%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU198+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 4.92s 1.20s
% Output : CNFRefutation 4.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 77 ( 28 ~; 26 |; 15 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 50 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f112,lemma,
! [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/sandbox/benchmark/theBenchmark.p') ).
fof(f113,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
inference(negated_conjecture,[status(cth)],[f113]) ).
fof(f323,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f324,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)],[f323]) ).
fof(f325,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)],[f324]) ).
fof(f326,plain,
( ! [A,B] :
( ( ~ in(sK26_skl(B,A),B)
& in(sK26_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,[sK26_skl]),skolemize(C,sK26_skl(B,A))],[f325]) ).
fof(f328,plain,
! [X0,X1] :
( in(sK26_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f326]) ).
fof(f329,plain,
! [X0,X1] :
( ~ in(sK26_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f326]) ).
fof(f556,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)],[f112]) ).
fof(f557,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)],[f556]) ).
fof(f558,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)],[f557]) ).
fof(f559,plain,
! [X0,X1,X2] :
( in(X1,X2)
| ~ in(X1,relation_rng(relation_rng_restriction(X2,X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f558]) ).
fof(f562,plain,
? [A,B] :
( ~ subset(relation_rng(relation_rng_restriction(A,B)),A)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f114]) ).
fof(f563,plain,
? [B] :
( ? [A] : ~ subset(relation_rng(relation_rng_restriction(A,B)),A)
& relation(B) ),
inference(miniscoping,[status(thm)],[f562]) ).
fof(f564,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),sK54_skl)
& relation(sK53_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl,sK54_skl]),skolemize(B,sK53_skl),skolemize(A,sK54_skl)],[f563]) ).
fof(f565,plain,
relation(sK53_skl),
inference(cnf_transformation,[status(thm)],[f564]) ).
fof(f566,plain,
~ subset(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),sK54_skl),
inference(cnf_transformation,[status(thm)],[f564]) ).
fof(f977,plain,
! [X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,sK53_skl))) ),
inference(resolution,[status(thm)],[f559,f565]) ).
fof(f1226,plain,
! [X0,X1] :
( in(sK26_skl(X1,relation_rng(relation_rng_restriction(X0,sK53_skl))),X0)
| subset(relation_rng(relation_rng_restriction(X0,sK53_skl)),X1) ),
inference(resolution,[status(thm)],[f328,f977]) ).
fof(f1902,plain,
! [X0] :
( subset(relation_rng(relation_rng_restriction(X0,sK53_skl)),X0)
| subset(relation_rng(relation_rng_restriction(X0,sK53_skl)),X0) ),
inference(resolution,[status(thm)],[f1226,f329]) ).
fof(f1918,plain,
! [X0] : subset(relation_rng(relation_rng_restriction(X0,sK53_skl)),X0),
inference(duplicate_literals_removal,[status(thm)],[f1902]) ).
fof(f1919,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f566,f1918]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU198+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n026.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 05:59:37 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 4.92/1.20 % Refutation found
% 4.92/1.20 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.92/1.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.18/1.24 % Elapsed time: 0.793325 seconds
% 3.18/1.24 % CPU time: 5.837086 seconds
% 3.18/1.24 % Total memory used: 158.062 MB
% 3.18/1.24 % Net memory used: 150.503 MB
%------------------------------------------------------------------------------