%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU213+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 02:24:16 PM UTC 2026
% Result : Theorem 210.27s 36.44s
% Output : CNFRefutation 210.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 13 unt; 0 def)
% Number of atoms : 260 ( 28 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 336 ( 131 ~; 141 |; 37 &)
% ( 9 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-5 aty)
% Number of variables : 96 ( 1 sgn 49 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) )
& ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(t21_funct_1,conjecture,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(apply(X3,X1),relation_dom(X2))
& in(X1,relation_dom(X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(fc1_funct_1,axiom,
! [X1,X2] :
( ( function(X2)
& relation(X2)
& function(X1)
& relation(X1) )
=> ( function(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(d8_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_composition(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ? [X6] :
( in(ordered_pair(X6,X5),X2)
& in(ordered_pair(X4,X6),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X2)
& relation(X1) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(t20_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X2,relation_rng(X3))
& in(X1,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(t8_funct_1,lemma,
! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( X2 = apply(X3,X1)
& in(X1,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
fof(c_0_7,plain,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) )
& ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
fof(c_0_8,plain,
! [X40,X41,X42] :
( ( ~ function(X40)
| ~ relation(X40)
| in(X41,relation_dom(X40))
| X42 = apply(X40,X41)
| X42 != empty_set )
& ( ~ function(X40)
| ~ relation(X40)
| in(X41,relation_dom(X40))
| X42 = empty_set
| X42 != apply(X40,X41) )
& ( ~ function(X40)
| ~ relation(X40)
| ~ in(X41,relation_dom(X40))
| X42 = apply(X40,X41)
| ~ in(ordered_pair(X41,X42),X40) )
& ( ~ function(X40)
| ~ relation(X40)
| ~ in(X41,relation_dom(X40))
| in(ordered_pair(X41,X42),X40)
| X42 != apply(X40,X41) ) ),
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_7])])])])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(apply(X3,X1),relation_dom(X2))
& in(X1,relation_dom(X3)) ) ) ) ),
inference(assume_negation,[status(cth)],[t21_funct_1]) ).
cnf(c_0_10,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| in(ordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,negated_conjecture,
( ( in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
| in(apply(esk3_0,esk1_0),relation_dom(esk2_0)) )
& ( in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
| in(esk1_0,relation_dom(esk3_0)) )
& ( ~ in(apply(esk3_0,esk1_0),relation_dom(esk2_0))
| ~ in(esk1_0,relation_dom(esk3_0))
| ~ in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))) )
& function(esk3_0)
& relation(esk3_0)
& function(esk2_0)
& relation(esk2_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
cnf(c_0_12,plain,
( ~ in(X1,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| in(ordered_pair(X1,apply(X2,X1)),X2) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
| in(esk1_0,relation_dom(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X74,X75] :
( ( ~ function(X75)
| ~ relation(X75)
| ~ function(X74)
| ~ relation(X74)
| function(relation_composition(X74,X75)) )
& ( ~ function(X75)
| ~ relation(X75)
| ~ function(X74)
| ~ relation(X74)
| relation(relation_composition(X74,X75)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])])]) ).
fof(c_0_15,plain,
! [X46,X47,X48,X49,X50,X52,X53,X54,X57] :
( ( ~ relation(X46)
| ~ relation(X47)
| ~ relation(X48)
| X48 = relation_composition(X46,X47)
| in(ordered_pair(esk10_3(X46,X47,X48),esk11_3(X46,X47,X48)),X48)
| in(ordered_pair(esk12_3(X46,X47,X48),esk11_3(X46,X47,X48)),X47) )
& ( ~ relation(X46)
| ~ relation(X47)
| ~ relation(X48)
| X48 = relation_composition(X46,X47)
| in(ordered_pair(esk10_3(X46,X47,X48),esk11_3(X46,X47,X48)),X48)
| in(ordered_pair(esk10_3(X46,X47,X48),esk12_3(X46,X47,X48)),X46) )
& ( ~ relation(X46)
| ~ relation(X47)
| ~ relation(X48)
| X48 = relation_composition(X46,X47)
| ~ in(ordered_pair(X57,esk11_3(X46,X47,X48)),X47)
| ~ in(ordered_pair(esk10_3(X46,X47,X48),X57),X46)
| ~ in(ordered_pair(esk10_3(X46,X47,X48),esk11_3(X46,X47,X48)),X48) )
& ( ~ relation(X46)
| ~ relation(X47)
| ~ relation(X48)
| X48 != relation_composition(X46,X47)
| in(ordered_pair(X52,X53),X48)
| ~ in(ordered_pair(X54,X53),X47)
| ~ in(ordered_pair(X52,X54),X46) )
& ( ~ relation(X46)
| ~ relation(X47)
| ~ relation(X48)
| X48 != relation_composition(X46,X47)
| ~ in(ordered_pair(X49,X50),X48)
| in(ordered_pair(esk9_5(X46,X47,X48,X49,X50),X50),X47) )
& ( ~ relation(X46)
| ~ relation(X47)
| ~ relation(X48)
| X48 != relation_composition(X46,X47)
| ~ in(ordered_pair(X49,X50),X48)
| in(ordered_pair(X49,esk9_5(X46,X47,X48,X49,X50)),X46) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_relat_1])])])])])])]) ).
fof(c_0_16,plain,
! [X59,X60] :
( relation(relation_composition(X59,X60))
| ~ relation(X60)
| ~ relation(X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ function(relation_composition(esk3_0,esk2_0))
| ~ relation(relation_composition(esk3_0,esk2_0))
| in(esk1_0,relation_dom(esk3_0))
| in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| function(relation_composition(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
function(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,negated_conjecture,
function(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,plain,
( ~ relation(X2)
| ~ relation(X3)
| ~ relation(X4)
| X4 != relation_composition(X2,X3)
| ~ in(ordered_pair(X1,X5),X4)
| in(ordered_pair(X1,esk9_5(X2,X3,X4,X1,X5)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( ~ relation(X2)
| ~ relation(X1)
| relation(relation_composition(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( ~ relation(relation_composition(esk3_0,esk2_0))
| in(esk1_0,relation_dom(esk3_0))
| in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22])]) ).
fof(c_0_26,lemma,
! [X33,X34,X35] :
( ( ~ relation(X35)
| ~ in(ordered_pair(X33,X34),X35)
| in(X34,relation_rng(X35)) )
& ( ~ relation(X35)
| ~ in(ordered_pair(X33,X34),X35)
| in(X33,relation_dom(X35)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])])]) ).
cnf(c_0_27,plain,
( ~ in(ordered_pair(X1,X4),relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(ordered_pair(X1,esk9_5(X2,X3,relation_composition(X2,X3),X1,X4)),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( in(esk1_0,relation_dom(esk3_0))
| in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_19]),c_0_20])]) ).
cnf(c_0_29,plain,
( ~ relation(X3)
| ~ relation(X5)
| ~ relation(X6)
| X6 != relation_composition(X3,X5)
| ~ in(ordered_pair(X2,X4),X5)
| ~ in(ordered_pair(X1,X2),X3)
| in(ordered_pair(X1,X4),X6) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_30,negated_conjecture,
( in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
| in(apply(esk3_0,esk1_0),relation_dom(esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,lemma,
( ~ relation(X2)
| ~ in(ordered_pair(X1,X3),X2)
| in(X1,relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( in(esk1_0,relation_dom(esk3_0))
| in(ordered_pair(esk1_0,esk9_5(esk3_0,esk2_0,relation_composition(esk3_0,esk2_0),esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0))),esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_19]),c_0_20])]) ).
cnf(c_0_33,plain,
( ~ in(ordered_pair(X1,X5),X3)
| ~ in(ordered_pair(X5,X2),X4)
| ~ relation(X3)
| ~ relation(X4)
| in(ordered_pair(X1,X2),relation_composition(X3,X4)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_24]) ).
cnf(c_0_34,negated_conjecture,
( in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
| in(ordered_pair(apply(esk3_0,esk1_0),apply(esk2_0,apply(esk3_0,esk1_0))),esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_30]),c_0_19]),c_0_21])]) ).
cnf(c_0_35,lemma,
in(esk1_0,relation_dom(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20])]) ).
cnf(c_0_36,negated_conjecture,
( ~ in(ordered_pair(X1,apply(esk3_0,esk1_0)),X2)
| ~ relation(X2)
| in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
| in(ordered_pair(X1,apply(esk2_0,apply(esk3_0,esk1_0))),relation_composition(X2,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_19])]) ).
cnf(c_0_37,lemma,
in(ordered_pair(esk1_0,apply(esk3_0,esk1_0)),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_35]),c_0_20]),c_0_22])]) ).
cnf(c_0_38,lemma,
( in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
| in(ordered_pair(esk1_0,apply(esk2_0,apply(esk3_0,esk1_0))),relation_composition(esk3_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_20])]) ).
cnf(c_0_39,lemma,
( ~ relation(relation_composition(esk3_0,esk2_0))
| in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))) ),
inference(spm,[status(thm)],[c_0_31,c_0_38]) ).
cnf(c_0_40,lemma,
in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_24]),c_0_19]),c_0_20])]) ).
cnf(c_0_41,lemma,
( ~ function(relation_composition(esk3_0,esk2_0))
| ~ relation(relation_composition(esk3_0,esk2_0))
| in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_40]) ).
cnf(c_0_42,lemma,
( ~ relation(relation_composition(esk3_0,esk2_0))
| in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22])]) ).
fof(c_0_43,lemma,
! [X43,X44,X45] :
( ( ~ function(X45)
| ~ relation(X45)
| in(ordered_pair(X43,X44),X45)
| X44 != apply(X45,X43)
| ~ in(X43,relation_dom(X45)) )
& ( ~ function(X45)
| ~ relation(X45)
| ~ in(ordered_pair(X43,X44),X45)
| X44 = apply(X45,X43) )
& ( ~ function(X45)
| ~ relation(X45)
| ~ in(ordered_pair(X43,X44),X45)
| in(X43,relation_dom(X45)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_funct_1])])])]) ).
cnf(c_0_44,lemma,
in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_24]),c_0_19]),c_0_20])]) ).
cnf(c_0_45,plain,
( ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3)
| in(ordered_pair(esk9_5(X1,X2,X3,X4,X5),X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_46,lemma,
( ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X1),X2)
| X1 = apply(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_47,lemma,
in(ordered_pair(esk1_0,esk9_5(esk3_0,esk2_0,relation_composition(esk3_0,esk2_0),esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0))),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_44]),c_0_19]),c_0_20])]) ).
cnf(c_0_48,negated_conjecture,
( ~ in(apply(esk3_0,esk1_0),relation_dom(esk2_0))
| ~ in(esk1_0,relation_dom(esk3_0))
| ~ in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_49,plain,
( ~ in(ordered_pair(X3,X4),relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(esk9_5(X1,X2,relation_composition(X1,X2),X3,X4),X4),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_45]),c_0_24]) ).
cnf(c_0_50,lemma,
esk9_5(esk3_0,esk2_0,relation_composition(esk3_0,esk2_0),esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)) = apply(esk3_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_20]),c_0_22])]) ).
cnf(c_0_51,negated_conjecture,
( ~ in(apply(esk3_0,esk1_0),relation_dom(esk2_0))
| ~ in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_35])]) ).
cnf(c_0_52,lemma,
in(ordered_pair(apply(esk3_0,esk1_0),apply(relation_composition(esk3_0,esk2_0),esk1_0)),esk2_0),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_19]),c_0_20])]),c_0_50]) ).
cnf(c_0_53,negated_conjecture,
~ in(apply(esk3_0,esk1_0),relation_dom(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_40])]) ).
cnf(c_0_54,lemma,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_52]),c_0_19])]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU213+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.41 % Computer : n010.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Mon Sep 21 05:59:16 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.47 Running first-order theorem proving
% 0.14/5.47 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
% 210.27/36.44 % Version: 3.5.1
% 210.27/36.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 210.27/36.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 210.27/36.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 210.27/36.44 % Starting new_bool_3 with 300s (1) cores
% 210.27/36.44 % Starting new_bool_1 with 300s (1) cores
% 210.27/36.44 % Starting sh5l with 300s (1) cores
% 210.27/36.44 % new_bool_1 with pid 169326 completed with status 0
% 210.27/36.44 % Result found by new_bool_1
% 210.27/36.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 210.27/36.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 210.27/36.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 210.27/36.44 % Starting new_bool_3 with 300s (1) cores
% 210.27/36.44 % Starting new_bool_1 with 300s (1) cores
% 210.27/36.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 210.27/36.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 210.27/36.44 % Search class: FGHSM-FFMM31-SFFFFFNN
% 210.27/36.44 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 210.27/36.44 % Starting SubtermCWHack with 28s (1) cores
% 210.27/36.44 % SubtermCWHack with pid 169328 completed with status 8
% 210.27/36.44 % Starting new_bool_1 with 31s (1) cores
% 210.27/36.44 % new_bool_1 with pid 169337 completed with status 0
% 210.27/36.44 % Result found by new_bool_1
% 210.27/36.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 210.27/36.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 210.27/36.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 210.27/36.44 % Starting new_bool_3 with 300s (1) cores
% 210.27/36.44 % Starting new_bool_1 with 300s (1) cores
% 210.27/36.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 210.27/36.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 210.27/36.44 % Search class: FGHSM-FFMM31-SFFFFFNN
% 210.27/36.44 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 210.27/36.44 % Starting SubtermCWHack with 28s (1) cores
% 210.27/36.44 % SubtermCWHack with pid 169328 completed with status 8
% 210.27/36.44 % Starting new_bool_1 with 31s (1) cores
% 210.27/36.44 % Preprocessing time : 0.005 s
% 210.27/36.44 % Presaturation interreduction done
% 210.27/36.44
% 210.27/36.44 % Proof found!
% 210.27/36.44 % SZS status Theorem
% 210.27/36.44 % SZS output start CNFRefutation
% See solution above
% 210.27/36.44 % Parsed axioms : 217
% 210.27/36.44 % Removed by relevancy pruning/SinE : 154
% 210.27/36.44 % Initial clauses : 123
% 210.27/36.44 % Removed in clause preprocessing : 2
% 210.27/36.44 % Initial clauses in saturation : 121
% 210.27/36.44 % Processed clauses : 7625
% 210.27/36.44 % ...of these trivial : 21
% 210.27/36.44 % ...subsumed : 6339
% 210.27/36.44 % ...remaining for further processing : 1265
% 210.27/36.44 % Other redundant clauses eliminated : 141
% 210.27/36.44 % Clauses deleted for lack of memory : 0
% 210.27/36.44 % Backward-subsumed : 107
% 210.27/36.44 % Backward-rewritten : 147
% 210.27/36.44 % Generated clauses : 59969
% 210.27/36.44 % ...of the previous two non-redundant : 55194
% 210.27/36.44 % ...aggressively subsumed : 0
% 210.27/36.44 % Contextual simplify-reflections : 83
% 210.27/36.44 % Paramodulations : 59807
% 210.27/36.44 % Factorizations : 16
% 210.27/36.44 % NegExts : 0
% 210.27/36.44 % Equation resolutions : 143
% 210.27/36.44 % Disequality decompositions : 0
% 210.27/36.44 % Total rewrite steps : 14362
% 210.27/36.44 % ...of those cached : 14220
% 210.27/36.44 % Propositional unsat checks : 0
% 210.27/36.44 % Propositional check models : 0
% 210.27/36.44 % Propositional check unsatisfiable : 0
% 210.27/36.44 % Propositional clauses : 0
% 210.27/36.44 % Propositional clauses after purity: 0
% 210.27/36.44 % Propositional unsat core size : 0
% 210.27/36.44 % Propositional preprocessing time : 0.000
% 210.27/36.44 % Propositional encoding time : 0.000
% 210.27/36.44 % Propositional solver time : 0.000
% 210.27/36.44 % Success case prop preproc time : 0.000
% 210.27/36.44 % Success case prop encoding time : 0.000
% 210.27/36.44 % Success case prop solver time : 0.000
% 210.27/36.44 % Current number of processed clauses : 884
% 210.27/36.44 % Positive orientable unit clauses : 59
% 210.27/36.44 % Positive unorientable unit clauses: 0
% 210.27/36.44 % Negative unit clauses : 29
% 210.27/36.44 % Non-unit-clauses : 796
% 210.27/36.44 % Current number of unprocessed clauses: 47223
% 210.27/36.44 % ...number of literals in the above : 233383
% 210.27/36.44 % Current number of archived formulas : 0
% 210.27/36.44 % Current number of archived clauses : 365
% 210.27/36.44 % Clause-clause subsumption calls (NU) : 173005
% 210.27/36.44 % Rec. Clause-clause subsumption calls : 87843
% 210.27/36.44 % Non-unit clause-clause subsumptions : 4161
% 210.27/36.44 % Unit Clause-clause subsumption calls : 1688
% 210.27/36.44 % Rewrite failures with RHS unbound : 0
% 210.27/36.44 % BW rewrite match attempts : 19
% 210.27/36.44 % BW rewrite match successes : 10
% 210.27/36.44 % Condensation attempts : 0
% 210.27/36.44 % Condensation successes : 0
% 210.27/36.44 % Termbank termtop insertions : 873961
% 210.27/36.44 % Search garbage collected termcells : 3085
% 210.27/36.44
% 210.27/36.44 % -------------------------------------------------
% 210.27/36.44 % User time : 29.133 s
% 210.27/36.44 % System time : 1.129 s
% 210.27/36.44 % Total time : 30.263 s
% 210.27/36.44 % Maximum resident set size: 3832 pages
% 210.27/36.44
% 210.27/36.44 % -------------------------------------------------
% 210.27/36.44 % User time : 29.144 s
% 210.27/36.44 % System time : 1.138 s
% 210.27/36.44 % Total time : 30.282 s
% 210.27/36.44 % Maximum resident set size: 4864 pages
% 210.27/36.44 % E exiting
%------------------------------------------------------------------------------