%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET639+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 02:43:41 PM UTC 2026
% Result : Theorem 8.37s 1.55s
% Output : Proof 8.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 21 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 5 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f5_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c11,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f9,conjecture,
! [B,C] :
( ( intersection(C,B) = empty_set
& subset(B,C) )
=> B = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th121) ).
fof(f9_neg,negated_conjecture,
~ ! [B,C] :
( ( intersection(C,B) = empty_set
& subset(B,C) )
=> B = empty_set ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_nnf,plain,
? [B,C] :
( B != empty_set
& intersection(C,B) = empty_set
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f9_neg]) ).
fof(f9_sk,plain,
( sk3 != empty_set
& intersection(sk4,sk3) = empty_set
& subset(sk3,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f9_nnf]) ).
cnf(c22,plain,
intersection(sk4,sk3) = empty_set,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p26,plain,
sk3 = empty_set,
inference(superposition,[status(thm)],[c11,c22]) ).
cnf(c23,plain,
sk3 != empty_set,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p29,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p26,c23]) ).
cnf(p33,plain,
$false,
inference(equality_resolution,[status(thm)],[p29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET639+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.02/0.36 % Computer : n018.cluster.edu
% 0.02/0.36 % Model : x86_64 x86_64
% 0.02/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.36 % Memory : 8046.5625MB
% 0.02/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Thu Sep 24 11:34:19 UTC 2026
% 0.02/0.37 % CPUTime :
% 0.02/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.37/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.37/1.55 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------