%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU198+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:19:38 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 6 unt; 2 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 91 ( 36 ~; 30 |; 15 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f37,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f39]) ).
fof(f42,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f77,plain,
! [A,B,C] :
( ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f78,plain,
! [A,B,C] :
( ( ( ~ in(A,relation_rng(C))
| ~ in(A,B)
| in(A,relation_rng(relation_rng_restriction(B,C))) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
! [C] :
( ( ! [A,B] :
( ~ in(A,relation_rng(C))
| ~ in(A,B)
| in(A,relation_rng(relation_rng_restriction(B,C))) )
& ! [A,B] :
( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( in(X1,X2)
| ~ in(X1,relation_rng(relation_rng_restriction(X2,X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f83,plain,
? [A,B] :
( ~ subset(relation_rng(relation_rng_restriction(A,B)),A)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f84,plain,
? [B] :
( ? [A] : ~ subset(relation_rng(relation_rng_restriction(A,B)),A)
& relation(B) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f85,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK9_skl,sK8_skl)),sK9_skl)
& relation(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(B,sK8_skl),skolemize(A,sK9_skl)],[f84]) ).
fof(f86,plain,
relation(sK8_skl),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
~ subset(relation_rng(relation_rng_restriction(sK9_skl,sK8_skl)),sK9_skl),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f130,plain,
~ in(sK0_skl(sK9_skl,relation_rng(relation_rng_restriction(sK9_skl,sK8_skl))),sK9_skl),
inference(resolution,[status(thm)],[f43,f87]) ).
fof(f131,plain,
! [X0] :
( ~ in(sK0_skl(sK9_skl,relation_rng(relation_rng_restriction(sK9_skl,sK8_skl))),relation_rng(relation_rng_restriction(sK9_skl,X0)))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f130,f80]) ).
fof(f135,plain,
( subset(relation_rng(relation_rng_restriction(sK9_skl,sK8_skl)),sK9_skl)
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f131,f42]) ).
fof(f138,definition,
( sQ4_spl
<=> relation(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ4_spl
| ~ relation(sK8_skl) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,definition,
( sQ5_spl
<=> subset(relation_rng(relation_rng_restriction(sK9_skl,sK8_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ5_spl
| subset(relation_rng(relation_rng_restriction(sK9_skl,sK8_skl)),sK9_skl) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f135,f138,f141]) ).
fof(f145,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f86]) ).
fof(f146,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f145]) ).
fof(f147,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f87]) ).
fof(f148,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f149,plain,
$false,
inference(sat_refutation,[status(thm)],[f144,f146,f148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU198+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n005.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:56:48 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.48 % Refutation found
% 0.17/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.52 % Elapsed time: 0.071983 seconds
% 0.17/0.52 % CPU time: 0.183908 seconds
% 0.17/0.52 % Total memory used: 68.237 MB
% 0.17/0.52 % Net memory used: 68.133 MB
%------------------------------------------------------------------------------