%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU199+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 20.50s 13.01s
% Output : CNFRefutation 20.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 4 unt; 0 def)
% Number of atoms : 148 ( 9 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 193 ( 77 ~; 78 |; 24 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 98 ( 88 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
inference(negated_conjecture,[status(cth)],[f114]) ).
fof(f228,plain,
! [A,B] :
( ! [C] :
( ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f229,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ( ! [D,E] :
( ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f228]) ).
fof(f230,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f229]) ).
fof(f231,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( ( ( in(ordered_pair(sK4_skl(A,C,B),sK5_skl(A,C,B)),B)
& in(sK5_skl(A,C,B),A) )
| in(ordered_pair(sK4_skl(A,C,B),sK5_skl(A,C,B)),C) )
& ( ~ in(ordered_pair(sK4_skl(A,C,B),sK5_skl(A,C,B)),B)
| ~ in(sK5_skl(A,C,B),A)
| ~ in(ordered_pair(sK4_skl(A,C,B),sK5_skl(A,C,B)),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(D,sK4_skl(A,C,B)),skolemize(E,sK5_skl(A,C,B))],[f230]) ).
fof(f233,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X1)
| X1 != relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f318,plain,
! [A] :
( ! [B] :
( ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f319,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) )
| subset(A,B) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f318]) ).
fof(f320,plain,
! [A] :
( ! [B] :
( ( ( ( ~ in(ordered_pair(sK24_skl(B,A),sK25_skl(B,A)),B)
& in(ordered_pair(sK24_skl(B,A),sK25_skl(B,A)),A) )
| subset(A,B) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl]),skolemize(C,sK24_skl(B,A)),skolemize(D,sK25_skl(B,A))],[f319]) ).
fof(f322,plain,
! [X0,X1] :
( in(ordered_pair(sK24_skl(X1,X0),sK25_skl(X1,X0)),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f323,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK24_skl(X1,X0),sK25_skl(X1,X0)),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f434,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f61]) ).
fof(f435,plain,
! [B] :
( ! [A] : relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f434]) ).
fof(f436,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f566,plain,
? [A,B] :
( ~ subset(relation_rng_restriction(A,B),B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f115]) ).
fof(f567,plain,
? [B] :
( ? [A] : ~ subset(relation_rng_restriction(A,B),B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f566]) ).
fof(f568,plain,
( ~ subset(relation_rng_restriction(sK54_skl,sK53_skl),sK53_skl)
& relation(sK53_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl,sK54_skl]),skolemize(B,sK53_skl),skolemize(A,sK54_skl)],[f567]) ).
fof(f569,plain,
relation(sK53_skl),
inference(cnf_transformation,[status(thm)],[f568]) ).
fof(f570,plain,
~ subset(relation_rng_restriction(sK54_skl,sK53_skl),sK53_skl),
inference(cnf_transformation,[status(thm)],[f568]) ).
fof(f804,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f233]) ).
fof(f862,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X2),relation_rng_restriction(X3,X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f804,f436]) ).
fof(f4148,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK24_skl(X2,relation_rng_restriction(X0,X1)),sK25_skl(X2,relation_rng_restriction(X0,X1))),X1)
| ~ relation(X1)
| subset(relation_rng_restriction(X0,X1),X2)
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f322,f862]) ).
fof(f4166,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK24_skl(X0,relation_rng_restriction(X1,X2)),sK25_skl(X0,relation_rng_restriction(X1,X2))),X2)
| ~ relation(X2)
| subset(relation_rng_restriction(X1,X2),X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4148,f436]) ).
fof(f9685,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X1,X0),X0)
| ~ relation(X0)
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| subset(relation_rng_restriction(X1,X0),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f4166,f323]) ).
fof(f9714,plain,
! [X0,X1] :
( ~ relation(relation_rng_restriction(X1,X0))
| subset(relation_rng_restriction(X1,X0),X0)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f9685]) ).
fof(f9715,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X1,X0),X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f9714,f436]) ).
fof(f9730,plain,
~ relation(sK53_skl),
inference(resolution,[status(thm)],[f9715,f570]) ).
fof(f9799,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f9730,f569]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU199+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n026.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Mon Sep 21 06:00:05 UTC 2026
% 0.08/10.38 % CPUTime :
% 0.13/10.40 % Drodi V4.1.1
% 20.50/13.01 % Refutation found
% 20.50/13.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 20.50/13.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 20.50/13.07 % Elapsed time: 2.672675 seconds
% 20.50/13.07 % CPU time: 20.920004 seconds
% 20.50/13.07 % Total memory used: 276.895 MB
% 20.50/13.07 % Net memory used: 246.000 MB
%------------------------------------------------------------------------------