%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU191+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:19:36 PM UTC 2026
% Result : Theorem 0.07s 0.36s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 27
% Syntax : Number of formulae : 138 ( 17 unt; 17 def)
% Number of atoms : 507 ( 51 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 635 ( 266 ~; 283 |; 50 &)
% ( 27 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 18 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-5 aty)
% Number of variables : 240 ( 213 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,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/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f36,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [A,B] :
( ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
! [A,B] :
( ( ( ? [C,D] :
( ( ( C = D
& in(C,A) )
| in(ordered_pair(C,D),B) )
& ( C != D
| ~ in(C,A)
| ~ in(ordered_pair(C,D),B) ) )
| B = identity_relation(A) )
& ( ! [C,D] :
( ( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [B] :
( ( ! [A] :
( ? [C,D] :
( ( ( C = D
& in(C,A) )
| in(ordered_pair(C,D),B) )
& ( C != D
| ~ in(C,A)
| ~ in(ordered_pair(C,D),B) ) )
| B = identity_relation(A) )
& ! [A] :
( ( ! [C,D] :
( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [B] :
( ( ! [A] :
( ( ( ( sK0_skl(A,B) = sK1_skl(A,B)
& in(sK0_skl(A,B),A) )
| in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B) )
& ( sK0_skl(A,B) != sK1_skl(A,B)
| ~ in(sK0_skl(A,B),A)
| ~ in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B) ) )
| B = identity_relation(A) )
& ! [A] :
( ( ! [C,D] :
( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(A,B)),skolemize(D,sK1_skl(A,B))],[f40]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( in(X2,X1)
| ~ in(ordered_pair(X2,X3),X0)
| X0 != identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X2,X3),X0)
| X0 != identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( X2 != X3
| ~ in(X2,X1)
| in(ordered_pair(X2,X3),X0)
| X0 != identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f49,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)],[f6]) ).
fof(f50,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)],[f49]) ).
fof(f51,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)],[f50]) ).
fof(f52,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ( ( in(ordered_pair(sK5_skl(C,B,A),sK4_skl(C,B,A)),B)
& in(ordered_pair(sK3_skl(C,B,A),sK5_skl(C,B,A)),A) )
| in(ordered_pair(sK3_skl(C,B,A),sK4_skl(C,B,A)),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,sK4_skl(C,B,A)),B)
| ~ in(ordered_pair(sK3_skl(C,B,A),F),A) )
| ~ in(ordered_pair(sK3_skl(C,B,A),sK4_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(sK2_skl(E,D,C,B,A),E),B)
& in(ordered_pair(D,sK2_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,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(F,sK2_skl(E,D,C,B,A)),skolemize(D,sK3_skl(C,B,A)),skolemize(E,sK4_skl(C,B,A)),skolemize(F,sK5_skl(C,B,A))],[f51]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X3,sK2_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)],[f52]) ).
fof(f54,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK2_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)],[f52]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0)
| in(ordered_pair(X3,X4),X2)
| X2 != relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f57,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK3_skl(X2,X1,X0),sK5_skl(X2,X1,X0)),X0)
| in(ordered_pair(sK3_skl(X2,X1,X0),sK4_skl(X2,X1,X0)),X2)
| X2 = relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f58,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK5_skl(X2,X1,X0),sK4_skl(X2,X1,X0)),X1)
| in(ordered_pair(sK3_skl(X2,X1,X0),sK4_skl(X2,X1,X0)),X2)
| X2 = relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f59,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f60,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f67,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f72,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f79,plain,
empty(sK8_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f23]) ).
fof(f80,plain,
empty(sK8_skl),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f92,plain,
? [A,B,C,D] :
( ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<~> ( in(ordered_pair(A,B),D)
& in(A,C) ) )
& relation(D) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f93,plain,
? [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),D)
| ~ in(A,C)
| ~ in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) )
& ( ( in(ordered_pair(A,B),D)
& in(A,C) )
| in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) )
& relation(D) ),
inference(NNF_transformation,[status(thm)],[f92]) ).
fof(f94,plain,
? [D] :
( ? [A,B,C] :
( ( ~ in(ordered_pair(A,B),D)
| ~ in(A,C)
| ~ in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) )
& ( ( in(ordered_pair(A,B),D)
& in(A,C) )
| in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) ) )
& relation(D) ),
inference(miniscoping,[status(thm)],[f93]) ).
fof(f95,plain,
( ( ~ in(ordered_pair(sK12_skl,sK13_skl),sK11_skl)
| ~ in(sK12_skl,sK14_skl)
| ~ in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl)) )
& ( ( in(ordered_pair(sK12_skl,sK13_skl),sK11_skl)
& in(sK12_skl,sK14_skl) )
| in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl)) )
& relation(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(D,sK11_skl),skolemize(A,sK12_skl),skolemize(B,sK13_skl),skolemize(C,sK14_skl)],[f94]) ).
fof(f96,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
( in(sK12_skl,sK14_skl)
| in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl)) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f98,plain,
( in(ordered_pair(sK12_skl,sK13_skl),sK11_skl)
| in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl)) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f99,plain,
( ~ in(ordered_pair(sK12_skl,sK13_skl),sK11_skl)
| ~ in(sK12_skl,sK14_skl)
| ~ in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl)) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f100,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f101,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f106,definition,
( sQ0_spl
<=> in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ0_spl
| in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl)) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f108,plain,
( sQ0_spl
| ~ in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl)) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,definition,
( sQ1_spl
<=> in(sK12_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ1_spl
| in(sK12_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f111,plain,
( sQ1_spl
| ~ in(sK12_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f97,f106,f109]) ).
fof(f113,definition,
( sQ2_spl
<=> in(ordered_pair(sK12_skl,sK13_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( sQ2_spl
| ~ in(ordered_pair(sK12_skl,sK13_skl),sK11_skl) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f98,f106,f113]) ).
fof(f117,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f99,f106,f109,f113]) ).
fof(f118,plain,
! [X0,X1,X2] :
( in(X1,X0)
| ~ in(ordered_pair(X1,X2),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f42]) ).
fof(f119,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f43]) ).
fof(f120,plain,
! [X0,X1] :
( ~ in(X1,X0)
| in(ordered_pair(X1,X1),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f44]) ).
fof(f121,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,sK2_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)],[f53]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK2_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)],[f54]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),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)],[f55]) ).
fof(f125,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),identity_relation(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f61]) ).
fof(f126,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ in(ordered_pair(X0,X1),identity_relation(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f61]) ).
fof(f127,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(ordered_pair(X0,X0),identity_relation(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f61]) ).
fof(f152,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X0)
| in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f123,f60]) ).
fof(f155,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,sK2_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)],[f121,f60]) ).
fof(f156,plain,
( ~ sQ0_spl
| in(ordered_pair(sK12_skl,sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl))),identity_relation(sK14_skl))
| ~ relation(sK11_skl)
| ~ relation(identity_relation(sK14_skl)) ),
inference(resolution,[status(thm)],[f155,f107]) ).
fof(f157,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X0)
| ~ relation(X1)
| ~ relation(X0)
| in(ordered_pair(X2,sK2_skl(X3,X2,relation_composition(X0,X1),X1,X0)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f155,f152]) ).
fof(f158,definition,
( sQ3_spl
<=> relation(identity_relation(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( sQ3_spl
| ~ relation(identity_relation(sK14_skl)) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,definition,
( sQ4_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( sQ4_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,definition,
( sQ5_spl
<=> in(ordered_pair(sK12_skl,sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl))),identity_relation(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( ~ sQ5_spl
| in(ordered_pair(sK12_skl,sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl))),identity_relation(sK14_skl)) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f156,f158,f161,f164,f106]) ).
fof(f168,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X0)
| in(ordered_pair(X2,sK2_skl(X3,X2,relation_composition(X0,X1),X1,X0)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f157]) ).
fof(f169,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK2_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)],[f122,f60]) ).
fof(f170,plain,
( ~ sQ0_spl
| in(ordered_pair(sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl)),sK13_skl),sK11_skl)
| ~ relation(sK11_skl)
| ~ relation(identity_relation(sK14_skl)) ),
inference(resolution,[status(thm)],[f169,f107]) ).
fof(f171,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,X2),X1)
| ~ in(ordered_pair(X3,X4),X0)
| ~ relation(X1)
| ~ relation(X0)
| in(ordered_pair(sK2_skl(X2,X3,relation_composition(X0,X1),X1,X0),X2),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f169,f152]) ).
fof(f172,definition,
( sQ6_spl
<=> in(ordered_pair(sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl)),sK13_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ6_spl
| in(ordered_pair(sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl)),sK13_skl),sK11_skl) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f170,f158,f161,f172,f106]) ).
fof(f176,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,X2),X1)
| ~ in(ordered_pair(X3,X4),X0)
| in(ordered_pair(sK2_skl(X2,X3,relation_composition(X0,X1),X1,X0),X2),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f171]) ).
fof(f177,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f96]) ).
fof(f178,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f179,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f160,f61]) ).
fof(f180,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f179]) ).
fof(f203,plain,
( ~ sQ5_spl
| sK12_skl = sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl)) ),
inference(resolution,[status(thm)],[f165,f126]) ).
fof(f204,plain,
( ~ sQ5_spl
| in(sK12_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f165,f125]) ).
fof(f207,plain,
( ~ sQ5_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f111]) ).
fof(f208,plain,
( ~ sQ5_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f209,plain,
! [X0] :
( sQ0_spl
| ~ in(ordered_pair(X0,sK13_skl),sK11_skl)
| ~ in(ordered_pair(sK12_skl,X0),identity_relation(sK14_skl))
| ~ relation(sK11_skl)
| ~ relation(identity_relation(sK14_skl)) ),
inference(resolution,[status(thm)],[f108,f152]) ).
fof(f210,definition,
! [X0] :
( sQ7_spl
<=> ( ~ in(ordered_pair(X0,sK13_skl),sK11_skl)
| ~ in(ordered_pair(sK12_skl,X0),identity_relation(sK14_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f211,plain,
! [X0] :
( ~ sQ7_spl
| ~ in(ordered_pair(X0,sK13_skl),sK11_skl)
| ~ in(ordered_pair(sK12_skl,X0),identity_relation(sK14_skl)) ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,plain,
( sQ0_spl
| sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f209,f158,f161,f210,f106]) ).
fof(f214,plain,
( ~ sQ1_spl
| in(ordered_pair(sK12_skl,sK12_skl),identity_relation(sK14_skl)) ),
inference(resolution,[status(thm)],[f110,f127]) ).
fof(f224,plain,
! [X0] : ~ in(X0,sK8_skl),
inference(resolution,[status(thm)],[f102,f80]) ).
fof(f226,plain,
! [X0] : ~ in(X0,empty_set),
inference(resolution,[status(thm)],[f67,f102]) ).
fof(f238,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| in(ordered_pair(sK12_skl,sK13_skl),sK11_skl) ),
inference(forward_demodulation,[status(thm)],[f203,f173]) ).
fof(f241,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f238]) ).
fof(f242,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f241]) ).
fof(f252,plain,
! [X0,X1] :
( in(ordered_pair(sK3_skl(X1,empty_set,X0),sK4_skl(X1,empty_set,X0)),X1)
| X1 = relation_composition(X0,empty_set)
| ~ relation(X1)
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f226,f58]) ).
fof(f253,plain,
! [X0,X1] :
( in(ordered_pair(sK3_skl(X1,X0,empty_set),sK4_skl(X1,X0,empty_set)),X1)
| X1 = relation_composition(empty_set,X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f226,f57]) ).
fof(f254,definition,
! [X0,X1] :
( sQ8_spl
<=> ( in(ordered_pair(sK3_skl(X1,empty_set,X0),sK4_skl(X1,empty_set,X0)),X1)
| X1 = relation_composition(X0,empty_set)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f257,definition,
( sQ9_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ9_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f252,f254,f257]) ).
fof(f261,definition,
! [X0,X1] :
( sQ10_spl
<=> ( in(ordered_pair(sK3_skl(X1,X0,empty_set),sK4_skl(X1,X0,empty_set)),X1)
| X1 = relation_composition(empty_set,X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f253,f257,f261]) ).
fof(f265,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f72]) ).
fof(f266,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f265]) ).
fof(f268,plain,
! [X0,X1] :
( in(ordered_pair(sK3_skl(X1,sK8_skl,X0),sK4_skl(X1,sK8_skl,X0)),X1)
| X1 = relation_composition(X0,sK8_skl)
| ~ relation(X1)
| ~ relation(sK8_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f224,f58]) ).
fof(f269,plain,
! [X0,X1] :
( in(ordered_pair(sK3_skl(X1,X0,sK8_skl),sK4_skl(X1,X0,sK8_skl)),X1)
| X1 = relation_composition(sK8_skl,X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f224,f57]) ).
fof(f270,definition,
! [X0,X1] :
( sQ11_spl
<=> ( in(ordered_pair(sK3_skl(X1,sK8_skl,X0),sK4_skl(X1,sK8_skl,X0)),X1)
| X1 = relation_composition(X0,sK8_skl)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f273,definition,
( sQ12_spl
<=> relation(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( sQ12_spl
| ~ relation(sK8_skl) ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,plain,
( ~ sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f268,f270,f273]) ).
fof(f277,definition,
! [X0,X1] :
( sQ13_spl
<=> ( in(ordered_pair(sK3_skl(X1,X0,sK8_skl),sK4_skl(X1,X0,sK8_skl)),X1)
| X1 = relation_composition(sK8_skl,X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f269,f273,f277]) ).
fof(f281,plain,
( sQ12_spl
| ~ empty(sK8_skl) ),
inference(resolution,[status(thm)],[f275,f36]) ).
fof(f282,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f80]) ).
fof(f283,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f282]) ).
fof(f328,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ in(ordered_pair(X1,sK12_skl),X0)
| in(ordered_pair(X1,sK2_skl(sK12_skl,X1,relation_composition(X0,identity_relation(sK14_skl)),identity_relation(sK14_skl),X0)),X0)
| ~ relation(identity_relation(sK14_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f168,f214]) ).
fof(f335,definition,
! [X0,X1] :
( sQ14_spl
<=> ( ~ in(ordered_pair(X1,sK12_skl),X0)
| in(ordered_pair(X1,sK2_skl(sK12_skl,X1,relation_composition(X0,identity_relation(sK14_skl)),identity_relation(sK14_skl),X0)),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f338,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f328,f335,f158,f109]) ).
fof(f348,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ in(ordered_pair(X1,sK12_skl),X0)
| in(ordered_pair(sK2_skl(sK12_skl,X1,relation_composition(X0,identity_relation(sK14_skl)),identity_relation(sK14_skl),X0),sK12_skl),identity_relation(sK14_skl))
| ~ relation(identity_relation(sK14_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f176,f214]) ).
fof(f355,definition,
! [X0,X1] :
( sQ16_spl
<=> ( ~ in(ordered_pair(X1,sK12_skl),X0)
| in(ordered_pair(sK2_skl(sK12_skl,X1,relation_composition(X0,identity_relation(sK14_skl)),identity_relation(sK14_skl),X0),sK12_skl),identity_relation(sK14_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f358,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f348,f355,f158,f109]) ).
fof(f460,definition,
( sQ19_spl
<=> relation(identity_relation(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( sQ19_spl
| ~ relation(identity_relation(sK11_skl)) ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f468,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f462,f61]) ).
fof(f469,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f468]) ).
fof(f470,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ in(ordered_pair(sK12_skl,sK13_skl),sK11_skl) ),
inference(resolution,[status(thm)],[f211,f214]) ).
fof(f471,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f470,f113,f210,f109]) ).
fof(f472,plain,
$false,
inference(sat_refutation,[status(thm)],[f112,f116,f117,f167,f175,f178,f180,f208,f213,f242,f260,f264,f266,f276,f280,f283,f338,f358,f469,f471]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU191+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 05:56:37 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.07/0.36 % Refutation found
% 0.07/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.38 % Elapsed time: 0.067646 seconds
% 0.07/0.38 % CPU time: 0.310896 seconds
% 0.07/0.38 % Total memory used: 112.039 MB
% 0.07/0.38 % Net memory used: 111.229 MB
%------------------------------------------------------------------------------