%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET592+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 : 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 02:43:32 PM UTC 2026
% Result : Theorem 25.07s 4.09s
% Output : Proof 25.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 45 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 15 ~; 10 |; 11 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( ( subset(B,D)
& subset(B,C) )
=> subset(B,intersection(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subsets) ).
fof(f1_nnf,plain,
! [B,C,D] :
( subset(B,intersection(C,D))
| ~ subset(B,D)
| ~ subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( subset(B,intersection(C,D))
| ~ subset(B,D)
| ~ subset(B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( subset(X0,intersection(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f10,conjecture,
! [B,C,D] :
( ( intersection(C,D) = empty_set
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th51) ).
fof(f10_neg,negated_conjecture,
~ ! [B,C,D] :
( ( intersection(C,D) = empty_set
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [B,C,D] :
( B != empty_set
& intersection(C,D) = empty_set
& subset(B,D)
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( sk3 != empty_set
& intersection(sk4,sk5) = empty_set
& subset(sk3,sk5)
& subset(sk3,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f10_nnf]) ).
cnf(c22,plain,
subset(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p27,plain,
( subset(sk3,intersection(sk4,X0))
| ~ subset(sk3,X0) ),
inference(resolution,[status(thm)],[c1,c22]) ).
cnf(c23,plain,
subset(sk3,sk5),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p31,plain,
subset(sk3,empty_set),
inference(resolution,[status(thm)],[p27,c23]) ).
fof(f0,axiom,
! [B] :
( subset(B,empty_set)
=> B = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_empty_set_is_empty_set) ).
fof(f0_nnf,plain,
! [B] :
( B = empty_set
| ~ subset(B,empty_set) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B] :
( B = empty_set
| ~ subset(B,empty_set) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p33,plain,
sk3 = empty_set,
inference(resolution,[status(thm)],[p31,c0]) ).
cnf(c25,plain,
sk3 != empty_set,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p36,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p33,c25]) ).
cnf(p41,plain,
$false,
inference(equality_resolution,[status(thm)],[p36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET592+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 11:27:27 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.07/4.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.07/4.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------