%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET627+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 02:43:39 PM UTC 2026
% Result : Theorem 2.84s 1.33s
% Output : Proof 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 41 ( 20 ~; 12 |; 7 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 1 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f1_nnf,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| intersect(B,C) )
& ( ( member(sk0(B,C),C)
& member(sk0(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c2,plain,
( member(sk0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f2,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f2_nnf,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c5,plain,
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f5,conjecture,
! [B] : disjoint(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th104) ).
fof(f5_neg,negated_conjecture,
~ ! [B] : disjoint(B,empty_set),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [B] : ~ disjoint(B,empty_set),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
~ disjoint(sk2,empty_set),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f5_nnf]) ).
cnf(c9,plain,
~ disjoint(sk2,empty_set),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p10,plain,
intersect(sk2,empty_set),
inference(resolution,[status(thm)],[c5,c9]) ).
cnf(p13,plain,
member(sk0(sk2,empty_set),empty_set),
inference(resolution,[status(thm)],[c2,p10]) ).
fof(f0,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/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(p16,plain,
$false,
inference(resolution,[status(thm)],[p13,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET627+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.57 % Computer : n006.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Thu Sep 24 11:29:58 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.84/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.84/1.33 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------