TSTP Solution File: SEU218+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU218+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n011.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 : 600s
% DateTime : Tue Jul 19 09:17:57 EDT 2022
% Result : Theorem 1.08s 177.24s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 9
% Syntax : Number of formulae : 153 ( 29 unt; 0 def)
% Number of atoms : 575 ( 268 equ)
% Maximal formula atoms : 65 ( 3 avg)
% Number of connectives : 672 ( 250 ~; 336 |; 54 &)
% ( 10 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 124 ( 14 sgn 60 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t54_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = function_inverse(X1)
<=> ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) )
=> ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) )
=> ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t54_funct_1) ).
fof(d9_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d9_funct_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(d7_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_inverse(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> in(ordered_pair(X4,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d7_relat_1) ).
fof(t37_relat_1,axiom,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t37_relat_1) ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d5_relat_1) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d4_relat_1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',dt_k2_funct_1) ).
fof(d4_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d4_funct_1) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = function_inverse(X1)
<=> ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) )
=> ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) )
=> ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t54_funct_1]) ).
fof(c_0_10,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2)
| function_inverse(X2) = relation_inverse(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_funct_1])]) ).
fof(c_0_11,negated_conjecture,
! [X9,X10,X9,X10] :
( relation(esk1_0)
& function(esk1_0)
& one_to_one(esk1_0)
& relation(esk2_0)
& function(esk2_0)
& ( in(esk6_0,relation_dom(esk1_0))
| in(esk3_0,relation_rng(esk1_0))
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk2_0 != function_inverse(esk1_0) )
& ( esk5_0 = apply(esk1_0,esk6_0)
| in(esk3_0,relation_rng(esk1_0))
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk2_0 != function_inverse(esk1_0) )
& ( ~ in(esk5_0,relation_rng(esk1_0))
| esk6_0 != apply(esk2_0,esk5_0)
| in(esk3_0,relation_rng(esk1_0))
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk2_0 != function_inverse(esk1_0) )
& ( in(esk6_0,relation_dom(esk1_0))
| esk4_0 = apply(esk2_0,esk3_0)
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk2_0 != function_inverse(esk1_0) )
& ( esk5_0 = apply(esk1_0,esk6_0)
| esk4_0 = apply(esk2_0,esk3_0)
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk2_0 != function_inverse(esk1_0) )
& ( ~ in(esk5_0,relation_rng(esk1_0))
| esk6_0 != apply(esk2_0,esk5_0)
| esk4_0 = apply(esk2_0,esk3_0)
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk2_0 != function_inverse(esk1_0) )
& ( in(esk6_0,relation_dom(esk1_0))
| ~ in(esk4_0,relation_dom(esk1_0))
| esk3_0 != apply(esk1_0,esk4_0)
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk2_0 != function_inverse(esk1_0) )
& ( esk5_0 = apply(esk1_0,esk6_0)
| ~ in(esk4_0,relation_dom(esk1_0))
| esk3_0 != apply(esk1_0,esk4_0)
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk2_0 != function_inverse(esk1_0) )
& ( ~ in(esk5_0,relation_rng(esk1_0))
| esk6_0 != apply(esk2_0,esk5_0)
| ~ in(esk4_0,relation_dom(esk1_0))
| esk3_0 != apply(esk1_0,esk4_0)
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk2_0 != function_inverse(esk1_0) )
& ( relation_dom(esk2_0) = relation_rng(esk1_0)
| esk2_0 = function_inverse(esk1_0) )
& ( in(X10,relation_dom(esk1_0))
| ~ in(X9,relation_rng(esk1_0))
| X10 != apply(esk2_0,X9)
| esk2_0 = function_inverse(esk1_0) )
& ( X9 = apply(esk1_0,X10)
| ~ in(X9,relation_rng(esk1_0))
| X10 != apply(esk2_0,X9)
| esk2_0 = function_inverse(esk1_0) )
& ( in(X9,relation_rng(esk1_0))
| ~ in(X10,relation_dom(esk1_0))
| X9 != apply(esk1_0,X10)
| esk2_0 = function_inverse(esk1_0) )
& ( X10 = apply(esk2_0,X9)
| ~ in(X10,relation_dom(esk1_0))
| X9 != apply(esk1_0,X10)
| esk2_0 = function_inverse(esk1_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])])])]) ).
fof(c_0_12,plain,
! [X2] :
( ~ relation(X2)
| relation_inverse(relation_inverse(X2)) = X2 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1])]) ).
cnf(c_0_13,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
one_to_one(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
function(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X5,X6,X7,X8,X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X6)
| in(ordered_pair(X8,X7),X5)
| X6 != relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X8,X7),X5)
| in(ordered_pair(X7,X8),X6)
| X6 != relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk20_2(X5,X6),esk21_2(X5,X6)),X6)
| ~ in(ordered_pair(esk21_2(X5,X6),esk20_2(X5,X6)),X5)
| X6 = relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk20_2(X5,X6),esk21_2(X5,X6)),X6)
| in(ordered_pair(esk21_2(X5,X6),esk20_2(X5,X6)),X5)
| X6 = relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_relat_1])])])])])])]) ).
fof(c_0_18,plain,
! [X2] :
( ( relation_rng(X2) = relation_dom(relation_inverse(X2))
| ~ relation(X2) )
& ( relation_dom(X2) = relation_rng(relation_inverse(X2))
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_relat_1])])]) ).
cnf(c_0_19,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
relation_inverse(esk1_0) = function_inverse(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_21,plain,
( X2 = relation_inverse(X1)
| in(ordered_pair(esk21_2(X1,X2),esk20_2(X1,X2)),X1)
| in(ordered_pair(esk20_2(X1,X2),esk21_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,plain,
( relation_dom(X1) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
relation_inverse(function_inverse(esk1_0)) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_15]),c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( esk2_0 = function_inverse(esk1_0)
| relation_dom(esk2_0) = relation_rng(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_26,plain,
! [X5,X6,X7,X7,X9,X6,X11] :
( ( ~ in(X7,X6)
| in(ordered_pair(esk7_3(X5,X6,X7),X7),X5)
| X6 != relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(esk8_2(X5,X6),X6)
| ~ in(ordered_pair(X11,esk8_2(X5,X6)),X5)
| X6 = relation_rng(X5)
| ~ relation(X5) )
& ( in(esk8_2(X5,X6),X6)
| in(ordered_pair(esk9_2(X5,X6),esk8_2(X5,X6)),X5)
| X6 = relation_rng(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_relat_1])])])])])])]) ).
cnf(c_0_27,negated_conjecture,
( relation_inverse(X1) = esk2_0
| in(ordered_pair(esk20_2(X1,esk2_0),esk21_2(X1,esk2_0)),esk2_0)
| in(ordered_pair(esk21_2(X1,esk2_0),esk20_2(X1,esk2_0)),X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
relation_rng(relation_inverse(esk2_0)) = relation_dom(esk2_0),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( relation_rng(esk1_0) = relation_dom(esk2_0)
| relation_inverse(esk2_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(esk20_2(esk1_0,esk2_0),esk21_2(esk1_0,esk2_0)),esk2_0)
| in(ordered_pair(esk21_2(esk1_0,esk2_0),esk20_2(esk1_0,esk2_0)),esk1_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_15]),c_0_20]) ).
cnf(c_0_32,negated_conjecture,
relation_rng(esk1_0) = relation_dom(esk2_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_33,plain,
! [X5,X6,X7,X7,X9,X6,X11] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk10_3(X5,X6,X7)),X5)
| X6 != relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6)
| X6 != relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(esk11_2(X5,X6),X6)
| ~ in(ordered_pair(esk11_2(X5,X6),X11),X5)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk11_2(X5,X6),X6)
| in(ordered_pair(esk11_2(X5,X6),esk12_2(X5,X6)),X5)
| X6 = relation_dom(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_relat_1])])])])])])]) ).
cnf(c_0_34,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(esk20_2(esk1_0,esk2_0),esk21_2(esk1_0,esk2_0)),esk2_0)
| in(esk20_2(esk1_0,esk2_0),X1)
| X1 != relation_dom(esk2_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_15])]) ).
cnf(c_0_35,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(esk20_2(esk1_0,esk2_0),esk21_2(esk1_0,esk2_0)),esk2_0)
| in(esk20_2(esk1_0,esk2_0),relation_dom(esk2_0)) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( esk2_0 = function_inverse(esk1_0)
| in(X1,relation_dom(esk1_0))
| X1 != apply(esk2_0,X2)
| ~ in(X2,relation_rng(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_38,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(esk20_2(esk1_0,esk2_0),relation_dom(esk2_0))
| in(esk20_2(esk1_0,esk2_0),X1)
| X1 != relation_dom(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_22])]) ).
cnf(c_0_39,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(X1,relation_dom(esk1_0))
| X1 != apply(esk2_0,X2)
| ~ in(X2,relation_dom(esk2_0)) ),
inference(rw,[status(thm)],[c_0_37,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(esk20_2(esk1_0,esk2_0),relation_dom(esk2_0)) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( esk2_0 = function_inverse(esk1_0)
| X2 = apply(esk1_0,X1)
| X1 != apply(esk2_0,X2)
| ~ in(X2,relation_rng(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_42,plain,
! [X2] :
( ( relation(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( function(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_43,plain,
! [X4,X5,X6,X6,X5,X6,X6] :
( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( ~ in(ordered_pair(X5,X6),X4)
| X6 = apply(X4,X5)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X6 != apply(X4,X5)
| X6 = empty_set
| in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X6 != empty_set
| X6 = apply(X4,X5)
| in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_funct_1])])])])])])]) ).
cnf(c_0_44,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(X1,relation_dom(esk1_0))
| X1 != apply(esk2_0,esk20_2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( X1 = apply(esk1_0,X2)
| function_inverse(esk1_0) = esk2_0
| X2 != apply(esk2_0,X1)
| ~ in(X1,relation_dom(esk2_0)) ),
inference(rw,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_46,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_47,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(apply(esk2_0,esk20_2(esk1_0,esk2_0)),relation_dom(esk1_0)) ),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( esk20_2(esk1_0,esk2_0) = apply(esk1_0,X1)
| function_inverse(esk1_0) = esk2_0
| X1 != apply(esk2_0,esk20_2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_45,c_0_40]) ).
cnf(c_0_51,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(esk20_2(esk1_0,esk2_0),esk21_2(esk1_0,esk2_0)),esk2_0)
| in(ordered_pair(esk20_2(esk1_0,esk2_0),esk21_2(esk1_0,esk2_0)),X1)
| relation_inverse(X1) != esk1_0
| ~ relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_31]),c_0_15])]) ).
cnf(c_0_52,negated_conjecture,
relation(function_inverse(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_15]),c_0_16])]) ).
cnf(c_0_53,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,plain,
( relation_rng(X1) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_55,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(apply(esk2_0,esk20_2(esk1_0,esk2_0)),X1),esk1_0)
| X1 != apply(esk1_0,apply(esk2_0,esk20_2(esk1_0,esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_15]),c_0_16])]) ).
cnf(c_0_56,negated_conjecture,
( apply(esk1_0,apply(esk2_0,esk20_2(esk1_0,esk2_0))) = esk20_2(esk1_0,esk2_0)
| function_inverse(esk1_0) = esk2_0 ),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_57,plain,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_58,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(esk20_2(esk1_0,esk2_0),esk21_2(esk1_0,esk2_0)),function_inverse(esk1_0))
| in(ordered_pair(esk20_2(esk1_0,esk2_0),esk21_2(esk1_0,esk2_0)),esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_24]),c_0_52])]) ).
cnf(c_0_59,negated_conjecture,
function(function_inverse(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_15]),c_0_16])]) ).
cnf(c_0_60,negated_conjecture,
relation_dom(function_inverse(esk1_0)) = relation_dom(esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_15]),c_0_20]),c_0_32]) ).
cnf(c_0_61,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(apply(esk2_0,esk20_2(esk1_0,esk2_0)),X1),esk1_0)
| X1 != esk20_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = apply(function_inverse(esk1_0),esk20_2(esk1_0,esk2_0))
| function_inverse(esk1_0) = esk2_0
| in(ordered_pair(esk20_2(esk1_0,esk2_0),esk21_2(esk1_0,esk2_0)),esk2_0)
| ~ in(esk20_2(esk1_0,esk2_0),relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_52]),c_0_59]),c_0_60])]) ).
cnf(c_0_63,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(apply(esk2_0,esk20_2(esk1_0,esk2_0)),esk20_2(esk1_0,esk2_0)),esk1_0) ),
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_64,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = apply(function_inverse(esk1_0),esk20_2(esk1_0,esk2_0))
| function_inverse(esk1_0) = esk2_0
| in(ordered_pair(esk20_2(esk1_0,esk2_0),esk21_2(esk1_0,esk2_0)),esk2_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_40]) ).
cnf(c_0_65,negated_conjecture,
function(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_66,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(esk20_2(esk1_0,esk2_0),apply(esk2_0,esk20_2(esk1_0,esk2_0))),X1)
| relation_inverse(X1) != esk1_0
| ~ relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_63]),c_0_15])]) ).
cnf(c_0_67,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = apply(function_inverse(esk1_0),esk20_2(esk1_0,esk2_0))
| esk21_2(esk1_0,esk2_0) = apply(esk2_0,esk20_2(esk1_0,esk2_0))
| function_inverse(esk1_0) = esk2_0
| ~ in(esk20_2(esk1_0,esk2_0),relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_64]),c_0_22]),c_0_65])]) ).
cnf(c_0_68,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(esk20_2(esk1_0,esk2_0),apply(esk2_0,esk20_2(esk1_0,esk2_0))),function_inverse(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_24]),c_0_52])]) ).
cnf(c_0_69,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = apply(function_inverse(esk1_0),esk20_2(esk1_0,esk2_0))
| esk21_2(esk1_0,esk2_0) = apply(esk2_0,esk20_2(esk1_0,esk2_0))
| function_inverse(esk1_0) = esk2_0 ),
inference(spm,[status(thm)],[c_0_67,c_0_40]) ).
cnf(c_0_70,negated_conjecture,
( apply(function_inverse(esk1_0),esk20_2(esk1_0,esk2_0)) = apply(esk2_0,esk20_2(esk1_0,esk2_0))
| function_inverse(esk1_0) = esk2_0
| ~ in(esk20_2(esk1_0,esk2_0),relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_68]),c_0_52]),c_0_59]),c_0_60])]) ).
cnf(c_0_71,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = apply(esk2_0,esk20_2(esk1_0,esk2_0))
| function_inverse(esk1_0) = esk2_0
| apply(function_inverse(esk1_0),esk20_2(esk1_0,esk2_0)) != apply(esk2_0,esk20_2(esk1_0,esk2_0)) ),
inference(ef,[status(thm)],[c_0_69]) ).
cnf(c_0_72,negated_conjecture,
( apply(function_inverse(esk1_0),esk20_2(esk1_0,esk2_0)) = apply(esk2_0,esk20_2(esk1_0,esk2_0))
| function_inverse(esk1_0) = esk2_0 ),
inference(spm,[status(thm)],[c_0_70,c_0_40]) ).
cnf(c_0_73,plain,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk21_2(X1,X2),esk20_2(X1,X2)),X1)
| ~ in(ordered_pair(esk20_2(X1,X2),esk21_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_74,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = apply(esk2_0,esk20_2(esk1_0,esk2_0))
| function_inverse(esk1_0) = esk2_0 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(esk20_2(esk1_0,esk2_0),X1),esk2_0)
| X1 != apply(esk2_0,esk20_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_40]),c_0_22]),c_0_65])]) ).
cnf(c_0_76,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| ~ in(ordered_pair(esk20_2(esk1_0,esk2_0),apply(esk2_0,esk20_2(esk1_0,esk2_0))),esk2_0)
| ~ in(ordered_pair(apply(esk2_0,esk20_2(esk1_0,esk2_0)),esk20_2(esk1_0,esk2_0)),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_20]),c_0_22]),c_0_15])]) ).
cnf(c_0_77,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| in(ordered_pair(esk20_2(esk1_0,esk2_0),apply(esk2_0,esk20_2(esk1_0,esk2_0))),esk2_0) ),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_78,negated_conjecture,
( in(esk3_0,relation_rng(esk1_0))
| in(esk6_0,relation_dom(esk1_0))
| esk2_0 != function_inverse(esk1_0)
| relation_dom(esk2_0) != relation_rng(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_79,negated_conjecture,
( function_inverse(esk1_0) = esk2_0
| ~ in(ordered_pair(apply(esk2_0,esk20_2(esk1_0,esk2_0)),esk20_2(esk1_0,esk2_0)),esk1_0) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_80,negated_conjecture,
( esk4_0 = apply(esk2_0,esk3_0)
| in(esk6_0,relation_dom(esk1_0))
| esk2_0 != function_inverse(esk1_0)
| relation_dom(esk2_0) != relation_rng(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_81,negated_conjecture,
( in(esk3_0,relation_dom(esk2_0))
| in(esk6_0,relation_dom(esk1_0))
| function_inverse(esk1_0) != esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_32]),c_0_32])]) ).
cnf(c_0_82,negated_conjecture,
function_inverse(esk1_0) = esk2_0,
inference(spm,[status(thm)],[c_0_79,c_0_63]) ).
cnf(c_0_83,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| in(esk6_0,relation_dom(esk1_0))
| function_inverse(esk1_0) != esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_32])]) ).
cnf(c_0_84,negated_conjecture,
( in(esk3_0,relation_dom(esk2_0))
| in(esk6_0,relation_dom(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]) ).
cnf(c_0_85,negated_conjecture,
( in(esk3_0,relation_rng(esk1_0))
| esk5_0 = apply(esk1_0,esk6_0)
| esk2_0 != function_inverse(esk1_0)
| relation_dom(esk2_0) != relation_rng(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_86,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| in(esk6_0,relation_dom(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_82])]) ).
cnf(c_0_87,negated_conjecture,
( esk4_0 = apply(esk2_0,esk3_0)
| esk5_0 = apply(esk1_0,esk6_0)
| esk2_0 != function_inverse(esk1_0)
| relation_dom(esk2_0) != relation_rng(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_88,negated_conjecture,
( in(ordered_pair(esk6_0,X1),esk1_0)
| in(esk3_0,relation_dom(esk2_0))
| X1 != apply(esk1_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_84]),c_0_15]),c_0_16])]) ).
cnf(c_0_89,negated_conjecture,
( apply(esk1_0,esk6_0) = esk5_0
| in(esk3_0,relation_dom(esk2_0))
| function_inverse(esk1_0) != esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_32]),c_0_32])]) ).
cnf(c_0_90,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| in(ordered_pair(esk6_0,X1),esk1_0)
| X1 != apply(esk1_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_86]),c_0_15]),c_0_16])]) ).
cnf(c_0_91,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| apply(esk1_0,esk6_0) = esk5_0
| function_inverse(esk1_0) != esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_32])]) ).
cnf(c_0_92,negated_conjecture,
( in(ordered_pair(esk6_0,apply(esk1_0,esk6_0)),esk1_0)
| in(esk3_0,relation_dom(esk2_0)) ),
inference(er,[status(thm)],[c_0_88]) ).
cnf(c_0_93,negated_conjecture,
( apply(esk1_0,esk6_0) = esk5_0
| in(esk3_0,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_82])]) ).
cnf(c_0_94,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| in(ordered_pair(esk6_0,apply(esk1_0,esk6_0)),esk1_0) ),
inference(er,[status(thm)],[c_0_90]) ).
cnf(c_0_95,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| apply(esk1_0,esk6_0) = esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_82])]) ).
cnf(c_0_96,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_97,negated_conjecture,
( in(ordered_pair(esk6_0,esk5_0),esk1_0)
| in(esk3_0,relation_dom(esk2_0)) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| in(ordered_pair(esk6_0,esk5_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
( in(ordered_pair(esk5_0,esk6_0),X1)
| in(esk3_0,relation_dom(esk2_0))
| X1 != esk2_0
| ~ relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_20]),c_0_82]),c_0_15])]) ).
cnf(c_0_100,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| in(ordered_pair(esk5_0,esk6_0),X1)
| X1 != esk2_0
| ~ relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_98]),c_0_20]),c_0_82]),c_0_15])]) ).
cnf(c_0_101,negated_conjecture,
( in(esk3_0,relation_rng(esk1_0))
| esk2_0 != function_inverse(esk1_0)
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk6_0 != apply(esk2_0,esk5_0)
| ~ in(esk5_0,relation_rng(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_102,negated_conjecture,
( in(ordered_pair(esk5_0,esk6_0),esk2_0)
| in(esk3_0,relation_dom(esk2_0)) ),
inference(spm,[status(thm)],[c_0_99,c_0_22]) ).
cnf(c_0_103,negated_conjecture,
( in(esk3_0,relation_dom(esk2_0))
| in(esk5_0,X1)
| X1 != relation_dom(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_97]),c_0_32]),c_0_15])]) ).
cnf(c_0_104,negated_conjecture,
( esk4_0 = apply(esk2_0,esk3_0)
| esk2_0 != function_inverse(esk1_0)
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk6_0 != apply(esk2_0,esk5_0)
| ~ in(esk5_0,relation_rng(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_105,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| in(ordered_pair(esk5_0,esk6_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_100,c_0_22]) ).
cnf(c_0_106,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| in(esk5_0,X1)
| X1 != relation_dom(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_98]),c_0_32]),c_0_15])]) ).
cnf(c_0_107,negated_conjecture,
( in(esk3_0,relation_dom(esk2_0))
| esk6_0 != apply(esk2_0,esk5_0)
| function_inverse(esk1_0) != esk2_0
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_32]),c_0_32]),c_0_32])]) ).
cnf(c_0_108,negated_conjecture,
( esk6_0 = apply(esk2_0,esk5_0)
| in(esk3_0,relation_dom(esk2_0))
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_102]),c_0_22]),c_0_65])]) ).
cnf(c_0_109,negated_conjecture,
( in(esk3_0,relation_dom(esk2_0))
| in(esk5_0,relation_dom(esk2_0)) ),
inference(er,[status(thm)],[c_0_103]) ).
cnf(c_0_110,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| esk6_0 != apply(esk2_0,esk5_0)
| function_inverse(esk1_0) != esk2_0
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_32]),c_0_32])]) ).
cnf(c_0_111,negated_conjecture,
( esk6_0 = apply(esk2_0,esk5_0)
| apply(esk2_0,esk3_0) = esk4_0
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_105]),c_0_22]),c_0_65])]) ).
cnf(c_0_112,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| in(esk5_0,relation_dom(esk2_0)) ),
inference(er,[status(thm)],[c_0_106]) ).
cnf(c_0_113,negated_conjecture,
( in(esk3_0,relation_dom(esk2_0))
| esk6_0 != apply(esk2_0,esk5_0)
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_82])]) ).
cnf(c_0_114,negated_conjecture,
( esk6_0 = apply(esk2_0,esk5_0)
| in(esk3_0,relation_dom(esk2_0)) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_115,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| esk6_0 != apply(esk2_0,esk5_0)
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_82])]) ).
cnf(c_0_116,negated_conjecture,
( esk6_0 = apply(esk2_0,esk5_0)
| apply(esk2_0,esk3_0) = esk4_0 ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_117,negated_conjecture,
( in(esk3_0,relation_dom(esk2_0))
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
( apply(esk2_0,esk3_0) = esk4_0
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_119,negated_conjecture,
in(esk3_0,relation_dom(esk2_0)),
inference(spm,[status(thm)],[c_0_117,c_0_109]) ).
cnf(c_0_120,negated_conjecture,
apply(esk2_0,esk3_0) = esk4_0,
inference(spm,[status(thm)],[c_0_118,c_0_112]) ).
cnf(c_0_121,negated_conjecture,
( in(ordered_pair(esk3_0,X1),esk2_0)
| X1 != esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_119]),c_0_120]),c_0_22]),c_0_65])]) ).
cnf(c_0_122,negated_conjecture,
in(ordered_pair(esk3_0,esk4_0),esk2_0),
inference(er,[status(thm)],[c_0_121]) ).
cnf(c_0_123,negated_conjecture,
relation_inverse(esk2_0) = esk1_0,
inference(rw,[status(thm)],[c_0_24,c_0_82]) ).
cnf(c_0_124,negated_conjecture,
relation_rng(function_inverse(esk1_0)) = relation_dom(esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_15]),c_0_20]) ).
cnf(c_0_125,negated_conjecture,
( in(ordered_pair(esk4_0,esk3_0),X1)
| X1 != esk1_0
| ~ relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_122]),c_0_123]),c_0_22])]) ).
cnf(c_0_126,negated_conjecture,
relation_rng(esk2_0) = relation_dom(esk1_0),
inference(rw,[status(thm)],[c_0_124,c_0_82]) ).
cnf(c_0_127,negated_conjecture,
( in(esk6_0,relation_dom(esk1_0))
| esk2_0 != function_inverse(esk1_0)
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk3_0 != apply(esk1_0,esk4_0)
| ~ in(esk4_0,relation_dom(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_128,negated_conjecture,
in(ordered_pair(esk4_0,esk3_0),esk1_0),
inference(spm,[status(thm)],[c_0_125,c_0_15]) ).
cnf(c_0_129,negated_conjecture,
( in(esk4_0,X1)
| X1 != relation_dom(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_122]),c_0_126]),c_0_22])]) ).
cnf(c_0_130,negated_conjecture,
( esk5_0 = apply(esk1_0,esk6_0)
| esk2_0 != function_inverse(esk1_0)
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk3_0 != apply(esk1_0,esk4_0)
| ~ in(esk4_0,relation_dom(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_131,negated_conjecture,
( in(esk6_0,relation_dom(esk1_0))
| esk3_0 != apply(esk1_0,esk4_0)
| function_inverse(esk1_0) != esk2_0
| ~ in(esk4_0,relation_dom(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_32])]) ).
cnf(c_0_132,negated_conjecture,
( esk3_0 = apply(esk1_0,esk4_0)
| ~ in(esk4_0,relation_dom(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_128]),c_0_15]),c_0_16])]) ).
cnf(c_0_133,negated_conjecture,
in(esk4_0,relation_dom(esk1_0)),
inference(er,[status(thm)],[c_0_129]) ).
cnf(c_0_134,negated_conjecture,
( apply(esk1_0,esk6_0) = esk5_0
| esk3_0 != apply(esk1_0,esk4_0)
| function_inverse(esk1_0) != esk2_0
| ~ in(esk4_0,relation_dom(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_32])]) ).
cnf(c_0_135,negated_conjecture,
( in(esk6_0,relation_dom(esk1_0))
| esk3_0 != apply(esk1_0,esk4_0)
| ~ in(esk4_0,relation_dom(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_82])]) ).
cnf(c_0_136,negated_conjecture,
esk3_0 = apply(esk1_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133])]) ).
cnf(c_0_137,negated_conjecture,
( apply(esk1_0,esk6_0) = esk5_0
| esk3_0 != apply(esk1_0,esk4_0)
| ~ in(esk4_0,relation_dom(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_82])]) ).
cnf(c_0_138,negated_conjecture,
in(esk6_0,relation_dom(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_133])]),c_0_136])]) ).
cnf(c_0_139,negated_conjecture,
apply(esk1_0,esk6_0) = esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_133])]),c_0_136])]) ).
cnf(c_0_140,negated_conjecture,
( in(ordered_pair(esk6_0,X1),esk1_0)
| X1 != esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_138]),c_0_139]),c_0_15]),c_0_16])]) ).
cnf(c_0_141,negated_conjecture,
in(ordered_pair(esk6_0,esk5_0),esk1_0),
inference(er,[status(thm)],[c_0_140]) ).
cnf(c_0_142,negated_conjecture,
( esk2_0 != function_inverse(esk1_0)
| relation_dom(esk2_0) != relation_rng(esk1_0)
| esk3_0 != apply(esk1_0,esk4_0)
| ~ in(esk4_0,relation_dom(esk1_0))
| esk6_0 != apply(esk2_0,esk5_0)
| ~ in(esk5_0,relation_rng(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_143,negated_conjecture,
( in(ordered_pair(esk5_0,esk6_0),X1)
| X1 != esk2_0
| ~ relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_141]),c_0_20]),c_0_82]),c_0_15])]) ).
cnf(c_0_144,negated_conjecture,
( esk3_0 != apply(esk1_0,esk4_0)
| esk6_0 != apply(esk2_0,esk5_0)
| function_inverse(esk1_0) != esk2_0
| ~ in(esk4_0,relation_dom(esk1_0))
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_32]),c_0_32])]) ).
cnf(c_0_145,negated_conjecture,
in(ordered_pair(esk5_0,esk6_0),esk2_0),
inference(spm,[status(thm)],[c_0_143,c_0_22]) ).
cnf(c_0_146,negated_conjecture,
( in(esk5_0,X1)
| X1 != relation_dom(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_141]),c_0_32]),c_0_15])]) ).
cnf(c_0_147,negated_conjecture,
( esk3_0 != apply(esk1_0,esk4_0)
| esk6_0 != apply(esk2_0,esk5_0)
| ~ in(esk4_0,relation_dom(esk1_0))
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_82])]) ).
cnf(c_0_148,negated_conjecture,
( esk6_0 = apply(esk2_0,esk5_0)
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_145]),c_0_22]),c_0_65])]) ).
cnf(c_0_149,negated_conjecture,
in(esk5_0,relation_dom(esk2_0)),
inference(er,[status(thm)],[c_0_146]) ).
cnf(c_0_150,negated_conjecture,
( esk6_0 != apply(esk2_0,esk5_0)
| ~ in(esk5_0,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_133])]),c_0_136])]) ).
cnf(c_0_151,negated_conjecture,
esk6_0 = apply(esk2_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_149])]) ).
cnf(c_0_152,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_149])]),c_0_151])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU218+3 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 04:22:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.34/23.40 eprover: CPU time limit exceeded, terminating
% 0.34/23.41 eprover: CPU time limit exceeded, terminating
% 0.34/23.41 eprover: CPU time limit exceeded, terminating
% 0.34/23.41 eprover: CPU time limit exceeded, terminating
% 0.47/46.42 eprover: CPU time limit exceeded, terminating
% 0.47/46.42 eprover: CPU time limit exceeded, terminating
% 0.47/46.43 eprover: CPU time limit exceeded, terminating
% 0.47/46.43 eprover: CPU time limit exceeded, terminating
% 0.57/69.43 eprover: CPU time limit exceeded, terminating
% 0.57/69.44 eprover: CPU time limit exceeded, terminating
% 0.57/69.44 eprover: CPU time limit exceeded, terminating
% 0.57/69.45 eprover: CPU time limit exceeded, terminating
% 0.68/92.46 eprover: CPU time limit exceeded, terminating
% 0.68/92.46 eprover: CPU time limit exceeded, terminating
% 0.68/92.46 eprover: CPU time limit exceeded, terminating
% 0.68/92.46 eprover: CPU time limit exceeded, terminating
% 0.79/115.47 eprover: CPU time limit exceeded, terminating
% 0.79/115.47 eprover: eprover: CPU time limit exceeded, terminatingCPU time limit exceeded, terminating
% 0.79/115.47
% 0.79/115.47 eprover: CPU time limit exceeded, terminating
% 0.90/138.48 eprover: CPU time limit exceeded, terminating
% 0.90/138.49 eprover: CPU time limit exceeded, terminating
% 0.90/138.49 eprover: CPU time limit exceeded, terminating
% 0.90/138.51 eprover: CPU time limit exceeded, terminating
% 1.02/161.50 eprover: CPU time limit exceeded, terminating
% 1.02/161.50 eprover: CPU time limit exceeded, terminating
% 1.02/161.51 eprover: CPU time limit exceeded, terminating
% 1.02/161.53 eprover: CPU time limit exceeded, terminating
% 1.08/177.24 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 1.08/177.24
% 1.08/177.24 # Failure: Resource limit exceeded (time)
% 1.08/177.24 # OLD status Res
% 1.08/177.24 # Preprocessing time : 0.019 s
% 1.08/177.24 # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 1.08/177.24
% 1.08/177.24 # Failure: Resource limit exceeded (time)
% 1.08/177.24 # OLD status Res
% 1.08/177.24 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 1.08/177.24 # Preprocessing time : 0.011 s
% 1.08/177.24 # Running protocol protocol_eprover_a172c605141d0894bf6fdc293a5220c6c2a32117 for 23 seconds:
% 1.08/177.24
% 1.08/177.24 # Failure: Resource limit exceeded (time)
% 1.08/177.24 # OLD status Res
% 1.08/177.24 # Preprocessing time : 0.010 s
% 1.08/177.24 # Running protocol protocol_eprover_f8b0f932169414d689b89e2a8b18d4600533b975 for 23 seconds:
% 1.08/177.24
% 1.08/177.24 # Failure: Resource limit exceeded (time)
% 1.08/177.24 # OLD status Res
% 1.08/177.24 # Preprocessing time : 0.010 s
% 1.08/177.24 # Running protocol protocol_eprover_fc511518e5f98a6b2c7baef820b71b6d1abb3e55 for 23 seconds:
% 1.08/177.24
% 1.08/177.24 # Failure: Resource limit exceeded (time)
% 1.08/177.24 # OLD status Res
% 1.08/177.24 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,02,80,1.0)
% 1.08/177.24 # Preprocessing time : 0.010 s
% 1.08/177.24 # Running protocol protocol_eprover_95b56b3f38545d2cfee43b45856d192a814b65d5 for 23 seconds:
% 1.08/177.24
% 1.08/177.24 # Failure: Resource limit exceeded (time)
% 1.08/177.24 # OLD status Res
% 1.08/177.24 # Preprocessing time : 0.010 s
% 1.08/177.24 # Running protocol protocol_eprover_6017f334107ca4679a9978dd19d7c76a8bd36e48 for 23 seconds:
% 1.08/177.24
% 1.08/177.24 # Failure: Resource limit exceeded (time)
% 1.08/177.24 # OLD status Res
% 1.08/177.24 # SinE strategy is GSinE(CountFormulas,,1.4,,02,20000,1.0)
% 1.08/177.24 # Preprocessing time : 0.011 s
% 1.08/177.24 # Running protocol protocol_eprover_29f46a864b4eba32a7d0333eeab34cc2a3bfeeb2 for 23 seconds:
% 1.08/177.24 # SinE strategy is GSinE(CountFormulas,hypos,1.1,,04,500,1.0)
% 1.08/177.24 # Preprocessing time : 0.021 s
% 1.08/177.24
% 1.08/177.24 # Proof found!
% 1.08/177.24 # SZS status Theorem
% 1.08/177.24 # SZS output start CNFRefutation
% See solution above
% 1.08/177.25 # Proof object total steps : 153
% 1.08/177.25 # Proof object clause steps : 134
% 1.08/177.25 # Proof object formula steps : 19
% 1.08/177.25 # Proof object conjectures : 123
% 1.08/177.25 # Proof object clause conjectures : 120
% 1.08/177.25 # Proof object formula conjectures : 3
% 1.08/177.25 # Proof object initial clauses used : 31
% 1.08/177.25 # Proof object initial formulas used : 9
% 1.08/177.25 # Proof object generating inferences : 75
% 1.08/177.25 # Proof object simplifying inferences : 165
% 1.08/177.25 # Training examples: 0 positive, 0 negative
% 1.08/177.25 # Parsed axioms : 50
% 1.08/177.25 # Removed by relevancy pruning/SinE : 16
% 1.08/177.25 # Initial clauses : 83
% 1.08/177.25 # Removed in clause preprocessing : 4
% 1.08/177.25 # Initial clauses in saturation : 79
% 1.08/177.25 # Processed clauses : 26183
% 1.08/177.25 # ...of these trivial : 502
% 1.08/177.25 # ...subsumed : 16495
% 1.08/177.25 # ...remaining for further processing : 9185
% 1.08/177.25 # Other redundant clauses eliminated : 0
% 1.08/177.25 # Clauses deleted for lack of memory : 0
% 1.08/177.25 # Backward-subsumed : 1467
% 1.08/177.25 # Backward-rewritten : 4873
% 1.08/177.25 # Generated clauses : 205253
% 1.08/177.25 # ...of the previous two non-trivial : 205802
% 1.08/177.25 # Contextual simplify-reflections : 0
% 1.08/177.25 # Paramodulations : 204375
% 1.08/177.25 # Factorizations : 25
% 1.08/177.25 # Equation resolutions : 853
% 1.08/177.25 # Current number of processed clauses : 2845
% 1.08/177.25 # Positive orientable unit clauses : 454
% 1.08/177.25 # Positive unorientable unit clauses: 0
% 1.08/177.25 # Negative unit clauses : 12
% 1.08/177.25 # Non-unit-clauses : 2379
% 1.08/177.25 # Current number of unprocessed clauses: 47192
% 1.08/177.25 # ...number of literals in the above : 212056
% 1.08/177.25 # Current number of archived formulas : 0
% 1.08/177.25 # Current number of archived clauses : 6340
% 1.08/177.25 # Clause-clause subsumption calls (NU) : 3522513
% 1.08/177.25 # Rec. Clause-clause subsumption calls : 345737
% 1.08/177.25 # Non-unit clause-clause subsumptions : 17685
% 1.08/177.25 # Unit Clause-clause subsumption calls : 300894
% 1.08/177.25 # Rewrite failures with RHS unbound : 0
% 1.08/177.25 # BW rewrite match attempts : 30361
% 1.08/177.25 # BW rewrite match successes : 88
% 1.08/177.25 # Condensation attempts : 0
% 1.08/177.25 # Condensation successes : 0
% 1.08/177.25 # Termbank termtop insertions : 7383495
% 1.08/177.25
% 1.08/177.25 # -------------------------------------------------
% 1.08/177.25 # User time : 15.138 s
% 1.08/177.25 # System time : 0.093 s
% 1.08/177.25 # Total time : 15.231 s
% 1.08/177.25 # Maximum resident set size: 111092 pages
% 1.08/184.52 eprover: CPU time limit exceeded, terminating
% 1.08/184.52 eprover: CPU time limit exceeded, terminating
% 1.08/184.54 eprover: CPU time limit exceeded, terminating
% 1.08/184.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 1.08/184.54 eprover: No such file or directory
% 1.08/184.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.08/184.54 eprover: No such file or directory
% 1.08/184.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 1.08/184.55 eprover: No such file or directory
% 1.08/184.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.08/184.55 eprover: No such file or directory
% 1.08/184.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 1.08/184.55 eprover: No such file or directory
% 1.08/184.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.08/184.55 eprover: No such file or directory
% 1.08/184.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.08/184.55 eprover: No such file or directory
% 1.08/184.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 1.08/184.55 eprover: No such file or directory
% 1.08/184.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.08/184.56 eprover: No such file or directory
% 1.08/184.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.08/184.56 eprover: No such file or directory
% 1.08/184.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.08/184.57 eprover: No such file or directory
% 1.08/184.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.08/184.57 eprover: No such file or directory
%------------------------------------------------------------------------------