TSTP Solution File: SEU063+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU063+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 16:22:19 EDT 2023
% Result : Theorem 143.88s 143.91s
% Output : CNFRefutation 143.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 41
% Syntax : Number of formulae : 116 ( 11 unt; 36 typ; 0 def)
% Number of atoms : 340 ( 87 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 427 ( 167 ~; 213 |; 32 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 25 >; 12 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 11 con; 0-3 aty)
% Number of variables : 126 ( 4 sgn; 44 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
function: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
one_to_one: $i > $o ).
tff(decl_27,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_dom: $i > $i ).
tff(decl_29,type,
apply: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
relation_rng: $i > $i ).
tff(decl_32,type,
element: ( $i * $i ) > $o ).
tff(decl_33,type,
empty_set: $i ).
tff(decl_34,type,
relation_empty_yielding: $i > $o ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
subset: ( $i * $i ) > $o ).
tff(decl_37,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk6_1: $i > $i ).
tff(decl_43,type,
esk7_1: $i > $i ).
tff(decl_44,type,
esk8_1: $i > $i ).
tff(decl_45,type,
esk9_0: $i ).
tff(decl_46,type,
esk10_0: $i ).
tff(decl_47,type,
esk11_1: $i > $i ).
tff(decl_48,type,
esk12_0: $i ).
tff(decl_49,type,
esk13_0: $i ).
tff(decl_50,type,
esk14_0: $i ).
tff(decl_51,type,
esk15_1: $i > $i ).
tff(decl_52,type,
esk16_0: $i ).
tff(decl_53,type,
esk17_0: $i ).
tff(decl_54,type,
esk18_0: $i ).
tff(decl_55,type,
esk19_0: $i ).
tff(decl_56,type,
esk20_0: $i ).
tff(decl_57,type,
esk21_1: $i > $i ).
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t144_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2] :
~ ( in(X2,relation_rng(X1))
& ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3) )
<=> one_to_one(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
fof(d8_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(d13_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(c_0_5,plain,
! [X25,X26,X27,X29,X30,X31,X33] :
( ( in(esk3_3(X25,X26,X27),relation_dom(X25))
| ~ in(X27,X26)
| X26 != relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) )
& ( X27 = apply(X25,esk3_3(X25,X26,X27))
| ~ in(X27,X26)
| X26 != relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) )
& ( ~ in(X30,relation_dom(X25))
| X29 != apply(X25,X30)
| in(X29,X26)
| X26 != relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) )
& ( ~ in(esk4_2(X25,X31),X31)
| ~ in(X33,relation_dom(X25))
| esk4_2(X25,X31) != apply(X25,X33)
| X31 = relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) )
& ( in(esk5_2(X25,X31),relation_dom(X25))
| in(esk4_2(X25,X31),X31)
| X31 = relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) )
& ( esk4_2(X25,X31) = apply(X25,esk5_2(X25,X31))
| in(esk4_2(X25,X31),X31)
| X31 = relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) ) ),
inference(distribute,[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_6,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2] :
~ ( in(X2,relation_rng(X1))
& ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3) )
<=> one_to_one(X1) ) ),
inference(assume_negation,[status(cth)],[t144_funct_1]) ).
cnf(c_0_7,plain,
( in(X3,X4)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| X4 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X35,X36,X37] :
( ( ~ one_to_one(X35)
| ~ in(X36,relation_dom(X35))
| ~ in(X37,relation_dom(X35))
| apply(X35,X36) != apply(X35,X37)
| X36 = X37
| ~ relation(X35)
| ~ function(X35) )
& ( in(esk6_1(X35),relation_dom(X35))
| one_to_one(X35)
| ~ relation(X35)
| ~ function(X35) )
& ( in(esk7_1(X35),relation_dom(X35))
| one_to_one(X35)
| ~ relation(X35)
| ~ function(X35) )
& ( apply(X35,esk6_1(X35)) = apply(X35,esk7_1(X35))
| one_to_one(X35)
| ~ relation(X35)
| ~ function(X35) )
& ( esk6_1(X35) != esk7_1(X35)
| one_to_one(X35)
| ~ relation(X35)
| ~ function(X35) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
fof(c_0_9,plain,
! [X18,X19,X20,X21,X22,X23] :
( ( ~ in(X20,X19)
| X20 = X18
| X19 != singleton(X18) )
& ( X21 != X18
| in(X21,X19)
| X19 != singleton(X18) )
& ( ~ in(esk2_2(X22,X23),X23)
| esk2_2(X22,X23) != X22
| X23 = singleton(X22) )
& ( in(esk2_2(X22,X23),X23)
| esk2_2(X22,X23) = X22
| X23 = singleton(X22) ) ),
inference(distribute,[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])])])])])]) ).
fof(c_0_10,negated_conjecture,
! [X63,X64] :
( relation(esk19_0)
& function(esk19_0)
& ( in(esk20_0,relation_rng(esk19_0))
| ~ one_to_one(esk19_0) )
& ( relation_inverse_image(esk19_0,singleton(esk20_0)) != singleton(X63)
| ~ one_to_one(esk19_0) )
& ( ~ in(X64,relation_rng(esk19_0))
| relation_inverse_image(esk19_0,singleton(X64)) = singleton(esk21_1(X64))
| one_to_one(esk19_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
cnf(c_0_11,plain,
( in(apply(X1,X2),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_7])]) ).
cnf(c_0_12,plain,
( in(esk7_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X10,X11,X12,X13,X14,X15,X16] :
( ( in(X13,relation_dom(X10))
| ~ in(X13,X12)
| X12 != relation_inverse_image(X10,X11)
| ~ relation(X10)
| ~ function(X10) )
& ( in(apply(X10,X13),X11)
| ~ in(X13,X12)
| X12 != relation_inverse_image(X10,X11)
| ~ relation(X10)
| ~ function(X10) )
& ( ~ in(X14,relation_dom(X10))
| ~ in(apply(X10,X14),X11)
| in(X14,X12)
| X12 != relation_inverse_image(X10,X11)
| ~ relation(X10)
| ~ function(X10) )
& ( ~ in(esk1_3(X10,X15,X16),X16)
| ~ in(esk1_3(X10,X15,X16),relation_dom(X10))
| ~ in(apply(X10,esk1_3(X10,X15,X16)),X15)
| X16 = relation_inverse_image(X10,X15)
| ~ relation(X10)
| ~ function(X10) )
& ( in(esk1_3(X10,X15,X16),relation_dom(X10))
| in(esk1_3(X10,X15,X16),X16)
| X16 = relation_inverse_image(X10,X15)
| ~ relation(X10)
| ~ function(X10) )
& ( in(apply(X10,esk1_3(X10,X15,X16)),X15)
| in(esk1_3(X10,X15,X16),X16)
| X16 = relation_inverse_image(X10,X15)
| ~ relation(X10)
| ~ function(X10) ) ),
inference(distribute,[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])])])])])]) ).
cnf(c_0_14,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( relation_inverse_image(esk19_0,singleton(X1)) = singleton(esk21_1(X1))
| one_to_one(esk19_0)
| ~ in(X1,relation_rng(esk19_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( one_to_one(X1)
| in(apply(X1,esk7_1(X1)),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
function(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X3 != relation_inverse_image(X2,X4)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).
cnf(c_0_21,negated_conjecture,
( singleton(esk21_1(apply(esk19_0,esk7_1(esk19_0)))) = relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk7_1(esk19_0))))
| one_to_one(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_22,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,X4)
| X4 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_inverse_image(X2,X3)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( one_to_one(esk19_0)
| in(esk21_1(apply(esk19_0,esk7_1(esk19_0))),relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk7_1(esk19_0))))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,plain,
( in(apply(X1,X2),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( in(X1,X4)
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,negated_conjecture,
( one_to_one(esk19_0)
| in(esk21_1(apply(esk19_0,esk7_1(esk19_0))),relation_dom(esk19_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]),c_0_18])]) ).
cnf(c_0_29,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( one_to_one(esk19_0)
| in(apply(esk19_0,esk21_1(apply(esk19_0,esk7_1(esk19_0)))),singleton(apply(esk19_0,esk7_1(esk19_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_17]),c_0_18])]) ).
cnf(c_0_31,plain,
( in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( one_to_one(esk19_0)
| in(apply(esk19_0,esk21_1(apply(esk19_0,esk7_1(esk19_0)))),relation_rng(esk19_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_28]),c_0_17]),c_0_18])]) ).
cnf(c_0_33,negated_conjecture,
( apply(esk19_0,esk21_1(apply(esk19_0,esk7_1(esk19_0)))) = apply(esk19_0,esk7_1(esk19_0))
| one_to_one(esk19_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( one_to_one(X1)
| in(esk7_1(X1),relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(apply(X1,esk7_1(X1)),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_12]) ).
cnf(c_0_35,negated_conjecture,
( one_to_one(esk19_0)
| in(apply(esk19_0,esk7_1(esk19_0)),relation_rng(esk19_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( one_to_one(esk19_0)
| in(esk7_1(esk19_0),relation_inverse_image(esk19_0,relation_rng(esk19_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_17]),c_0_18])]) ).
cnf(c_0_37,plain,
( in(esk6_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_38,plain,
( apply(X1,esk6_1(X1)) = apply(X1,esk7_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_39,negated_conjecture,
( one_to_one(esk19_0)
| in(esk7_1(esk19_0),relation_dom(esk19_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_36]),c_0_17]),c_0_18])]) ).
cnf(c_0_40,plain,
( one_to_one(X1)
| in(esk6_1(X1),relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(apply(X1,esk6_1(X1)),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( one_to_one(esk19_0)
| in(apply(esk19_0,esk6_1(esk19_0)),relation_rng(esk19_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_38]),c_0_17]),c_0_18])]) ).
cnf(c_0_42,negated_conjecture,
( one_to_one(esk19_0)
| in(esk7_1(esk19_0),relation_inverse_image(esk19_0,X1))
| ~ in(apply(esk19_0,esk7_1(esk19_0)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_39]),c_0_17]),c_0_18])]) ).
cnf(c_0_43,negated_conjecture,
( one_to_one(esk19_0)
| in(esk6_1(esk19_0),relation_inverse_image(esk19_0,relation_rng(esk19_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_17]),c_0_18])]) ).
cnf(c_0_44,negated_conjecture,
( X1 = esk21_1(apply(esk19_0,esk7_1(esk19_0)))
| one_to_one(esk19_0)
| ~ in(X1,relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk7_1(esk19_0))))) ),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_45,negated_conjecture,
( one_to_one(esk19_0)
| in(esk7_1(esk19_0),relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk7_1(esk19_0))))) ),
inference(spm,[status(thm)],[c_0_42,c_0_20]) ).
cnf(c_0_46,negated_conjecture,
( one_to_one(esk19_0)
| in(esk6_1(esk19_0),relation_dom(esk19_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_43]),c_0_17]),c_0_18])]) ).
cnf(c_0_47,negated_conjecture,
( esk21_1(apply(esk19_0,esk7_1(esk19_0))) = esk7_1(esk19_0)
| one_to_one(esk19_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( one_to_one(esk19_0)
| in(esk6_1(esk19_0),relation_inverse_image(esk19_0,X1))
| ~ in(apply(esk19_0,esk6_1(esk19_0)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_46]),c_0_17]),c_0_18])]) ).
cnf(c_0_49,negated_conjecture,
( singleton(esk21_1(apply(esk19_0,esk6_1(esk19_0)))) = relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk6_1(esk19_0))))
| one_to_one(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_38]),c_0_17]),c_0_18])]) ).
cnf(c_0_50,negated_conjecture,
( esk21_1(apply(esk19_0,esk6_1(esk19_0))) = esk7_1(esk19_0)
| one_to_one(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_38]),c_0_17]),c_0_18])]) ).
cnf(c_0_51,negated_conjecture,
( one_to_one(esk19_0)
| in(esk6_1(esk19_0),relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk6_1(esk19_0))))) ),
inference(spm,[status(thm)],[c_0_48,c_0_20]) ).
cnf(c_0_52,negated_conjecture,
( relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk6_1(esk19_0)))) = singleton(esk7_1(esk19_0))
| one_to_one(esk19_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( one_to_one(esk19_0)
| in(esk6_1(esk19_0),singleton(esk7_1(esk19_0))) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,plain,
( one_to_one(X1)
| esk6_1(X1) != esk7_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_55,negated_conjecture,
( esk7_1(esk19_0) = esk6_1(esk19_0)
| one_to_one(esk19_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_53]) ).
cnf(c_0_56,plain,
( X1 = apply(X2,esk3_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_57,negated_conjecture,
( in(esk20_0,relation_rng(esk19_0))
| ~ one_to_one(esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_58,negated_conjecture,
one_to_one(esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_17]),c_0_18])]) ).
cnf(c_0_59,plain,
( in(esk3_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_60,plain,
( apply(X1,esk3_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_61,negated_conjecture,
in(esk20_0,relation_rng(esk19_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_62,plain,
( in(esk3_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_59]) ).
cnf(c_0_63,plain,
( in(esk2_2(X1,X2),X2)
| esk2_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_64,plain,
( X2 = X3
| ~ one_to_one(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_65,negated_conjecture,
apply(esk19_0,esk3_3(esk19_0,relation_rng(esk19_0),esk20_0)) = esk20_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_17]),c_0_18])]) ).
cnf(c_0_66,negated_conjecture,
in(esk3_3(esk19_0,relation_rng(esk19_0),esk20_0),relation_dom(esk19_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_61]),c_0_17]),c_0_18])]) ).
cnf(c_0_67,plain,
( esk2_2(X1,relation_inverse_image(X2,X3)) = X1
| relation_inverse_image(X2,X3) = singleton(X1)
| in(apply(X2,esk2_2(X1,relation_inverse_image(X2,X3))),X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_63]) ).
cnf(c_0_68,negated_conjecture,
( relation_inverse_image(esk19_0,singleton(esk20_0)) != singleton(X1)
| ~ one_to_one(esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_69,negated_conjecture,
( esk3_3(esk19_0,relation_rng(esk19_0),esk20_0) = X1
| apply(esk19_0,X1) != esk20_0
| ~ in(X1,relation_dom(esk19_0)) ),
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_64,c_0_65]),c_0_58]),c_0_17]),c_0_18])]),c_0_66])]) ).
cnf(c_0_70,plain,
( apply(X1,esk2_2(X2,relation_inverse_image(X1,singleton(X3)))) = X3
| esk2_2(X2,relation_inverse_image(X1,singleton(X3))) = X2
| relation_inverse_image(X1,singleton(X3)) = singleton(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_67]) ).
cnf(c_0_71,negated_conjecture,
relation_inverse_image(esk19_0,singleton(esk20_0)) != singleton(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_58])]) ).
cnf(c_0_72,negated_conjecture,
( esk2_2(X1,relation_inverse_image(esk19_0,singleton(esk20_0))) = esk3_3(esk19_0,relation_rng(esk19_0),esk20_0)
| esk2_2(X1,relation_inverse_image(esk19_0,singleton(esk20_0))) = X1
| ~ in(esk2_2(X1,relation_inverse_image(esk19_0,singleton(esk20_0))),relation_dom(esk19_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_69,c_0_70]),c_0_17]),c_0_18])])]),c_0_71]) ).
cnf(c_0_73,plain,
( esk2_2(X1,relation_inverse_image(X2,X3)) = X1
| relation_inverse_image(X2,X3) = singleton(X1)
| in(esk2_2(X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_63]) ).
cnf(c_0_74,negated_conjecture,
( esk2_2(X1,relation_inverse_image(esk19_0,singleton(esk20_0))) = esk3_3(esk19_0,relation_rng(esk19_0),esk20_0)
| esk2_2(X1,relation_inverse_image(esk19_0,singleton(esk20_0))) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_17]),c_0_18])]),c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( in(esk3_3(esk19_0,relation_rng(esk19_0),esk20_0),relation_inverse_image(esk19_0,X1))
| ~ in(esk20_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_66]),c_0_17]),c_0_18]),c_0_65])]) ).
cnf(c_0_76,plain,
( X2 = singleton(X1)
| ~ in(esk2_2(X1,X2),X2)
| esk2_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_77,negated_conjecture,
esk2_2(esk3_3(esk19_0,relation_rng(esk19_0),esk20_0),relation_inverse_image(esk19_0,singleton(esk20_0))) = esk3_3(esk19_0,relation_rng(esk19_0),esk20_0),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_74])]) ).
cnf(c_0_78,negated_conjecture,
in(esk3_3(esk19_0,relation_rng(esk19_0),esk20_0),relation_inverse_image(esk19_0,singleton(esk20_0))),
inference(spm,[status(thm)],[c_0_75,c_0_20]) ).
cnf(c_0_79,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78])]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU063+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 17:20:09 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.60 start to proof: theBenchmark
% 143.88/143.91 % Version : CSE_E---1.5
% 143.88/143.91 % Problem : theBenchmark.p
% 143.88/143.91 % Proof found
% 143.88/143.91 % SZS status Theorem for theBenchmark.p
% 143.88/143.91 % SZS output start Proof
% See solution above
% 143.88/143.92 % Total time : 143.235000 s
% 143.88/143.92 % SZS output end Proof
% 143.88/143.92 % Total time : 143.243000 s
%------------------------------------------------------------------------------