%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU354+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:51:49 PM UTC 2026
% Result : Theorem 57.47s 7.81s
% Output : Proof 57.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 54 ( 22 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 59 ( 26 ~; 19 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f101,axiom,
! [A,B] :
( element(B,A)
=> ( proper_element(B,A)
<=> B != union(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
fof(f101_nnf,plain,
! [A,B] :
( ( ( B = union(A)
| proper_element(B,A) )
& ( B != union(A)
| ~ proper_element(B,A) ) )
| ~ element(B,A) ),
inference(nnf_transformation,[status(thm)],[f101]) ).
fof(f101_sk,plain,
! [B,A] :
( ( ( B = union(A)
| proper_element(B,A) )
& ( B != union(A)
| ~ proper_element(B,A) ) )
| ~ element(B,A) ),
inference(skolemisation,[status(esa)],[f101_nnf]) ).
cnf(c378,plain,
( X1 = union(X0)
| proper_element(X1,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
fof(f626,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
fof(f626_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
inference(negated_conjecture,[status(cth)],[f626]) ).
fof(f626_nnf,plain,
? [A,B] :
( ( ( B != A
& ~ proper_element(B,powerset(A)) )
| ( B = A
& proper_element(B,powerset(A)) ) )
& element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f626_neg]) ).
fof(f626_sk,plain,
( ( ( sk447 != sk446
& ~ proper_element(sk447,powerset(sk446)) )
| ( sk447 = sk446
& proper_element(sk447,powerset(sk446)) ) )
& element(sk447,powerset(sk446)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk446,sk447])],[f626_nnf]) ).
cnf(c3049,plain,
element(sk447,powerset(sk446)),
inference(cnf_transformation,[status(esa)],[f626_sk]) ).
cnf(p2418,plain,
( sk447 = sk446
| proper_element(sk447,powerset(sk446)) ),
inference(resolution,[status(thm)],[c378,c3049]) ).
cnf(c3052,plain,
( ~ proper_element(sk447,powerset(sk446))
| sk447 = sk446 ),
inference(cnf_transformation,[status(esa)],[f626_sk]) ).
cnf(p2421,plain,
( sk447 = sk446
| sk447 = sk446 ),
inference(resolution,[status(thm)],[p2418,c3052]) ).
cnf(p2422,plain,
sk447 = sk446,
inference(factoring,[status(thm)],[p2421]) ).
cnf(c377,plain,
( X1 != union(X0)
| ~ proper_element(X1,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
cnf(p2406,plain,
( sk447 != sk446
| ~ proper_element(sk447,powerset(sk446)) ),
inference(resolution,[status(thm)],[c377,c3049]) ).
cnf(p2427,plain,
( sk446 != sk446
| ~ proper_element(sk446,powerset(sk446)) ),
inference(demodulation,[status(thm)],[p2422,p2406]) ).
cnf(p2431,plain,
~ proper_element(sk446,powerset(sk446)),
inference(equality_resolution,[status(thm)],[p2427]) ).
cnf(c3051,plain,
( sk447 != sk446
| proper_element(sk447,powerset(sk446)) ),
inference(cnf_transformation,[status(esa)],[f626_sk]) ).
cnf(p2424,plain,
( sk446 != sk446
| proper_element(sk446,powerset(sk446)) ),
inference(demodulation,[status(thm)],[p2422,c3051]) ).
cnf(p2428,plain,
proper_element(sk446,powerset(sk446)),
inference(equality_resolution,[status(thm)],[p2424]) ).
cnf(p2432,plain,
$false,
inference(resolution,[status(thm)],[p2431,p2428]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU354+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.43 % Computer : n002.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Thu Sep 24 13:51:50 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 57.47/7.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 57.47/7.81 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------