%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU143+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/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 05:10:45 PM UTC 2026
% Result : Theorem 1.26s 1.70s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 35 ( 21 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 39 ( 18 ~; 13 |; 4 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(l1_zfmisc_1,conjecture,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(c_0_3,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_4,plain,
! [X16,X17,X18,X19,X20,X21] :
( ( ~ in(X18,X17)
| X18 = X16
| X17 != singleton(X16) )
& ( X19 != X16
| in(X19,X17)
| X17 != singleton(X16) )
& ( ~ in(esk1_2(X20,X21),X21)
| esk1_2(X20,X21) != X20
| X21 = singleton(X20) )
& ( in(esk1_2(X20,X21),X21)
| esk1_2(X20,X21) = X20
| X21 = singleton(X20) ) ),
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])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] : singleton(X1) != empty_set,
inference(assume_negation,[status(cth)],[l1_zfmisc_1]) ).
fof(c_0_6,plain,
! [X23,X24,X25] :
( ( X23 != empty_set
| ~ in(X24,X23) )
& ( in(esk2_1(X25),X25)
| X25 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).
cnf(c_0_7,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
singleton(esk3_0) = empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_7])]) ).
cnf(c_0_11,negated_conjecture,
singleton(esk3_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU143+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/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 02:45:01 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.26/1.70 % Version : CSE_E---1.7
% 1.26/1.70 % Problem : theBenchmark.p
% 1.26/1.70 % SZS status Theorem for theBenchmark.p
% 1.26/1.70 % SZS output start CNFRefutation
% See solution above
% 1.26/1.70 % Total time : 1.367s
%------------------------------------------------------------------------------