%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU225+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:19:47 PM UTC 2026
% Result : Theorem 0.03s 0.33s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 81 ( 10 unt; 11 def)
% Number of atoms : 304 ( 71 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 371 ( 148 ~; 147 |; 44 &)
% ( 19 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 102 ( 94 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,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(f9,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,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(f24,axiom,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [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(f44,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(f45,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)],[f44]) ).
fof(f60,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)],[f7]) ).
fof(f61,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)],[f60]) ).
fof(f62,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)],[f61]) ).
fof(f66,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)],[f62]) ).
fof(f68,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f69,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f87,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)],[f19]) ).
fof(f88,plain,
! [A] :
( ( ! [B] : function(relation_dom_restriction(A,B))
& ! [B] : relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f87]) ).
fof(f90,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f100,plain,
! [A,B,C] :
( ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) )
| ~ function(C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f101,plain,
! [A,B,C] :
( ( ( ~ in(B,A)
| ~ in(B,relation_dom(C))
| in(B,relation_dom(relation_dom_restriction(C,A))) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) ) )
| ~ function(C)
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
! [C] :
( ( ! [A,B] :
( ~ in(B,A)
| ~ in(B,relation_dom(C))
| in(B,relation_dom(relation_dom_restriction(C,A))) )
& ! [A,B] :
( ( in(B,A)
& in(B,relation_dom(C)) )
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) ) )
| ~ function(C)
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,relation_dom(X0))
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f154,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)],[f42]) ).
fof(f155,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)],[f154]) ).
fof(f156,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)],[f155]) ).
fof(f157,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK11_skl(A,C,B)) != apply(C,sK11_skl(A,C,B))
& in(sK11_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,[sK11_skl]),skolemize(D,sK11_skl(A,C,B))],[f156]) ).
fof(f159,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)],[f157]) ).
fof(f164,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)],[f45]) ).
fof(f165,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)],[f164]) ).
fof(f166,plain,
( apply(relation_dom_restriction(sK12_skl,sK13_skl),sK14_skl) != apply(sK12_skl,sK14_skl)
& in(sK14_skl,sK13_skl)
& function(sK12_skl)
& relation(sK12_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(C,sK12_skl),skolemize(A,sK13_skl),skolemize(B,sK14_skl)],[f165]) ).
fof(f167,plain,
relation(sK12_skl),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f168,plain,
function(sK12_skl),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f169,plain,
in(sK14_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f170,plain,
apply(relation_dom_restriction(sK12_skl,sK13_skl),sK14_skl) != apply(sK12_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f239,definition,
( sQ3_spl
<=> relation(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ3_spl
| ~ relation(sK12_skl) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,definition,
( sQ4_spl
<=> function(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( sQ4_spl
| ~ function(sK12_skl) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f252,definition,
( sQ7_spl
<=> relation(relation_dom_restriction(sK12_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( sQ7_spl
| ~ relation(relation_dom_restriction(sK12_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ8_spl
<=> function(relation_dom_restriction(sK12_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ8_spl
| ~ function(relation_dom_restriction(sK12_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f263,definition,
( sQ10_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( sQ10_spl
| empty_set != empty_set ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f267,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f244,f168]) ).
fof(f268,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f267]) ).
fof(f269,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f241,f167]) ).
fof(f270,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f269]) ).
fof(f271,plain,
( sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f265]) ).
fof(f272,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f271]) ).
fof(f273,plain,
! [X0] :
( ~ in(sK14_skl,relation_dom(relation_dom_restriction(sK12_skl,sK13_skl)))
| relation_dom_restriction(sK12_skl,sK13_skl) != relation_dom_restriction(sK12_skl,X0)
| ~ function(sK12_skl)
| ~ relation(sK12_skl)
| ~ function(relation_dom_restriction(sK12_skl,sK13_skl))
| ~ relation(relation_dom_restriction(sK12_skl,sK13_skl)) ),
inference(resolution,[status(thm)],[f159,f170]) ).
fof(f275,definition,
! [X0] :
( sQ11_spl
<=> relation_dom_restriction(sK12_skl,sK13_skl) != relation_dom_restriction(sK12_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f276,plain,
! [X0] :
( ~ sQ11_spl
| relation_dom_restriction(sK12_skl,sK13_skl) != relation_dom_restriction(sK12_skl,X0) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,definition,
( sQ12_spl
<=> in(sK14_skl,relation_dom(relation_dom_restriction(sK12_skl,sK13_skl))) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ12_spl
| ~ in(sK14_skl,relation_dom(relation_dom_restriction(sK12_skl,sK13_skl))) ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,plain,
( ~ sQ12_spl
| sQ11_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f273,f252,f255,f239,f242,f275,f278]) ).
fof(f285,definition,
( sQ14_spl
<=> in(sK14_skl,relation_dom(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ14_spl
| ~ in(sK14_skl,relation_dom(sK12_skl)) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f294,plain,
( sQ8_spl
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f257,f90]) ).
fof(f296,plain,
( sQ8_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f294,f239,f242,f255]) ).
fof(f297,plain,
( sQ7_spl
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f254,f70]) ).
fof(f299,plain,
( sQ7_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f297,f239,f252]) ).
fof(f307,plain,
( ~ sQ11_spl
| $false ),
inference(equality_resolution,[status(thm)],[f276]) ).
fof(f308,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f343,plain,
( sQ12_spl
| ~ in(sK14_skl,sK13_skl)
| ~ in(sK14_skl,relation_dom(sK12_skl))
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f280,f105]) ).
fof(f344,plain,
! [X0] :
( sQ12_spl
| X0 != empty_set
| X0 = apply(relation_dom_restriction(sK12_skl,sK13_skl),sK14_skl)
| ~ function(relation_dom_restriction(sK12_skl,sK13_skl))
| ~ relation(relation_dom_restriction(sK12_skl,sK13_skl)) ),
inference(resolution,[status(thm)],[f280,f66]) ).
fof(f346,definition,
( sQ21_spl
<=> in(sK14_skl,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( sQ21_spl
| ~ in(sK14_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f349,plain,
( sQ12_spl
| ~ sQ21_spl
| ~ sQ14_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f343,f239,f242,f285,f346,f278]) ).
fof(f350,definition,
! [X0] :
( sQ22_spl
<=> ( X0 != empty_set
| X0 = apply(relation_dom_restriction(sK12_skl,sK13_skl),sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f351,plain,
! [X0] :
( ~ sQ22_spl
| X0 != empty_set
| X0 = apply(relation_dom_restriction(sK12_skl,sK13_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,plain,
( sQ12_spl
| sQ22_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f344,f252,f255,f350,f278]) ).
fof(f358,plain,
! [X0] :
( sQ14_spl
| X0 != empty_set
| X0 = apply(sK12_skl,sK14_skl)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f287,f66]) ).
fof(f360,definition,
! [X0] :
( sQ24_spl
<=> ( X0 != empty_set
| X0 = apply(sK12_skl,sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f361,plain,
! [X0] :
( ~ sQ24_spl
| X0 != empty_set
| X0 = apply(sK12_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,plain,
( sQ14_spl
| sQ24_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f358,f239,f242,f360,f285]) ).
fof(f368,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f348,f169]) ).
fof(f369,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f368]) ).
fof(f411,plain,
( ~ sQ22_spl
| apply(sK12_skl,sK14_skl) != empty_set ),
inference(resolution,[status(thm)],[f351,f170]) ).
fof(f417,plain,
( ~ sQ24_spl
| ~ sQ22_spl
| empty_set != empty_set ),
inference(resolution,[status(thm)],[f411,f361]) ).
fof(f419,plain,
( ~ sQ24_spl
| ~ sQ22_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f417,f263,f350,f360]) ).
fof(f421,plain,
$false,
inference(sat_refutation,[status(thm)],[f268,f270,f272,f281,f296,f299,f308,f349,f353,f363,f369,f419]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU225+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 06:00:21 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.03/0.33 % Refutation found
% 0.03/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.37 % Elapsed time: 0.067399 seconds
% 0.03/0.37 % CPU time: 0.173732 seconds
% 0.03/0.37 % Total memory used: 35.198 MB
% 0.03/0.37 % Net memory used: 34.879 MB
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