%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET027+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 31.65s 4.50s
% Output : Proof 31.65s
% 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(f0,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f0_nnf,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,X] :
( ( ( ~ member(sk0(A,B),B)
& member(sk0(A,B),A) )
| subset(A,B) )
& ( member(X,B)
| ~ member(X,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f11,conjecture,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI03) ).
fof(f11_neg,negated_conjecture,
~ ! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [A,B,C] :
( ~ subset(A,C)
& subset(B,C)
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( ~ subset(sk3,sk5)
& subset(sk4,sk5)
& subset(sk3,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f11_nnf]) ).
cnf(c29,plain,
subset(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p32,plain,
( member(X0,sk4)
| ~ member(X0,sk3) ),
inference(resolution,[status(thm)],[c0,c29]) ).
cnf(p35,plain,
( member(sk0(sk3,X0),sk4)
| subset(sk3,X0) ),
inference(resolution,[status(thm)],[c1,p32]) ).
cnf(c30,plain,
subset(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p33,plain,
( member(X0,sk5)
| ~ member(X0,sk4) ),
inference(resolution,[status(thm)],[c0,c30]) ).
cnf(p234,plain,
( member(sk0(sk3,X0),sk5)
| subset(sk3,X0) ),
inference(resolution,[status(thm)],[p35,p33]) ).
cnf(c2,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p2223,plain,
( subset(sk3,sk5)
| subset(sk3,sk5) ),
inference(resolution,[status(thm)],[p234,c2]) ).
cnf(p2252,plain,
subset(sk3,sk5),
inference(factoring,[status(thm)],[p2223]) ).
cnf(c31,plain,
~ subset(sk3,sk5),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p2253,plain,
$false,
inference(resolution,[status(thm)],[p2252,c31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET027+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 09:17:19 UTC 2026
% 0.02/0.37 % CPUTime :
% 0.02/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 31.65/4.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.65/4.50 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------