%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU214+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 02:19:42 PM UTC 2026
% Result : Theorem 53.66s 7.27s
% Output : CNFRefutation 53.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 98 ( 12 unt; 12 def)
% Number of atoms : 404 ( 55 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 507 ( 201 ~; 207 |; 60 &)
% ( 24 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 13 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-5 aty)
% Number of variables : 162 ( 138 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,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(f36,conjecture,
! [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(f37,negated_conjecture,
~ ! [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)) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f49,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)],[f5]) ).
fof(f50,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)],[f49]) ).
fof(f51,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)],[f50]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f56,plain,
! [A] :
( ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f57,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK1_skl(B,A),sK2_skl(B,A)),A)
| in(sK1_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK1_skl(B,A),D),A)
| ~ in(sK1_skl(B,A),B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(C,sK0_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(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))],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK0_skl(X2,X1,X0)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f65,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f66,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_composition(A,B) )
& ( ! [D,E] :
( ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_composition(A,B) )
& ( ( ! [D,E] :
( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f68,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ( ( in(ordered_pair(sK6_skl(C,B,A),sK5_skl(C,B,A)),B)
& in(ordered_pair(sK4_skl(C,B,A),sK6_skl(C,B,A)),A) )
| in(ordered_pair(sK4_skl(C,B,A),sK5_skl(C,B,A)),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,sK5_skl(C,B,A)),B)
| ~ in(ordered_pair(sK4_skl(C,B,A),F),A) )
| ~ in(ordered_pair(sK4_skl(C,B,A),sK5_skl(C,B,A)),C) ) )
| C = relation_composition(A,B) )
& ( ( ! [D,E] :
( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(sK3_skl(E,D,C,B,A),E),B)
& in(ordered_pair(D,sK3_skl(E,D,C,B,A)),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(F,sK3_skl(E,D,C,B,A)),skolemize(D,sK4_skl(C,B,A)),skolemize(E,sK5_skl(C,B,A)),skolemize(F,sK6_skl(C,B,A))],[f67]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X3,sK3_skl(X4,X3,X2,X1,X0)),X0)
| ~ in(ordered_pair(X3,X4),X2)
| X2 != relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK3_skl(X4,X3,X2,X1,X0),X4),X1)
| ~ in(ordered_pair(X3,X4),X2)
| X2 != relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f75,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f76,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f85,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)],[f20]) ).
fof(f87,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f120,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)],[f37]) ).
fof(f121,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)],[f120]) ).
fof(f122,plain,
( apply(relation_composition(sK15_skl,sK14_skl),sK16_skl) != apply(sK14_skl,apply(sK15_skl,sK16_skl))
& in(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)))
& function(sK15_skl)
& relation(sK15_skl)
& function(sK14_skl)
& relation(sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(B,sK14_skl),skolemize(C,sK15_skl),skolemize(A,sK16_skl)],[f121]) ).
fof(f123,plain,
relation(sK14_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
function(sK14_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f125,plain,
relation(sK15_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f126,plain,
function(sK15_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f127,plain,
in(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl))),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f128,plain,
apply(relation_composition(sK15_skl,sK14_skl),sK16_skl) != apply(sK14_skl,apply(sK15_skl,sK16_skl)),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f142,plain,
! [X0,X1] :
( in(ordered_pair(X1,sK0_skl(X1,relation_dom(X0),X0)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f60]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f61]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,sK3_skl(X3,X2,relation_composition(X0,X1),X1,X0)),X0)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f145,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK3_skl(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f70]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| X1 = apply(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f53,f143]) ).
fof(f152,plain,
( in(ordered_pair(sK16_skl,sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl))),relation_composition(sK15_skl,sK14_skl))
| ~ relation(relation_composition(sK15_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f127,f142]) ).
fof(f155,definition,
( sQ0_spl
<=> relation(relation_composition(sK15_skl,sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( sQ0_spl
| ~ relation(relation_composition(sK15_skl,sK14_skl)) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,definition,
( sQ1_spl
<=> in(ordered_pair(sK16_skl,sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl))),relation_composition(sK15_skl,sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( ~ sQ1_spl
| in(ordered_pair(sK16_skl,sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl))),relation_composition(sK15_skl,sK14_skl)) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f152,f155,f158]) ).
fof(f162,definition,
( sQ2_spl
<=> function(relation_composition(sK15_skl,sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( sQ2_spl
| ~ function(relation_composition(sK15_skl,sK14_skl)) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f171,plain,
( sQ0_spl
| ~ relation(sK14_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f76,f157]) ).
fof(f172,definition,
( sQ4_spl
<=> relation(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( sQ4_spl
| ~ relation(sK15_skl) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
( sQ5_spl
<=> relation(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( sQ5_spl
| ~ relation(sK14_skl) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f171,f172,f175,f155]) ).
fof(f179,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f125]) ).
fof(f180,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f179]) ).
fof(f181,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f123]) ).
fof(f182,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f181]) ).
fof(f195,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,sK3_skl(X3,X2,relation_composition(X0,X1),X1,X0)),X0)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f76]) ).
fof(f198,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK3_skl(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f76]) ).
fof(f211,plain,
( ~ sQ1_spl
| in(ordered_pair(sK3_skl(sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl)),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl),sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl))),sK14_skl)
| ~ relation(sK14_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f159,f198]) ).
fof(f212,plain,
( ~ sQ1_spl
| in(ordered_pair(sK16_skl,sK3_skl(sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl)),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl)),sK15_skl)
| ~ relation(sK14_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f159,f195]) ).
fof(f215,definition,
( sQ6_spl
<=> in(ordered_pair(sK3_skl(sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl)),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl),sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl))),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( ~ sQ6_spl
| in(ordered_pair(sK3_skl(sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl)),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl),sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl))),sK14_skl) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( ~ sQ1_spl
| sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f211,f172,f175,f215,f158]) ).
fof(f219,definition,
( sQ7_spl
<=> in(ordered_pair(sK16_skl,sK3_skl(sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl)),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl)),sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( ~ sQ7_spl
| in(ordered_pair(sK16_skl,sK3_skl(sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl)),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl)),sK15_skl) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( ~ sQ1_spl
| sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f212,f172,f175,f219,f158]) ).
fof(f227,plain,
( sQ2_spl
| ~ function(sK14_skl)
| ~ relation(sK14_skl)
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f87,f164]) ).
fof(f228,definition,
( sQ9_spl
<=> function(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ9_spl
| ~ function(sK15_skl) ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,definition,
( sQ10_spl
<=> function(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ10_spl
| ~ function(sK14_skl) ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( sQ2_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f227,f172,f228,f175,f231,f162]) ).
fof(f235,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f124]) ).
fof(f236,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f237,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f126]) ).
fof(f238,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f237]) ).
fof(f267,plain,
( ~ sQ1_spl
| sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl)) = apply(relation_composition(sK15_skl,sK14_skl),sK16_skl)
| ~ function(relation_composition(sK15_skl,sK14_skl))
| ~ relation(relation_composition(sK15_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f151,f159]) ).
fof(f275,definition,
( sQ14_spl
<=> sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl)) = apply(relation_composition(sK15_skl,sK14_skl),sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( ~ sQ14_spl
| sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl)) = apply(relation_composition(sK15_skl,sK14_skl),sK16_skl) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,plain,
( ~ sQ1_spl
| sQ14_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f267,f155,f162,f275,f158]) ).
fof(f316,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| in(ordered_pair(sK3_skl(apply(relation_composition(sK15_skl,sK14_skl),sK16_skl),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl),sK0_skl(sK16_skl,relation_dom(relation_composition(sK15_skl,sK14_skl)),relation_composition(sK15_skl,sK14_skl))),sK14_skl) ),
inference(forward_demodulation,[status(thm)],[f276,f216]) ).
fof(f317,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| in(ordered_pair(sK3_skl(apply(relation_composition(sK15_skl,sK14_skl),sK16_skl),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl),apply(relation_composition(sK15_skl,sK14_skl),sK16_skl)),sK14_skl) ),
inference(forward_demodulation,[status(thm)],[f276,f316]) ).
fof(f334,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| in(ordered_pair(sK16_skl,sK3_skl(apply(relation_composition(sK15_skl,sK14_skl),sK16_skl),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl)),sK15_skl) ),
inference(forward_demodulation,[status(thm)],[f276,f220]) ).
fof(f336,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| sK3_skl(apply(relation_composition(sK15_skl,sK14_skl),sK16_skl),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl) = apply(sK15_skl,sK16_skl)
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f334,f151]) ).
fof(f343,definition,
( sQ21_spl
<=> sK3_skl(apply(relation_composition(sK15_skl,sK14_skl),sK16_skl),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl) = apply(sK15_skl,sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( ~ sQ21_spl
| sK3_skl(apply(relation_composition(sK15_skl,sK14_skl),sK16_skl),sK16_skl,relation_composition(sK15_skl,sK14_skl),sK14_skl,sK15_skl) = apply(sK15_skl,sK16_skl) ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f346,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| sQ21_spl
| ~ sQ9_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f336,f172,f228,f343,f275,f219]) ).
fof(f9687,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ21_spl
| in(ordered_pair(apply(sK15_skl,sK16_skl),apply(relation_composition(sK15_skl,sK14_skl),sK16_skl)),sK14_skl) ),
inference(backward_demodulation,[status(thm)],[f344,f317]) ).
fof(f10129,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ21_spl
| apply(relation_composition(sK15_skl,sK14_skl),sK16_skl) = apply(sK14_skl,apply(sK15_skl,sK16_skl))
| ~ function(sK14_skl)
| ~ relation(sK14_skl) ),
inference(resolution,[status(thm)],[f9687,f151]) ).
fof(f10137,definition,
( sQ647_spl
<=> apply(relation_composition(sK15_skl,sK14_skl),sK16_skl) = apply(sK14_skl,apply(sK15_skl,sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ647_spl])],[split_symbol_definition]) ).
fof(f10138,plain,
( ~ sQ647_spl
| apply(relation_composition(sK15_skl,sK14_skl),sK16_skl) = apply(sK14_skl,apply(sK15_skl,sK16_skl)) ),
inference(component_clause,[status(thm)],[f10137]) ).
fof(f10140,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ21_spl
| sQ647_spl
| ~ sQ10_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f10129,f175,f231,f10137,f343,f275,f215]) ).
fof(f10146,plain,
( ~ sQ647_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10138,f128]) ).
fof(f10147,plain,
~ sQ647_spl,
inference(contradiction_clause,[status(thm)],[f10146]) ).
fof(f10148,plain,
$false,
inference(sat_refutation,[status(thm)],[f161,f178,f180,f182,f218,f222,f234,f236,f238,f278,f346,f10140,f10147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU214+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 06:03:38 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 53.66/7.27 % Refutation found
% 53.66/7.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 53.66/7.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.90/7.33 % Elapsed time: 6.941922 seconds
% 1.90/7.33 % CPU time: 54.394452 seconds
% 1.90/7.33 % Total memory used: 318.133 MB
% 1.90/7.33 % Net memory used: 292.244 MB
%------------------------------------------------------------------------------