%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET987+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n019.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 05:09:05 PM UTC 2026
% Result : Theorem 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 23 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 3 |; 2 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 18 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t141_zfmisc_1,conjecture,
! [X1,X2] :
( ~ in(X1,X2)
=> set_difference(set_union2(X2,singleton(X1)),singleton(X1)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_zfmisc_1) ).
fof(t40_xboole_1,axiom,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(t65_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
( ~ in(X1,X2)
=> set_difference(set_union2(X2,singleton(X1)),singleton(X1)) = X2 ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t141_zfmisc_1])]) ).
fof(c_0_4,negated_conjecture,
( ~ in(esk3_0,esk4_0)
& set_difference(set_union2(esk4_0,singleton(esk3_0)),singleton(esk3_0)) != esk4_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X34,X35] : set_difference(set_union2(X34,X35),X35) = set_difference(X34,X35),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(c_0_6,plain,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[t65_zfmisc_1]) ).
cnf(c_0_7,negated_conjecture,
set_difference(set_union2(esk4_0,singleton(esk3_0)),singleton(esk3_0)) != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X36,X37] :
( ( set_difference(X36,singleton(X37)) != X36
| ~ in(X37,X36) )
& ( in(X37,X36)
| set_difference(X36,singleton(X37)) = X36 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
cnf(c_0_10,negated_conjecture,
set_difference(esk4_0,singleton(esk3_0)) != esk4_0,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( in(X1,X2)
| set_difference(X2,singleton(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
~ in(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
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 : SET987+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:41:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.19/0.34 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Theorem for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------