%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU168+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:10:54 PM UTC 2026
% Result : Theorem 1.74s 1.82s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of formulae : 85 ( 13 unt; 0 def)
% Number of atoms : 346 ( 7 equ)
% Maximal formula atoms : 72 ( 4 avg)
% Number of connectives : 431 ( 170 ~; 195 |; 54 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 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 : 133 ( 1 sgn 51 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t9_tarski,axiom,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& ! [X5] :
( subset(X5,X3)
=> in(X5,X4) ) ) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t136_zfmisc_1,conjecture,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_5,plain,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& ! [X5] :
( subset(X5,X3)
=> in(X5,X4) ) ) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[t9_tarski]) ).
fof(c_0_6,plain,
! [X32,X33,X34,X35,X36,X37] :
( ( ~ in(X34,X33)
| subset(X34,X32)
| X33 != powerset(X32) )
& ( ~ subset(X35,X32)
| in(X35,X33)
| X33 != powerset(X32) )
& ( ~ in(esk1_2(X36,X37),X37)
| ~ subset(esk1_2(X36,X37),X36)
| X37 = powerset(X36) )
& ( in(esk1_2(X36,X37),X37)
| subset(esk1_2(X36,X37),X36)
| X37 = powerset(X36) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_zfmisc_1])])])])])]) ).
fof(c_0_7,plain,
! [X39,X40,X41,X42,X43] :
( ( ~ subset(X39,X40)
| ~ in(X41,X39)
| in(X41,X40) )
& ( in(esk2_2(X42,X43),X42)
| subset(X42,X43) )
& ( ~ in(esk2_2(X42,X43),X43)
| subset(X42,X43) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
fof(c_0_8,plain,
! [X52,X54,X55,X56,X58,X59] :
( in(X52,esk8_1(X52))
& ( ~ in(X54,esk8_1(X52))
| ~ subset(X55,X54)
| in(X55,esk8_1(X52)) )
& ( in(esk9_2(X52,X56),esk8_1(X52))
| ~ in(X56,esk8_1(X52)) )
& ( ~ subset(X58,X56)
| in(X58,esk9_2(X52,X56))
| ~ in(X56,esk8_1(X52)) )
& ( ~ subset(X59,esk8_1(X52))
| are_equipotent(X59,esk8_1(X52))
| in(X59,esk8_1(X52)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
cnf(c_0_9,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( in(X1,esk9_2(X3,X2))
| ~ subset(X1,X2)
| ~ in(X2,esk8_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t136_zfmisc_1])]) ).
cnf(c_0_15,plain,
( in(X3,esk8_1(X2))
| ~ in(X1,esk8_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( in(esk9_2(X1,X2),esk8_1(X1))
| ~ in(X2,esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( subset(X1,esk9_2(X2,X3))
| ~ subset(esk2_2(X1,esk9_2(X2,X3)),X3)
| ~ in(X3,esk8_1(X2)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,plain,
( subset(esk2_2(powerset(X1),X2),X1)
| subset(powerset(X1),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_19,negated_conjecture,
! [X47] :
( ( subset(esk7_1(X47),X47)
| in(esk6_1(X47),X47)
| in(esk4_1(X47),X47)
| ~ in(esk3_0,X47) )
& ( ~ are_equipotent(esk7_1(X47),X47)
| in(esk6_1(X47),X47)
| in(esk4_1(X47),X47)
| ~ in(esk3_0,X47) )
& ( ~ in(esk7_1(X47),X47)
| in(esk6_1(X47),X47)
| in(esk4_1(X47),X47)
| ~ in(esk3_0,X47) )
& ( subset(esk7_1(X47),X47)
| ~ in(powerset(esk6_1(X47)),X47)
| in(esk4_1(X47),X47)
| ~ in(esk3_0,X47) )
& ( ~ are_equipotent(esk7_1(X47),X47)
| ~ in(powerset(esk6_1(X47)),X47)
| in(esk4_1(X47),X47)
| ~ in(esk3_0,X47) )
& ( ~ in(esk7_1(X47),X47)
| ~ in(powerset(esk6_1(X47)),X47)
| in(esk4_1(X47),X47)
| ~ in(esk3_0,X47) )
& ( subset(esk7_1(X47),X47)
| in(esk6_1(X47),X47)
| subset(esk5_1(X47),esk4_1(X47))
| ~ in(esk3_0,X47) )
& ( ~ are_equipotent(esk7_1(X47),X47)
| in(esk6_1(X47),X47)
| subset(esk5_1(X47),esk4_1(X47))
| ~ in(esk3_0,X47) )
& ( ~ in(esk7_1(X47),X47)
| in(esk6_1(X47),X47)
| subset(esk5_1(X47),esk4_1(X47))
| ~ in(esk3_0,X47) )
& ( subset(esk7_1(X47),X47)
| ~ in(powerset(esk6_1(X47)),X47)
| subset(esk5_1(X47),esk4_1(X47))
| ~ in(esk3_0,X47) )
& ( ~ are_equipotent(esk7_1(X47),X47)
| ~ in(powerset(esk6_1(X47)),X47)
| subset(esk5_1(X47),esk4_1(X47))
| ~ in(esk3_0,X47) )
& ( ~ in(esk7_1(X47),X47)
| ~ in(powerset(esk6_1(X47)),X47)
| subset(esk5_1(X47),esk4_1(X47))
| ~ in(esk3_0,X47) )
& ( subset(esk7_1(X47),X47)
| in(esk6_1(X47),X47)
| ~ in(esk5_1(X47),X47)
| ~ in(esk3_0,X47) )
& ( ~ are_equipotent(esk7_1(X47),X47)
| in(esk6_1(X47),X47)
| ~ in(esk5_1(X47),X47)
| ~ in(esk3_0,X47) )
& ( ~ in(esk7_1(X47),X47)
| in(esk6_1(X47),X47)
| ~ in(esk5_1(X47),X47)
| ~ in(esk3_0,X47) )
& ( subset(esk7_1(X47),X47)
| ~ in(powerset(esk6_1(X47)),X47)
| ~ in(esk5_1(X47),X47)
| ~ in(esk3_0,X47) )
& ( ~ are_equipotent(esk7_1(X47),X47)
| ~ in(powerset(esk6_1(X47)),X47)
| ~ in(esk5_1(X47),X47)
| ~ in(esk3_0,X47) )
& ( ~ in(esk7_1(X47),X47)
| ~ in(powerset(esk6_1(X47)),X47)
| ~ in(esk5_1(X47),X47)
| ~ in(esk3_0,X47) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_20,plain,
( in(X1,esk8_1(X2))
| ~ subset(X1,esk9_2(X2,X3))
| ~ in(X3,esk8_1(X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( subset(powerset(X1),esk9_2(X2,X1))
| ~ in(X1,esk8_1(X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( subset(esk7_1(X1),X1)
| in(esk4_1(X1),X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( in(powerset(X1),esk8_1(X2))
| ~ in(X1,esk8_1(X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( subset(esk7_1(X1),X1)
| in(esk6_1(X1),X1)
| in(esk4_1(X1),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( subset(esk7_1(esk8_1(X1)),esk8_1(X1))
| in(esk4_1(esk8_1(X1)),esk8_1(X1))
| ~ in(esk3_0,esk8_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,plain,
in(X1,esk8_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
( subset(esk7_1(X1),X1)
| subset(esk5_1(X1),esk4_1(X1))
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( subset(esk7_1(X1),X1)
| in(esk6_1(X1),X1)
| subset(esk5_1(X1),esk4_1(X1))
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( subset(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_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( subset(esk5_1(esk8_1(X1)),esk4_1(esk8_1(X1)))
| subset(esk7_1(esk8_1(X1)),esk8_1(X1))
| ~ in(esk3_0,esk8_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_23]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( subset(esk7_1(X1),X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk5_1(X1),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,negated_conjecture,
( subset(esk7_1(X1),X1)
| in(esk6_1(X1),X1)
| ~ in(esk5_1(X1),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_33,negated_conjecture,
( subset(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(X1,esk8_1(esk3_0))
| ~ subset(X1,esk4_1(esk8_1(esk3_0))) ),
inference(spm,[status(thm)],[c_0_15,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( subset(esk5_1(esk8_1(esk3_0)),esk4_1(esk8_1(esk3_0)))
| subset(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_35,negated_conjecture,
( subset(esk7_1(esk8_1(X1)),esk8_1(X1))
| ~ in(esk5_1(esk8_1(X1)),esk8_1(X1))
| ~ in(esk3_0,esk8_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_23]),c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( subset(esk7_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_33,c_0_34]) ).
cnf(c_0_37,plain,
( are_equipotent(X1,esk8_1(X2))
| in(X1,esk8_1(X2))
| ~ subset(X1,esk8_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_38,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_35,c_0_36]),c_0_26])]) ).
cnf(c_0_39,negated_conjecture,
( in(esk4_1(X1),X1)
| ~ are_equipotent(esk7_1(X1),X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_40,negated_conjecture,
( are_equipotent(esk7_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_37,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk4_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| ~ in(powerset(esk6_1(esk8_1(esk3_0))),esk8_1(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_26])]) ).
cnf(c_0_42,negated_conjecture,
( ~ are_equipotent(esk7_1(X1),X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk5_1(X1),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_43,negated_conjecture,
( in(esk6_1(X1),X1)
| in(esk4_1(X1),X1)
| ~ are_equipotent(esk7_1(X1),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_44,negated_conjecture,
( in(esk4_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| ~ in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_23]) ).
cnf(c_0_45,negated_conjecture,
( in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| ~ in(powerset(esk6_1(esk8_1(esk3_0))),esk8_1(esk3_0))
| ~ in(esk5_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_40]),c_0_26])]) ).
cnf(c_0_46,negated_conjecture,
( in(esk4_1(X1),X1)
| ~ in(esk7_1(X1),X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_47,negated_conjecture,
( in(esk6_1(X1),X1)
| in(esk4_1(X1),X1)
| ~ in(esk7_1(X1),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_48,negated_conjecture,
( in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| 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_43,c_0_40]),c_0_26])]),c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( in(esk6_1(X1),X1)
| subset(esk5_1(X1),esk4_1(X1))
| ~ are_equipotent(esk7_1(X1),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_50,negated_conjecture,
( in(esk6_1(X1),X1)
| ~ are_equipotent(esk7_1(X1),X1)
| ~ in(esk5_1(X1),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_51,negated_conjecture,
( in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| ~ in(esk5_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| ~ in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_45,c_0_23]) ).
cnf(c_0_52,negated_conjecture,
( in(esk4_1(esk8_1(X1)),esk8_1(X1))
| ~ in(esk7_1(esk8_1(X1)),esk8_1(X1))
| ~ in(esk3_0,esk8_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_23]),c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(X1,esk8_1(esk3_0))
| ~ subset(X1,esk4_1(esk8_1(esk3_0))) ),
inference(spm,[status(thm)],[c_0_15,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( subset(esk5_1(esk8_1(esk3_0)),esk4_1(esk8_1(esk3_0)))
| in(esk7_1(esk8_1(esk3_0)),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_49,c_0_40]),c_0_26])]) ).
cnf(c_0_55,negated_conjecture,
( in(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| ~ 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_50,c_0_40]),c_0_26])]),c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( in(X1,esk8_1(X2))
| ~ subset(X1,esk4_1(esk8_1(X2)))
| ~ in(esk7_1(esk8_1(X2)),esk8_1(X2))
| ~ in(esk3_0,esk8_1(X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_52]) ).
cnf(c_0_57,negated_conjecture,
( in(esk6_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(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_58,negated_conjecture,
( in(esk6_1(X1),X1)
| subset(esk5_1(X1),esk4_1(X1))
| ~ in(esk7_1(X1),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_59,negated_conjecture,
( in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(X1,esk8_1(esk3_0))
| ~ subset(X1,esk4_1(esk8_1(esk3_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_26])]) ).
cnf(c_0_60,negated_conjecture,
( subset(esk5_1(esk8_1(esk3_0)),esk4_1(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_58,c_0_57]),c_0_26])]) ).
cnf(c_0_61,plain,
( in(X1,esk8_1(X2))
| ~ subset(X1,powerset(X3))
| ~ in(X3,esk8_1(X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_62,negated_conjecture,
( in(esk6_1(X1),X1)
| ~ in(esk7_1(X1),X1)
| ~ in(esk5_1(X1),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_63,negated_conjecture,
( in(esk5_1(esk8_1(esk3_0)),esk8_1(esk3_0))
| in(esk6_1(esk8_1(esk3_0)),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,plain,
( subset(powerset(powerset(X1)),X2)
| in(esk2_2(powerset(powerset(X1)),X2),esk8_1(X3))
| ~ in(X1,esk8_1(X3)) ),
inference(spm,[status(thm)],[c_0_61,c_0_18]) ).
cnf(c_0_65,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_62,c_0_63]),c_0_26])]),c_0_57]) ).
cnf(c_0_66,negated_conjecture,
( subset(powerset(powerset(esk6_1(esk8_1(esk3_0)))),X1)
| in(esk2_2(powerset(powerset(esk6_1(esk8_1(esk3_0)))),X1),esk8_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_67,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_68,negated_conjecture,
subset(powerset(powerset(esk6_1(esk8_1(esk3_0)))),esk8_1(esk3_0)),
inference(spm,[status(thm)],[c_0_10,c_0_66]) ).
cnf(c_0_69,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_70,negated_conjecture,
( in(X1,esk8_1(esk3_0))
| ~ in(X1,powerset(powerset(esk6_1(esk8_1(esk3_0))))) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_69]) ).
fof(c_0_72,plain,
! [X45] : subset(X45,X45),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_73,negated_conjecture,
( in(X1,esk8_1(esk3_0))
| ~ subset(X1,powerset(esk6_1(esk8_1(esk3_0)))) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_74,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_75,negated_conjecture,
in(powerset(esk6_1(esk8_1(esk3_0))),esk8_1(esk3_0)),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_76,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_46,c_0_75]),c_0_26])]),c_0_48]) ).
cnf(c_0_77,negated_conjecture,
( ~ in(esk7_1(X1),X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk5_1(X1),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_78,negated_conjecture,
( in(X1,esk8_1(esk3_0))
| ~ subset(X1,esk4_1(esk8_1(esk3_0))) ),
inference(spm,[status(thm)],[c_0_15,c_0_76]) ).
cnf(c_0_79,negated_conjecture,
( subset(esk5_1(X1),esk4_1(X1))
| ~ in(esk7_1(X1),X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_80,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_77,c_0_75]),c_0_26])]),c_0_55]) ).
cnf(c_0_81,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_78,c_0_79]),c_0_75]),c_0_26])]),c_0_80]) ).
cnf(c_0_82,negated_conjecture,
( subset(esk5_1(X1),esk4_1(X1))
| ~ are_equipotent(esk7_1(X1),X1)
| ~ in(powerset(esk6_1(X1)),X1)
| ~ in(esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_83,negated_conjecture,
are_equipotent(esk7_1(esk8_1(esk3_0)),esk8_1(esk3_0)),
inference(sr,[status(thm)],[c_0_40,c_0_81]) ).
cnf(c_0_84,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_82]),c_0_75]),c_0_26])]),c_0_80]),c_0_83])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU168+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n006.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:45:46 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.74/1.82 % Version : CSE_E---1.7
% 1.74/1.82 % Problem : theBenchmark.p
% 1.74/1.82 % SZS status Theorem for theBenchmark.p
% 1.74/1.82 % SZS output start CNFRefutation
% See solution above
% 1.74/1.82 % Total time : 1.372s
%------------------------------------------------------------------------------