%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET062+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 02:41:51 PM UTC 2026
% Result : Theorem 1.20s 0.90s
% Output : Proof 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 27 ( 14 ~; 7 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 2 sgn 14 !; 2 ?)
% 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(c2,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f0,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f0_nnf,plain,
! [B] : ~ member(B,empty_set),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B] : ~ member(B,empty_set),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p8,plain,
subset(empty_set,X0),
inference(resolution,[status(thm)],[c2,c0]) ).
fof(f4,conjecture,
! [B] : subset(empty_set,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_empty_set_subset) ).
fof(f4_neg,negated_conjecture,
~ ! [B] : subset(empty_set,B),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [B] : ~ subset(empty_set,B),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
~ subset(empty_set,sk2),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f4_nnf]) ).
cnf(c7,plain,
~ subset(empty_set,sk2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p10,plain,
$false,
inference(resolution,[status(thm)],[p8,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET062+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n001.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 09:35:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.20/0.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.20/0.90 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------