%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU120+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 02:50:59 PM UTC 2026
% Result : Theorem 3.59s 1.08s
% Output : Proof 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 6 unt; 0 def)
% Number of atoms : 58 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 63 ( 29 ~; 18 |; 14 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 3 sgn 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f4_nnf,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c14,plain,
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f2,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f2_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ( in(sk0(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c3,plain,
( in(sk0(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f13,conjecture,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f13_neg,negated_conjecture,
~ ! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [A,B] :
( ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
| ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
! [C] :
( ( disjoint(sk5,sk6)
& in(sk7,set_intersection2(sk5,sk6)) )
| ( ~ in(C,set_intersection2(sk5,sk6))
& ~ disjoint(sk5,sk6) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6,sk7])],[f13_nnf]) ).
cnf(c28,plain,
( disjoint(sk5,sk6)
| ~ in(X2,set_intersection2(sk5,sk6)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p31,plain,
( disjoint(sk5,sk6)
| set_intersection2(sk5,sk6) = empty_set ),
inference(resolution,[status(thm)],[c3,c28]) ).
cnf(p42,plain,
( disjoint(sk5,sk6)
| disjoint(sk5,sk6) ),
inference(resolution,[status(thm)],[c14,p31]) ).
cnf(p43,plain,
disjoint(sk5,sk6),
inference(factoring,[status(thm)],[p42]) ).
cnf(c13,plain,
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p46,plain,
set_intersection2(sk5,sk6) = empty_set,
inference(resolution,[status(thm)],[p43,c13]) ).
cnf(c25,plain,
( in(sk7,set_intersection2(sk5,sk6))
| ~ disjoint(sk5,sk6) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p44,plain,
in(sk7,set_intersection2(sk5,sk6)),
inference(resolution,[status(thm)],[p43,c25]) ).
cnf(p47,plain,
in(sk7,empty_set),
inference(demodulation,[status(thm)],[p46,p44]) ).
cnf(c2,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p30,plain,
~ in(X0,empty_set),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p51,plain,
$false,
inference(resolution,[status(thm)],[p47,p30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU120+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:53:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.59/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.59/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------