%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU144+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 : n021.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 05:10:46 PM UTC 2026
% Result : Theorem 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 4 unt; 0 def)
% Number of atoms : 63 ( 16 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 66 ( 25 ~; 29 |; 6 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l2_zfmisc_1,conjecture,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_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(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
inference(assume_negation,[status(cth)],[l2_zfmisc_1]) ).
fof(c_0_4,plain,
! [X25,X26,X27,X28,X29] :
( ( ~ subset(X25,X26)
| ~ in(X27,X25)
| in(X27,X26) )
& ( in(esk2_2(X28,X29),X28)
| subset(X28,X29) )
& ( ~ in(esk2_2(X28,X29),X29)
| subset(X28,X29) ) ),
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_5,negated_conjecture,
( ( ~ subset(singleton(esk3_0),esk4_0)
| ~ in(esk3_0,esk4_0) )
& ( subset(singleton(esk3_0),esk4_0)
| in(esk3_0,esk4_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_6,plain,
! [X18,X19,X20,X21,X22,X23] :
( ( ~ in(X20,X19)
| X20 = X18
| X19 != singleton(X18) )
& ( X21 != X18
| in(X21,X19)
| X19 != singleton(X18) )
& ( ~ in(esk1_2(X22,X23),X23)
| esk1_2(X22,X23) != X22
| X23 = singleton(X22) )
& ( in(esk1_2(X22,X23),X23)
| esk1_2(X22,X23) = X22
| X23 = singleton(X22) ) ),
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_tarski])])])])])]) ).
cnf(c_0_7,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
( subset(singleton(esk3_0),esk4_0)
| in(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
( in(esk3_0,esk4_0)
| in(X1,esk4_0)
| ~ in(X1,singleton(esk3_0)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_13,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,negated_conjecture,
( ~ subset(singleton(esk3_0),esk4_0)
| ~ in(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
in(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_18,plain,
( esk2_2(singleton(X1),X2) = X1
| subset(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
~ subset(singleton(esk3_0),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_20,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU144+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 : n021.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 02:45:55 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.369s
%------------------------------------------------------------------------------