%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET027+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 : n001.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 02:41:36 PM UTC 2026
% Result : Theorem 2.28s 0.77s
% Output : Proof 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 44 ( 15 ~; 15 |; 10 &)
% ( 1 <=>; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 15 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,conjecture,
! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).
fof(f2_neg,negated_conjecture,
~ ! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
? [B,C,D] :
( ~ subset(B,D)
& subset(C,D)
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
( ~ subset(sk1,sk3)
& subset(sk2,sk3)
& subset(sk1,sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f2_nnf]) ).
cnf(c4,plain,
subset(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f0,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f0_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)],[f0]) ).
fof(f0_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])],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p7,plain,
( member(X0,sk2)
| ~ member(X0,sk1) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p9,plain,
( subset(sk1,X0)
| member(sk0(sk1,X0),sk2) ),
inference(resolution,[status(thm)],[p7,c1]) ).
cnf(c5,plain,
subset(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p8,plain,
( member(X0,sk3)
| ~ member(X0,sk2) ),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(p11,plain,
( member(sk0(sk1,X0),sk3)
| subset(sk1,X0) ),
inference(resolution,[status(thm)],[p9,p8]) ).
cnf(c2,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p12,plain,
( subset(sk1,sk3)
| subset(sk1,sk3) ),
inference(resolution,[status(thm)],[p11,c2]) ).
cnf(p13,plain,
subset(sk1,sk3),
inference(factoring,[status(thm)],[p12]) ).
cnf(c6,plain,
~ subset(sk1,sk3),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p15,plain,
$false,
inference(resolution,[status(thm)],[p13,c6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET027+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 09:22:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.28/0.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.28/0.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------