%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU014+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 : n019.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 6.97s 1.56s
% Output : CNFRefutation 6.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 25
% Syntax : Number of formulae : 114 ( 14 unt; 19 def)
% Number of atoms : 389 ( 53 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 472 ( 197 ~; 201 |; 37 &)
% ( 21 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 20 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 64 !; 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(f28,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( subset(relation_rng(B),relation_dom(A))
& one_to_one(relation_composition(B,A)) )
=> one_to_one(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( subset(relation_rng(B),relation_dom(A))
& one_to_one(relation_composition(B,A)) )
=> one_to_one(B) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f45,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(f46,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)],[f45]) ).
fof(f47,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))],[f46]) ).
fof(f48,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)],[f47]) ).
fof(f49,plain,
! [X0] :
( in(sK0_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X0] :
( in(sK1_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,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)],[f47]) ).
fof(f52,plain,
! [X0] :
( sK0_skl(X0) != sK1_skl(X0)
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f53,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f54,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f63,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(f65,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f110,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f111,plain,
! [B] :
( ! [C] :
( ! [A] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B)) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f110]) ).
fof(f112,plain,
! [X0,X1,X2] :
( apply(relation_composition(X0,X1),X2) = apply(X1,apply(X0,X2))
| ~ in(X2,relation_dom(X0))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f119,plain,
! [A] :
( ! [B] :
( relation_dom(relation_composition(A,B)) = relation_dom(A)
| ~ subset(relation_rng(A),relation_dom(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f120,plain,
! [X0,X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
? [A] :
( ? [B] :
( ~ one_to_one(B)
& subset(relation_rng(B),relation_dom(A))
& one_to_one(relation_composition(B,A))
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f122,plain,
( ~ one_to_one(sK12_skl)
& subset(relation_rng(sK12_skl),relation_dom(sK11_skl))
& one_to_one(relation_composition(sK12_skl,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)],[f121]) ).
fof(f123,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
function(sK11_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f125,plain,
relation(sK12_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f126,plain,
function(sK12_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f127,plain,
one_to_one(relation_composition(sK12_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f128,plain,
subset(relation_rng(sK12_skl),relation_dom(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f129,plain,
~ one_to_one(sK12_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f145,plain,
( apply(sK12_skl,sK0_skl(sK12_skl)) = apply(sK12_skl,sK1_skl(sK12_skl))
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f129,f51]) ).
fof(f146,plain,
( in(sK1_skl(sK12_skl),relation_dom(sK12_skl))
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f129,f50]) ).
fof(f147,plain,
( in(sK0_skl(sK12_skl),relation_dom(sK12_skl))
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f129,f49]) ).
fof(f148,definition,
( sQ0_spl
<=> relation(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( sQ0_spl
| ~ relation(sK12_skl) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,definition,
( sQ1_spl
<=> function(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( sQ1_spl
| ~ function(sK12_skl) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
( sQ2_spl
<=> apply(sK12_skl,sK0_skl(sK12_skl)) = apply(sK12_skl,sK1_skl(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ2_spl
| apply(sK12_skl,sK0_skl(sK12_skl)) = apply(sK12_skl,sK1_skl(sK12_skl)) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f145,f148,f151,f154]) ).
fof(f158,definition,
( sQ3_spl
<=> in(sK1_skl(sK12_skl),relation_dom(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( ~ sQ3_spl
| in(sK1_skl(sK12_skl),relation_dom(sK12_skl)) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f146,f148,f151,f158]) ).
fof(f162,definition,
( sQ4_spl
<=> in(sK0_skl(sK12_skl),relation_dom(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( ~ sQ4_spl
| in(sK0_skl(sK12_skl),relation_dom(sK12_skl)) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,plain,
( sQ4_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f147,f148,f151,f162]) ).
fof(f166,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f126]) ).
fof(f167,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f150,f125]) ).
fof(f169,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f177,definition,
( sQ5_spl
<=> one_to_one(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ5_spl
| one_to_one(sK12_skl) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,definition,
( sQ6_spl
<=> sK0_skl(sK12_skl) = sK1_skl(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ6_spl
| sK0_skl(sK12_skl) = sK1_skl(sK12_skl) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f191,plain,
( relation_dom(relation_composition(sK12_skl,sK11_skl)) = relation_dom(sK12_skl)
| ~ relation(sK11_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f120,f128]) ).
fof(f193,definition,
( sQ8_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ8_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,definition,
( sQ9_spl
<=> relation_dom(relation_composition(sK12_skl,sK11_skl)) = relation_dom(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( ~ sQ9_spl
| relation_dom(relation_composition(sK12_skl,sK11_skl)) = relation_dom(sK12_skl) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,plain,
( sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f191,f148,f193,f196]) ).
fof(f200,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f123]) ).
fof(f201,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f211,definition,
( sQ11_spl
<=> relation(relation_composition(sK12_skl,sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ11_spl
| ~ relation(relation_composition(sK12_skl,sK11_skl)) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f233,plain,
( sQ11_spl
| ~ relation(sK11_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f213,f54]) ).
fof(f243,plain,
( sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f233,f148,f193,f211]) ).
fof(f250,plain,
! [X0] :
( ~ sQ4_spl
| apply(relation_composition(sK12_skl,X0),sK0_skl(sK12_skl)) = apply(X0,apply(sK12_skl,sK0_skl(sK12_skl)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f112,f163]) ).
fof(f251,plain,
! [X0] :
( ~ sQ3_spl
| apply(relation_composition(sK12_skl,X0),sK1_skl(sK12_skl)) = apply(X0,apply(sK12_skl,sK1_skl(sK12_skl)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f112,f159]) ).
fof(f253,definition,
! [X0] :
( sQ18_spl
<=> ( apply(relation_composition(sK12_skl,X0),sK0_skl(sK12_skl)) = apply(X0,apply(sK12_skl,sK0_skl(sK12_skl)))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f254,plain,
! [X0] :
( ~ sQ18_spl
| apply(relation_composition(sK12_skl,X0),sK0_skl(sK12_skl)) = apply(X0,apply(sK12_skl,sK0_skl(sK12_skl)))
| ~ function(X0)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ4_spl
| sQ18_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f250,f148,f151,f253,f162]) ).
fof(f257,definition,
! [X0] :
( sQ19_spl
<=> ( apply(relation_composition(sK12_skl,X0),sK1_skl(sK12_skl)) = apply(X0,apply(sK12_skl,sK1_skl(sK12_skl)))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f258,plain,
! [X0] :
( ~ sQ19_spl
| apply(relation_composition(sK12_skl,X0),sK1_skl(sK12_skl)) = apply(X0,apply(sK12_skl,sK1_skl(sK12_skl)))
| ~ function(X0)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( ~ sQ3_spl
| sQ19_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f251,f148,f151,f257,f158]) ).
fof(f261,definition,
( sQ20_spl
<=> function(relation_composition(sK12_skl,sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ20_spl
| ~ function(relation_composition(sK12_skl,sK11_skl)) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f268,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ2_spl
| apply(relation_composition(sK12_skl,X0),sK1_skl(sK12_skl)) = apply(X0,apply(sK12_skl,sK0_skl(sK12_skl)))
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f155,f258]) ).
fof(f292,plain,
( ~ sQ18_spl
| apply(relation_composition(sK12_skl,sK11_skl),sK0_skl(sK12_skl)) = apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl)))
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f254,f124]) ).
fof(f306,definition,
( sQ29_spl
<=> apply(relation_composition(sK12_skl,sK11_skl),sK0_skl(sK12_skl)) = apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( ~ sQ29_spl
| apply(relation_composition(sK12_skl,sK11_skl),sK0_skl(sK12_skl)) = apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl))) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( ~ sQ18_spl
| sQ29_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f292,f193,f306,f253]) ).
fof(f313,plain,
( sQ20_spl
| ~ function(sK11_skl)
| ~ relation(sK11_skl)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f263,f65]) ).
fof(f315,definition,
( sQ30_spl
<=> function(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( sQ30_spl
| ~ function(sK11_skl) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,plain,
( sQ20_spl
| ~ sQ30_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f313,f148,f151,f193,f315,f261]) ).
fof(f363,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f317,f124]) ).
fof(f364,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f363]) ).
fof(f889,plain,
! [X0] :
( ~ sQ29_spl
| X0 = sK0_skl(sK12_skl)
| apply(relation_composition(sK12_skl,sK11_skl),X0) != apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl)))
| ~ in(sK0_skl(sK12_skl),relation_dom(relation_composition(sK12_skl,sK11_skl)))
| ~ in(X0,relation_dom(relation_composition(sK12_skl,sK11_skl)))
| ~ one_to_one(relation_composition(sK12_skl,sK11_skl))
| ~ function(relation_composition(sK12_skl,sK11_skl))
| ~ relation(relation_composition(sK12_skl,sK11_skl)) ),
inference(paramodulation,[status(thm)],[f307,f48]) ).
fof(f891,definition,
( sQ70_spl
<=> one_to_one(relation_composition(sK12_skl,sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f893,plain,
( sQ70_spl
| ~ one_to_one(relation_composition(sK12_skl,sK11_skl)) ),
inference(component_clause,[status(thm)],[f891]) ).
fof(f894,definition,
! [X0] :
( sQ71_spl
<=> ( X0 = sK0_skl(sK12_skl)
| apply(relation_composition(sK12_skl,sK11_skl),X0) != apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl)))
| ~ in(X0,relation_dom(relation_composition(sK12_skl,sK11_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f895,plain,
! [X0] :
( ~ sQ71_spl
| X0 = sK0_skl(sK12_skl)
| apply(relation_composition(sK12_skl,sK11_skl),X0) != apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl)))
| ~ in(X0,relation_dom(relation_composition(sK12_skl,sK11_skl))) ),
inference(component_clause,[status(thm)],[f894]) ).
fof(f897,definition,
( sQ72_spl
<=> in(sK0_skl(sK12_skl),relation_dom(relation_composition(sK12_skl,sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f899,plain,
( sQ72_spl
| ~ in(sK0_skl(sK12_skl),relation_dom(relation_composition(sK12_skl,sK11_skl))) ),
inference(component_clause,[status(thm)],[f897]) ).
fof(f900,plain,
( ~ sQ29_spl
| ~ sQ72_spl
| sQ71_spl
| ~ sQ70_spl
| ~ sQ20_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f889,f211,f261,f891,f894,f897,f306]) ).
fof(f902,plain,
( sQ72_spl
| ~ sQ9_spl
| ~ in(sK0_skl(sK12_skl),relation_dom(sK12_skl)) ),
inference(forward_demodulation,[status(thm)],[f197,f899]) ).
fof(f903,plain,
( sQ72_spl
| ~ sQ9_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f902,f163]) ).
fof(f904,plain,
( sQ72_spl
| ~ sQ9_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f903]) ).
fof(f905,plain,
! [X0] :
( ~ sQ71_spl
| ~ sQ9_spl
| X0 = sK0_skl(sK12_skl)
| apply(relation_composition(sK12_skl,sK11_skl),X0) != apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl)))
| ~ in(X0,relation_dom(sK12_skl)) ),
inference(forward_demodulation,[status(thm)],[f197,f895]) ).
fof(f906,plain,
( sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f893,f127]) ).
fof(f907,plain,
sQ70_spl,
inference(contradiction_clause,[status(thm)],[f906]) ).
fof(f4781,plain,
( ~ sQ3_spl
| ~ sQ71_spl
| ~ sQ9_spl
| sK1_skl(sK12_skl) = sK0_skl(sK12_skl)
| apply(relation_composition(sK12_skl,sK11_skl),sK1_skl(sK12_skl)) != apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl))) ),
inference(resolution,[status(thm)],[f905,f159]) ).
fof(f4787,definition,
( sQ228_spl
<=> apply(relation_composition(sK12_skl,sK11_skl),sK1_skl(sK12_skl)) = apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f4790,plain,
( ~ sQ3_spl
| ~ sQ71_spl
| ~ sQ9_spl
| sQ6_spl
| ~ sQ228_spl ),
inference(split_clause,[status(thm)],[f4781,f4787,f180,f196,f894,f158]) ).
fof(f4803,plain,
( ~ sQ6_spl
| one_to_one(sK12_skl)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f181,f52]) ).
fof(f4808,plain,
( ~ sQ6_spl
| sQ5_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f4803,f148,f151,f177,f180]) ).
fof(f4834,plain,
( ~ sQ19_spl
| ~ sQ2_spl
| apply(relation_composition(sK12_skl,sK11_skl),sK1_skl(sK12_skl)) = apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl)))
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f268,f124]) ).
fof(f4853,plain,
( ~ sQ19_spl
| ~ sQ2_spl
| sQ228_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4834,f193,f4787,f154,f257]) ).
fof(f4858,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f129]) ).
fof(f4859,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f4858]) ).
fof(f4860,plain,
$false,
inference(sat_refutation,[status(thm)],[f157,f161,f165,f167,f169,f199,f201,f243,f256,f260,f309,f318,f364,f900,f904,f907,f4790,f4808,f4853,f4859]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU014+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 05:47:20 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.15/0.40 % Drodi V4.1.1
% 6.97/1.56 % Refutation found
% 6.97/1.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.97/1.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.97/1.60 % Elapsed time: 1.200930 seconds
% 6.97/1.60 % CPU time: 9.132259 seconds
% 6.97/1.60 % Total memory used: 173.010 MB
% 6.97/1.60 % Net memory used: 163.907 MB
%------------------------------------------------------------------------------