.14/0.45 % Result found by sh5l
% 0.14/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.45 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.45 % SubtermCWHack with pid 2345406 completed with status 0
% 0.14/0.45 % Result found by SubtermCWHack
% 0.14/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.45 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.45 % Preprocessing time : 0.002 s
% 0.14/0.45
% 0.14/0.45 % Proof found!
% 0.14/0.45 % SZS status Theorem
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
% 0.14/0.45 % Parsed axioms : 39
% 0.14/0.45 % Removed by relevancy pruning/SinE : 0
% 0.14/0.45 % Initial clauses : 71
% 0.14/0.45 % Removed in clause preprocessing : 5
% 0.14/0.45 % Initial clauses in saturation : 66
% 0.14/0.45 % Processed clauses : 533
% 0.14/0.45 % ...of these trivial : 14
% 0.14/0.45 % ...subsumed : 95
% 0.14/0.45 % ...remaining for further processing : 424
% 0.14/0.45 % Other redundant clauses eliminated : 2
% 0.14/0.45 % Clauses deleted for lack of memory : 0
% 0.14/0.45 % Backward-subsumed : 9
% 0.14/0.45 % Backward-rewritten : 2
% 0.14/0.45 % Generated clauses : 1458
% 0.14/0.45 % ...of the previous two non-redundant : 1404
% 0.14/0.45 % ...aggressively subsumed : 0
% 0.14/0.45 % Contextual simplify-reflections : 1
% 0.14/0.45 % Paramodulations : 1456
% 0.14/0.45 % Factorizations : 0
% 0.14/0.45 % NegExts : 0
% 0.14/0.45 % Equation resolutions : 2
% 0.14/0.45 % Disequality decompositions : 0
% 0.14/0.45 % Total rewrite steps : 177
% 0.14/0.45 % ...of those cached : 114
% 0.14/0.45 % Propositional unsat checks : 0
% 0.14/0.45 % Propositional check models : 0
% 0.14/0.45 % Propositional check unsatisfiable : 0
% 0.14/0.45 % Propositional clauses : 0
% 0.14/0.45 % Propositional clauses after purity: 0
% 0.14/0.45 % Propositional unsat core size : 0
% 0.14/0.45 % Propositional preprocessing time : 0.000
% 0.14/0.45 % Propositional encoding time : 0.000
% 0.14/0.45 % Propositional solver time : 0.000
% 0.14/0.45 % Success case prop preproc time : 0.000
% 0.14/0.45 % Success case prop encoding time : 0.000
% 0.14/0.45 % Success case prop solver time : 0.000
% 0.14/0.45 % Current number of processed clauses : 412
% 0.14/0.45 % Positive orientable unit clauses : 117
% 0.14/0.45 % Positive unorientable unit clauses: 0
% 0.14/0.45 % Negative unit clauses : 3
% 0.14/0.45 % Non-unit-clauses : 292
% 0.14/0.45 % Current number of unprocessed clauses: 936
% 0.14/0.45 % ...number of literals in the above : 2554
% 0.14/0.45 % Current number of archived formulas : 0
% 0.14/0.45 % Current number of archived clauses : 11
% 0.14/0.45 % Clause-clause subsumption calls (NU) : 11882
% 0.14/0.45 % Rec. Clause-clause subsumption calls : 7552
% 0.14/0.45 % Non-unit clause-clause subsumptions : 80
% 0.14/0.45 % Unit Clause-clause subsumption calls : 3437
% 0.14/0.45 % Rewrite failures with RHS unbound : 0
% 0.14/0.45 % BW rewrite match attempts : 71
% 0.14/0.45 % BW rewrite match successes : 2
% 0.14/0.45 % Condensation attempts : 0
% 0.14/0.45 % Condensation successes : 0
% 0.14/0.45 % Termbank termtop insertions : 29314
% 0.14/0.45 % Search garbage collected termcells : 1636
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.044 s
% 0.14/0.45 % System time : 0.006 s
% 0.14/0.45 % Total time : 0.050 s
% 0.14/0.45 % Maximum resident set size: 3940 pages
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.046 s
% 0.14/0.45 % System time : 0.012 s
% 0.14/0.45 % Total time : 0.057 s
% 0.14/0.45 % Maximum resident set size: 4864 pages
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------