%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET927+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n016.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 05:08:59 PM UTC 2026
% Result : Theorem 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 69 ( 36 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 76 ( 28 ~; 34 |; 10 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 1 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l39_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(t70_zfmisc_1,conjecture,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).
fof(c_0_2,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
inference(fof_simplification,[status(thm)],[l39_zfmisc_1]) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t70_zfmisc_1])]) ).
fof(c_0_4,plain,
! [X25,X26,X27] :
( ( ~ in(X25,X27)
| set_difference(unordered_pair(X25,X26),X27) != singleton(X25) )
& ( in(X26,X27)
| X25 = X26
| set_difference(unordered_pair(X25,X26),X27) != singleton(X25) )
& ( ~ in(X26,X27)
| in(X25,X27)
| set_difference(unordered_pair(X25,X26),X27) = singleton(X25) )
& ( X25 != X26
| in(X25,X27)
| set_difference(unordered_pair(X25,X26),X27) = singleton(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).
fof(c_0_5,negated_conjecture,
( ( ~ in(esk4_0,esk5_0)
| in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0) )
& ( esk3_0 != esk4_0
| in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0) )
& ( ~ in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0) )
& ( in(esk4_0,esk5_0)
| esk3_0 = esk4_0
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
cnf(c_0_6,plain,
( ~ in(X1,X2)
| set_difference(unordered_pair(X1,X3),X2) != singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0)
| ~ in(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( in(X1,X2)
| X3 = X1
| set_difference(unordered_pair(X3,X1),X2) != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
( in(esk4_0,esk5_0)
| esk3_0 = esk4_0
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( in(esk3_0,esk5_0)
| ~ in(esk4_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( in(X3,X2)
| set_difference(unordered_pair(X3,X1),X2) = singleton(X3)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
~ in(esk3_0,esk5_0),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( esk4_0 = esk3_0
| in(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
~ in(esk4_0,esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( in(esk3_0,esk5_0)
| esk3_0 != esk4_0
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
esk4_0 = esk3_0,
inference(sr,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( in(X1,X3)
| set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_18,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk3_0),esk5_0) != singleton(esk3_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16])]),c_0_12]) ).
cnf(c_0_19,plain,
( set_difference(unordered_pair(X1,X1),X2) = singleton(X1)
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET927+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n016.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 02:39:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Theorem for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------