%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU223+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 : n001.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 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 8 unt; 4 def)
% Number of atoms : 157 ( 34 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 187 ( 74 ~; 70 |; 28 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 63 ( 55 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f216,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f220,conjecture,
! [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(f221,negated_conjecture,
~ ! [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) ) ),
inference(negated_conjecture,[status(cth)],[f220]) ).
fof(f521,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f522,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f521]) ).
fof(f523,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f522]) ).
fof(f568,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(f569,plain,
! [A] :
( ( ! [B] : function(relation_dom_restriction(A,B))
& ! [B] : relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f568]) ).
fof(f571,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f569]) ).
fof(f942,plain,
! [A,B] :
( ! [C] :
( ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f216]) ).
fof(f943,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f942]) ).
fof(f944,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f943]) ).
fof(f945,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK78_skl(A,C,B)) != apply(C,sK78_skl(A,C,B))
& in(sK78_skl(A,C,B),relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78_skl]),skolemize(D,sK78_skl(A,C,B))],[f944]) ).
fof(f947,plain,
! [X0,X1,X2,X3] :
( apply(X0,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X0))
| X0 != relation_dom_restriction(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f945]) ).
fof(f955,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(f956,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)],[f955]) ).
fof(f957,plain,
( apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl) != apply(sK79_skl,sK81_skl)
& in(sK81_skl,relation_dom(relation_dom_restriction(sK79_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)],[f956]) ).
fof(f958,plain,
relation(sK79_skl),
inference(cnf_transformation,[status(thm)],[f957]) ).
fof(f959,plain,
function(sK79_skl),
inference(cnf_transformation,[status(thm)],[f957]) ).
fof(f960,plain,
in(sK81_skl,relation_dom(relation_dom_restriction(sK79_skl,sK80_skl))),
inference(cnf_transformation,[status(thm)],[f957]) ).
fof(f961,plain,
apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl) != apply(sK79_skl,sK81_skl),
inference(cnf_transformation,[status(thm)],[f957]) ).
fof(f1110,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X1),X2) = apply(X0,X2)
| ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f947]) ).
fof(f1118,definition,
( sQ0_spl
<=> relation(sK79_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1120,plain,
( sQ0_spl
| ~ relation(sK79_skl) ),
inference(component_clause,[status(thm)],[f1118]) ).
fof(f1125,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1120,f958]) ).
fof(f1126,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1125]) ).
fof(f1162,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X1),X2) = apply(X0,X2)
| ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1110,f523]) ).
fof(f1163,plain,
( ~ in(sK81_skl,relation_dom(relation_dom_restriction(sK79_skl,sK80_skl)))
| ~ function(sK79_skl)
| ~ relation(sK79_skl)
| ~ function(relation_dom_restriction(sK79_skl,sK80_skl)) ),
inference(resolution,[status(thm)],[f1162,f961]) ).
fof(f1164,definition,
( sQ3_spl
<=> function(relation_dom_restriction(sK79_skl,sK80_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1166,plain,
( sQ3_spl
| ~ function(relation_dom_restriction(sK79_skl,sK80_skl)) ),
inference(component_clause,[status(thm)],[f1164]) ).
fof(f1167,definition,
( sQ4_spl
<=> function(sK79_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1169,plain,
( sQ4_spl
| ~ function(sK79_skl) ),
inference(component_clause,[status(thm)],[f1167]) ).
fof(f1170,definition,
( sQ5_spl
<=> in(sK81_skl,relation_dom(relation_dom_restriction(sK79_skl,sK80_skl))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1172,plain,
( sQ5_spl
| ~ in(sK81_skl,relation_dom(relation_dom_restriction(sK79_skl,sK80_skl))) ),
inference(component_clause,[status(thm)],[f1170]) ).
fof(f1173,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1163,f1164,f1118,f1167,f1170]) ).
fof(f1174,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1172,f960]) ).
fof(f1175,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f1174]) ).
fof(f1227,plain,
( sQ3_spl
| ~ function(sK79_skl)
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1166,f571]) ).
fof(f1228,plain,
( sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1227,f1118,f1167,f1164]) ).
fof(f1229,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1169,f959]) ).
fof(f1230,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f1229]) ).
fof(f1231,plain,
$false,
inference(sat_refutation,[status(thm)],[f1126,f1173,f1175,f1228,f1230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU223+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n001.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 06:05:45 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.076901 seconds
% 0.12/0.44 % CPU time: 0.216159 seconds
% 0.12/0.44 % Total memory used: 122.712 MB
% 0.12/0.44 % Net memory used: 122.340 MB
%------------------------------------------------------------------------------