%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRA002+3 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:30:38 PM UTC 2026
% Result : Theorem 0.22s 10.52s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 91 ( 13 unt; 11 def)
% Number of atoms : 315 ( 45 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 349 ( 125 ~; 124 |; 71 &)
% ( 13 <=>; 12 =>; 1 <=; 3 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 12 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 193 ( 168 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [V1,V2,P] :
( path(V1,V2,P)
=> ( ? [E] :
( ( ( P = path_cons(E,empty)
& V2 = head_of(E) )
<~> ? [TP] :
( P = path_cons(E,TP)
& path(head_of(E),V2,TP) ) )
& V1 = tail_of(E)
& edge(E) )
& vertex(V2)
& vertex(V1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [P,V1,V2] :
( path(V1,V2,P)
=> ! [E1,E2] :
( precedes(E1,E2,P)
<= ( ( ? [E3] :
( precedes(E3,E2,P)
& sequential(E1,E3) )
| sequential(E1,E2) )
& on_path(E2,P)
& on_path(E1,P) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [V1,V2,SP] :
( shortest_path(V1,V2,SP)
<=> ( ! [P] :
( path(V1,V2,P)
=> less_or_equal(length_of(SP),length_of(P)) )
& V1 != V2
& path(V1,V2,SP) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [V1,V2,P] :
( path(V1,V2,P)
=> number_of_in(sequential_pairs,P) = minus(length_of(P),n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [P,V1,V2] :
( ( ! [E1,E2] :
( ( sequential(E1,E2)
& on_path(E2,P)
& on_path(E1,P) )
=> ? [E3] : triangle(E1,E2,E3) )
& path(V1,V2,P) )
=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Things,InThese] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,lemma,
( complete
=> ! [V1,V2,E1,E2,P] :
( ( sequential(E1,E2)
& precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ? [E3] : triangle(E1,E2,E3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f38,plain,
! [V1,V2,P] :
( ( ? [E] :
( ( ( P = path_cons(E,empty)
& V2 = head_of(E) )
<~> ? [TP] :
( P = path_cons(E,TP)
& path(head_of(E),V2,TP) ) )
& V1 = tail_of(E)
& edge(E) )
& vertex(V2)
& vertex(V1) )
| ~ path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f39,definition,
! [V2,P,E] :
( sP1_prd(E,P,V2)
<=> ( P = path_cons(E,empty)
& V2 = head_of(E) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f40,plain,
! [V1,V2,P] :
( ( ? [E] :
( ( sP1_prd(E,P,V2)
<~> ? [TP] :
( P = path_cons(E,TP)
& path(head_of(E),V2,TP) ) )
& V1 = tail_of(E)
& edge(E) )
& vertex(V2)
& vertex(V1) )
| ~ path(V1,V2,P) ),
inference(formula_renaming,[status(thm)],[f38,f39]) ).
fof(f41,plain,
! [V1,V2,P] :
( ( ? [E] :
( ( ! [TP] :
( P != path_cons(E,TP)
| ~ path(head_of(E),V2,TP) )
| ~ sP1_prd(E,P,V2) )
& ( ? [TP] :
( P = path_cons(E,TP)
& path(head_of(E),V2,TP) )
| sP1_prd(E,P,V2) )
& V1 = tail_of(E)
& edge(E) )
& vertex(V2)
& vertex(V1) )
| ~ path(V1,V2,P) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [V1,V2,P] :
( ( ( ! [TP] :
( P != path_cons(sK1_skl(P,V2,V1),TP)
| ~ path(head_of(sK1_skl(P,V2,V1)),V2,TP) )
| ~ sP1_prd(sK1_skl(P,V2,V1),P,V2) )
& ( ( P = path_cons(sK1_skl(P,V2,V1),sK2_skl(P,V2,V1))
& path(head_of(sK1_skl(P,V2,V1)),V2,sK2_skl(P,V2,V1)) )
| sP1_prd(sK1_skl(P,V2,V1),P,V2) )
& V1 = tail_of(sK1_skl(P,V2,V1))
& edge(sK1_skl(P,V2,V1))
& vertex(V2)
& vertex(V1) )
| ~ path(V1,V2,P) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(E,sK1_skl(P,V2,V1)),skolemize(TP,sK2_skl(P,V2,V1))],[f41]) ).
fof(f45,plain,
! [X0,X1,X2] :
( edge(sK1_skl(X2,X1,X0))
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f68,plain,
! [P,V1,V2] :
( ! [E1,E2] :
( ( ! [E3] :
( ~ precedes(E3,E2,P)
| ~ sequential(E1,E3) )
& ~ sequential(E1,E2) )
| ~ on_path(E2,P)
| ~ on_path(E1,P)
| precedes(E1,E2,P) )
| ~ path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f69,plain,
! [P] :
( ! [E1,E2] :
( ( ! [E3] :
( ~ precedes(E3,E2,P)
| ~ sequential(E1,E3) )
& ~ sequential(E1,E2) )
| ~ on_path(E2,P)
| ~ on_path(E1,P)
| precedes(E1,E2,P) )
| ! [V1,V2] : ~ path(V1,V2,P) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f81,plain,
! [V1,V2,SP] :
( shortest_path(V1,V2,SP)
<=> ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f82,plain,
! [V1,V2,SP] :
( ( ? [P] :
( ~ less_or_equal(length_of(SP),length_of(P))
& path(V1,V2,P) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ( ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) )
| ~ shortest_path(V1,V2,SP) ) ),
inference(NNF_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
( ! [V1,V2,SP] :
( ? [P] :
( ~ less_or_equal(length_of(SP),length_of(P))
& path(V1,V2,P) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ! [V1,V2,SP] :
( ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) )
| ~ shortest_path(V1,V2,SP) ) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f84,plain,
( ! [V1,V2,SP] :
( ( ~ less_or_equal(length_of(SP),length_of(sK5_skl(SP,V2,V1)))
& path(V1,V2,sK5_skl(SP,V2,V1)) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ! [V1,V2,SP] :
( ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) )
| ~ shortest_path(V1,V2,SP) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(P,sK5_skl(SP,V2,V1))],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f106,plain,
! [V1,V2,P] :
( number_of_in(sequential_pairs,P) = minus(length_of(P),n1)
| ~ path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f107,plain,
! [P] :
( number_of_in(sequential_pairs,P) = minus(length_of(P),n1)
| ! [V1,V2] : ~ path(V1,V2,P) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f108,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [P,V1,V2] :
( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
| ? [E1,E2] :
( ! [E3] : ~ triangle(E1,E2,E3)
& sequential(E1,E2)
& on_path(E2,P)
& on_path(E1,P) )
| ~ path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f110,plain,
! [P] :
( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
| ? [E1,E2] :
( ! [E3] : ~ triangle(E1,E2,E3)
& sequential(E1,E2)
& on_path(E2,P)
& on_path(E1,P) )
| ! [V1,V2] : ~ path(V1,V2,P) ),
inference(miniscoping,[status(thm)],[f109]) ).
fof(f111,plain,
! [P] :
( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
| ( ! [E3] : ~ triangle(sK6_skl(P),sK7_skl(P),E3)
& sequential(sK6_skl(P),sK7_skl(P))
& on_path(sK7_skl(P),P)
& on_path(sK6_skl(P),P) )
| ! [V1,V2] : ~ path(V1,V2,P) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(E1,sK6_skl(P)),skolemize(E2,sK7_skl(P))],[f110]) ).
fof(f112,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| on_path(sK6_skl(X2),X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| on_path(sK7_skl(X2),X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f114,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| sequential(sK6_skl(X2),sK7_skl(X2))
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ triangle(sK6_skl(X2),sK7_skl(X2),X3)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f116,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f117,plain,
( ! [V1,V2,E1,E2,P] :
( ? [E3] : triangle(E1,E2,E3)
| ~ sequential(E1,E2)
| ~ precedes(E1,E2,P)
| ~ shortest_path(V1,V2,P) )
| ~ complete ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f118,plain,
( ! [E1,E2] :
( ? [E3] : triangle(E1,E2,E3)
| ~ sequential(E1,E2)
| ! [P] :
( ~ precedes(E1,E2,P)
| ! [V1,V2] : ~ shortest_path(V1,V2,P) ) )
| ~ complete ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
( ! [E1,E2] :
( triangle(E1,E2,sK8_skl(E2,E1))
| ~ sequential(E1,E2)
| ! [P] :
( ~ precedes(E1,E2,P)
| ! [V1,V2] : ~ shortest_path(V1,V2,P) ) )
| ~ complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(E3,sK8_skl(E2,E1))],[f118]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4] :
( triangle(X3,X4,sK8_skl(X4,X3))
| ~ sequential(X3,X4)
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2)
| ~ complete ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
( ? [P,V1,V2] :
( ~ less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph))
& shortest_path(V1,V2,P) )
& complete ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f122,plain,
( ? [P] :
( ~ less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph))
& ? [V1,V2] : shortest_path(V1,V2,P) )
& complete ),
inference(miniscoping,[status(thm)],[f121]) ).
fof(f123,plain,
( ~ less_or_equal(minus(length_of(sK9_skl),n1),number_of_in(triangles,graph))
& shortest_path(sK10_skl,sK11_skl,sK9_skl)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl]),skolemize(P,sK9_skl),skolemize(V1,sK10_skl),skolemize(V2,sK11_skl)],[f122]) ).
fof(f124,plain,
complete,
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
shortest_path(sK10_skl,sK11_skl,sK9_skl),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f126,plain,
~ less_or_equal(minus(length_of(sK9_skl),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f137,definition,
( sQ0_spl
<=> complete ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( sQ0_spl
| ~ complete ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f156,definition,
! [X0,X1,X2,X3,X4] :
( sQ5_spl
<=> ( triangle(X3,X4,sK8_skl(X4,X3))
| ~ sequential(X3,X4)
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f157,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ5_spl
| triangle(X3,X4,sK8_skl(X4,X3))
| ~ sequential(X3,X4)
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f120,f137,f156]) ).
fof(f171,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f124]) ).
fof(f172,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f173,plain,
path(sK10_skl,sK11_skl,sK9_skl),
inference(resolution,[status(thm)],[f85,f125]) ).
fof(f179,plain,
number_of_in(sequential_pairs,sK9_skl) = minus(length_of(sK9_skl),n1),
inference(resolution,[status(thm)],[f173,f108]) ).
fof(f180,plain,
~ less_or_equal(number_of_in(sequential_pairs,sK9_skl),number_of_in(triangles,graph)),
inference(backward_demodulation,[status(thm)],[f179,f126]) ).
fof(f188,plain,
edge(sK1_skl(sK9_skl,sK11_skl,sK10_skl)),
inference(resolution,[status(thm)],[f45,f173]) ).
fof(f231,definition,
( sQ12_spl
<=> edge(sK1_skl(sK9_skl,sK11_skl,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ12_spl
| ~ edge(sK1_skl(sK9_skl,sK11_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f301,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| ~ on_path(X1,sK9_skl)
| ~ on_path(X0,sK9_skl)
| precedes(X0,X1,sK9_skl) ),
inference(resolution,[status(thm)],[f173,f70]) ).
fof(f363,plain,
( number_of_in(sequential_pairs,sK9_skl) = number_of_in(triangles,sK9_skl)
| on_path(sK6_skl(sK9_skl),sK9_skl) ),
inference(resolution,[status(thm)],[f112,f173]) ).
fof(f364,definition,
( sQ23_spl
<=> on_path(sK6_skl(sK9_skl),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f367,definition,
( sQ24_spl
<=> number_of_in(sequential_pairs,sK9_skl) = number_of_in(triangles,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( ~ sQ24_spl
| number_of_in(sequential_pairs,sK9_skl) = number_of_in(triangles,sK9_skl) ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,plain,
( sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f363,f364,f367]) ).
fof(f390,plain,
( ~ sQ24_spl
| less_or_equal(number_of_in(sequential_pairs,sK9_skl),number_of_in(triangles,graph)) ),
inference(paramodulation,[status(thm)],[f368,f116]) ).
fof(f391,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f390,f180]) ).
fof(f392,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f391]) ).
fof(f424,plain,
( number_of_in(sequential_pairs,sK9_skl) = number_of_in(triangles,sK9_skl)
| on_path(sK7_skl(sK9_skl),sK9_skl) ),
inference(resolution,[status(thm)],[f113,f173]) ).
fof(f425,definition,
( sQ29_spl
<=> on_path(sK7_skl(sK9_skl),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f428,plain,
( sQ24_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f424,f425,f367]) ).
fof(f429,plain,
( number_of_in(sequential_pairs,sK9_skl) = number_of_in(triangles,sK9_skl)
| sequential(sK6_skl(sK9_skl),sK7_skl(sK9_skl)) ),
inference(resolution,[status(thm)],[f114,f173]) ).
fof(f430,definition,
( sQ30_spl
<=> sequential(sK6_skl(sK9_skl),sK7_skl(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( ~ sQ30_spl
| sequential(sK6_skl(sK9_skl),sK7_skl(sK9_skl)) ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,plain,
( sQ24_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f429,f430,f367]) ).
fof(f434,plain,
! [X0] :
( number_of_in(sequential_pairs,sK9_skl) = number_of_in(triangles,sK9_skl)
| ~ triangle(sK6_skl(sK9_skl),sK7_skl(sK9_skl),X0) ),
inference(resolution,[status(thm)],[f115,f173]) ).
fof(f435,definition,
! [X0] :
( sQ31_spl
<=> ~ triangle(sK6_skl(sK9_skl),sK7_skl(sK9_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f436,plain,
! [X0] :
( ~ sQ31_spl
| ~ triangle(sK6_skl(sK9_skl),sK7_skl(sK9_skl),X0) ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,plain,
( sQ24_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f434,f435,f367]) ).
fof(f503,plain,
( ~ sQ30_spl
| ~ on_path(sK7_skl(sK9_skl),sK9_skl)
| ~ on_path(sK6_skl(sK9_skl),sK9_skl)
| precedes(sK6_skl(sK9_skl),sK7_skl(sK9_skl),sK9_skl) ),
inference(resolution,[status(thm)],[f431,f301]) ).
fof(f508,definition,
( sQ36_spl
<=> precedes(sK6_skl(sK9_skl),sK7_skl(sK9_skl),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( ~ sQ36_spl
| precedes(sK6_skl(sK9_skl),sK7_skl(sK9_skl),sK9_skl) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,plain,
( ~ sQ30_spl
| ~ sQ29_spl
| ~ sQ23_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f503,f508,f364,f425,f430]) ).
fof(f706,plain,
! [X0,X1] :
( ~ sQ5_spl
| triangle(X0,X1,sK8_skl(X1,X0))
| ~ sequential(X0,X1)
| ~ precedes(X0,X1,sK9_skl) ),
inference(resolution,[status(thm)],[f157,f125]) ).
fof(f891,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f188]) ).
fof(f892,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f891]) ).
fof(f1095,plain,
( ~ sQ5_spl
| ~ sQ36_spl
| triangle(sK6_skl(sK9_skl),sK7_skl(sK9_skl),sK8_skl(sK7_skl(sK9_skl),sK6_skl(sK9_skl)))
| ~ sequential(sK6_skl(sK9_skl),sK7_skl(sK9_skl)) ),
inference(resolution,[status(thm)],[f509,f706]) ).
fof(f1103,definition,
( sQ96_spl
<=> triangle(sK6_skl(sK9_skl),sK7_skl(sK9_skl),sK8_skl(sK7_skl(sK9_skl),sK6_skl(sK9_skl))) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1104,plain,
( ~ sQ96_spl
| triangle(sK6_skl(sK9_skl),sK7_skl(sK9_skl),sK8_skl(sK7_skl(sK9_skl),sK6_skl(sK9_skl))) ),
inference(component_clause,[status(thm)],[f1103]) ).
fof(f1106,plain,
( ~ sQ5_spl
| ~ sQ36_spl
| sQ96_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1095,f430,f1103,f508,f156]) ).
fof(f1120,plain,
( ~ sQ96_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1104,f436]) ).
fof(f1121,plain,
( ~ sQ96_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f1120]) ).
fof(f1122,plain,
$false,
inference(sat_refutation,[status(thm)],[f159,f172,f370,f392,f428,f433,f438,f511,f892,f1106,f1121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRA002+3 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/10.44 % Computer : n008.cluster.edu
% 0.17/10.44 % Model : x86_64 x86_64
% 0.17/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.44 % Memory : 8046.5625MB
% 0.17/10.44 % OS : Linux 6.8.0-71-generic
% 0.17/10.44 % CPULimit : 300
% 0.17/10.44 % WCLimit : 300
% 0.17/10.44 % DateTime : Sun Sep 20 18:19:20 UTC 2026
% 0.17/10.44 % CPUTime :
% 0.17/10.45 % Drodi V4.1.1
% 0.22/10.52 % Refutation found
% 0.22/10.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/10.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/10.55 % Elapsed time: 0.097965 seconds
% 0.22/10.55 % CPU time: 0.428419 seconds
% 0.22/10.55 % Total memory used: 68.071 MB
% 0.22/10.55 % Net memory used: 67.669 MB
%------------------------------------------------------------------------------