%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU063+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 02:23:45 PM UTC 2026
% Result : Theorem 259.22s 37.78s
% Output : CNFRefutation 259.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 94 ( 18 unt; 0 def)
% Number of atoms : 377 ( 88 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 471 ( 188 ~; 231 |; 34 &)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-3 aty)
% Number of variables : 154 ( 5 sgn 56 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t144_funct_1,conjecture,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ! [X2] :
~ ( ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3)
& in(X2,relation_rng(X1)) )
<=> one_to_one(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_funct_1) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X1,X4)
& in(X4,relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(d13_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(apply(X1,X4),X2)
& in(X4,relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( in(X1,X2)
| empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(d8_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( apply(X1,X2) = apply(X1,X3)
& in(X3,relation_dom(X1))
& in(X2,relation_dom(X1)) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ empty(singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ! [X2] :
~ ( ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3)
& in(X2,relation_rng(X1)) )
<=> one_to_one(X1) ) ),
inference(assume_negation,[status(cth)],[t144_funct_1]) ).
fof(c_0_9,plain,
! [X43,X44,X45,X47,X48,X49,X51] :
( ( ~ function(X43)
| ~ relation(X43)
| X49 = relation_rng(X43)
| in(esk10_2(X43,X49),X49)
| esk10_2(X43,X49) = apply(X43,esk11_2(X43,X49)) )
& ( ~ function(X43)
| ~ relation(X43)
| X49 = relation_rng(X43)
| in(esk10_2(X43,X49),X49)
| in(esk11_2(X43,X49),relation_dom(X43)) )
& ( ~ function(X43)
| ~ relation(X43)
| X49 = relation_rng(X43)
| esk10_2(X43,X49) != apply(X43,X51)
| ~ in(X51,relation_dom(X43))
| ~ in(esk10_2(X43,X49),X49) )
& ( ~ function(X43)
| ~ relation(X43)
| X44 != relation_rng(X43)
| in(X47,X44)
| X47 != apply(X43,X48)
| ~ in(X48,relation_dom(X43)) )
& ( ~ function(X43)
| ~ relation(X43)
| X44 != relation_rng(X43)
| ~ in(X45,X44)
| X45 = apply(X43,esk9_3(X43,X44,X45)) )
& ( ~ function(X43)
| ~ relation(X43)
| X44 != relation_rng(X43)
| ~ in(X45,X44)
| in(esk9_3(X43,X44,X45),relation_dom(X43)) ) ),
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)],[d5_funct_1])])])])])])]) ).
fof(c_0_10,plain,
! [X27,X28,X29,X30,X31,X32,X33] :
( ( ~ function(X27)
| ~ relation(X27)
| X33 = relation_inverse_image(X27,X32)
| in(esk8_3(X27,X32,X33),X33)
| in(apply(X27,esk8_3(X27,X32,X33)),X32) )
& ( ~ function(X27)
| ~ relation(X27)
| X33 = relation_inverse_image(X27,X32)
| in(esk8_3(X27,X32,X33),X33)
| in(esk8_3(X27,X32,X33),relation_dom(X27)) )
& ( ~ function(X27)
| ~ relation(X27)
| X33 = relation_inverse_image(X27,X32)
| ~ in(apply(X27,esk8_3(X27,X32,X33)),X32)
| ~ in(esk8_3(X27,X32,X33),relation_dom(X27))
| ~ in(esk8_3(X27,X32,X33),X33) )
& ( ~ function(X27)
| ~ relation(X27)
| X29 != relation_inverse_image(X27,X28)
| in(X31,X29)
| ~ in(apply(X27,X31),X28)
| ~ in(X31,relation_dom(X27)) )
& ( ~ function(X27)
| ~ relation(X27)
| X29 != relation_inverse_image(X27,X28)
| ~ in(X30,X29)
| in(apply(X27,X30),X28) )
& ( ~ function(X27)
| ~ relation(X27)
| X29 != relation_inverse_image(X27,X28)
| ~ in(X30,X29)
| in(X30,relation_dom(X27)) ) ),
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)],[d13_funct_1])])])])])])]) ).
fof(c_0_11,plain,
! [X39,X40] :
( in(X39,X40)
| empty(X40)
| ~ element(X39,X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
fof(c_0_12,plain,
! [X70] : element(esk18_1(X70),X70),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ! [X2] :
~ ( ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3)
& in(X2,relation_rng(X1)) )
<=> one_to_one(X1) ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ function(X2)
| ~ relation(X2)
| X4 != relation_rng(X2)
| X3 != apply(X2,X1)
| ~ in(X1,relation_dom(X2))
| in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X11,X12,X13] :
( ( ~ function(X11)
| ~ relation(X11)
| one_to_one(X11)
| esk4_1(X11) != esk5_1(X11) )
& ( ~ function(X11)
| ~ relation(X11)
| one_to_one(X11)
| apply(X11,esk4_1(X11)) = apply(X11,esk5_1(X11)) )
& ( ~ function(X11)
| ~ relation(X11)
| one_to_one(X11)
| in(esk5_1(X11),relation_dom(X11)) )
& ( ~ function(X11)
| ~ relation(X11)
| one_to_one(X11)
| in(esk4_1(X11),relation_dom(X11)) )
& ( ~ function(X11)
| ~ relation(X11)
| X12 = X13
| apply(X11,X12) != apply(X11,X13)
| ~ in(X13,relation_dom(X11))
| ~ in(X12,relation_dom(X11))
| ~ one_to_one(X11) ) ),
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)],[d8_funct_1])])])])])]) ).
cnf(c_0_16,plain,
( ~ function(X2)
| ~ relation(X2)
| X3 != relation_inverse_image(X2,X4)
| ~ in(X1,X3)
| in(X1,relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
element(esk18_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X17,X18,X19,X20,X21,X22] :
( ( X22 = singleton(X21)
| esk7_2(X21,X22) = X21
| in(esk7_2(X21,X22),X22) )
& ( X22 = singleton(X21)
| esk7_2(X21,X22) != X21
| ~ in(esk7_2(X21,X22),X22) )
& ( X18 != singleton(X17)
| in(X20,X18)
| X20 != X17 )
& ( X18 != singleton(X17)
| X19 = X17
| ~ in(X19,X18) ) ),
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)],[d1_tarski])])])])])])]) ).
cnf(c_0_20,plain,
( ~ function(X1)
| ~ relation(X1)
| X4 != relation_inverse_image(X1,X3)
| ~ in(X2,X4)
| in(apply(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_21,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(c_0_22,negated_conjecture,
! [X7,X8] :
( ( one_to_one(esk1_0)
| relation_inverse_image(esk1_0,singleton(X8)) = singleton(esk3_1(X8))
| ~ in(X8,relation_rng(esk1_0)) )
& ( ~ one_to_one(esk1_0)
| relation_inverse_image(esk1_0,singleton(esk2_0)) != singleton(X7) )
& ( ~ one_to_one(esk1_0)
| in(esk2_0,relation_rng(esk1_0)) )
& function(esk1_0)
& relation(esk1_0) ),
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)],[c_0_13])])])])])]) ).
cnf(c_0_23,plain,
( ~ in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X2),relation_rng(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).
cnf(c_0_24,plain,
( ~ function(X1)
| ~ relation(X1)
| one_to_one(X1)
| in(esk5_1(X1),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( ~ in(X1,relation_inverse_image(X2,X3))
| ~ function(X2)
| ~ relation(X2)
| in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
( in(esk18_1(X1),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_27,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( ~ in(X2,relation_inverse_image(X1,X3))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X2),X3) ),
inference(er,[status(thm)],[c_0_20]) ).
fof(c_0_29,plain,
! [X24] : ~ empty(singleton(X24)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_21])]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(X1,relation_rng(esk1_0))
| one_to_one(esk1_0)
| relation_inverse_image(esk1_0,singleton(X1)) = singleton(esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( ~ function(X1)
| ~ relation(X1)
| in(apply(X1,esk5_1(X1)),relation_rng(X1))
| one_to_one(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,negated_conjecture,
function(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_34,plain,
( ~ function(X1)
| ~ relation(X1)
| in(esk18_1(relation_inverse_image(X1,X2)),relation_dom(X1))
| empty(relation_inverse_image(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
( ~ function(X1)
| ~ relation(X1)
| in(apply(X1,esk18_1(relation_inverse_image(X1,X2))),X2)
| empty(relation_inverse_image(X1,X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_37,plain,
( ~ function(X2)
| ~ relation(X2)
| X4 != relation_inverse_image(X2,X3)
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2))
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_38,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
( one_to_one(esk1_0)
| singleton(esk3_1(apply(esk1_0,esk5_1(esk1_0)))) = relation_inverse_image(esk1_0,singleton(apply(esk1_0,esk5_1(esk1_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_40,plain,
( ~ function(X1)
| ~ relation(X1)
| in(apply(X1,esk18_1(relation_inverse_image(X1,X2))),relation_rng(X1))
| empty(relation_inverse_image(X1,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_41,plain,
( ~ function(X1)
| ~ relation(X1)
| empty(relation_inverse_image(X1,singleton(X2)))
| apply(X1,esk18_1(relation_inverse_image(X1,singleton(X2)))) = X2 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
( ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| ~ function(X2)
| ~ relation(X2)
| in(X1,relation_inverse_image(X2,X3)) ),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( ~ empty(relation_inverse_image(esk1_0,singleton(apply(esk1_0,esk5_1(esk1_0)))))
| one_to_one(esk1_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( ~ function(X1)
| ~ relation(X1)
| in(X2,relation_rng(X1))
| empty(relation_inverse_image(X1,singleton(X2))) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
( ~ in(apply(X1,esk5_1(X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| in(esk5_1(X1),relation_inverse_image(X1,X2))
| one_to_one(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_24]) ).
cnf(c_0_46,negated_conjecture,
( in(apply(esk1_0,esk5_1(esk1_0)),relation_rng(esk1_0))
| one_to_one(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_32]),c_0_33])]) ).
cnf(c_0_47,plain,
( ~ function(X1)
| ~ relation(X1)
| one_to_one(X1)
| apply(X1,esk4_1(X1)) = apply(X1,esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_48,negated_conjecture,
( in(esk5_1(esk1_0),relation_inverse_image(esk1_0,relation_rng(esk1_0)))
| one_to_one(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_32]),c_0_33])]) ).
cnf(c_0_49,plain,
( ~ function(X1)
| ~ relation(X1)
| one_to_one(X1)
| in(esk4_1(X1),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_50,negated_conjecture,
( ~ empty(relation_inverse_image(esk1_0,singleton(apply(esk1_0,esk4_1(esk1_0)))))
| one_to_one(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_47]),c_0_32]),c_0_33])]) ).
cnf(c_0_51,negated_conjecture,
( in(esk5_1(esk1_0),relation_dom(esk1_0))
| one_to_one(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_48]),c_0_32]),c_0_33])]) ).
cnf(c_0_52,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_53,plain,
( ~ in(apply(X1,esk4_1(X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| in(esk4_1(X1),relation_inverse_image(X1,X2))
| one_to_one(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( in(apply(esk1_0,esk4_1(esk1_0)),relation_rng(esk1_0))
| one_to_one(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_44]),c_0_32]),c_0_33])]) ).
cnf(c_0_55,negated_conjecture,
( ~ in(apply(esk1_0,esk5_1(esk1_0)),X1)
| in(esk5_1(esk1_0),relation_inverse_image(esk1_0,X1))
| one_to_one(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_51]),c_0_32]),c_0_33])]) ).
cnf(c_0_56,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_52])]) ).
cnf(c_0_57,negated_conjecture,
( in(esk4_1(esk1_0),relation_inverse_image(esk1_0,relation_rng(esk1_0)))
| one_to_one(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_32]),c_0_33])]) ).
cnf(c_0_58,negated_conjecture,
( ~ in(X1,relation_inverse_image(esk1_0,singleton(apply(esk1_0,esk5_1(esk1_0)))))
| one_to_one(esk1_0)
| X1 = esk3_1(apply(esk1_0,esk5_1(esk1_0))) ),
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_59,negated_conjecture,
( in(esk5_1(esk1_0),relation_inverse_image(esk1_0,singleton(apply(esk1_0,esk5_1(esk1_0)))))
| one_to_one(esk1_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
( in(esk4_1(esk1_0),relation_dom(esk1_0))
| one_to_one(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_57]),c_0_32]),c_0_33])]) ).
cnf(c_0_61,negated_conjecture,
( one_to_one(esk1_0)
| esk3_1(apply(esk1_0,esk5_1(esk1_0))) = esk5_1(esk1_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_62,negated_conjecture,
( ~ in(apply(esk1_0,esk4_1(esk1_0)),X1)
| in(esk4_1(esk1_0),relation_inverse_image(esk1_0,X1))
| one_to_one(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_60]),c_0_32]),c_0_33])]) ).
cnf(c_0_63,negated_conjecture,
( one_to_one(esk1_0)
| singleton(esk3_1(apply(esk1_0,esk4_1(esk1_0)))) = relation_inverse_image(esk1_0,singleton(apply(esk1_0,esk4_1(esk1_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_47]),c_0_32]),c_0_33])]) ).
cnf(c_0_64,negated_conjecture,
( one_to_one(esk1_0)
| esk3_1(apply(esk1_0,esk4_1(esk1_0))) = esk5_1(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_47]),c_0_32]),c_0_33])]) ).
cnf(c_0_65,negated_conjecture,
( in(esk4_1(esk1_0),relation_inverse_image(esk1_0,singleton(apply(esk1_0,esk4_1(esk1_0)))))
| one_to_one(esk1_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_56]) ).
cnf(c_0_66,negated_conjecture,
( one_to_one(esk1_0)
| relation_inverse_image(esk1_0,singleton(apply(esk1_0,esk4_1(esk1_0)))) = singleton(esk5_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
( in(esk4_1(esk1_0),singleton(esk5_1(esk1_0)))
| one_to_one(esk1_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_68,plain,
( ~ function(X1)
| ~ relation(X1)
| esk4_1(X1) != esk5_1(X1)
| one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_69,negated_conjecture,
( one_to_one(esk1_0)
| esk5_1(esk1_0) = esk4_1(esk1_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_67]) ).
cnf(c_0_70,plain,
( ~ function(X2)
| ~ relation(X2)
| X3 != relation_rng(X2)
| ~ in(X1,X3)
| X1 = apply(X2,esk9_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_71,negated_conjecture,
( ~ one_to_one(esk1_0)
| in(esk2_0,relation_rng(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_72,negated_conjecture,
one_to_one(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_32]),c_0_33])]) ).
cnf(c_0_73,plain,
( ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2)
| in(esk9_3(X1,X2,X3),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_74,plain,
( ~ in(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| apply(X1,esk9_3(X1,relation_rng(X1),X2)) = X2 ),
inference(er,[status(thm)],[c_0_70]) ).
cnf(c_0_75,negated_conjecture,
in(esk2_0,relation_rng(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).
cnf(c_0_76,plain,
( ~ in(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| in(esk9_3(X1,relation_rng(X1),X2),relation_dom(X1)) ),
inference(er,[status(thm)],[c_0_73]) ).
cnf(c_0_77,plain,
( X2 = singleton(X1)
| esk7_2(X1,X2) = X1
| in(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_78,plain,
( ~ function(X1)
| ~ relation(X1)
| apply(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_79,negated_conjecture,
apply(esk1_0,esk9_3(esk1_0,relation_rng(esk1_0),esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_32]),c_0_33])]) ).
cnf(c_0_80,negated_conjecture,
in(esk9_3(esk1_0,relation_rng(esk1_0),esk2_0),relation_dom(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_75]),c_0_32]),c_0_33])]) ).
cnf(c_0_81,plain,
( ~ function(X2)
| ~ relation(X2)
| in(apply(X2,esk7_2(X1,relation_inverse_image(X2,X3))),X3)
| relation_inverse_image(X2,X3) = singleton(X1)
| esk7_2(X1,relation_inverse_image(X2,X3)) = X1 ),
inference(spm,[status(thm)],[c_0_28,c_0_77]) ).
cnf(c_0_82,negated_conjecture,
( ~ one_to_one(esk1_0)
| relation_inverse_image(esk1_0,singleton(esk2_0)) != singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_83,negated_conjecture,
( ~ in(X1,relation_dom(esk1_0))
| apply(esk1_0,X1) != esk2_0
| esk9_3(esk1_0,relation_rng(esk1_0),esk2_0) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_72]),c_0_32]),c_0_33])]),c_0_80])]) ).
cnf(c_0_84,plain,
( ~ function(X1)
| ~ relation(X1)
| relation_inverse_image(X1,singleton(X3)) = singleton(X2)
| esk7_2(X2,relation_inverse_image(X1,singleton(X3))) = X2
| apply(X1,esk7_2(X2,relation_inverse_image(X1,singleton(X3)))) = X3 ),
inference(spm,[status(thm)],[c_0_35,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
relation_inverse_image(esk1_0,singleton(esk2_0)) != singleton(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_72])]) ).
cnf(c_0_86,negated_conjecture,
( ~ in(esk7_2(X1,relation_inverse_image(esk1_0,singleton(esk2_0))),relation_dom(esk1_0))
| esk7_2(X1,relation_inverse_image(esk1_0,singleton(esk2_0))) = X1
| esk7_2(X1,relation_inverse_image(esk1_0,singleton(esk2_0))) = esk9_3(esk1_0,relation_rng(esk1_0),esk2_0) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_32]),c_0_33])])]),c_0_85]) ).
cnf(c_0_87,plain,
( ~ function(X2)
| ~ relation(X2)
| in(esk7_2(X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| relation_inverse_image(X2,X3) = singleton(X1)
| esk7_2(X1,relation_inverse_image(X2,X3)) = X1 ),
inference(spm,[status(thm)],[c_0_25,c_0_77]) ).
cnf(c_0_88,negated_conjecture,
( esk7_2(X1,relation_inverse_image(esk1_0,singleton(esk2_0))) = X1
| esk7_2(X1,relation_inverse_image(esk1_0,singleton(esk2_0))) = esk9_3(esk1_0,relation_rng(esk1_0),esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_32]),c_0_33])]),c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( ~ in(esk2_0,X1)
| in(esk9_3(esk1_0,relation_rng(esk1_0),esk2_0),relation_inverse_image(esk1_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_80]),c_0_32]),c_0_33]),c_0_79])]) ).
cnf(c_0_90,plain,
( esk7_2(X1,X2) != X1
| ~ in(esk7_2(X1,X2),X2)
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_91,negated_conjecture,
esk7_2(esk9_3(esk1_0,relation_rng(esk1_0),esk2_0),relation_inverse_image(esk1_0,singleton(esk2_0))) = esk9_3(esk1_0,relation_rng(esk1_0),esk2_0),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_88])]) ).
cnf(c_0_92,negated_conjecture,
in(esk9_3(esk1_0,relation_rng(esk1_0),esk2_0),relation_inverse_image(esk1_0,singleton(esk2_0))),
inference(spm,[status(thm)],[c_0_89,c_0_56]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92])]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU063+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:47:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 259.22/37.78 % Version: 3.5.1
% 259.22/37.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 259.22/37.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 259.22/37.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 259.22/37.78 % Starting new_bool_3 with 300s (1) cores
% 259.22/37.78 % Starting new_bool_1 with 300s (1) cores
% 259.22/37.78 % Starting sh5l with 300s (1) cores
% 259.22/37.78 % new_bool_3 with pid 61616 completed with status 0
% 259.22/37.78 % Result found by new_bool_3
% 259.22/37.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 259.22/37.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 259.22/37.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 259.22/37.78 % Starting new_bool_3 with 300s (1) cores
% 259.22/37.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 259.22/37.78 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 259.22/37.78 % Search class: FGHSM-FFMM31-SFFFFFNN
% 259.22/37.78 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 259.22/37.78 % Starting SubtermCWHack with 28s (1) cores
% 259.22/37.78 % SubtermCWHack with pid 61623 completed with status 8
% 259.22/37.78 % Starting new_bool_3 with 31s (1) cores
% 259.22/37.78 % new_bool_3 with pid 61655 completed with status 0
% 259.22/37.78 % Result found by new_bool_3
% 259.22/37.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 259.22/37.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 259.22/37.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 259.22/37.78 % Starting new_bool_3 with 300s (1) cores
% 259.22/37.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 259.22/37.78 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 259.22/37.78 % Search class: FGHSM-FFMM31-SFFFFFNN
% 259.22/37.78 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 259.22/37.78 % Starting SubtermCWHack with 28s (1) cores
% 259.22/37.78 % SubtermCWHack with pid 61623 completed with status 8
% 259.22/37.78 % Starting new_bool_3 with 31s (1) cores
% 259.22/37.78 % Preprocessing time : 0.002 s
% 259.22/37.78 % Presaturation interreduction done
% 259.22/37.78
% 259.22/37.78 % Proof found!
% 259.22/37.78 % SZS status Theorem
% 259.22/37.78 % SZS output start CNFRefutation
% See solution above
% 259.22/37.78 % Parsed axioms : 39
% 259.22/37.78 % Removed by relevancy pruning/SinE : 5
% 259.22/37.78 % Initial clauses : 69
% 259.22/37.78 % Removed in clause preprocessing : 2
% 259.22/37.78 % Initial clauses in saturation : 67
% 259.22/37.78 % Processed clauses : 38065
% 259.22/37.78 % ...of these trivial : 11
% 259.22/37.78 % ...subsumed : 33706
% 259.22/37.78 % ...remaining for further processing : 4348
% 259.22/37.78 % Other redundant clauses eliminated : 1466
% 259.22/37.78 % Clauses deleted for lack of memory : 0
% 259.22/37.78 % Backward-subsumed : 449
% 259.22/37.78 % Backward-rewritten : 1283
% 259.22/37.78 % Generated clauses : 295670
% 259.22/37.78 % ...of the previous two non-redundant : 289025
% 259.22/37.78 % ...aggressively subsumed : 0
% 259.22/37.78 % Contextual simplify-reflections : 184
% 259.22/37.78 % Paramodulations : 294181
% 259.22/37.78 % Factorizations : 22
% 259.22/37.78 % NegExts : 0
% 259.22/37.78 % Equation resolutions : 1469
% 259.22/37.78 % Disequality decompositions : 0
% 259.22/37.78 % Total rewrite steps : 17175
% 259.22/37.78 % ...of those cached : 16921
% 259.22/37.78 % Propositional unsat checks : 0
% 259.22/37.78 % Propositional check models : 0
% 259.22/37.78 % Propositional check unsatisfiable : 0
% 259.22/37.78 % Propositional clauses : 0
% 259.22/37.78 % Propositional clauses after purity: 0
% 259.22/37.78 % Propositional unsat core size : 0
% 259.22/37.78 % Propositional preprocessing time : 0.000
% 259.22/37.78 % Propositional encoding time : 0.000
% 259.22/37.78 % Propositional solver time : 0.000
% 259.22/37.78 % Success case prop preproc time : 0.000
% 259.22/37.78 % Success case prop encoding time : 0.000
% 259.22/37.78 % Success case prop solver time : 0.000
% 259.22/37.78 % Current number of processed clauses : 2541
% 259.22/37.78 % Positive orientable unit clauses : 56
% 259.22/37.78 % Positive unorientable unit clauses: 0
% 259.22/37.78 % Negative unit clauses : 29
% 259.22/37.78 % Non-unit-clauses : 2456
% 259.22/37.78 % Current number of unprocessed clauses: 233739
% 259.22/37.78 % ...number of literals in the above : 1726451
% 259.22/37.78 % Current number of archived formulas : 0
% 259.22/37.78 % Current number of archived clauses : 1799
% 259.22/37.78 % Clause-clause subsumption calls (NU) : 5136635
% 259.22/37.78 % Rec. Clause-clause subsumption calls : 1081965
% 259.22/37.78 % Non-unit clause-clause subsumptions : 25208
% 259.22/37.78 % Unit Clause-clause subsumption calls : 16271
% 259.22/37.78 % Rewrite failures with RHS unbound : 0
% 259.22/37.78 % BW rewrite match attempts : 28
% 259.22/37.78 % BW rewrite match successes : 10
% 259.22/37.78 % Condensation attempts : 0
% 259.22/37.78 % Condensation successes : 0
% 259.22/37.78 % Termbank termtop insertions : 5470899
% 259.22/37.78 % Search garbage collected termcells : 1072
% 259.22/37.78
% 259.22/37.78 % -------------------------------------------------
% 259.22/37.78 % User time : 35.402 s
% 259.22/37.78 % System time : 1.225 s
% 259.22/37.78 % Total time : 36.627 s
% 259.22/37.78 % Maximum resident set size: 3664 pages
% 259.22/37.78
% 259.22/37.78 % -------------------------------------------------
% 259.22/37.78 % User time : 35.404 s
% 259.22/37.78 % System time : 1.233 s
% 259.22/37.78 % Total time : 36.637 s
% 259.22/37.78 % Maximum resident set size: 4864 pages
% 259.22/37.78 % E exiting
%------------------------------------------------------------------------------