%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU216+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 02:24:17 PM UTC 2026
% Result : Theorem 2.55s 0.99s
% Output : CNFRefutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 70 ( 18 unt; 0 def)
% Number of atoms : 287 ( 118 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 355 ( 138 ~; 166 |; 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 : 126 ( 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(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(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(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,
! [X57,X58,X59] :
( ( ~ function(X59)
| ~ relation(X59)
| in(ordered_pair(X57,X58),X59)
| X58 != apply(X59,X57)
| ~ in(X57,relation_dom(X59)) )
& ( ~ function(X59)
| ~ relation(X59)
| ~ in(ordered_pair(X57,X58),X59)
| X58 = apply(X59,X57) )
& ( ~ function(X59)
| ~ relation(X59)
| ~ in(ordered_pair(X57,X58),X59)
| in(X57,relation_dom(X59)) ) ),
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])])])])])])]) ).
cnf(c_0_12,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_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]) ).
cnf(c_0_15,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_16,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_17,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_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]) ).
cnf(c_0_19,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_15,c_0_13]) ).
fof(c_0_20,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]) ).
fof(c_0_21,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_16])])])])]) ).
cnf(c_0_22,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_17,c_0_18]) ).
cnf(c_0_23,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_19,c_0_18]) ).
fof(c_0_24,negated_conjecture,
! [X50] :
( ( esk11_0 = identity_relation(esk10_0)
| apply(esk11_0,X50) = X50
| ~ in(X50,esk10_0) )
& ( esk11_0 = identity_relation(esk10_0)
| relation_dom(esk11_0) = esk10_0 )
& ( esk11_0 != identity_relation(esk10_0)
| relation_dom(esk11_0) != esk10_0
| apply(esk11_0,esk12_0) != esk12_0 )
& ( esk11_0 != identity_relation(esk10_0)
| relation_dom(esk11_0) != esk10_0
| in(esk12_0,esk10_0) )
& function(esk11_0)
& relation(esk11_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_20])])])])])]) ).
cnf(c_0_25,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_26,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_21]) ).
cnf(c_0_27,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_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
function(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,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_25,c_0_13]) ).
cnf(c_0_31,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_26,c_0_13]) ).
cnf(c_0_32,negated_conjecture,
( in(esk1_2(X1,esk11_0),X1)
| in(esk1_2(X1,esk11_0),relation_dom(esk11_0))
| identity_relation(X1) = esk11_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,negated_conjecture,
( esk11_0 = identity_relation(esk10_0)
| relation_dom(esk11_0) = esk10_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,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_30,c_0_18]) ).
cnf(c_0_35,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_31,c_0_18]) ).
cnf(c_0_36,negated_conjecture,
( in(esk1_2(X1,esk11_0),X1)
| in(esk1_2(X1,esk11_0),esk10_0)
| identity_relation(X1) = esk11_0
| identity_relation(esk10_0) = esk11_0 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,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_38,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_39,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_34,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( in(esk1_2(esk10_0,esk11_0),esk10_0)
| identity_relation(esk10_0) = esk11_0 ),
inference(ef,[status(thm)],[c_0_36]) ).
cnf(c_0_41,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_37,c_0_13]) ).
cnf(c_0_42,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_38,c_0_13]) ).
cnf(c_0_43,negated_conjecture,
( ~ in(esk1_2(esk10_0,esk11_0),relation_dom(esk11_0))
| esk2_2(esk10_0,esk11_0) != esk1_2(esk10_0,esk11_0)
| apply(esk11_0,esk1_2(esk10_0,esk11_0)) != esk2_2(esk10_0,esk11_0)
| identity_relation(esk10_0) = esk11_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_28]),c_0_29])]) ).
cnf(c_0_44,negated_conjecture,
( ~ in(X1,esk10_0)
| esk11_0 = identity_relation(esk10_0)
| apply(esk11_0,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_45,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_41,c_0_18]) ).
cnf(c_0_46,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_42,c_0_18]) ).
cnf(c_0_47,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_48,negated_conjecture,
( ~ in(esk1_2(esk10_0,esk11_0),relation_dom(esk11_0))
| esk2_2(esk10_0,esk11_0) != esk1_2(esk10_0,esk11_0)
| identity_relation(esk10_0) = esk11_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_40]) ).
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_45,c_0_46]) ).
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_47,c_0_13]) ).
fof(c_0_51,plain,
! [X52] :
( relation_rng(identity_relation(X52)) = X52
& relation_dom(identity_relation(X52)) = X52 ),
inference(variable_rename,[status(thm)],[t71_relat_1]) ).
cnf(c_0_52,negated_conjecture,
( esk2_2(esk10_0,esk11_0) != esk1_2(esk10_0,esk11_0)
| identity_relation(esk10_0) = esk11_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_33]),c_0_40]) ).
cnf(c_0_53,negated_conjecture,
( ~ in(esk1_2(X1,esk11_0),esk10_0)
| identity_relation(X1) = esk11_0
| identity_relation(esk10_0) = esk11_0
| esk2_2(X1,esk11_0) = esk1_2(X1,esk11_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_49]),c_0_28]),c_0_29])]) ).
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_31]) ).
fof(c_0_55,plain,
! [X24] : relation(identity_relation(X24)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_56,plain,
! [X29] :
( function(identity_relation(X29))
& relation(identity_relation(X29)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
cnf(c_0_57,plain,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,negated_conjecture,
identity_relation(esk10_0) = esk11_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_40]) ).
cnf(c_0_59,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_60,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( esk11_0 != identity_relation(esk10_0)
| relation_dom(esk11_0) != esk10_0
| apply(esk11_0,esk12_0) != esk12_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_63,negated_conjecture,
relation_dom(esk11_0) = esk10_0,
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,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_59]),c_0_60]),c_0_61]),c_0_57])]) ).
cnf(c_0_65,negated_conjecture,
( esk11_0 != identity_relation(esk10_0)
| relation_dom(esk11_0) != esk10_0
| in(esk12_0,esk10_0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_66,negated_conjecture,
apply(esk11_0,esk12_0) != esk12_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_58])]),c_0_63])]) ).
cnf(c_0_67,negated_conjecture,
( ~ in(X1,esk10_0)
| apply(esk11_0,X1) = X1 ),
inference(spm,[status(thm)],[c_0_64,c_0_58]) ).
cnf(c_0_68,negated_conjecture,
in(esk12_0,esk10_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_58])]),c_0_63])]) ).
cnf(c_0_69,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU216+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n017.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 05:53:56 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.49 Running first-order theorem proving
% 0.06/0.49 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
% 2.55/0.99 % Version: 3.5.1
% 2.55/0.99 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.55/0.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.55/0.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.55/0.99 % Starting new_bool_3 with 300s (1) cores
% 2.55/0.99 % Starting new_bool_1 with 300s (1) cores
% 2.55/0.99 % Starting sh5l with 300s (1) cores
% 2.55/0.99 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1581326 completed with status 0
% 2.55/0.99 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.55/0.99 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.55/0.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.55/0.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.55/0.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.55/0.99 % No SInE strategy applied
% 2.55/0.99 % Search class: FGHSM-FFMM21-MFFFFFNN
% 2.55/0.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.55/0.99 % Starting SubtermCWHack with 136s (1) cores
% 2.55/0.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.55/0.99 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 2.55/0.99 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 2.55/0.99 % Starting new_bool_3 with 136s (1) cores
% 2.55/0.99 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 1581333 completed with status 0
% 2.55/0.99 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y
% 2.55/0.99 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.55/0.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.55/0.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.55/0.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.55/0.99 % No SInE strategy applied
% 2.55/0.99 % Search class: FGHSM-FFMM21-MFFFFFNN
% 2.55/0.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.55/0.99 % Starting SubtermCWHack with 136s (1) cores
% 2.55/0.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.55/0.99 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 2.55/0.99 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 2.55/0.99 % Preprocessing time : 0.004 s
% 2.55/0.99
% 2.55/0.99 % Proof found!
% 2.55/0.99 % SZS status Theorem
% 2.55/0.99 % SZS output start CNFRefutation
% See solution above
% 2.55/0.99 % Parsed axioms : 42
% 2.55/0.99 % Removed by relevancy pruning/SinE : 0
% 2.55/0.99 % Initial clauses : 68
% 2.55/0.99 % Removed in clause preprocessing : 9
% 2.55/0.99 % Initial clauses in saturation : 59
% 2.55/0.99 % Processed clauses : 1838
% 2.55/0.99 % ...of these trivial : 6
% 2.55/0.99 % ...subsumed : 1380
% 2.55/0.99 % ...remaining for further processing : 452
% 2.55/0.99 % Other redundant clauses eliminated : 21
% 2.55/0.99 % Clauses deleted for lack of memory : 0
% 2.55/0.99 % Backward-subsumed : 78
% 2.55/0.99 % Backward-rewritten : 102
% 2.55/0.99 % Generated clauses : 8466
% 2.55/0.99 % ...of the previous two non-redundant : 7966
% 2.55/0.99 % ...aggressively subsumed : 0
% 2.55/0.99 % Contextual simplify-reflections : 38
% 2.55/0.99 % Paramodulations : 8399
% 2.55/0.99 % Factorizations : 8
% 2.55/0.99 % NegExts : 0
% 2.55/0.99 % Equation resolutions : 59
% 2.55/0.99 % Disequality decompositions : 0
% 2.55/0.99 % Total rewrite steps : 2085
% 2.55/0.99 % ...of those cached : 1998
% 2.55/0.99 % Propositional unsat checks : 0
% 2.55/0.99 % Propositional check models : 0
% 2.55/0.99 % Propositional check unsatisfiable : 0
% 2.55/0.99 % Propositional clauses : 0
% 2.55/0.99 % Propositional clauses after purity: 0
% 2.55/0.99 % Propositional unsat core size : 0
% 2.55/0.99 % Propositional preprocessing time : 0.000
% 2.55/0.99 % Propositional encoding time : 0.000
% 2.55/0.99 % Propositional solver time : 0.000
% 2.55/0.99 % Success case prop preproc time : 0.000
% 2.55/0.99 % Success case prop encoding time : 0.000
% 2.55/0.99 % Success case prop solver time : 0.000
% 2.55/0.99 % Current number of processed clauses : 271
% 2.55/0.99 % Positive orientable unit clauses : 25
% 2.55/0.99 % Positive unorientable unit clauses: 1
% 2.55/0.99 % Negative unit clauses : 12
% 2.55/0.99 % Non-unit-clauses : 233
% 2.55/0.99 % Current number of unprocessed clauses: 5518
% 2.55/0.99 % ...number of literals in the above : 29643
% 2.55/0.99 % Current number of archived formulas : 0
% 2.55/0.99 % Current number of archived clauses : 181
% 2.55/0.99 % Clause-clause subsumption calls (NU) : 35856
% 2.55/0.99 % Rec. Clause-clause subsumption calls : 18407
% 2.55/0.99 % Non-unit clause-clause subsumptions : 984
% 2.55/0.99 % Unit Clause-clause subsumption calls : 619
% 2.55/0.99 % Rewrite failures with RHS unbound : 0
% 2.55/0.99 % BW rewrite match attempts : 14
% 2.55/0.99 % BW rewrite match successes : 14
% 2.55/0.99 % Condensation attempts : 0
% 2.55/0.99 % Condensation successes : 0
% 2.55/0.99 % Termbank termtop insertions : 126723
% 2.55/0.99 % Search garbage collected termcells : 636
% 2.55/0.99
% 2.55/0.99 % -------------------------------------------------
% 2.55/0.99 % User time : 0.403 s
% 2.55/0.99 % System time : 0.013 s
% 2.55/0.99 % Total time : 0.416 s
% 2.55/0.99 % Maximum resident set size: 3404 pages
% 2.55/0.99
% 2.55/0.99 % -------------------------------------------------
% 2.55/0.99 % User time : 1.754 s
% 2.55/0.99 % System time : 0.070 s
% 2.55/0.99 % Total time : 1.825 s
% 2.55/0.99 % Maximum resident set size: 4608 pages
% 2.55/0.99 % E exiting
%------------------------------------------------------------------------------