%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRA010+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:30:40 PM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 4 unt; 3 def)
% Number of atoms : 112 ( 16 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 128 ( 47 ~; 43 |; 27 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 79 ( 64 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
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(f18,conjecture,
( complete
=> ! [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(f19,negated_conjecture,
~ ( complete
=> ! [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) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f108,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(f109,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)],[f108]) ).
fof(f110,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))],[f109]) ).
fof(f111,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)],[f110]) ).
fof(f112,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)],[f110]) ).
fof(f113,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)],[f110]) ).
fof(f114,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)],[f110]) ).
fof(f116,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) )
& complete ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f117,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) )
& complete ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f118,plain,
( number_of_in(sequential_pairs,sK8_skl) != number_of_in(triangles,sK8_skl)
& ! [E1,E2] :
( triangle(E1,E2,sK11_skl(E2,E1))
| ~ sequential(E1,E2)
| ~ on_path(E2,sK8_skl)
| ~ on_path(E1,sK8_skl) )
& path(sK9_skl,sK10_skl,sK8_skl)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl]),skolemize(P,sK8_skl),skolemize(V1,sK9_skl),skolemize(V2,sK10_skl),skolemize(E3,sK11_skl(E2,E1))],[f117]) ).
fof(f120,plain,
path(sK9_skl,sK10_skl,sK8_skl),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f121,plain,
! [X0,X1] :
( triangle(X0,X1,sK11_skl(X1,X0))
| ~ sequential(X0,X1)
| ~ on_path(X1,sK8_skl)
| ~ on_path(X0,sK8_skl) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f122,plain,
number_of_in(sequential_pairs,sK8_skl) != number_of_in(triangles,sK8_skl),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f251,definition,
! [X0,X1] :
( sQ5_spl
<=> ~ path(X0,X1,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f252,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ path(X0,X1,sK8_skl) ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f266,plain,
( ~ sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f120,f252]) ).
fof(f267,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f338,plain,
! [X0,X1] :
( on_path(sK6_skl(sK8_skl),sK8_skl)
| ~ path(X0,X1,sK8_skl) ),
inference(resolution,[status(thm)],[f111,f122]) ).
fof(f339,definition,
( sQ9_spl
<=> on_path(sK6_skl(sK8_skl),sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( sQ9_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f338,f251,f339]) ).
fof(f346,plain,
! [X0,X1] :
( on_path(sK7_skl(sK8_skl),sK8_skl)
| ~ path(X0,X1,sK8_skl) ),
inference(resolution,[status(thm)],[f112,f122]) ).
fof(f347,definition,
( sQ10_spl
<=> on_path(sK7_skl(sK8_skl),sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( sQ10_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f346,f251,f347]) ).
fof(f862,plain,
! [X0,X1,X2] :
( ~ sequential(sK6_skl(X2),sK7_skl(X2))
| ~ on_path(sK7_skl(X2),sK8_skl)
| ~ on_path(sK6_skl(X2),sK8_skl)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ path(X0,X1,X2) ),
inference(resolution,[status(thm)],[f114,f121]) ).
fof(f864,plain,
! [X0,X1,X2] :
( ~ on_path(sK7_skl(X2),sK8_skl)
| ~ on_path(sK6_skl(X2),sK8_skl)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ path(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f862,f113]) ).
fof(f910,plain,
! [X0,X1] :
( ~ on_path(sK7_skl(sK8_skl),sK8_skl)
| ~ on_path(sK6_skl(sK8_skl),sK8_skl)
| ~ path(X0,X1,sK8_skl) ),
inference(resolution,[status(thm)],[f864,f122]) ).
fof(f911,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f910,f251,f339,f347]) ).
fof(f912,plain,
$false,
inference(sat_refutation,[status(thm)],[f267,f342,f350,f911]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA010+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 18:18:26 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.45 % Refutation found
% 0.09/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.48 % Elapsed time: 0.101732 seconds
% 0.09/0.48 % CPU time: 0.515997 seconds
% 0.09/0.48 % Total memory used: 94.411 MB
% 0.09/0.48 % Net memory used: 93.615 MB
%------------------------------------------------------------------------------