%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET627+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 : Thu Sep 24 02:10:17 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 54 ( 25 ~; 17 |; 9 &)
% ( 2 <=>; 1 =>; 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 : 43 ( 39 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [B] : disjoint(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [B] : disjoint(B,empty_set),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,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)],[f2]) ).
fof(f10,plain,
( ! [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ! [B,C] :
( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f11,plain,
( ! [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ! [B,C] :
( ( member(sK0_skl(C,B),C)
& member(sK0_skl(C,B),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f15,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
( ! [B,C] :
( intersect(B,C)
| disjoint(B,C) )
& ! [B,C] :
( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [B,C] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
! [X0,X1] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f26,plain,
? [B] : ~ disjoint(B,empty_set),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f27,plain,
~ disjoint(sK2_skl,empty_set),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(B,sK2_skl)],[f26]) ).
fof(f28,plain,
~ disjoint(sK2_skl,empty_set),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
intersect(sK2_skl,empty_set),
inference(resolution,[status(thm)],[f18,f28]) ).
fof(f33,plain,
! [X0] : ~ intersect(empty_set,X0),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f34,plain,
! [X0] : ~ intersect(X0,empty_set),
inference(resolution,[status(thm)],[f33,f20]) ).
fof(f36,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f29,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET627+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n005.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Mon Sep 21 05:30:03 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.49 % Elapsed time: 0.053750 seconds
% 0.18/0.49 % CPU time: 0.128851 seconds
% 0.18/0.49 % Total memory used: 12.490 MB
% 0.18/0.49 % Net memory used: 12.092 MB
%------------------------------------------------------------------------------