%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET899+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 02:10:55 PM UTC 2026
% Result : Theorem 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 6 unt; 2 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 44 ( 18 ~; 15 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,plain,
? [A,B,C] :
( ~ subset(A,set_difference(B,singleton(C)))
& ~ in(C,A)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
? [A,B] :
( ? [C] :
( ~ subset(A,set_difference(B,singleton(C)))
& ~ in(C,A) )
& subset(A,B) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
( ~ subset(sK2_skl,set_difference(sK3_skl,singleton(sK4_skl)))
& ~ in(sK4_skl,sK2_skl)
& subset(sK2_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f17]) ).
fof(f19,plain,
subset(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
~ in(sK4_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
~ subset(sK2_skl,set_difference(sK3_skl,singleton(sK4_skl))),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,plain,
! [A,B,C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [A,B] :
( ! [C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A) )
| ~ subset(A,B) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
( in(sK4_skl,sK2_skl)
| ~ subset(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f24,f21]) ).
fof(f26,definition,
( sQ0_spl
<=> subset(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f28,plain,
( sQ0_spl
| ~ subset(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f29,definition,
( sQ1_spl
<=> in(sK4_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f30,plain,
( ~ sQ1_spl
| in(sK4_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f25,f26,f29]) ).
fof(f33,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f28,f19]) ).
fof(f34,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f33]) ).
fof(f35,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f20]) ).
fof(f36,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f35]) ).
fof(f37,plain,
$false,
inference(sat_refutation,[status(thm)],[f32,f34,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET899+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:38:43 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.032292 seconds
% 0.14/0.40 % CPU time: 0.042959 seconds
% 0.14/0.40 % Total memory used: 2.592 MB
% 0.14/0.40 % Net memory used: 2.512 MB
%------------------------------------------------------------------------------