%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET877+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:44:12 PM UTC 2026
% Result : Theorem 16.03s 2.66s
% Output : Proof 16.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 55 ( 37 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 53 ( 21 ~; 17 |; 10 &)
% ( 2 <=>; 3 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 25 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f4,axiom,
! [A,B] :
( set_intersection2(A,singleton(B)) = singleton(B)
=> in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_zfmisc_1) ).
fof(f4_nnf,plain,
! [A,B] :
( in(B,A)
| set_intersection2(A,singleton(B)) != singleton(B) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( in(B,A)
| set_intersection2(A,singleton(B)) != singleton(B) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c9,plain,
( in(X1,X0)
| set_intersection2(X0,singleton(X1)) != singleton(X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p17,plain,
( in(X0,X1)
| set_intersection2(singleton(X0),X1) != singleton(X0) ),
inference(superposition,[status(thm)],[c1,c9]) ).
fof(f7,conjecture,
! [A,B] :
( set_intersection2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B] :
( set_intersection2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B] :
( A != B
& set_intersection2(singleton(A),singleton(B)) = singleton(A) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( sk3 != sk4
& set_intersection2(singleton(sk3),singleton(sk4)) = singleton(sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f7_nnf]) ).
cnf(c12,plain,
set_intersection2(singleton(sk3),singleton(sk4)) = singleton(sk3),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p24,plain,
in(sk3,singleton(sk4)),
inference(resolution,[status(thm)],[p17,c12]) ).
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
& ~ in(C,B) )
| ( C != A
& in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,A,C] :
( ( ( sk0(A,B) = A
& ~ in(sk0(A,B),B) )
| ( sk0(A,B) != A
& in(sk0(A,B),B) )
| B = singleton(A) )
& ( ( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c2,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p18,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p26,plain,
sk3 = sk4,
inference(resolution,[status(thm)],[p24,p18]) ).
cnf(c13,plain,
sk3 != sk4,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p27,plain,
$false,
inference(resolution,[status(thm)],[p26,c13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET877+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:21:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.03/2.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.03/2.66 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------