%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET199+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 : n002.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 02:42:51 PM UTC 2026
% Result : Theorem 5.06s 1.19s
% Output : Proof 5.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 24 ~; 28 |; 15 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f1_nnf,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( ( ( ~ member(sk0(B,C),C)
& member(sk0(B,C),B) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ subset(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f5,conjecture,
! [B,C,D] :
( ( subset(B,D)
& subset(B,C) )
=> subset(B,intersection(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_of_subsets) ).
fof(f5_neg,negated_conjecture,
~ ! [B,C,D] :
( ( subset(B,D)
& subset(B,C) )
=> subset(B,intersection(C,D)) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [B,C,D] :
( ~ subset(B,intersection(C,D))
& subset(B,D)
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( ~ subset(sk2,intersection(sk3,sk4))
& subset(sk2,sk4)
& subset(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f5_nnf]) ).
cnf(c14,plain,
subset(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p22,plain,
( member(X0,sk3)
| ~ member(X0,sk2) ),
inference(resolution,[status(thm)],[c3,c14]) ).
cnf(c4,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p24,plain,
( subset(sk2,X0)
| member(sk0(sk2,X0),sk3) ),
inference(resolution,[status(thm)],[p22,c4]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f0_nnf,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [D,B,C] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c2,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p27,plain,
( ~ member(sk0(sk2,X0),X1)
| member(sk0(sk2,X0),intersection(sk3,X1))
| subset(sk2,X0) ),
inference(resolution,[status(thm)],[p24,c2]) ).
cnf(c15,plain,
subset(sk2,sk4),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p23,plain,
( member(X0,sk4)
| ~ member(X0,sk2) ),
inference(resolution,[status(thm)],[c3,c15]) ).
cnf(p25,plain,
( subset(sk2,X0)
| member(sk0(sk2,X0),sk4) ),
inference(resolution,[status(thm)],[p23,c4]) ).
cnf(p206,plain,
( subset(sk2,X0)
| member(sk0(sk2,X0),intersection(sk3,sk4))
| subset(sk2,X0) ),
inference(resolution,[status(thm)],[p27,p25]) ).
cnf(p311,plain,
( member(sk0(sk2,X0),intersection(sk3,sk4))
| subset(sk2,X0) ),
inference(factoring,[status(thm)],[p206]) ).
cnf(c5,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p312,plain,
( subset(sk2,intersection(sk3,sk4))
| subset(sk2,intersection(sk3,sk4)) ),
inference(resolution,[status(thm)],[p311,c5]) ).
cnf(p321,plain,
subset(sk2,intersection(sk3,sk4)),
inference(factoring,[status(thm)],[p312]) ).
cnf(c16,plain,
~ subset(sk2,intersection(sk3,sk4)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p323,plain,
$false,
inference(resolution,[status(thm)],[p321,c16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET199+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 10:16:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.06/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.06/1.19 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------