%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU208+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 : n004.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 02:19:40 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 96 ( 13 unt; 14 def)
% Number of atoms : 333 ( 26 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 388 ( 151 ~; 159 |; 47 &)
% ( 24 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-4 aty)
% Number of variables : 140 ( 109 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f30,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,plain,
! [A] :
( ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ! [D] :
( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK2_skl(C,B,A),B)
& in(ordered_pair(sK1_skl(C,B,A),sK2_skl(C,B,A)),A) )
| in(sK1_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(sK1_skl(C,B,A),E),A) )
| ~ in(sK1_skl(C,B,A),C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ! [D] :
( ( in(sK0_skl(D,C,B,A),B)
& in(ordered_pair(D,sK0_skl(D,C,B,A)),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(E,sK0_skl(D,C,B,A)),skolemize(D,sK1_skl(C,B,A)),skolemize(E,sK2_skl(C,B,A))],[f40]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X3,sK0_skl(X3,X1,X2,X0)),X0)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( in(sK0_skl(X3,X1,X2,X0),X2)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X3,X4),X0)
| in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f48,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f49,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK5_skl(B,A),sK4_skl(B,A)),A)
| in(sK4_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK4_skl(B,A)),A)
| ~ in(sK4_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK3_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(D,sK3_skl(C,B,A)),skolemize(C,sK4_skl(B,A)),skolemize(D,sK5_skl(B,A))],[f50]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f59,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f67,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f68,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f73,plain,
empty(sK8_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f23]) ).
fof(f74,plain,
empty(sK8_skl),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f80,plain,
? [A,B,C] :
( ( in(A,relation_inverse_image(C,B))
<~> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) )
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f81,plain,
? [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| in(A,relation_inverse_image(C,B)) )
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
? [C] :
( ? [A,B] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| in(A,relation_inverse_image(C,B)) ) )
& relation(C) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,plain,
( ( ! [D] :
( ~ in(D,sK13_skl)
| ~ in(ordered_pair(sK12_skl,D),sK11_skl)
| ~ in(D,relation_rng(sK11_skl)) )
| ~ in(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl)) )
& ( ( in(sK14_skl,sK13_skl)
& in(ordered_pair(sK12_skl,sK14_skl),sK11_skl)
& in(sK14_skl,relation_rng(sK11_skl)) )
| in(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl)) )
& relation(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(C,sK11_skl),skolemize(A,sK12_skl),skolemize(B,sK13_skl),skolemize(D,sK14_skl)],[f82]) ).
fof(f84,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
( in(sK14_skl,relation_rng(sK11_skl))
| in(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl)) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f86,plain,
( in(ordered_pair(sK12_skl,sK14_skl),sK11_skl)
| in(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl)) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f87,plain,
( in(sK14_skl,sK13_skl)
| in(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl)) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f88,plain,
! [X0] :
( ~ in(X0,sK13_skl)
| ~ in(ordered_pair(sK12_skl,X0),sK11_skl)
| ~ in(X0,relation_rng(sK11_skl))
| ~ in(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl)) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f93,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f94,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f101,definition,
( sQ0_spl
<=> in(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ0_spl
| in(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,definition,
( sQ1_spl
<=> in(sK14_skl,relation_rng(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( ~ sQ1_spl
| in(sK14_skl,relation_rng(sK11_skl)) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f85,f101,f104]) ).
fof(f108,definition,
( sQ2_spl
<=> in(ordered_pair(sK12_skl,sK14_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( ~ sQ2_spl
| in(ordered_pair(sK12_skl,sK14_skl),sK11_skl) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f86,f101,f108]) ).
fof(f112,definition,
( sQ3_spl
<=> in(sK14_skl,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ3_spl
| in(sK14_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f87,f101,f112]) ).
fof(f116,definition,
! [X0] :
( sQ4_spl
<=> ( ~ in(X0,sK13_skl)
| ~ in(ordered_pair(sK12_skl,X0),sK11_skl)
| ~ in(X0,relation_rng(sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f117,plain,
! [X0] :
( ~ sQ4_spl
| ~ in(X0,sK13_skl)
| ~ in(ordered_pair(sK12_skl,X0),sK11_skl)
| ~ in(X0,relation_rng(sK11_skl)) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f88,f101,f116]) ).
fof(f120,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,sK0_skl(X1,relation_inverse_image(X0,X2),X2,X0)),X0)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f42]) ).
fof(f121,plain,
! [X0,X1,X2] :
( in(sK0_skl(X1,relation_inverse_image(X0,X2),X2,X0),X2)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f43]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X1,X3),X0)
| in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f44]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f128,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(sK14_skl,X0)
| in(sK12_skl,relation_inverse_image(sK11_skl,X0))
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f122,f109]) ).
fof(f129,definition,
( sQ5_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( sQ5_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,definition,
! [X0] :
( sQ6_spl
<=> ( ~ in(sK14_skl,X0)
| in(sK12_skl,relation_inverse_image(sK11_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f133,plain,
! [X0] :
( ~ sQ6_spl
| ~ in(sK14_skl,X0)
| in(sK12_skl,relation_inverse_image(sK11_skl,X0)) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,plain,
( ~ sQ2_spl
| sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f128,f129,f132,f108]) ).
fof(f140,plain,
empty(relation_rng(sK8_skl)),
inference(resolution,[status(thm)],[f74,f68]) ).
fof(f146,plain,
( ~ sQ0_spl
| in(sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl),sK13_skl,sK11_skl),sK13_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f102,f121]) ).
fof(f147,plain,
( ~ sQ0_spl
| in(ordered_pair(sK12_skl,sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl),sK13_skl,sK11_skl)),sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f102,f120]) ).
fof(f149,definition,
( sQ7_spl
<=> in(sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl),sK13_skl,sK11_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( ~ sQ0_spl
| sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f146,f129,f149,f101]) ).
fof(f153,definition,
( sQ8_spl
<=> in(ordered_pair(sK12_skl,sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl),sK13_skl,sK11_skl)),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ8_spl
| in(ordered_pair(sK12_skl,sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl),sK13_skl,sK11_skl)),sK11_skl) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( ~ sQ0_spl
| sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f147,f129,f153,f101]) ).
fof(f157,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f84]) ).
fof(f158,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f203,definition,
( sQ17_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( sQ17_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,definition,
( sQ18_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f214,plain,
relation_rng(sK8_skl) = empty_set,
inference(resolution,[status(thm)],[f94,f140]) ).
fof(f217,plain,
sK8_skl = empty_set,
inference(resolution,[status(thm)],[f94,f74]) ).
fof(f232,plain,
relation_rng(empty_set) = empty_set,
inference(forward_demodulation,[status(thm)],[f217,f214]) ).
fof(f234,plain,
( relation(empty_set)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f232,f69]) ).
fof(f237,plain,
( sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f234,f203,f206]) ).
fof(f238,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f59]) ).
fof(f239,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f251,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| in(sK12_skl,relation_inverse_image(sK11_skl,relation_rng(sK11_skl))) ),
inference(resolution,[status(thm)],[f133,f105]) ).
fof(f252,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| in(sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,relation_rng(sK11_skl)),relation_rng(sK11_skl),sK11_skl),relation_rng(sK11_skl))
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f251,f121]) ).
fof(f253,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| in(ordered_pair(sK12_skl,sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,relation_rng(sK11_skl)),relation_rng(sK11_skl),sK11_skl)),sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f251,f120]) ).
fof(f255,definition,
( sQ19_spl
<=> in(sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,relation_rng(sK11_skl)),relation_rng(sK11_skl),sK11_skl),relation_rng(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| sQ19_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f252,f129,f255,f132,f104]) ).
fof(f259,definition,
( sQ20_spl
<=> in(ordered_pair(sK12_skl,sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,relation_rng(sK11_skl)),relation_rng(sK11_skl),sK11_skl)),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| sQ20_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f253,f129,f259,f132,f104]) ).
fof(f264,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ in(sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl),sK13_skl,sK11_skl),sK13_skl)
| ~ in(sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl),sK13_skl,sK11_skl),relation_rng(sK11_skl)) ),
inference(resolution,[status(thm)],[f154,f117]) ).
fof(f265,plain,
( ~ sQ8_spl
| in(sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl),sK13_skl,sK11_skl),relation_rng(sK11_skl))
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f154,f124]) ).
fof(f268,definition,
( sQ21_spl
<=> in(sK0_skl(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl),sK13_skl,sK11_skl),relation_rng(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f264,f268,f149,f153,f116]) ).
fof(f272,plain,
( ~ sQ8_spl
| sQ21_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f265,f129,f268,f153]) ).
fof(f277,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| in(sK12_skl,relation_inverse_image(sK11_skl,sK13_skl)) ),
inference(resolution,[status(thm)],[f113,f133]) ).
fof(f279,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f277,f101,f112,f132]) ).
fof(f280,plain,
$false,
inference(sat_refutation,[status(thm)],[f107,f111,f115,f119,f135,f152,f156,f158,f237,f239,f258,f262,f271,f272,f279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU208+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n004.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 05:57:50 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.51 % Elapsed time: 0.064510 seconds
% 0.18/0.51 % CPU time: 0.176073 seconds
% 0.18/0.51 % Total memory used: 61.547 MB
% 0.18/0.51 % Net memory used: 61.443 MB
%------------------------------------------------------------------------------