%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET602+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:10:12 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 38 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 38 ( 17 ~; 12 |; 7 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 24 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [B] : difference(B,B) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [B] : difference(B,B) = empty_set,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [B,C] :
( ( ~ subset(B,C)
| difference(B,C) = empty_set )
& ( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
( ! [B,C] :
( ~ subset(B,C)
| difference(B,C) = empty_set )
& ! [B,C] :
( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f20,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
( ! [B,C] :
( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f38,plain,
? [B] : difference(B,B) != empty_set,
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
difference(sK2_skl,sK2_skl) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(B,sK2_skl)],[f38]) ).
fof(f40,plain,
difference(sK2_skl,sK2_skl) != empty_set,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f22]) ).
fof(f44,plain,
! [X0] : difference(X0,X0) = empty_set,
inference(resolution,[status(thm)],[f41,f13]) ).
fof(f45,plain,
empty_set != empty_set,
inference(backward_demodulation,[status(thm)],[f44,f40]) ).
fof(f48,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET602+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:28:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.052694 seconds
% 0.13/0.42 % CPU time: 0.140782 seconds
% 0.13/0.42 % Total memory used: 37.471 MB
% 0.13/0.42 % Net memory used: 37.290 MB
%------------------------------------------------------------------------------