%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU381+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 : n012.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 02:24:55 PM UTC 2026
% Result : Theorem 5.30s 1.17s
% Output : CNFRefutation 5.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 81 ( 18 unt; 0 def)
% Number of atoms : 332 ( 3 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 395 ( 144 ~; 162 |; 68 &)
% ( 7 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 122 ( 3 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t11_waybel_7,conjecture,
! [X1,X2] :
( element(X2,powerset(the_carrier(boole_POSet(X1))))
=> ( upper_relstr_subset(X2,boole_POSet(X1))
<=> ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X1)
& subset(X3,X4) )
=> in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_waybel_7) ).
fof(d20_waybel_0,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( upper_relstr_subset(X2,X1)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( ( related(X1,X3,X4)
& in(X3,X2) )
=> in(X4,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_waybel_0) ).
fof(t4_waybel_7,axiom,
! [X1] : the_carrier(boole_POSet(X1)) = powerset(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_waybel_7) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(dt_k3_yellow_1,axiom,
! [X1] :
( rel_str(boole_POSet(X1))
& strict_rel_str(boole_POSet(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
fof(redefinition_r3_orders_2,axiom,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& rel_str(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1) )
=> ( related_reflexive(X1,X2,X3)
<=> related(X1,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
fof(fc1_waybel_1,axiom,
! [X1] :
( distributive_relstr(boole_POSet(X1))
& join_complete_relstr(boole_POSet(X1))
& up_complete_relstr(boole_POSet(X1))
& bounded_relstr(boole_POSet(X1))
& upper_bounded_relstr(boole_POSet(X1))
& lower_bounded_relstr(boole_POSet(X1))
& complete_relstr(boole_POSet(X1))
& with_infima_relstr(boole_POSet(X1))
& with_suprema_relstr(boole_POSet(X1))
& antisymmetric_relstr(boole_POSet(X1))
& transitive_relstr(boole_POSet(X1))
& reflexive_relstr(boole_POSet(X1))
& strict_rel_str(boole_POSet(X1))
& ~ empty_carrier(boole_POSet(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel_1) ).
fof(t2_yellow_1,axiom,
! [X1,X2] :
( element(X2,the_carrier(boole_POSet(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_POSet(X1)))
=> ( related_reflexive(boole_POSet(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yellow_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X3))
& in(X1,X2) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(the_carrier(boole_POSet(X1))))
=> ( upper_relstr_subset(X2,boole_POSet(X1))
<=> ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X1)
& subset(X3,X4) )
=> in(X4,X2) ) ) ),
inference(assume_negation,[status(cth)],[t11_waybel_7]) ).
fof(c_0_10,plain,
! [X43,X44,X45,X46] :
( ( ~ rel_str(X43)
| ~ element(X44,powerset(the_carrier(X43)))
| upper_relstr_subset(X44,X43)
| ~ in(esk2_2(X43,X44),X44) )
& ( ~ rel_str(X43)
| ~ element(X44,powerset(the_carrier(X43)))
| upper_relstr_subset(X44,X43)
| related(X43,esk1_2(X43,X44),esk2_2(X43,X44)) )
& ( ~ rel_str(X43)
| ~ element(X44,powerset(the_carrier(X43)))
| upper_relstr_subset(X44,X43)
| in(esk1_2(X43,X44),X44) )
& ( ~ rel_str(X43)
| ~ element(X44,powerset(the_carrier(X43)))
| upper_relstr_subset(X44,X43)
| element(esk2_2(X43,X44),the_carrier(X43)) )
& ( ~ rel_str(X43)
| ~ element(X44,powerset(the_carrier(X43)))
| upper_relstr_subset(X44,X43)
| element(esk1_2(X43,X44),the_carrier(X43)) )
& ( ~ rel_str(X43)
| ~ element(X44,powerset(the_carrier(X43)))
| in(X46,X44)
| ~ related(X43,X45,X46)
| ~ in(X45,X44)
| ~ element(X46,the_carrier(X43))
| ~ element(X45,the_carrier(X43))
| ~ upper_relstr_subset(X44,X43) ) ),
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)],[d20_waybel_0])])])])])]) ).
fof(c_0_11,plain,
! [X149] : the_carrier(boole_POSet(X149)) = powerset(X149),
inference(variable_rename,[status(thm)],[t4_waybel_7]) ).
fof(c_0_12,negated_conjecture,
! [X135,X136] :
( ( in(X136,esk36_0)
| ~ in(X135,esk36_0)
| ~ subset(X136,esk35_0)
| ~ subset(X135,X136)
| upper_relstr_subset(esk36_0,boole_POSet(esk35_0)) )
& ( ~ upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| ~ in(esk38_0,esk36_0) )
& ( ~ upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| in(esk37_0,esk36_0) )
& ( ~ upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| subset(esk38_0,esk35_0) )
& ( ~ upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| subset(esk37_0,esk38_0) )
& element(esk36_0,powerset(the_carrier(boole_POSet(esk35_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_9])])])])])]) ).
fof(c_0_13,plain,
! [X144,X145] :
( ( element(X144,powerset(X145))
| ~ subset(X144,X145) )
& ( subset(X144,X145)
| ~ element(X144,powerset(X145)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
cnf(c_0_14,plain,
( ~ rel_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| upper_relstr_subset(X2,X1)
| element(esk2_2(X1,X2),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
the_carrier(boole_POSet(X1)) = powerset(X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
element(esk36_0,powerset(the_carrier(boole_POSet(esk35_0)))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X51] :
( rel_str(boole_POSet(X51))
& strict_rel_str(boole_POSet(X51)) ),
inference(variable_rename,[status(thm)],[dt_k3_yellow_1]) ).
fof(c_0_18,plain,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& rel_str(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1) )
=> ( related_reflexive(X1,X2,X3)
<=> related(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_orders_2]) ).
fof(c_0_19,plain,
! [X1] :
( distributive_relstr(boole_POSet(X1))
& join_complete_relstr(boole_POSet(X1))
& up_complete_relstr(boole_POSet(X1))
& bounded_relstr(boole_POSet(X1))
& upper_bounded_relstr(boole_POSet(X1))
& lower_bounded_relstr(boole_POSet(X1))
& complete_relstr(boole_POSet(X1))
& with_infima_relstr(boole_POSet(X1))
& with_suprema_relstr(boole_POSet(X1))
& antisymmetric_relstr(boole_POSet(X1))
& transitive_relstr(boole_POSet(X1))
& reflexive_relstr(boole_POSet(X1))
& strict_rel_str(boole_POSet(X1))
& ~ empty_carrier(boole_POSet(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_waybel_1]) ).
cnf(c_0_20,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ element(X2,the_carrier(boole_POSet(the_carrier(X1))))
| ~ rel_str(X1)
| element(esk2_2(X1,X2),the_carrier(X1))
| upper_relstr_subset(X2,X1) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,negated_conjecture,
element(esk36_0,the_carrier(boole_POSet(the_carrier(boole_POSet(esk35_0))))),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_23,plain,
rel_str(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,plain,
! [X124,X125,X126] :
( ( ~ element(X126,the_carrier(X124))
| ~ element(X125,the_carrier(X124))
| ~ rel_str(X124)
| ~ reflexive_relstr(X124)
| empty_carrier(X124)
| related_reflexive(X124,X125,X126)
| ~ related(X124,X125,X126) )
& ( ~ element(X126,the_carrier(X124))
| ~ element(X125,the_carrier(X124))
| ~ rel_str(X124)
| ~ reflexive_relstr(X124)
| empty_carrier(X124)
| related(X124,X125,X126)
| ~ related_reflexive(X124,X125,X126) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_25,plain,
! [X72] :
( distributive_relstr(boole_POSet(X72))
& join_complete_relstr(boole_POSet(X72))
& up_complete_relstr(boole_POSet(X72))
& bounded_relstr(boole_POSet(X72))
& upper_bounded_relstr(boole_POSet(X72))
& lower_bounded_relstr(boole_POSet(X72))
& complete_relstr(boole_POSet(X72))
& with_infima_relstr(boole_POSet(X72))
& with_suprema_relstr(boole_POSet(X72))
& antisymmetric_relstr(boole_POSet(X72))
& transitive_relstr(boole_POSet(X72))
& reflexive_relstr(boole_POSet(X72))
& strict_rel_str(boole_POSet(X72))
& ~ empty_carrier(boole_POSet(X72)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
cnf(c_0_26,plain,
( ~ rel_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| upper_relstr_subset(X2,X1)
| element(esk1_2(X1,X2),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,plain,
( ~ rel_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| upper_relstr_subset(X2,X1)
| related(X1,esk1_2(X1,X2),esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,plain,
( ~ element(X1,the_carrier(boole_POSet(X2)))
| subset(X1,X2) ),
inference(rw,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_29,negated_conjecture,
( element(esk2_2(boole_POSet(esk35_0),esk36_0),the_carrier(boole_POSet(esk35_0)))
| upper_relstr_subset(esk36_0,boole_POSet(esk35_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_30,plain,
( ~ rel_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| upper_relstr_subset(X2,X1)
| in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_31,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1)
| ~ reflexive_relstr(X1)
| ~ related(X1,X2,X3)
| empty_carrier(X1)
| related_reflexive(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
reflexive_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
~ empty_carrier(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
( ~ element(X2,the_carrier(boole_POSet(the_carrier(X1))))
| ~ rel_str(X1)
| element(esk1_2(X1,X2),the_carrier(X1))
| upper_relstr_subset(X2,X1) ),
inference(rw,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_35,plain,
( ~ element(X2,the_carrier(boole_POSet(the_carrier(X1))))
| ~ rel_str(X1)
| related(X1,esk1_2(X1,X2),esk2_2(X1,X2))
| upper_relstr_subset(X2,X1) ),
inference(rw,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_36,negated_conjecture,
( ~ in(X1,esk36_0)
| ~ subset(X2,esk35_0)
| ~ subset(X1,X2)
| in(X2,esk36_0)
| upper_relstr_subset(esk36_0,boole_POSet(esk35_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,negated_conjecture,
( upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| subset(esk2_2(boole_POSet(esk35_0),esk36_0),esk35_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
( ~ element(X2,the_carrier(boole_POSet(the_carrier(X1))))
| ~ rel_str(X1)
| in(esk1_2(X1,X2),X2)
| upper_relstr_subset(X2,X1) ),
inference(rw,[status(thm)],[c_0_30,c_0_15]) ).
fof(c_0_39,plain,
! [X141,X142,X143] :
( ( ~ element(X142,the_carrier(boole_POSet(X141)))
| ~ element(X143,the_carrier(boole_POSet(X141)))
| related_reflexive(boole_POSet(X141),X142,X143)
| ~ subset(X142,X143) )
& ( ~ element(X142,the_carrier(boole_POSet(X141)))
| ~ element(X143,the_carrier(boole_POSet(X141)))
| subset(X142,X143)
| ~ related_reflexive(boole_POSet(X141),X142,X143) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_yellow_1])])])])]) ).
cnf(c_0_40,negated_conjecture,
( ~ element(X1,the_carrier(boole_POSet(esk35_0)))
| ~ related(boole_POSet(esk35_0),X1,esk2_2(boole_POSet(esk35_0),esk36_0))
| upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| related_reflexive(boole_POSet(esk35_0),X1,esk2_2(boole_POSet(esk35_0),esk36_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_32]),c_0_23])]),c_0_33]) ).
cnf(c_0_41,negated_conjecture,
( element(esk1_2(boole_POSet(esk35_0),esk36_0),the_carrier(boole_POSet(esk35_0)))
| upper_relstr_subset(esk36_0,boole_POSet(esk35_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_22]),c_0_23])]) ).
cnf(c_0_42,negated_conjecture,
( upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| related(boole_POSet(esk35_0),esk1_2(boole_POSet(esk35_0),esk36_0),esk2_2(boole_POSet(esk35_0),esk36_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_22]),c_0_23])]) ).
cnf(c_0_43,negated_conjecture,
( ~ in(X1,esk36_0)
| ~ subset(X1,esk2_2(boole_POSet(esk35_0),esk36_0))
| in(esk2_2(boole_POSet(esk35_0),esk36_0),esk36_0)
| upper_relstr_subset(esk36_0,boole_POSet(esk35_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( in(esk1_2(boole_POSet(esk35_0),esk36_0),esk36_0)
| upper_relstr_subset(esk36_0,boole_POSet(esk35_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_22]),c_0_23])]) ).
cnf(c_0_45,plain,
( ~ element(X2,the_carrier(boole_POSet(X1)))
| ~ element(X3,the_carrier(boole_POSet(X1)))
| ~ related_reflexive(boole_POSet(X1),X2,X3)
| subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| related_reflexive(boole_POSet(esk35_0),esk1_2(boole_POSet(esk35_0),esk36_0),esk2_2(boole_POSet(esk35_0),esk36_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_47,plain,
( ~ rel_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(esk2_2(X1,X2),X2)
| upper_relstr_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_48,negated_conjecture,
( ~ subset(esk1_2(boole_POSet(esk35_0),esk36_0),esk2_2(boole_POSet(esk35_0),esk36_0))
| in(esk2_2(boole_POSet(esk35_0),esk36_0),esk36_0)
| upper_relstr_subset(esk36_0,boole_POSet(esk35_0)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| subset(esk1_2(boole_POSet(esk35_0),esk36_0),esk2_2(boole_POSet(esk35_0),esk36_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_41]),c_0_29]) ).
cnf(c_0_50,plain,
( ~ element(X2,the_carrier(boole_POSet(the_carrier(X1))))
| ~ in(esk2_2(X1,X2),X2)
| ~ rel_str(X1)
| upper_relstr_subset(X2,X1) ),
inference(rw,[status(thm)],[c_0_47,c_0_15]) ).
cnf(c_0_51,negated_conjecture,
( in(esk2_2(boole_POSet(esk35_0),esk36_0),esk36_0)
| upper_relstr_subset(esk36_0,boole_POSet(esk35_0)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_52,plain,
! [X146,X147,X148] :
( element(X146,X148)
| ~ element(X147,powerset(X148))
| ~ in(X146,X147) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
cnf(c_0_53,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_54,negated_conjecture,
( ~ upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| subset(esk38_0,esk35_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_55,negated_conjecture,
upper_relstr_subset(esk36_0,boole_POSet(esk35_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_22]),c_0_23])]) ).
cnf(c_0_56,plain,
( ~ element(X2,powerset(X3))
| ~ in(X1,X2)
| element(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,plain,
( ~ rel_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ related(X2,X3,X4)
| ~ in(X3,X1)
| ~ element(X4,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| ~ upper_relstr_subset(X1,X2)
| in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_58,plain,
( ~ subset(X1,X2)
| element(X1,the_carrier(boole_POSet(X2))) ),
inference(rw,[status(thm)],[c_0_53,c_0_15]) ).
cnf(c_0_59,negated_conjecture,
subset(esk38_0,esk35_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_60,plain,
( ~ element(X2,the_carrier(boole_POSet(X3)))
| ~ in(X1,X2)
| element(X1,X3) ),
inference(rw,[status(thm)],[c_0_56,c_0_15]) ).
cnf(c_0_61,negated_conjecture,
( ~ upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| in(esk37_0,esk36_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_62,plain,
( ~ element(X1,the_carrier(boole_POSet(the_carrier(X2))))
| ~ element(X3,the_carrier(X2))
| ~ element(X4,the_carrier(X2))
| ~ related(X2,X3,X4)
| ~ upper_relstr_subset(X1,X2)
| ~ in(X3,X1)
| ~ rel_str(X2)
| in(X4,X1) ),
inference(rw,[status(thm)],[c_0_57,c_0_15]) ).
cnf(c_0_63,plain,
( ~ element(X1,the_carrier(boole_POSet(X3)))
| ~ element(X2,the_carrier(boole_POSet(X3)))
| ~ subset(X1,X2)
| related_reflexive(boole_POSet(X3),X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_64,negated_conjecture,
element(esk38_0,the_carrier(boole_POSet(esk35_0))),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( ~ upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| subset(esk37_0,esk38_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_66,negated_conjecture,
( ~ in(X1,esk36_0)
| element(X1,the_carrier(boole_POSet(esk35_0))) ),
inference(spm,[status(thm)],[c_0_60,c_0_22]) ).
cnf(c_0_67,negated_conjecture,
in(esk37_0,esk36_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_55])]) ).
cnf(c_0_68,plain,
( ~ rel_str(X3)
| ~ in(X4,X2)
| ~ element(X1,the_carrier(X3))
| ~ element(X2,the_carrier(boole_POSet(the_carrier(X3))))
| ~ upper_relstr_subset(X2,X3)
| ~ related(X3,X4,X1)
| in(X1,X2) ),
inference(csr,[status(thm)],[c_0_62,c_0_60]) ).
cnf(c_0_69,negated_conjecture,
( ~ upper_relstr_subset(esk36_0,boole_POSet(esk35_0))
| ~ in(esk38_0,esk36_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_70,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1)
| ~ reflexive_relstr(X1)
| ~ related_reflexive(X1,X2,X3)
| empty_carrier(X1)
| related(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_71,negated_conjecture,
( ~ element(X1,the_carrier(boole_POSet(esk35_0)))
| ~ subset(X1,esk38_0)
| related_reflexive(boole_POSet(esk35_0),X1,esk38_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,negated_conjecture,
subset(esk37_0,esk38_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_55])]) ).
cnf(c_0_73,negated_conjecture,
element(esk37_0,the_carrier(boole_POSet(esk35_0))),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( ~ in(X2,X1)
| ~ element(X1,the_carrier(boole_POSet(the_carrier(boole_POSet(esk35_0)))))
| ~ upper_relstr_subset(X1,boole_POSet(esk35_0))
| ~ related(boole_POSet(esk35_0),X2,esk38_0)
| in(esk38_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_64]),c_0_23])]) ).
cnf(c_0_75,negated_conjecture,
~ in(esk38_0,esk36_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_55])]) ).
cnf(c_0_76,negated_conjecture,
( ~ element(X1,the_carrier(boole_POSet(esk35_0)))
| ~ related_reflexive(boole_POSet(esk35_0),X1,esk38_0)
| related(boole_POSet(esk35_0),X1,esk38_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_64]),c_0_32]),c_0_23])]),c_0_33]) ).
cnf(c_0_77,negated_conjecture,
related_reflexive(boole_POSet(esk35_0),esk37_0,esk38_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_78,negated_conjecture,
( ~ in(X1,esk36_0)
| ~ related(boole_POSet(esk35_0),X1,esk38_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_55]),c_0_22])]),c_0_75]) ).
cnf(c_0_79,negated_conjecture,
related(boole_POSet(esk35_0),esk37_0,esk38_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_73])]) ).
cnf(c_0_80,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_67]),c_0_79])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU381+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n012.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:17:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 5.30/1.17 % Version: 3.5.1
% 5.30/1.17 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.30/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.30/1.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.30/1.17 % Starting new_bool_3 with 300s (1) cores
% 5.30/1.17 % Starting new_bool_1 with 300s (1) cores
% 5.30/1.17 % Starting sh5l with 300s (1) cores
% 5.30/1.17 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1726994 completed with status 0
% 5.30/1.17 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 5.30/1.17 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.30/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.30/1.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.30/1.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.30/1.17 % No SInE strategy applied
% 5.30/1.17 % Search class: FGHSM-FSLM21-MFFFFFNN
% 5.30/1.17 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 5.30/1.17 % Starting SubtermCWHack with 136s (1) cores
% 5.30/1.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 5.30/1.17 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 5.30/1.17 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 5.30/1.17 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 5.30/1.17 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1727002 completed with status 0
% 5.30/1.17 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 5.30/1.17 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.30/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.30/1.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.30/1.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.30/1.17 % No SInE strategy applied
% 5.30/1.17 % Search class: FGHSM-FSLM21-MFFFFFNN
% 5.30/1.17 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 5.30/1.17 % Starting SubtermCWHack with 136s (1) cores
% 5.30/1.17 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 5.30/1.17 % Preprocessing time : 0.004 s
% 5.30/1.17 % Presaturation interreduction done
% 5.30/1.17
% 5.30/1.17 % Proof found!
% 5.30/1.17 % SZS status Theorem
% 5.30/1.17 % SZS output start CNFRefutation
% See solution above
% 5.30/1.17 % Parsed axioms : 108
% 5.30/1.17 % Removed by relevancy pruning/SinE : 0
% 5.30/1.17 % Initial clauses : 490
% 5.30/1.17 % Removed in clause preprocessing : 82
% 5.30/1.17 % Initial clauses in saturation : 408
% 5.30/1.17 % Processed clauses : 5648
% 5.30/1.17 % ...of these trivial : 77
% 5.30/1.17 % ...subsumed : 2972
% 5.30/1.17 % ...remaining for further processing : 2599
% 5.30/1.17 % Other redundant clauses eliminated : 12
% 5.30/1.17 % Clauses deleted for lack of memory : 0
% 5.30/1.17 % Backward-subsumed : 110
% 5.30/1.17 % Backward-rewritten : 443
% 5.30/1.17 % Generated clauses : 17503
% 5.30/1.17 % ...of the previous two non-redundant : 16537
% 5.30/1.17 % ...aggressively subsumed : 0
% 5.30/1.17 % Contextual simplify-reflections : 60
% 5.30/1.17 % Paramodulations : 17489
% 5.30/1.17 % Factorizations : 0
% 5.30/1.17 % NegExts : 0
% 5.30/1.17 % Equation resolutions : 14
% 5.30/1.17 % Disequality decompositions : 0
% 5.30/1.17 % Total rewrite steps : 4247
% 5.30/1.17 % ...of those cached : 3848
% 5.30/1.17 % Propositional unsat checks : 0
% 5.30/1.17 % Propositional check models : 0
% 5.30/1.17 % Propositional check unsatisfiable : 0
% 5.30/1.17 % Propositional clauses : 0
% 5.30/1.17 % Propositional clauses after purity: 0
% 5.30/1.17 % Propositional unsat core size : 0
% 5.30/1.17 % Propositional preprocessing time : 0.000
% 5.30/1.17 % Propositional encoding time : 0.000
% 5.30/1.17 % Propositional solver time : 0.000
% 5.30/1.17 % Success case prop preproc time : 0.000
% 5.30/1.17 % Success case prop encoding time : 0.000
% 5.30/1.17 % Success case prop solver time : 0.000
% 5.30/1.17 % Current number of processed clauses : 1719
% 5.30/1.17 % Positive orientable unit clauses : 336
% 5.30/1.17 % Positive unorientable unit clauses: 0
% 5.30/1.17 % Negative unit clauses : 50
% 5.30/1.17 % Non-unit-clauses : 1333
% 5.30/1.17 % Current number of unprocessed clauses: 11410
% 5.30/1.17 % ...number of literals in the above : 53867
% 5.30/1.17 % Current number of archived formulas : 0
% 5.30/1.17 % Current number of archived clauses : 881
% 5.30/1.17 % Clause-clause subsumption calls (NU) : 520908
% 5.30/1.17 % Rec. Clause-clause subsumption calls : 223413
% 5.30/1.17 % Non-unit clause-clause subsumptions : 2502
% 5.30/1.17 % Unit Clause-clause subsumption calls : 21807
% 5.30/1.17 % Rewrite failures with RHS unbound : 0
% 5.30/1.17 % BW rewrite match attempts : 379
% 5.30/1.17 % BW rewrite match successes : 26
% 5.30/1.17 % Condensation attempts : 0
% 5.30/1.17 % Condensation successes : 0
% 5.30/1.17 % Termbank termtop insertions : 330331
% 5.30/1.17 % Search garbage collected termcells : 3617
% 5.30/1.17
% 5.30/1.17 % -------------------------------------------------
% 5.30/1.17 % User time : 0.724 s
% 5.30/1.17 % System time : 0.021 s
% 5.30/1.17 % Total time : 0.744 s
% 5.30/1.17 % Maximum resident set size: 4520 pages
% 5.30/1.17
% 5.30/1.17 % -------------------------------------------------
% 5.30/1.17 % User time : 3.578 s
% 5.30/1.17 % System time : 0.110 s
% 5.30/1.17 % Total time : 3.688 s
% 5.30/1.17 % Maximum resident set size: 4864 pages
% 5.30/1.17 % E exiting
%------------------------------------------------------------------------------