%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU168+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 02:24:06 PM UTC 2026
% Result : Theorem 2.54s 0.91s
% Output : CNFRefutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of formulae : 86 ( 13 unt; 0 def)
% Number of atoms : 355 ( 7 equ)
% Maximal formula atoms : 72 ( 4 avg)
% Number of connectives : 444 ( 175 ~; 195 |; 60 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 139 ( 1 sgn 56 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t9_tarski,axiom,
! [X1] :
? [X2] :
( ! [X3] :
~ ( ~ in(X3,X2)
& ~ are_equipotent(X3,X2)
& subset(X3,X2) )
& ! [X3] :
~ ( ! [X4] :
~ ( ! [X5] :
( subset(X5,X3)
=> in(X5,X4) )
& in(X4,X2) )
& in(X3,X2) )
& ! [X3,X4] :
( ( subset(X4,X3)
& in(X3,X2) )
=> in(X4,X2) )
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(t136_zfmisc_1,conjecture,
! [X1] :
? [X2] :
( ! [X3] :
~ ( ~ in(X3,X2)
& ~ are_equipotent(X3,X2)
& subset(X3,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3,X4] :
( ( subset(X4,X3)
& in(X3,X2) )
=> in(X4,X2) )
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_5,plain,
! [X1] :
? [X2] :
( ! [X3] :
~ ( ~ in(X3,X2)
& ~ are_equipotent(X3,X2)
& subset(X3,X2) )
& ! [X3] :
~ ( ! [X4] :
~ ( ! [X5] :
( subset(X5,X3)
=> in(X5,X4) )
& in(X4,X2) )
& in(X3,X2) )
& ! [X3,X4] :
( ( subset(X4,X3)
& in(X3,X2) )
=> in(X4,X2) )
& in(X1,X2) ),
inference(fof_simplification,[status(thm)],[t9_tarski]) ).
fof(c_0_6,plain,
! [X8,X9,X10,X11,X12,X13] :
( ( X13 = powerset(X12)
| subset(esk1_2(X12,X13),X12)
| in(esk1_2(X12,X13),X13) )
& ( X13 = powerset(X12)
| ~ subset(esk1_2(X12,X13),X12)
| ~ in(esk1_2(X12,X13),X13) )
& ( X9 != powerset(X8)
| in(X11,X9)
| ~ subset(X11,X8) )
& ( X9 != powerset(X8)
| subset(X10,X8)
| ~ in(X10,X9) ) ),
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)],[d1_zfmisc_1])])])])])])]) ).
fof(c_0_7,plain,
! [X15,X16,X17,X18,X19] :
( ( subset(X18,X19)
| ~ in(esk2_2(X18,X19),X19) )
& ( subset(X18,X19)
| in(esk2_2(X18,X19),X18) )
& ( in(X17,X16)
| ~ in(X17,X15)
| ~ subset(X15,X16) ) ),
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)],[d3_tarski])])])])])])]) ).
fof(c_0_8,plain,
! [X28,X30,X31,X32,X34,X35] :
( ( in(X35,esk8_1(X28))
| are_equipotent(X35,esk8_1(X28))
| ~ subset(X35,esk8_1(X28)) )
& ( ~ in(X32,esk8_1(X28))
| in(X34,esk9_2(X28,X32))
| ~ subset(X34,X32) )
& ( ~ in(X32,esk8_1(X28))
| in(esk9_2(X28,X32),esk8_1(X28)) )
& ( in(X31,esk8_1(X28))
| ~ subset(X31,X30)
| ~ in(X30,esk8_1(X28)) )
& in(X28,esk8_1(X28)) ),
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_5])])])])])]) ).
cnf(c_0_9,plain,
( X2 != powerset(X3)
| ~ in(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
? [X2] :
( ! [X3] :
~ ( ~ in(X3,X2)
& ~ are_equipotent(X3,X2)
& subset(X3,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3,X4] :
( ( subset(X4,X3)
& in(X3,X2) )
=> in(X4,X2) )
& in(X1,X2) ),
inference(assume_negation,[status(cth)],[t136_zfmisc_1]) ).
cnf(c_0_11,plain,
( ~ in(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( ~ in(X2,esk8_1(X3))
| ~ subset(X1,X2)
| in(X1,esk9_2(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ in(X1,powerset(X2))
| subset(X1,X2) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| in(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
? [X2] :
( ! [X3] :
~ ( ~ in(X3,X2)
& ~ are_equipotent(X3,X2)
& subset(X3,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3,X4] :
( ( subset(X4,X3)
& in(X3,X2) )
=> in(X4,X2) )
& in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ subset(X3,X1)
| ~ in(X1,esk8_1(X2))
| in(X3,esk8_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( ~ in(X2,esk8_1(X1))
| in(esk9_2(X1,X2),esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
( ~ in(X3,esk8_1(X2))
| ~ subset(esk2_2(X1,esk9_2(X2,X3)),X3)
| subset(X1,esk9_2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
( subset(powerset(X1),X2)
| subset(esk2_2(powerset(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_20,negated_conjecture,
! [X23] :
( ( ~ in(esk3_0,X23)
| ~ in(esk5_1(X23),X23)
| ~ in(powerset(esk6_1(X23)),X23)
| ~ in(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| ~ in(esk5_1(X23),X23)
| ~ in(powerset(esk6_1(X23)),X23)
| ~ are_equipotent(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| ~ in(esk5_1(X23),X23)
| ~ in(powerset(esk6_1(X23)),X23)
| subset(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| ~ in(esk5_1(X23),X23)
| in(esk6_1(X23),X23)
| ~ in(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| ~ in(esk5_1(X23),X23)
| in(esk6_1(X23),X23)
| ~ are_equipotent(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| ~ in(esk5_1(X23),X23)
| in(esk6_1(X23),X23)
| subset(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| subset(esk5_1(X23),esk4_1(X23))
| ~ in(powerset(esk6_1(X23)),X23)
| ~ in(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| subset(esk5_1(X23),esk4_1(X23))
| ~ in(powerset(esk6_1(X23)),X23)
| ~ are_equipotent(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| subset(esk5_1(X23),esk4_1(X23))
| ~ in(powerset(esk6_1(X23)),X23)
| subset(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| subset(esk5_1(X23),esk4_1(X23))
| in(esk6_1(X23),X23)
| ~ in(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| subset(esk5_1(X23),esk4_1(X23))
| in(esk6_1(X23),X23)
| ~ are_equipotent(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| subset(esk5_1(X23),esk4_1(X23))
| in(esk6_1(X23),X23)
| subset(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| in(esk4_1(X23),X23)
| ~ in(powerset(esk6_1(X23)),X23)
| ~ in(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| in(esk4_1(X23),X23)
| ~ in(powerset(esk6_1(X23)),X23)
| ~ are_equipotent(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| in(esk4_1(X23),X23)
| ~ in(powerset(esk6_1(X23)),X23)
| subset(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| in(esk4_1(X23),X23)
| in(esk6_1(X23),X23)
| ~ in(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| in(esk4_1(X23),X23)
| in(esk6_1(X23),X23)
| ~ are_equipotent(esk7_1(X23),X23) )
& ( ~ in(esk3_0,X23)
| in(esk4_1(X23),X23)
| in(esk6_1(X23),X23)
| subset(esk7_1(X23),X23) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
cnf(c_0_21,plain,
( ~ in(X3,esk8_1(X2))
| ~ subset(X1,esk9_2(X2,X3))
| in(X1,esk8_1(X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( ~ in(X1,esk8_1(X2))
| subset(powerset(X1),esk9_2(X2,X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(powerset(esk6_1(X1)),X1)
| in(esk4_1(X1),X1)
| subset(esk7_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
( ~ in(X1,esk8_1(X2))
| in(powerset(X1),esk8_1(X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( ~ in(esk3_0,X1)
| in(esk4_1(X1),X1)
| in(esk6_1(X1),X1)
| subset(esk7_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( ~ in(esk3_0,esk8_1(X1))
| in(esk4_1(esk8_1(X1)),esk8_1(X1))
| subset(esk7_1(esk8_1(X1)),esk8_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_27,plain,
in(X1,esk8_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(powerset(esk6_1(X1)),X1)
| subset(esk5_1(X1),esk4_1(X1))
| subset(esk7_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( ~ in(esk3_0,X1)
| subset(esk5_1(X1),esk4_1(X1))
| in(esk6_1(X1),X1)
| subset(esk7_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( in(esk4_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| subset(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
( ~ in(esk3_0,esk8_1(X1))
| subset(esk7_1(esk8_1(X1)),esk8_1(X1))
| subset(esk5_1(esk8_1(X1)),esk4_1(esk8_1(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(esk5_1(X1),X1)
| ~ in(powerset(esk6_1(X1)),X1)
| subset(esk7_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(esk5_1(X1),X1)
| in(esk6_1(X1),X1)
| subset(esk7_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_34,negated_conjecture,
( ~ subset(X1,esk4_1(esk8_1(esk3_0)))
| in(X1,esk8_1(esk3_0))
| subset(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( subset(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| subset(esk5_1(esk8_1(esk3_0)),esk4_1(esk8_1(esk3_0))) ),
inference(spm,[status(thm)],[c_0_31,c_0_27]) ).
cnf(c_0_36,negated_conjecture,
( ~ in(esk3_0,esk8_1(X1))
| ~ in(esk5_1(esk8_1(X1)),esk8_1(X1))
| subset(esk7_1(esk8_1(X1)),esk8_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( in(esk5_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| subset(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
( ~ subset(X1,esk8_1(X2))
| in(X1,esk8_1(X2))
| are_equipotent(X1,esk8_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_39,negated_conjecture,
subset(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_27])]) ).
cnf(c_0_40,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ are_equipotent(esk7_1(X1),X1)
| in(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_41,negated_conjecture,
( in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| are_equipotent(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( ~ in(powerset(esk6_1(esk8_1(esk3_0))),esk8_1(esk3_0))
| in(esk4_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_27])]) ).
cnf(c_0_43,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(esk5_1(X1),X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ are_equipotent(esk7_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_44,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ are_equipotent(esk7_1(X1),X1)
| in(esk4_1(X1),X1)
| in(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_45,negated_conjecture,
( ~ in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk4_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_24]) ).
cnf(c_0_46,negated_conjecture,
( ~ in(esk5_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| ~ in(powerset(esk6_1(esk8_1(esk3_0))),esk8_1(esk3_0))
| in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_41]),c_0_27])]) ).
cnf(c_0_47,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk7_1(X1),X1)
| in(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_48,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(esk7_1(X1),X1)
| in(esk4_1(X1),X1)
| in(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_49,negated_conjecture,
( in(esk4_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_41]),c_0_27])]),c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ are_equipotent(esk7_1(X1),X1)
| subset(esk5_1(X1),esk4_1(X1))
| in(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_51,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(esk5_1(X1),X1)
| ~ are_equipotent(esk7_1(X1),X1)
| in(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_52,negated_conjecture,
( ~ in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| ~ in(esk5_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_46,c_0_24]) ).
cnf(c_0_53,negated_conjecture,
( ~ in(esk3_0,esk8_1(X1))
| ~ in(esk7_1(esk8_1(X1)),esk8_1(X1))
| in(esk4_1(esk8_1(X1)),esk8_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_24]),c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( ~ subset(X1,esk4_1(esk8_1(esk3_0)))
| in(X1,esk8_1(esk3_0))
| in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| subset(esk5_1(esk8_1(esk3_0)),esk4_1(esk8_1(esk3_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_41]),c_0_27])]) ).
cnf(c_0_56,negated_conjecture,
( ~ in(esk5_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_41]),c_0_27])]),c_0_52]) ).
cnf(c_0_57,negated_conjecture,
( ~ in(esk3_0,esk8_1(X2))
| ~ in(esk7_1(esk8_1(X2)),esk8_1(X2))
| ~ subset(X1,esk4_1(esk8_1(X2)))
| in(X1,esk8_1(X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_53]) ).
cnf(c_0_58,negated_conjecture,
( in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(esk7_1(X1),X1)
| subset(esk5_1(X1),esk4_1(X1))
| in(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_60,negated_conjecture,
( ~ subset(X1,esk4_1(esk8_1(esk3_0)))
| in(X1,esk8_1(esk3_0))
| in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_27])]) ).
cnf(c_0_61,negated_conjecture,
( in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| subset(esk5_1(esk8_1(esk3_0)),esk4_1(esk8_1(esk3_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_58]),c_0_27])]) ).
cnf(c_0_62,plain,
( ~ in(X3,esk8_1(X2))
| ~ subset(X1,powerset(X3))
| in(X1,esk8_1(X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_63,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(esk5_1(X1),X1)
| ~ in(esk7_1(X1),X1)
| in(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_64,negated_conjecture,
( in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk5_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
( ~ in(X1,esk8_1(X3))
| in(esk2_2(powerset(powerset(X1)),X2),esk8_1(X3))
| subset(powerset(powerset(X1)),X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_19]) ).
cnf(c_0_66,negated_conjecture,
in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_27])]),c_0_58]) ).
cnf(c_0_67,negated_conjecture,
( in(esk2_2(powerset(powerset(esk6_1(esk8_1(esk3_0)))),X1),esk8_1(esk3_0))
| subset(powerset(powerset(esk6_1(esk8_1(esk3_0)))),X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_68,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_69,negated_conjecture,
subset(powerset(powerset(esk6_1(esk8_1(esk3_0)))),esk8_1(esk3_0)),
inference(spm,[status(thm)],[c_0_11,c_0_67]) ).
cnf(c_0_70,plain,
( X3 != powerset(X2)
| ~ subset(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_71,negated_conjecture,
( ~ in(X1,powerset(powerset(esk6_1(esk8_1(esk3_0)))))
| in(X1,esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_72,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_70]) ).
fof(c_0_73,plain,
! [X21] : subset(X21,X21),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_74,negated_conjecture,
( ~ subset(X1,powerset(esk6_1(esk8_1(esk3_0))))
| in(X1,esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_76,negated_conjecture,
in(powerset(esk6_1(esk8_1(esk3_0))),esk8_1(esk3_0)),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_77,negated_conjecture,
in(esk4_1(esk8_1(esk3_0)),esk8_1(esk3_0)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_76]),c_0_27])]),c_0_49]) ).
cnf(c_0_78,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(esk5_1(X1),X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk7_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_79,negated_conjecture,
( ~ subset(X1,esk4_1(esk8_1(esk3_0)))
| in(X1,esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_77]) ).
cnf(c_0_80,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk7_1(X1),X1)
| subset(esk5_1(X1),esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_81,negated_conjecture,
~ in(esk5_1(esk8_1(esk3_0)),esk8_1(esk3_0)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_76]),c_0_27])]),c_0_56]) ).
cnf(c_0_82,negated_conjecture,
( ~ in(esk3_0,X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ are_equipotent(esk7_1(X1),X1)
| subset(esk5_1(X1),esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_83,negated_conjecture,
~ in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_76]),c_0_27])]),c_0_81]) ).
cnf(c_0_84,negated_conjecture,
~ are_equipotent(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_82]),c_0_76]),c_0_27])]),c_0_81]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_41,c_0_83]),c_0_84]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU168+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n014.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 05:54:04 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 2.54/0.91 % Version: 3.5.1
% 2.54/0.91 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.54/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.54/0.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.54/0.91 % Starting new_bool_3 with 300s (1) cores
% 2.54/0.91 % Starting new_bool_1 with 300s (1) cores
% 2.54/0.91 % Starting sh5l with 300s (1) cores
% 2.54/0.91 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3282346 completed with status 0
% 2.54/0.91 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.54/0.91 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.54/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.54/0.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.54/0.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.54/0.91 % No SInE strategy applied
% 2.54/0.91 % Search class: FGHSS-FFMF21-SFFFFFNN
% 2.54/0.91 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.54/0.91 % Starting SubtermCWHack with 136s (1) cores
% 2.54/0.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.54/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 2.54/0.91 % Starting new_bool_3 with 136s (1) cores
% 2.54/0.91 % Starting new_bool_1 with 136s (1) cores
% 2.54/0.91 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3282352 completed with status 0
% 2.54/0.91 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.54/0.91 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.54/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.54/0.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.54/0.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.54/0.91 % No SInE strategy applied
% 2.54/0.91 % Search class: FGHSS-FFMF21-SFFFFFNN
% 2.54/0.91 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.54/0.91 % Starting SubtermCWHack with 136s (1) cores
% 2.54/0.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.54/0.91 % Preprocessing time : 0.002 s
% 2.54/0.91 % Presaturation interreduction done
% 2.54/0.91
% 2.54/0.91 % Proof found!
% 2.54/0.91 % SZS status Theorem
% 2.54/0.91 % SZS output start CNFRefutation
% See solution above
% 2.54/0.91 % Parsed axioms : 7
% 2.54/0.91 % Removed by relevancy pruning/SinE : 0
% 2.54/0.91 % Initial clauses : 33
% 2.54/0.91 % Removed in clause preprocessing : 1
% 2.54/0.91 % Initial clauses in saturation : 32
% 2.54/0.91 % Processed clauses : 1260
% 2.54/0.91 % ...of these trivial : 0
% 2.54/0.91 % ...subsumed : 415
% 2.54/0.91 % ...remaining for further processing : 844
% 2.54/0.91 % Other redundant clauses eliminated : 2
% 2.54/0.91 % Clauses deleted for lack of memory : 0
% 2.54/0.91 % Backward-subsumed : 80
% 2.54/0.91 % Backward-rewritten : 16
% 2.54/0.91 % Generated clauses : 3109
% 2.54/0.91 % ...of the previous two non-redundant : 3078
% 2.54/0.91 % ...aggressively subsumed : 0
% 2.54/0.91 % Contextual simplify-reflections : 11
% 2.54/0.91 % Paramodulations : 3098
% 2.54/0.91 % Factorizations : 8
% 2.54/0.91 % NegExts : 0
% 2.54/0.91 % Equation resolutions : 2
% 2.54/0.91 % Disequality decompositions : 0
% 2.54/0.91 % Total rewrite steps : 117
% 2.54/0.91 % ...of those cached : 103
% 2.54/0.91 % Propositional unsat checks : 0
% 2.54/0.91 % Propositional check models : 0
% 2.54/0.91 % Propositional check unsatisfiable : 0
% 2.54/0.91 % Propositional clauses : 0
% 2.54/0.91 % Propositional clauses after purity: 0
% 2.54/0.91 % Propositional unsat core size : 0
% 2.54/0.91 % Propositional preprocessing time : 0.000
% 2.54/0.91 % Propositional encoding time : 0.000
% 2.54/0.91 % Propositional solver time : 0.000
% 2.54/0.91 % Success case prop preproc time : 0.000
% 2.54/0.91 % Success case prop encoding time : 0.000
% 2.54/0.91 % Success case prop solver time : 0.000
% 2.54/0.91 % Current number of processed clauses : 713
% 2.54/0.91 % Positive orientable unit clauses : 17
% 2.54/0.91 % Positive unorientable unit clauses: 0
% 2.54/0.91 % Negative unit clauses : 44
% 2.54/0.91 % Non-unit-clauses : 652
% 2.54/0.91 % Current number of unprocessed clauses: 1839
% 2.54/0.91 % ...number of literals in the above : 8315
% 2.54/0.91 % Current number of archived formulas : 0
% 2.54/0.91 % Current number of archived clauses : 129
% 2.54/0.91 % Clause-clause subsumption calls (NU) : 125533
% 2.54/0.91 % Rec. Clause-clause subsumption calls : 48796
% 2.54/0.91 % Non-unit clause-clause subsumptions : 436
% 2.54/0.91 % Unit Clause-clause subsumption calls : 4098
% 2.54/0.91 % Rewrite failures with RHS unbound : 0
% 2.54/0.91 % BW rewrite match attempts : 25
% 2.54/0.91 % BW rewrite match successes : 6
% 2.54/0.91 % Condensation attempts : 0
% 2.54/0.91 % Condensation successes : 0
% 2.54/0.91 % Termbank termtop insertions : 85664
% 2.54/0.91 % Search garbage collected termcells : 477
% 2.54/0.91
% 2.54/0.91 % -------------------------------------------------
% 2.54/0.91 % User time : 0.331 s
% 2.54/0.91 % System time : 0.014 s
% 2.54/0.91 % Total time : 0.345 s
% 2.54/0.91 % Maximum resident set size: 3636 pages
% 2.54/0.91
% 2.54/0.91 % -------------------------------------------------
% 2.54/0.91 % User time : 1.592 s
% 2.54/0.91 % System time : 0.070 s
% 2.54/0.91 % Total time : 1.662 s
% 2.54/0.91 % Maximum resident set size: 4864 pages
% 2.54/0.91 % E exiting
%------------------------------------------------------------------------------