TSTP Solution File: SEU216+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU216+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 16:23:26 EDT 2023
% Result : Theorem 9.53s 9.62s
% Output : CNFRefutation 9.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 39
% Syntax : Number of formulae : 99 ( 18 unt; 30 typ; 0 def)
% Number of atoms : 264 ( 107 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 312 ( 117 ~; 144 |; 30 &)
% ( 9 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 20 >; 8 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 10 con; 0-2 aty)
% Number of variables : 115 ( 5 sgn; 46 !; 0 ?; 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,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_27,type,
identity_relation: $i > $i ).
tff(decl_28,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_29,type,
relation_dom: $i > $i ).
tff(decl_30,type,
apply: ( $i * $i ) > $i ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
singleton: $i > $i ).
tff(decl_33,type,
element: ( $i * $i ) > $o ).
tff(decl_34,type,
relation_empty_yielding: $i > $o ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
relation_rng: $i > $i ).
tff(decl_37,type,
subset: ( $i * $i ) > $o ).
tff(decl_38,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk3_1: $i > $i ).
tff(decl_41,type,
esk4_0: $i ).
tff(decl_42,type,
esk5_0: $i ).
tff(decl_43,type,
esk6_1: $i > $i ).
tff(decl_44,type,
esk7_0: $i ).
tff(decl_45,type,
esk8_0: $i ).
tff(decl_46,type,
esk9_1: $i > $i ).
tff(decl_47,type,
esk10_0: $i ).
tff(decl_48,type,
esk11_0: $i ).
tff(decl_49,type,
esk12_0: $i ).
tff(decl_50,type,
esk13_0: $i ).
tff(decl_51,type,
esk14_0: $i ).
fof(d10_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X3 = X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t8_funct_1,axiom,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t34_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(t71_relat_1,axiom,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_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/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(c_0_9,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( in(X13,X11)
| ~ in(ordered_pair(X13,X14),X12)
| X12 != identity_relation(X11)
| ~ relation(X12) )
& ( X13 = X14
| ~ in(ordered_pair(X13,X14),X12)
| X12 != identity_relation(X11)
| ~ relation(X12) )
& ( ~ in(X15,X11)
| X15 != X16
| in(ordered_pair(X15,X16),X12)
| X12 != identity_relation(X11)
| ~ relation(X12) )
& ( ~ in(ordered_pair(esk1_2(X11,X12),esk2_2(X11,X12)),X12)
| ~ in(esk1_2(X11,X12),X11)
| esk1_2(X11,X12) != esk2_2(X11,X12)
| X12 = identity_relation(X11)
| ~ relation(X12) )
& ( in(esk1_2(X11,X12),X11)
| in(ordered_pair(esk1_2(X11,X12),esk2_2(X11,X12)),X12)
| X12 = identity_relation(X11)
| ~ relation(X12) )
& ( esk1_2(X11,X12) = esk2_2(X11,X12)
| in(ordered_pair(esk1_2(X11,X12),esk2_2(X11,X12)),X12)
| X12 = identity_relation(X11)
| ~ relation(X12) ) ),
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)],[d10_relat_1])])])])])]) ).
fof(c_0_10,plain,
! [X22,X23] : ordered_pair(X22,X23) = unordered_pair(unordered_pair(X22,X23),singleton(X22)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_11,plain,
! [X71,X72,X73] :
( ( in(X71,relation_dom(X73))
| ~ in(ordered_pair(X71,X72),X73)
| ~ relation(X73)
| ~ function(X73) )
& ( X72 = apply(X73,X71)
| ~ in(ordered_pair(X71,X72),X73)
| ~ relation(X73)
| ~ function(X73) )
& ( ~ in(X71,relation_dom(X73))
| X72 != apply(X73,X71)
| in(ordered_pair(X71,X72),X73)
| ~ relation(X73)
| ~ function(X73) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_funct_1])])]) ).
cnf(c_0_12,plain,
( in(esk1_2(X1,X2),X1)
| in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| X2 = identity_relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
inference(assume_negation,[status(cth)],[t34_funct_1]) ).
cnf(c_0_16,plain,
( in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( X2 = identity_relation(X1)
| in(esk1_2(X1,X2),X1)
| in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),singleton(esk1_2(X1,X2))),X2)
| ~ relation(X2) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,negated_conjecture,
! [X56] :
( relation(esk13_0)
& function(esk13_0)
& ( in(esk14_0,esk12_0)
| relation_dom(esk13_0) != esk12_0
| esk13_0 != identity_relation(esk12_0) )
& ( apply(esk13_0,esk14_0) != esk14_0
| relation_dom(esk13_0) != esk12_0
| esk13_0 != identity_relation(esk12_0) )
& ( relation_dom(esk13_0) = esk12_0
| esk13_0 = identity_relation(esk12_0) )
& ( ~ in(X56,esk12_0)
| apply(esk13_0,X56) = X56
| esk13_0 = identity_relation(esk12_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_15])])])])]) ).
fof(c_0_20,plain,
! [X66] :
( relation_dom(identity_relation(X66)) = X66
& relation_rng(identity_relation(X66)) = X66 ),
inference(variable_rename,[status(thm)],[t71_relat_1]) ).
cnf(c_0_21,plain,
( esk1_2(X1,X2) = esk2_2(X1,X2)
| in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| X2 = identity_relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,plain,
( in(X1,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2) ),
inference(rw,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_23,plain,
( X1 = identity_relation(X2)
| in(unordered_pair(singleton(esk1_2(X2,X1)),unordered_pair(esk1_2(X2,X1),esk2_2(X2,X1))),X1)
| in(esk1_2(X2,X1),X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( relation_dom(esk13_0) = esk12_0
| esk13_0 = identity_relation(esk12_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [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 ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
cnf(c_0_28,plain,
( X1 = apply(X2,X3)
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,plain,
( X2 = identity_relation(X1)
| esk2_2(X1,X2) = esk1_2(X1,X2)
| in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),singleton(esk1_2(X1,X2))),X2)
| ~ relation(X2) ),
inference(rw,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_30,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_31,negated_conjecture,
( identity_relation(X1) = esk13_0
| in(unordered_pair(singleton(esk1_2(X1,esk13_0)),unordered_pair(esk1_2(X1,esk13_0),esk2_2(X1,esk13_0))),esk13_0)
| in(esk1_2(X1,esk13_0),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
relation_dom(esk13_0) = esk12_0,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_34,plain,
! [X19,X20,X21] :
( ( X21 != apply(X19,X20)
| in(ordered_pair(X20,X21),X19)
| ~ in(X20,relation_dom(X19))
| ~ relation(X19)
| ~ function(X19) )
& ( ~ in(ordered_pair(X20,X21),X19)
| X21 = apply(X19,X20)
| ~ in(X20,relation_dom(X19))
| ~ relation(X19)
| ~ function(X19) )
& ( X21 != apply(X19,X20)
| X21 = empty_set
| in(X20,relation_dom(X19))
| ~ relation(X19)
| ~ function(X19) )
& ( X21 != empty_set
| X21 = apply(X19,X20)
| in(X20,relation_dom(X19))
| ~ relation(X19)
| ~ function(X19) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
cnf(c_0_35,plain,
( X1 = apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(rw,[status(thm)],[c_0_28,c_0_13]) ).
cnf(c_0_36,plain,
( esk2_2(X1,X2) = esk1_2(X1,X2)
| X2 = identity_relation(X1)
| in(unordered_pair(singleton(esk1_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))),X2)
| ~ relation(X2) ),
inference(rw,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_37,negated_conjecture,
( identity_relation(X1) = esk13_0
| in(esk1_2(X1,esk13_0),esk12_0)
| in(esk1_2(X1,esk13_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[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_24]),c_0_33])]) ).
cnf(c_0_38,plain,
( in(ordered_pair(X3,X1),X2)
| X1 != apply(X2,X3)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
( X2 = identity_relation(X1)
| ~ in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| ~ in(esk1_2(X1,X2),X1)
| esk1_2(X1,X2) != esk2_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_40,plain,
( X1 = apply(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_18]) ).
cnf(c_0_41,negated_conjecture,
( esk2_2(X1,esk13_0) = esk1_2(X1,esk13_0)
| identity_relation(X1) = esk13_0
| in(unordered_pair(singleton(esk1_2(X1,esk13_0)),unordered_pair(esk1_2(X1,esk13_0),esk2_2(X1,esk13_0))),esk13_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_24]) ).
cnf(c_0_42,negated_conjecture,
( apply(esk13_0,X1) = X1
| esk13_0 = identity_relation(esk12_0)
| ~ in(X1,esk12_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_43,negated_conjecture,
( identity_relation(esk12_0) = esk13_0
| in(esk1_2(esk12_0,esk13_0),esk12_0) ),
inference(ef,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
( in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
| X1 != apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(rw,[status(thm)],[c_0_38,c_0_13]) ).
cnf(c_0_45,plain,
( in(ordered_pair(X1,X3),X4)
| ~ in(X1,X2)
| X1 != X3
| X4 != identity_relation(X2)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_46,plain,
! [X24] : relation(identity_relation(X24)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
cnf(c_0_47,plain,
( X2 = identity_relation(X1)
| esk2_2(X1,X2) != esk1_2(X1,X2)
| ~ relation(X2)
| ~ in(esk1_2(X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),singleton(esk1_2(X1,X2))),X2) ),
inference(rw,[status(thm)],[c_0_39,c_0_13]) ).
cnf(c_0_48,negated_conjecture,
( apply(esk13_0,esk1_2(X1,esk13_0)) = esk2_2(X1,esk13_0)
| esk2_2(X1,esk13_0) = esk1_2(X1,esk13_0)
| identity_relation(X1) = esk13_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_24]),c_0_33])]) ).
cnf(c_0_49,negated_conjecture,
( apply(esk13_0,esk1_2(esk12_0,esk13_0)) = esk1_2(esk12_0,esk13_0)
| identity_relation(esk12_0) = esk13_0 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X2,X1))),X2)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_44]),c_0_18]) ).
cnf(c_0_51,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X4)
| X1 != X3
| X4 != identity_relation(X2)
| ~ relation(X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_45,c_0_13]) ).
cnf(c_0_52,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_53,plain,
! [X30] :
( relation(identity_relation(X30))
& function(identity_relation(X30)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
cnf(c_0_54,negated_conjecture,
( apply(esk13_0,esk14_0) != esk14_0
| relation_dom(esk13_0) != esk12_0
| esk13_0 != identity_relation(esk12_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_55,plain,
( X1 = identity_relation(X2)
| esk2_2(X2,X1) != esk1_2(X2,X1)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk1_2(X2,X1)),unordered_pair(esk1_2(X2,X1),esk2_2(X2,X1))),X1)
| ~ in(esk1_2(X2,X1),X2) ),
inference(rw,[status(thm)],[c_0_47,c_0_18]) ).
cnf(c_0_56,negated_conjecture,
( esk2_2(esk12_0,esk13_0) = esk1_2(esk12_0,esk13_0)
| identity_relation(esk12_0) = esk13_0 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,negated_conjecture,
( identity_relation(esk12_0) = esk13_0
| in(unordered_pair(singleton(esk1_2(esk12_0,esk13_0)),unordered_pair(esk1_2(esk12_0,esk13_0),esk1_2(esk12_0,esk13_0))),esk13_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_49]),c_0_24]),c_0_33]),c_0_32])]),c_0_43]) ).
cnf(c_0_58,plain,
( in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),identity_relation(X2))
| ~ in(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_51])]),c_0_52])]) ).
cnf(c_0_59,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( in(esk14_0,esk12_0)
| relation_dom(esk13_0) != esk12_0
| esk13_0 != identity_relation(esk12_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_61,negated_conjecture,
( apply(esk13_0,esk14_0) != esk14_0
| identity_relation(esk12_0) != esk13_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_32])]) ).
cnf(c_0_62,negated_conjecture,
identity_relation(esk12_0) = esk13_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_24])]),c_0_43]),c_0_57]) ).
cnf(c_0_63,plain,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_58]),c_0_52]),c_0_59])]) ).
cnf(c_0_64,negated_conjecture,
( in(esk14_0,esk12_0)
| identity_relation(esk12_0) != esk13_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_32])]) ).
cnf(c_0_65,negated_conjecture,
apply(esk13_0,esk14_0) != esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]) ).
cnf(c_0_66,negated_conjecture,
( apply(esk13_0,X1) = X1
| ~ in(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
in(esk14_0,esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_62])]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU216+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 18:11:16 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 9.53/9.62 % Version : CSE_E---1.5
% 9.53/9.62 % Problem : theBenchmark.p
% 9.53/9.62 % Proof found
% 9.53/9.62 % SZS status Theorem for theBenchmark.p
% 9.53/9.62 % SZS output start Proof
% See solution above
% 9.53/9.62 % Total time : 9.025000 s
% 9.53/9.62 % SZS output end Proof
% 9.53/9.62 % Total time : 9.029000 s
%------------------------------------------------------------------------------