%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU002+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 : n005.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 02:19:04 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 102 ( 15 unt; 13 def)
% Number of atoms : 373 ( 39 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 450 ( 179 ~; 182 |; 55 &)
% ( 19 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 105 ( 90 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
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(f19,axiom,
? [A] :
( relation(A)
& empty(A) ),
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(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,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,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_rng(relation_composition(C,B)))
=> in(A,relation_rng(B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_rng(relation_composition(C,B)))
=> in(A,relation_rng(B)) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f41,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f46,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK1_skl(B,A) = apply(A,sK2_skl(B,A))
& in(sK2_skl(B,A),relation_dom(A)) )
| in(sK1_skl(B,A),B) )
& ( ! [D] :
( sK1_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK1_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ( C = apply(A,sK0_skl(C,B,A))
& in(sK0_skl(C,B,A),relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(D,sK0_skl(C,B,A)),skolemize(C,sK1_skl(B,A)),skolemize(D,sK2_skl(B,A))],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( in(sK0_skl(X2,X1,X0),relation_dom(X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( X2 = apply(X0,sK0_skl(X2,X1,X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( X2 != apply(X0,X3)
| ~ in(X3,relation_dom(X0))
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f55,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f56,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f65,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(f67,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f88,plain,
( relation(sK5_skl)
& empty(sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f19]) ).
fof(f89,plain,
empty(sK5_skl),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f90,plain,
relation(sK5_skl),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f112,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)],[f28]) ).
fof(f113,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)],[f112]) ).
fof(f114,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)],[f113]) ).
fof(f116,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)],[f114]) ).
fof(f118,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)],[f29]) ).
fof(f119,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)],[f118]) ).
fof(f120,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)],[f119]) ).
fof(f121,plain,
? [A,B] :
( ? [C] :
( ~ in(A,relation_rng(B))
& in(A,relation_rng(relation_composition(C,B)))
& function(C)
& relation(C) )
& function(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f122,plain,
? [B] :
( ? [C] :
( ? [A] :
( ~ in(A,relation_rng(B))
& in(A,relation_rng(relation_composition(C,B))) )
& function(C)
& relation(C) )
& function(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f121]) ).
fof(f123,plain,
( ~ in(sK14_skl,relation_rng(sK12_skl))
& in(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)))
& function(sK13_skl)
& relation(sK13_skl)
& function(sK12_skl)
& relation(sK12_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(B,sK12_skl),skolemize(C,sK13_skl),skolemize(A,sK14_skl)],[f122]) ).
fof(f124,plain,
relation(sK12_skl),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
function(sK12_skl),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f126,plain,
relation(sK13_skl),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f127,plain,
function(sK13_skl),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f128,plain,
in(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl))),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f129,plain,
~ in(sK14_skl,relation_rng(sK12_skl)),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f150,plain,
! [X0,X1] :
( in(sK0_skl(X1,relation_rng(X0),X0),relation_dom(X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f49]) ).
fof(f151,plain,
! [X0,X1] :
( X1 = apply(X0,sK0_skl(X1,relation_rng(X0),X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f50]) ).
fof(f152,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| in(apply(X0,X1),relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f51]) ).
fof(f159,plain,
( sK14_skl = apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))
| ~ function(relation_composition(sK13_skl,sK12_skl))
| ~ relation(relation_composition(sK13_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f128,f151]) ).
fof(f160,plain,
( in(sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)),relation_dom(relation_composition(sK13_skl,sK12_skl)))
| ~ function(relation_composition(sK13_skl,sK12_skl))
| ~ relation(relation_composition(sK13_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f128,f150]) ).
fof(f162,definition,
( sQ0_spl
<=> relation(relation_composition(sK13_skl,sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( sQ0_spl
| ~ relation(relation_composition(sK13_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,definition,
( sQ1_spl
<=> function(relation_composition(sK13_skl,sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( sQ1_spl
| ~ function(relation_composition(sK13_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,definition,
( sQ2_spl
<=> sK14_skl = apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ2_spl
| sK14_skl = apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f159,f162,f165,f168]) ).
fof(f172,definition,
( sQ3_spl
<=> in(sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)),relation_dom(relation_composition(sK13_skl,sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ3_spl
| in(sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)),relation_dom(relation_composition(sK13_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f160,f162,f165,f172]) ).
fof(f192,plain,
( sQ1_spl
| ~ function(sK12_skl)
| ~ relation(sK12_skl)
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(resolution,[status(thm)],[f67,f167]) ).
fof(f193,definition,
( sQ4_spl
<=> relation(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ4_spl
| ~ relation(sK13_skl) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,definition,
( sQ5_spl
<=> function(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ5_spl
| ~ function(sK13_skl) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
( sQ6_spl
<=> relation(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( sQ6_spl
| ~ relation(sK12_skl) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
( sQ7_spl
<=> function(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( sQ7_spl
| ~ function(sK12_skl) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f192,f193,f196,f199,f202,f165]) ).
fof(f206,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f125]) ).
fof(f207,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f208,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f124]) ).
fof(f209,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f208]) ).
fof(f210,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f127]) ).
fof(f211,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f210]) ).
fof(f212,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f126]) ).
fof(f213,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f212]) ).
fof(f224,plain,
( sQ0_spl
| ~ relation(sK12_skl)
| ~ relation(sK13_skl) ),
inference(resolution,[status(thm)],[f164,f56]) ).
fof(f230,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f224,f193,f199,f162]) ).
fof(f268,definition,
( sQ18_spl
<=> relation(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( sQ18_spl
| ~ relation(sK5_skl) ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f344,definition,
( sQ23_spl
<=> function(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ23_spl
| ~ function(sK5_skl) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f356,plain,
( sQ23_spl
| ~ empty(sK5_skl) ),
inference(resolution,[status(thm)],[f346,f42]) ).
fof(f357,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f89]) ).
fof(f358,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f359,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f90]) ).
fof(f360,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f359]) ).
fof(f388,plain,
( ~ sQ3_spl
| in(apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))),relation_dom(sK12_skl))
| ~ function(sK13_skl)
| ~ relation(sK13_skl)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f116,f173]) ).
fof(f390,definition,
( sQ27_spl
<=> in(apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))),relation_dom(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( ~ sQ27_spl
| in(apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))),relation_dom(sK12_skl)) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,plain,
( ~ sQ3_spl
| sQ27_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f388,f199,f202,f193,f196,f390,f172]) ).
fof(f407,plain,
( ~ sQ27_spl
| in(apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))),relation_rng(sK12_skl))
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f391,f152]) ).
fof(f410,definition,
( sQ30_spl
<=> in(apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))),relation_rng(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f411,plain,
( ~ sQ30_spl
| in(apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))),relation_rng(sK12_skl)) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( ~ sQ27_spl
| sQ30_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f407,f199,f202,f410,f390]) ).
fof(f496,plain,
( ~ sQ3_spl
| apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))) = apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))))
| ~ function(sK13_skl)
| ~ relation(sK13_skl)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f120,f173]) ).
fof(f498,definition,
( sQ37_spl
<=> apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))) = apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( ~ sQ37_spl
| apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))) = apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,plain,
( ~ sQ3_spl
| sQ37_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f496,f199,f202,f193,f196,f498,f172]) ).
fof(f503,plain,
( ~ sQ37_spl
| ~ sQ2_spl
| sK14_skl = apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))) ),
inference(forward_demodulation,[status(thm)],[f169,f499]) ).
fof(f534,plain,
( ~ sQ30_spl
| ~ sQ37_spl
| ~ sQ2_spl
| in(sK14_skl,relation_rng(sK12_skl)) ),
inference(forward_demodulation,[status(thm)],[f503,f411]) ).
fof(f535,plain,
( ~ sQ30_spl
| ~ sQ37_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f129]) ).
fof(f536,plain,
( ~ sQ30_spl
| ~ sQ37_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f537,plain,
$false,
inference(sat_refutation,[status(thm)],[f171,f175,f205,f207,f209,f211,f213,f230,f358,f360,f393,f413,f501,f536]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU002+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:46:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.056224 seconds
% 0.14/0.43 % CPU time: 0.180635 seconds
% 0.14/0.43 % Total memory used: 83.744 MB
% 0.14/0.43 % Net memory used: 83.578 MB
%------------------------------------------------------------------------------