%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU216+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:28:34 PM UTC 2026
% Result : Theorem 0.22s 10.90s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 71 ( 18 unt; 0 def)
% Number of atoms : 286 ( 120 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 354 ( 139 ~; 164 |; 30 &)
% ( 9 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 125 ( 9 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_funct_1,axiom,
! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( X2 = apply(X3,X1)
& in(X1,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(d10_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( X3 = X4
& in(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
fof(d4_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) )
& ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t34_funct_1,conjecture,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( X2 = identity_relation(X1)
<=> ( ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 )
& relation_dom(X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(t71_relat_1,axiom,
! [X1] :
( relation_rng(identity_relation(X1)) = X1
& relation_dom(identity_relation(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( function(identity_relation(X1))
& relation(identity_relation(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(c_0_9,plain,
! [X71,X72,X73] :
( ( ~ function(X73)
| ~ relation(X73)
| in(ordered_pair(X71,X72),X73)
| X72 != apply(X73,X71)
| ~ in(X71,relation_dom(X73)) )
& ( ~ function(X73)
| ~ relation(X73)
| ~ in(ordered_pair(X71,X72),X73)
| X72 = apply(X73,X71) )
& ( ~ function(X73)
| ~ relation(X73)
| ~ in(ordered_pair(X71,X72),X73)
| in(X71,relation_dom(X73)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_funct_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,
! [X11,X12,X13,X14,X15,X16] :
( ( ~ relation(X12)
| X12 = identity_relation(X11)
| in(ordered_pair(esk1_2(X11,X12),esk2_2(X11,X12)),X12)
| esk1_2(X11,X12) = esk2_2(X11,X12) )
& ( ~ relation(X12)
| X12 = identity_relation(X11)
| in(ordered_pair(esk1_2(X11,X12),esk2_2(X11,X12)),X12)
| in(esk1_2(X11,X12),X11) )
& ( ~ relation(X12)
| X12 = identity_relation(X11)
| esk1_2(X11,X12) != esk2_2(X11,X12)
| ~ in(esk1_2(X11,X12),X11)
| ~ in(ordered_pair(esk1_2(X11,X12),esk2_2(X11,X12)),X12) )
& ( ~ relation(X12)
| X12 != identity_relation(X11)
| in(ordered_pair(X15,X16),X12)
| X15 != X16
| ~ in(X15,X11) )
& ( ~ relation(X12)
| X12 != identity_relation(X11)
| ~ in(ordered_pair(X13,X14),X12)
| X13 = X14 )
& ( ~ relation(X12)
| X12 != identity_relation(X11)
| ~ in(ordered_pair(X13,X14),X12)
| in(X13,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_relat_1])])])])])])]) ).
fof(c_0_12,plain,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) )
& ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
cnf(c_0_13,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),X2)
| in(X1,relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_16,plain,
( ~ relation(X2)
| X2 = identity_relation(X1)
| in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X19,X20,X21] :
( ( ~ function(X19)
| ~ relation(X19)
| in(X20,relation_dom(X19))
| X21 = apply(X19,X20)
| X21 != empty_set )
& ( ~ function(X19)
| ~ relation(X19)
| in(X20,relation_dom(X19))
| X21 = empty_set
| X21 != apply(X19,X20) )
& ( ~ function(X19)
| ~ relation(X19)
| ~ in(X20,relation_dom(X19))
| X21 = apply(X19,X20)
| ~ in(ordered_pair(X20,X21),X19) )
& ( ~ function(X19)
| ~ relation(X19)
| ~ in(X20,relation_dom(X19))
| in(ordered_pair(X20,X21),X19)
| X21 != apply(X19,X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).
cnf(c_0_18,plain,
( ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2)
| ~ relation(X2)
| ~ function(X2)
| in(X1,relation_dom(X2)) ),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( ~ relation(X2)
| in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),singleton(esk1_2(X1,X2))),X2)
| in(esk1_2(X1,X2),X1)
| X2 = identity_relation(X1) ),
inference(rw,[status(thm)],[c_0_16,c_0_14]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( X2 = identity_relation(X1)
<=> ( ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 )
& relation_dom(X2) = X1 ) ) ),
inference(assume_negation,[status(cth)],[t34_funct_1]) ).
cnf(c_0_22,plain,
( ~ relation(X2)
| esk1_2(X1,X2) != esk2_2(X1,X2)
| ~ in(esk1_2(X1,X2),X1)
| ~ in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| X2 = identity_relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| in(ordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2)
| ~ function(X2)
| ~ relation(X2)
| in(X1,relation_dom(X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( ~ relation(X1)
| in(esk1_2(X2,X1),X2)
| in(unordered_pair(singleton(esk1_2(X2,X1)),unordered_pair(esk1_2(X2,X1),esk2_2(X2,X1))),X1)
| X1 = identity_relation(X2) ),
inference(rw,[status(thm)],[c_0_20,c_0_19]) ).
fof(c_0_26,negated_conjecture,
! [X56] :
( ( esk13_0 = identity_relation(esk12_0)
| apply(esk13_0,X56) = X56
| ~ in(X56,esk12_0) )
& ( esk13_0 = identity_relation(esk12_0)
| relation_dom(esk13_0) = esk12_0 )
& ( esk13_0 != identity_relation(esk12_0)
| relation_dom(esk13_0) != esk12_0
| apply(esk13_0,esk14_0) != esk14_0 )
& ( esk13_0 != identity_relation(esk12_0)
| relation_dom(esk13_0) != esk12_0
| in(esk14_0,esk12_0) )
& function(esk13_0)
& relation(esk13_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])])]) ).
cnf(c_0_27,plain,
( ~ in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),singleton(esk1_2(X1,X2))),X2)
| ~ in(esk1_2(X1,X2),X1)
| ~ relation(X2)
| esk2_2(X1,X2) != esk1_2(X1,X2)
| X2 = identity_relation(X1) ),
inference(rw,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_28,plain,
( ~ in(X3,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2)
| X1 != apply(X2,X3)
| in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(rw,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_29,plain,
( ~ function(X1)
| ~ relation(X1)
| in(esk1_2(X2,X1),X2)
| in(esk1_2(X2,X1),relation_dom(X1))
| X1 = identity_relation(X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( ~ in(esk1_2(X2,X1),X2)
| ~ in(unordered_pair(singleton(esk1_2(X2,X1)),unordered_pair(esk1_2(X2,X1),esk2_2(X2,X1))),X1)
| ~ relation(X1)
| esk2_2(X2,X1) != esk1_2(X2,X1)
| X1 = identity_relation(X2) ),
inference(rw,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_33,plain,
( ~ in(X1,relation_dom(X3))
| ~ function(X3)
| ~ relation(X3)
| X2 != apply(X3,X1)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_34,negated_conjecture,
( in(esk1_2(X1,esk13_0),X1)
| in(esk1_2(X1,esk13_0),relation_dom(esk13_0))
| identity_relation(X1) = esk13_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X1),X2)
| X1 = apply(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_36,plain,
( ~ relation(X2)
| X2 = identity_relation(X1)
| in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| esk1_2(X1,X2) = esk2_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_37,plain,
( ~ in(esk1_2(X2,X1),X2)
| ~ in(esk1_2(X2,X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| esk2_2(X2,X1) != esk1_2(X2,X1)
| apply(X1,esk1_2(X2,X1)) != esk2_2(X2,X1)
| X1 = identity_relation(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( in(esk1_2(relation_dom(esk13_0),esk13_0),relation_dom(esk13_0))
| identity_relation(relation_dom(esk13_0)) = esk13_0 ),
inference(ef,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
( ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
| ~ relation(X2)
| ~ function(X2)
| X1 = apply(X2,X3) ),
inference(rw,[status(thm)],[c_0_35,c_0_14]) ).
cnf(c_0_40,plain,
( ~ relation(X2)
| in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),singleton(esk1_2(X1,X2))),X2)
| esk2_2(X1,X2) = esk1_2(X1,X2)
| X2 = identity_relation(X1) ),
inference(rw,[status(thm)],[c_0_36,c_0_14]) ).
cnf(c_0_41,negated_conjecture,
( esk2_2(relation_dom(esk13_0),esk13_0) != esk1_2(relation_dom(esk13_0),esk13_0)
| apply(esk13_0,esk1_2(relation_dom(esk13_0),esk13_0)) != esk2_2(relation_dom(esk13_0),esk13_0)
| identity_relation(relation_dom(esk13_0)) = esk13_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_30]),c_0_31])]),c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( esk13_0 = identity_relation(esk12_0)
| relation_dom(esk13_0) = esk12_0 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_43,plain,
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2)
| ~ function(X2)
| ~ relation(X2)
| X1 = apply(X2,X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_19]) ).
cnf(c_0_44,plain,
( ~ relation(X2)
| in(unordered_pair(singleton(esk1_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))),X2)
| X2 = identity_relation(X1)
| esk2_2(X1,X2) = esk1_2(X1,X2) ),
inference(rw,[status(thm)],[c_0_40,c_0_19]) ).
cnf(c_0_45,plain,
( ~ relation(X3)
| X3 != identity_relation(X4)
| ~ in(ordered_pair(X1,X2),X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_46,negated_conjecture,
( esk2_2(esk12_0,esk13_0) != esk1_2(esk12_0,esk13_0)
| apply(esk13_0,esk1_2(esk12_0,esk13_0)) != esk2_2(esk12_0,esk13_0)
| identity_relation(esk12_0) = esk13_0 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( ~ in(X1,esk12_0)
| esk13_0 = identity_relation(esk12_0)
| apply(esk13_0,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_48,negated_conjecture,
( in(esk1_2(esk12_0,esk13_0),esk12_0)
| identity_relation(esk12_0) = esk13_0 ),
inference(spm,[status(thm)],[c_0_38,c_0_42]) ).
cnf(c_0_49,plain,
( ~ function(X1)
| ~ relation(X1)
| X1 = identity_relation(X2)
| esk2_2(X2,X1) = esk1_2(X2,X1)
| apply(X1,esk1_2(X2,X1)) = esk2_2(X2,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| X3 != identity_relation(X4)
| X1 = X2 ),
inference(rw,[status(thm)],[c_0_45,c_0_14]) ).
cnf(c_0_51,negated_conjecture,
( esk2_2(esk12_0,esk13_0) != esk1_2(esk12_0,esk13_0)
| identity_relation(esk12_0) = esk13_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( ~ in(esk1_2(X1,esk13_0),esk12_0)
| identity_relation(X1) = esk13_0
| identity_relation(esk12_0) = esk13_0
| esk2_2(X1,esk13_0) = esk1_2(X1,esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_49]),c_0_30]),c_0_31])]) ).
fof(c_0_53,plain,
! [X66] :
( relation_rng(identity_relation(X66)) = X66
& relation_dom(identity_relation(X66)) = X66 ),
inference(variable_rename,[status(thm)],[t71_relat_1]) ).
cnf(c_0_54,plain,
( ~ in(X1,relation_dom(X3))
| ~ function(X3)
| ~ relation(X3)
| X3 != identity_relation(X4)
| X2 != apply(X3,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_50,c_0_28]) ).
fof(c_0_55,plain,
! [X24] : relation(identity_relation(X24)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_56,plain,
! [X30] :
( function(identity_relation(X30))
& relation(identity_relation(X30)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
cnf(c_0_57,negated_conjecture,
( esk13_0 != identity_relation(esk12_0)
| relation_dom(esk13_0) != esk12_0
| apply(esk13_0,esk14_0) != esk14_0 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_58,negated_conjecture,
identity_relation(esk12_0) = esk13_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_48]) ).
cnf(c_0_59,plain,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
( ~ in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X3)
| apply(X1,X2) = X2 ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_61,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,negated_conjecture,
( relation_dom(esk13_0) != esk12_0
| apply(esk13_0,esk14_0) != esk14_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_64,negated_conjecture,
relation_dom(esk13_0) = esk12_0,
inference(spm,[status(thm)],[c_0_59,c_0_58]) ).
cnf(c_0_65,plain,
( ~ in(X2,X1)
| apply(identity_relation(X1),X2) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_60]),c_0_61]),c_0_62]),c_0_59])]) ).
cnf(c_0_66,negated_conjecture,
( esk13_0 != identity_relation(esk12_0)
| relation_dom(esk13_0) != esk12_0
| in(esk14_0,esk12_0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_67,negated_conjecture,
apply(esk13_0,esk14_0) != esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
cnf(c_0_68,negated_conjecture,
( ~ in(X1,esk12_0)
| apply(esk13_0,X1) = X1 ),
inference(spm,[status(thm)],[c_0_65,c_0_58]) ).
cnf(c_0_69,negated_conjecture,
in(esk14_0,esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_58])]),c_0_64])]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU216+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/10.45 % Computer : n014.cluster.edu
% 0.19/10.45 % Model : x86_64 x86_64
% 0.19/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/10.45 % Memory : 8046.5625MB
% 0.19/10.45 % OS : Linux 6.8.0-71-generic
% 0.19/10.45 % CPULimit : 300
% 0.19/10.45 % WCLimit : 300
% 0.19/10.45 % DateTime : Mon Sep 21 05:59:16 UTC 2026
% 0.19/10.45 % CPUTime :
% 0.19/10.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/10.49 Running first-order theorem proving
% 0.19/10.49 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/10.90 % Version: 3.5.1
% 0.22/10.90 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/10.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/10.90 % Starting new_bool_3 with 300s (1) cores
% 0.22/10.90 % Starting new_bool_1 with 300s (1) cores
% 0.22/10.90 % Starting sh5l with 300s (1) cores
% 0.22/10.90 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3291799 completed with status 0
% 0.22/10.90 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.22/10.90 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/10.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/10.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/10.90 % No SInE strategy applied
% 0.22/10.90 % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.22/10.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/10.90 % Starting SubtermCWHack with 136s (1) cores
% 0.22/10.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/10.90 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.22/10.90 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.22/10.90 % Starting new_bool_3 with 136s (1) cores
% 0.22/10.90 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 3291808 completed with status 0
% 0.22/10.90 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y
% 0.22/10.90 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/10.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/10.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/10.90 % No SInE strategy applied
% 0.22/10.90 % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.22/10.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/10.90 % Starting SubtermCWHack with 136s (1) cores
% 0.22/10.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/10.90 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.22/10.90 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.22/10.90 % Preprocessing time : 0.003 s
% 0.22/10.90
% 0.22/10.90 % Proof found!
% 0.22/10.90 % SZS status Theorem
% 0.22/10.90 % SZS output start CNFRefutation
% See solution above
% 0.22/10.90 % Parsed axioms : 41
% 0.22/10.90 % Removed by relevancy pruning/SinE : 0
% 0.22/10.90 % Initial clauses : 70
% 0.22/10.90 % Removed in clause preprocessing : 1
% 0.22/10.90 % Initial clauses in saturation : 69
% 0.22/10.90 % Processed clauses : 2054
% 0.22/10.90 % ...of these trivial : 9
% 0.22/10.90 % ...subsumed : 1400
% 0.22/10.90 % ...remaining for further processing : 645
% 0.22/10.90 % Other redundant clauses eliminated : 42
% 0.22/10.90 % Clauses deleted for lack of memory : 0
% 0.22/10.90 % Backward-subsumed : 133
% 0.22/10.90 % Backward-rewritten : 127
% 0.22/10.90 % Generated clauses : 11558
% 0.22/10.90 % ...of the previous two non-redundant : 11022
% 0.22/10.90 % ...aggressively subsumed : 0
% 0.22/10.90 % Contextual simplify-reflections : 66
% 0.22/10.90 % Paramodulations : 11461
% 0.22/10.90 % Factorizations : 7
% 0.22/10.90 % NegExts : 0
% 0.22/10.90 % Equation resolutions : 90
% 0.22/10.90 % Disequality decompositions : 0
% 0.22/10.90 % Total rewrite steps : 2212
% 0.22/10.90 % ...of those cached : 2095
% 0.22/10.90 % Propositional unsat checks : 0
% 0.22/10.90 % Propositional check models : 0
% 0.22/10.90 % Propositional check unsatisfiable : 0
% 0.22/10.90 % Propositional clauses : 0
% 0.22/10.90 % Propositional clauses after purity: 0
% 0.22/10.90 % Propositional unsat core size : 0
% 0.22/10.90 % Propositional preprocessing time : 0.000
% 0.22/10.90 % Propositional encoding time : 0.000
% 0.22/10.90 % Propositional solver time : 0.000
% 0.22/10.90 % Success case prop preproc time : 0.000
% 0.22/10.90 % Success case prop encoding time : 0.000
% 0.22/10.90 % Success case prop solver time : 0.000
% 0.22/10.90 % Current number of processed clauses : 384
% 0.22/10.90 % Positive orientable unit clauses : 36
% 0.22/10.90 % Positive unorientable unit clauses: 1
% 0.22/10.90 % Negative unit clauses : 17
% 0.22/10.90 % Non-unit-clauses : 330
% 0.22/10.90 % Current number of unprocessed clauses: 8363
% 0.22/10.90 % ...number of literals in the above : 44720
% 0.22/10.90 % Current number of archived formulas : 0
% 0.22/10.90 % Current number of archived clauses : 261
% 0.22/10.90 % Clause-clause subsumption calls (NU) : 67473
% 0.22/10.90 % Rec. Clause-clause subsumption calls : 28106
% 0.22/10.90 % Non-unit clause-clause subsumptions : 1019
% 0.22/10.90 % Unit Clause-clause subsumption calls : 2508
% 0.22/10.90 % Rewrite failures with RHS unbound : 0
% 0.22/10.90 % BW rewrite match attempts : 24
% 0.22/10.90 % BW rewrite match successes : 15
% 0.22/10.90 % Condensation attempts : 0
% 0.22/10.90 % Condensation successes : 0
% 0.22/10.90 % Termbank termtop insertions : 198282
% 0.22/10.90 % Search garbage collected termcells : 726
% 0.22/10.90
% 0.22/10.90 % -------------------------------------------------
% 0.22/10.90 % User time : 0.360 s
% 0.22/10.90 % System time : 0.019 s
% 0.22/10.90 % Total time : 0.379 s
% 0.22/10.90 % Maximum resident set size: 3668 pages
% 0.22/10.90
% 0.22/10.90 % -------------------------------------------------
% 0.22/10.90 % User time : 1.816 s
% 0.22/10.90 % System time : 0.078 s
% 0.22/10.90 % Total time : 1.894 s
% 0.22/10.90 % Maximum resident set size: 4608 pages
% 0.22/10.90 % E exiting
%------------------------------------------------------------------------------