%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU225+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 : n006.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 02:19:46 PM UTC 2026
% Result : Theorem 0.07s 0.40s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 11 unt; 0 def)
% Number of atoms : 179 ( 37 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 216 ( 88 ~; 79 |; 31 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 82 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f91,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f221,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f223,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f224,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f223]) ).
fof(f229,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f414,plain,
! [A] :
( ! [B,C] :
( ( ( C = apply(A,B)
<=> C = empty_set )
| in(B,relation_dom(A)) )
& ( ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f415,plain,
! [A] :
( ! [B,C] :
( ( ( ( C != empty_set
| C = apply(A,B) )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f414]) ).
fof(f416,plain,
! [A] :
( ( ! [B] :
( ( ! [C] :
( C != empty_set
| C = apply(A,B) )
& ! [C] :
( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ! [B] :
( ( ! [C] :
( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ! [C] :
( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f419,plain,
! [X0,X1,X2] :
( X2 = empty_set
| X2 != apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f523,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f524,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f523]) ).
fof(f525,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f524]) ).
fof(f570,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f571,plain,
! [A] :
( ( ! [B] : function(relation_dom_restriction(A,B))
& ! [B] : relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f570]) ).
fof(f573,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f571]) ).
fof(f963,plain,
! [A,B,C] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,relation_dom(relation_dom_restriction(C,A)))
| ~ function(C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f221]) ).
fof(f964,plain,
! [C] :
( ! [A,B] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) )
| ~ function(C)
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f963]) ).
fof(f965,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X2),X1) = apply(X0,X1)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f964]) ).
fof(f969,plain,
? [A,B,C] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,A)
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f224]) ).
fof(f970,plain,
? [C] :
( ? [A,B] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,A) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f969]) ).
fof(f971,plain,
( apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl) != apply(sK79_skl,sK81_skl)
& in(sK81_skl,sK80_skl)
& function(sK79_skl)
& relation(sK79_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79_skl,sK80_skl,sK81_skl]),skolemize(C,sK79_skl),skolemize(A,sK80_skl),skolemize(B,sK81_skl)],[f970]) ).
fof(f972,plain,
relation(sK79_skl),
inference(cnf_transformation,[status(thm)],[f971]) ).
fof(f973,plain,
function(sK79_skl),
inference(cnf_transformation,[status(thm)],[f971]) ).
fof(f974,plain,
in(sK81_skl,sK80_skl),
inference(cnf_transformation,[status(thm)],[f971]) ).
fof(f975,plain,
apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl) != apply(sK79_skl,sK81_skl),
inference(cnf_transformation,[status(thm)],[f971]) ).
fof(f990,plain,
! [A,B,C] :
( ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f229]) ).
fof(f991,plain,
! [A,B,C] :
( ( ( ~ in(A,relation_dom(C))
| ~ in(A,B)
| in(A,relation_dom(relation_dom_restriction(C,B))) )
& ( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f990]) ).
fof(f992,plain,
! [C] :
( ( ! [A,B] :
( ~ in(A,relation_dom(C))
| ~ in(A,B)
| in(A,relation_dom(relation_dom_restriction(C,B))) )
& ! [A,B] :
( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f991]) ).
fof(f994,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(X0))
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f992]) ).
fof(f995,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(X0))
| ~ in(X1,X2)
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f992]) ).
fof(f1088,plain,
! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f419]) ).
fof(f1139,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X2),X1) = empty_set
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(relation_dom_restriction(X0,X2))
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f994,f1088]) ).
fof(f1140,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X2),X1) = empty_set
| ~ function(relation_dom_restriction(X0,X2))
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1139,f525]) ).
fof(f1179,plain,
( ~ in(sK81_skl,relation_dom(relation_dom_restriction(sK79_skl,sK80_skl)))
| ~ function(sK79_skl)
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f965,f975]) ).
fof(f1180,plain,
( ~ in(sK81_skl,relation_dom(relation_dom_restriction(sK79_skl,sK80_skl)))
| ~ function(sK79_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1179,f972]) ).
fof(f1191,plain,
~ in(sK81_skl,relation_dom(relation_dom_restriction(sK79_skl,sK80_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f1180,f973]) ).
fof(f1192,plain,
( ~ in(sK81_skl,relation_dom(sK79_skl))
| ~ in(sK81_skl,sK80_skl)
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1191,f995]) ).
fof(f1194,plain,
( ~ in(sK81_skl,relation_dom(sK79_skl))
| ~ in(sK81_skl,sK80_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1192,f972]) ).
fof(f1195,plain,
~ in(sK81_skl,relation_dom(sK79_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f1194,f974]) ).
fof(f1196,plain,
( apply(sK79_skl,sK81_skl) = empty_set
| ~ function(sK79_skl)
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1195,f1088]) ).
fof(f1197,plain,
( apply(sK79_skl,sK81_skl) = empty_set
| ~ function(sK79_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1196,f972]) ).
fof(f1198,plain,
apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl) != empty_set,
inference(backward_demodulation,[status(thm)],[f1199,f975]) ).
fof(f1199,plain,
apply(sK79_skl,sK81_skl) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[f1197,f973]) ).
fof(f1202,plain,
( ~ function(relation_dom_restriction(sK79_skl,sK80_skl))
| in(sK81_skl,relation_dom(sK79_skl))
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1198,f1140]) ).
fof(f1205,plain,
( ~ function(relation_dom_restriction(sK79_skl,sK80_skl))
| in(sK81_skl,relation_dom(sK79_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1202,f972]) ).
fof(f1207,plain,
~ function(relation_dom_restriction(sK79_skl,sK80_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f1205,f1195]) ).
fof(f1208,plain,
( ~ function(sK79_skl)
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1207,f573]) ).
fof(f1209,plain,
~ function(sK79_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1208,f972]) ).
fof(f1210,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1209,f973]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU225+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n006.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Mon Sep 21 06:00:27 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.07/0.40 % Refutation found
% 0.07/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.47 % Elapsed time: 0.123944 seconds
% 0.14/0.47 % CPU time: 0.241367 seconds
% 0.14/0.47 % Total memory used: 39.843 MB
% 0.14/0.47 % Net memory used: 39.555 MB
%------------------------------------------------------------------------------