%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET987+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 : n007.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 02:44:25 PM UTC 2026
% Result : Theorem 3.86s 1.03s
% Output : Proof 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 29 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 5 |; 4 &)
% ( 1 <=>; 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 : 22 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f9_nnf,plain,
! [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) = A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) = A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c11,plain,
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f8,axiom,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f8_nnf,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f7,conjecture,
! [A,B] :
( ~ in(A,B)
=> set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B] :
( set_difference(set_union2(B,singleton(A)),singleton(A)) != B
& ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( set_difference(set_union2(sk3,singleton(sk2)),singleton(sk2)) != sk3
& ~ in(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f7_nnf]) ).
cnf(c8,plain,
set_difference(set_union2(sk3,singleton(sk2)),singleton(sk2)) != sk3,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p13,plain,
set_difference(sk3,singleton(sk2)) != sk3,
inference(superposition,[status(thm)],[c9,c8]) ).
cnf(p20,plain,
in(sk2,sk3),
inference(resolution,[status(thm)],[c11,p13]) ).
cnf(c7,plain,
~ in(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p23,plain,
$false,
inference(resolution,[status(thm)],[p20,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET987+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.44 % Computer : n007.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Thu Sep 24 12:29:09 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.86/1.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.86/1.03 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------