%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET002+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 : n010.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 02:08:46 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 31 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 30 ( 14 ~; 9 |; 5 &)
% ( 1 <=>; 1 =>; 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 : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 20 ( 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [B] : union(B,B) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [B] : union(B,B) = B,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [B,C] :
( union(B,C) = C
| ~ subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] :
( union(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f17,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f18,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)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f38,plain,
? [B] : union(B,B) != B,
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
union(sK2_skl,sK2_skl) != sK2_skl,
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(B,sK2_skl)],[f38]) ).
fof(f40,plain,
union(sK2_skl,sK2_skl) != sK2_skl,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f47,plain,
~ subset(sK2_skl,sK2_skl),
inference(resolution,[status(thm)],[f11,f40]) ).
fof(f62,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f47,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.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
% 0.09/0.36 % DateTime : Mon Sep 21 04:41:11 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
% 0.09/0.43 % Elapsed time: 0.055022 seconds
% 0.09/0.43 % CPU time: 0.151148 seconds
% 0.09/0.43 % Total memory used: 101.428 MB
% 0.09/0.43 % Net memory used: 100.963 MB
%------------------------------------------------------------------------------