%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU013+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 02:19:05 PM UTC 2026
% Result : Theorem 49.26s 6.69s
% Output : CNFRefutation 49.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 27
% Syntax : Number of formulae : 125 ( 15 unt; 21 def)
% Number of atoms : 466 ( 41 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 589 ( 248 ~; 256 |; 45 &)
% ( 25 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 27 ( 25 usr; 22 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 79 ( 75 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( one_to_one(B)
& one_to_one(A) )
=> one_to_one(relation_composition(A,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( one_to_one(B)
& one_to_one(A) )
=> one_to_one(relation_composition(A,B)) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f43,plain,
! [A] :
( ( one_to_one(A)
<=> ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f44,plain,
! [A] :
( ( ( ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [A] :
( ( ( ( sK0_skl(A) != sK1_skl(A)
& apply(A,sK0_skl(A)) = apply(A,sK1_skl(A))
& in(sK1_skl(A),relation_dom(A))
& in(sK0_skl(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(B,sK0_skl(A)),skolemize(C,sK1_skl(A))],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0] :
( in(sK0_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
! [X0] :
( in(sK1_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,plain,
! [X0] :
( apply(X0,sK0_skl(X0)) = apply(X0,sK1_skl(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f50,plain,
! [X0] :
( sK0_skl(X0) != sK1_skl(X0)
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f51,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f61,plain,
! [A,B] :
( ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) )
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f63,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f103,plain,
! [A,B] :
( ! [C] :
( ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f104,plain,
! [A,B] :
( ! [C] :
( ( ( ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C))
| in(A,relation_dom(relation_composition(C,B))) )
& ( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C))
| in(A,relation_dom(relation_composition(C,B))) )
& ! [A] :
( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
! [X0,X1,X2] :
( in(X2,relation_dom(X1))
| ~ in(X2,relation_dom(relation_composition(X1,X0)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
! [X0,X1,X2] :
( in(apply(X1,X2),relation_dom(X0))
| ~ in(X2,relation_dom(relation_composition(X1,X0)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f109,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(C,B),A) = apply(B,apply(C,A))
| ~ in(A,relation_dom(relation_composition(C,B)))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f110,plain,
! [B] :
( ! [C] :
( ! [A] :
( apply(relation_composition(C,B),A) = apply(B,apply(C,A))
| ~ in(A,relation_dom(relation_composition(C,B))) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f109]) ).
fof(f111,plain,
! [X0,X1,X2] :
( apply(relation_composition(X1,X0),X2) = apply(X0,apply(X1,X2))
| ~ in(X2,relation_dom(relation_composition(X1,X0)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f118,plain,
? [A] :
( ? [B] :
( ~ one_to_one(relation_composition(A,B))
& one_to_one(B)
& one_to_one(A)
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f119,plain,
( ~ one_to_one(relation_composition(sK11_skl,sK12_skl))
& one_to_one(sK12_skl)
& one_to_one(sK11_skl)
& function(sK12_skl)
& relation(sK12_skl)
& function(sK11_skl)
& relation(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(A,sK11_skl),skolemize(B,sK12_skl)],[f118]) ).
fof(f120,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
function(sK11_skl),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f122,plain,
relation(sK12_skl),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f123,plain,
function(sK12_skl),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f124,plain,
one_to_one(sK11_skl),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f125,plain,
one_to_one(sK12_skl),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f126,plain,
~ one_to_one(relation_composition(sK11_skl,sK12_skl)),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f169,plain,
( apply(relation_composition(sK11_skl,sK12_skl),sK0_skl(relation_composition(sK11_skl,sK12_skl))) = apply(relation_composition(sK11_skl,sK12_skl),sK1_skl(relation_composition(sK11_skl,sK12_skl)))
| ~ function(relation_composition(sK11_skl,sK12_skl))
| ~ relation(relation_composition(sK11_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f49,f126]) ).
fof(f170,definition,
( sQ0_spl
<=> relation(relation_composition(sK11_skl,sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( sQ0_spl
| ~ relation(relation_composition(sK11_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,definition,
( sQ1_spl
<=> function(relation_composition(sK11_skl,sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( sQ1_spl
| ~ function(relation_composition(sK11_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,definition,
( sQ2_spl
<=> apply(relation_composition(sK11_skl,sK12_skl),sK0_skl(relation_composition(sK11_skl,sK12_skl))) = apply(relation_composition(sK11_skl,sK12_skl),sK1_skl(relation_composition(sK11_skl,sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( ~ sQ2_spl
| apply(relation_composition(sK11_skl,sK12_skl),sK0_skl(relation_composition(sK11_skl,sK12_skl))) = apply(relation_composition(sK11_skl,sK12_skl),sK1_skl(relation_composition(sK11_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f169,f170,f173,f176]) ).
fof(f180,plain,
( sK0_skl(relation_composition(sK11_skl,sK12_skl)) != sK1_skl(relation_composition(sK11_skl,sK12_skl))
| ~ function(relation_composition(sK11_skl,sK12_skl))
| ~ relation(relation_composition(sK11_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f50,f126]) ).
fof(f181,definition,
( sQ3_spl
<=> sK0_skl(relation_composition(sK11_skl,sK12_skl)) = sK1_skl(relation_composition(sK11_skl,sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f180,f170,f173,f181]) ).
fof(f185,plain,
( sQ1_spl
| ~ function(sK12_skl)
| ~ relation(sK12_skl)
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f175,f63]) ).
fof(f187,definition,
( sQ4_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( sQ4_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,definition,
( sQ5_spl
<=> function(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ5_spl
| ~ function(sK11_skl) ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,definition,
( sQ6_spl
<=> relation(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ6_spl
| ~ relation(sK12_skl) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,definition,
( sQ7_spl
<=> function(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ7_spl
| ~ function(sK12_skl) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f185,f187,f190,f193,f196,f173]) ).
fof(f200,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f123]) ).
fof(f201,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f202,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f122]) ).
fof(f203,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f121]) ).
fof(f205,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f206,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f120]) ).
fof(f207,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f210,plain,
( sQ0_spl
| ~ relation(sK12_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f172,f52]) ).
fof(f219,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f210,f187,f193,f170]) ).
fof(f224,definition,
( sQ10_spl
<=> one_to_one(relation_composition(sK11_skl,sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( ~ sQ10_spl
| one_to_one(relation_composition(sK11_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,definition,
( sQ11_spl
<=> in(sK0_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(relation_composition(sK11_skl,sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( ~ sQ11_spl
| in(sK0_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(relation_composition(sK11_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f229,plain,
( sQ11_spl
| ~ in(sK0_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(relation_composition(sK11_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,definition,
( sQ12_spl
<=> in(sK1_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(relation_composition(sK11_skl,sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( ~ sQ12_spl
| in(sK1_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(relation_composition(sK11_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f232,plain,
( sQ12_spl
| ~ in(sK1_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(relation_composition(sK11_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f240,plain,
( sQ12_spl
| one_to_one(relation_composition(sK11_skl,sK12_skl))
| ~ function(relation_composition(sK11_skl,sK12_skl))
| ~ relation(relation_composition(sK11_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f232,f48]) ).
fof(f241,plain,
( sQ12_spl
| sQ10_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f240,f170,f173,f224,f230]) ).
fof(f242,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f126]) ).
fof(f243,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f242]) ).
fof(f244,plain,
( ~ sQ12_spl
| in(sK1_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(sK11_skl))
| ~ function(sK11_skl)
| ~ relation(sK11_skl)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f231,f106]) ).
fof(f246,definition,
( sQ14_spl
<=> in(sK1_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( ~ sQ12_spl
| sQ14_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f244,f193,f196,f187,f190,f246,f230]) ).
fof(f1107,plain,
! [X0,X1] :
( apply(relation_composition(sK11_skl,X0),X1) = apply(X0,apply(sK11_skl,X1))
| ~ in(X1,relation_dom(relation_composition(sK11_skl,X0)))
| ~ relation(sK11_skl)
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f111,f121]) ).
fof(f1126,definition,
! [X0,X1] :
( sQ121_spl
<=> ( apply(relation_composition(sK11_skl,X0),X1) = apply(X0,apply(sK11_skl,X1))
| ~ in(X1,relation_dom(relation_composition(sK11_skl,X0)))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1127,plain,
! [X0,X1] :
( ~ sQ121_spl
| apply(relation_composition(sK11_skl,X0),X1) = apply(X0,apply(sK11_skl,X1))
| ~ in(X1,relation_dom(relation_composition(sK11_skl,X0)))
| ~ function(X0)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f1126]) ).
fof(f1129,plain,
( ~ sQ4_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f1107,f1126,f187]) ).
fof(f1686,plain,
! [X0] :
( ~ sQ121_spl
| apply(relation_composition(sK11_skl,sK12_skl),X0) = apply(sK12_skl,apply(sK11_skl,X0))
| ~ in(X0,relation_dom(relation_composition(sK11_skl,sK12_skl)))
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f1127,f123]) ).
fof(f1702,definition,
! [X0] :
( sQ199_spl
<=> ( apply(relation_composition(sK11_skl,sK12_skl),X0) = apply(sK12_skl,apply(sK11_skl,X0))
| ~ in(X0,relation_dom(relation_composition(sK11_skl,sK12_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f1703,plain,
! [X0] :
( ~ sQ199_spl
| apply(relation_composition(sK11_skl,sK12_skl),X0) = apply(sK12_skl,apply(sK11_skl,X0))
| ~ in(X0,relation_dom(relation_composition(sK11_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f1702]) ).
fof(f1705,plain,
( ~ sQ121_spl
| sQ199_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1686,f193,f1702,f1126]) ).
fof(f4473,plain,
( ~ sQ12_spl
| ~ sQ199_spl
| apply(relation_composition(sK11_skl,sK12_skl),sK1_skl(relation_composition(sK11_skl,sK12_skl))) = apply(sK12_skl,apply(sK11_skl,sK1_skl(relation_composition(sK11_skl,sK12_skl)))) ),
inference(resolution,[status(thm)],[f1703,f231]) ).
fof(f4480,plain,
( ~ sQ199_spl
| one_to_one(relation_composition(sK11_skl,sK12_skl))
| ~ function(relation_composition(sK11_skl,sK12_skl))
| ~ relation(relation_composition(sK11_skl,sK12_skl))
| apply(relation_composition(sK11_skl,sK12_skl),sK0_skl(relation_composition(sK11_skl,sK12_skl))) = apply(sK12_skl,apply(sK11_skl,sK0_skl(relation_composition(sK11_skl,sK12_skl)))) ),
inference(resolution,[status(thm)],[f1703,f47]) ).
fof(f4524,definition,
( sQ477_spl
<=> apply(relation_composition(sK11_skl,sK12_skl),sK0_skl(relation_composition(sK11_skl,sK12_skl))) = apply(sK12_skl,apply(sK11_skl,sK0_skl(relation_composition(sK11_skl,sK12_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ477_spl])],[split_symbol_definition]) ).
fof(f4525,plain,
( ~ sQ477_spl
| apply(relation_composition(sK11_skl,sK12_skl),sK0_skl(relation_composition(sK11_skl,sK12_skl))) = apply(sK12_skl,apply(sK11_skl,sK0_skl(relation_composition(sK11_skl,sK12_skl)))) ),
inference(component_clause,[status(thm)],[f4524]) ).
fof(f4527,plain,
( ~ sQ199_spl
| sQ10_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ477_spl ),
inference(split_clause,[status(thm)],[f4480,f4524,f170,f173,f224,f1702]) ).
fof(f22214,definition,
( sQ1888_spl
<=> one_to_one(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ1888_spl])],[split_symbol_definition]) ).
fof(f22216,plain,
( sQ1888_spl
| ~ one_to_one(sK12_skl) ),
inference(component_clause,[status(thm)],[f22214]) ).
fof(f22457,definition,
( sQ1894_spl
<=> one_to_one(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ1894_spl])],[split_symbol_definition]) ).
fof(f22459,plain,
( sQ1894_spl
| ~ one_to_one(sK11_skl) ),
inference(component_clause,[status(thm)],[f22457]) ).
fof(f23741,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ199_spl
| apply(relation_composition(sK11_skl,sK12_skl),sK0_skl(relation_composition(sK11_skl,sK12_skl))) = apply(sK12_skl,apply(sK11_skl,sK1_skl(relation_composition(sK11_skl,sK12_skl)))) ),
inference(backward_demodulation,[status(thm)],[f4473,f177]) ).
fof(f23839,plain,
( sQ11_spl
| one_to_one(relation_composition(sK11_skl,sK12_skl))
| ~ function(relation_composition(sK11_skl,sK12_skl))
| ~ relation(relation_composition(sK11_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f229,f47]) ).
fof(f23840,plain,
( sQ11_spl
| sQ10_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f23839,f170,f173,f224,f227]) ).
fof(f24492,plain,
( ~ sQ11_spl
| in(sK0_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(sK11_skl))
| ~ function(sK11_skl)
| ~ relation(sK11_skl)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f228,f106]) ).
fof(f24494,definition,
( sQ1925_spl
<=> in(sK0_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1925_spl])],[split_symbol_definition]) ).
fof(f24497,plain,
( ~ sQ11_spl
| sQ1925_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f24492,f193,f196,f187,f190,f24494,f227]) ).
fof(f24788,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ199_spl
| ~ sQ477_spl
| apply(sK12_skl,apply(sK11_skl,sK0_skl(relation_composition(sK11_skl,sK12_skl)))) = apply(sK12_skl,apply(sK11_skl,sK1_skl(relation_composition(sK11_skl,sK12_skl)))) ),
inference(backward_demodulation,[status(thm)],[f4525,f23741]) ).
fof(f24818,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ199_spl
| ~ sQ477_spl
| apply(sK11_skl,sK0_skl(relation_composition(sK11_skl,sK12_skl))) = apply(sK11_skl,sK1_skl(relation_composition(sK11_skl,sK12_skl)))
| ~ in(apply(sK11_skl,sK1_skl(relation_composition(sK11_skl,sK12_skl))),relation_dom(sK12_skl))
| ~ in(apply(sK11_skl,sK0_skl(relation_composition(sK11_skl,sK12_skl))),relation_dom(sK12_skl))
| ~ one_to_one(sK12_skl)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f24788,f46]) ).
fof(f24825,definition,
( sQ1943_spl
<=> in(apply(sK11_skl,sK0_skl(relation_composition(sK11_skl,sK12_skl))),relation_dom(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1943_spl])],[split_symbol_definition]) ).
fof(f24827,plain,
( sQ1943_spl
| ~ in(apply(sK11_skl,sK0_skl(relation_composition(sK11_skl,sK12_skl))),relation_dom(sK12_skl)) ),
inference(component_clause,[status(thm)],[f24825]) ).
fof(f24828,definition,
( sQ1944_spl
<=> in(apply(sK11_skl,sK1_skl(relation_composition(sK11_skl,sK12_skl))),relation_dom(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1944_spl])],[split_symbol_definition]) ).
fof(f24830,plain,
( sQ1944_spl
| ~ in(apply(sK11_skl,sK1_skl(relation_composition(sK11_skl,sK12_skl))),relation_dom(sK12_skl)) ),
inference(component_clause,[status(thm)],[f24828]) ).
fof(f24831,definition,
( sQ1945_spl
<=> apply(sK11_skl,sK0_skl(relation_composition(sK11_skl,sK12_skl))) = apply(sK11_skl,sK1_skl(relation_composition(sK11_skl,sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1945_spl])],[split_symbol_definition]) ).
fof(f24832,plain,
( ~ sQ1945_spl
| apply(sK11_skl,sK0_skl(relation_composition(sK11_skl,sK12_skl))) = apply(sK11_skl,sK1_skl(relation_composition(sK11_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f24831]) ).
fof(f24834,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ199_spl
| ~ sQ477_spl
| sQ1945_spl
| ~ sQ1944_spl
| ~ sQ1943_spl
| ~ sQ1888_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f24818,f193,f196,f22214,f24825,f24828,f24831,f4524,f1702,f230,f176]) ).
fof(f24940,plain,
( sQ1944_spl
| ~ in(sK1_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(relation_composition(sK11_skl,sK12_skl)))
| ~ function(sK11_skl)
| ~ relation(sK11_skl)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f24830,f107]) ).
fof(f24941,plain,
( sQ1944_spl
| ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f24940,f193,f196,f187,f190,f230,f24828]) ).
fof(f24942,plain,
( sQ1888_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22216,f125]) ).
fof(f24943,plain,
sQ1888_spl,
inference(contradiction_clause,[status(thm)],[f24942]) ).
fof(f25414,plain,
( sQ1943_spl
| ~ in(sK0_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(relation_composition(sK11_skl,sK12_skl)))
| ~ function(sK11_skl)
| ~ relation(sK11_skl)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f24827,f107]) ).
fof(f25415,plain,
( sQ1943_spl
| ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f25414,f193,f196,f187,f190,f227,f24825]) ).
fof(f25514,plain,
( ~ sQ1945_spl
| sK0_skl(relation_composition(sK11_skl,sK12_skl)) = sK1_skl(relation_composition(sK11_skl,sK12_skl))
| ~ in(sK1_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(sK11_skl))
| ~ in(sK0_skl(relation_composition(sK11_skl,sK12_skl)),relation_dom(sK11_skl))
| ~ one_to_one(sK11_skl)
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f24832,f46]) ).
fof(f25521,plain,
( ~ sQ1945_spl
| sQ3_spl
| ~ sQ14_spl
| ~ sQ1925_spl
| ~ sQ1894_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f25514,f187,f190,f22457,f24494,f246,f181,f24831]) ).
fof(f25540,plain,
( sQ1894_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22459,f124]) ).
fof(f25541,plain,
sQ1894_spl,
inference(contradiction_clause,[status(thm)],[f25540]) ).
fof(f25542,plain,
$false,
inference(sat_refutation,[status(thm)],[f179,f184,f199,f201,f203,f205,f207,f219,f241,f243,f249,f1129,f1705,f4527,f23840,f24497,f24834,f24941,f24943,f25415,f25521,f25541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU013+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:50:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 49.26/6.69 % Refutation found
% 49.26/6.69 % SZS status Theorem for theBenchmark: Theorem is valid
% 49.26/6.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.02/6.76 % Elapsed time: 6.378601 seconds
% 8.02/6.76 % CPU time: 50.298204 seconds
% 8.02/6.76 % Total memory used: 550.440 MB
% 8.02/6.76 % Net memory used: 506.396 MB
%------------------------------------------------------------------------------