%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO258+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:24:45 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 3 unt; 4 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 110 ( 42 ~; 49 |; 12 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 54 ( 50 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [L,A,B,C] :
( between_on_line(L,A,B,C)
<=> ( ( before_on_line(L,B,A)
& before_on_line(L,C,B) )
| ( before_on_line(L,B,C)
& before_on_line(L,A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [L,A,B,C] :
( between_on_line(L,A,B,C)
=> between_on_line(L,C,B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [L,A,B,C] :
( between_on_line(L,A,B,C)
=> between_on_line(L,C,B,A) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f84,plain,
! [L,A,B,C] :
( ( ( ( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B) )
& ( ~ before_on_line(L,B,C)
| ~ before_on_line(L,A,B) ) )
| between_on_line(L,A,B,C) )
& ( ( before_on_line(L,B,A)
& before_on_line(L,C,B) )
| ( before_on_line(L,B,C)
& before_on_line(L,A,B) )
| ~ between_on_line(L,A,B,C) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f85,plain,
( ! [L,A,B,C] :
( ( ( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B) )
& ( ~ before_on_line(L,B,C)
| ~ before_on_line(L,A,B) ) )
| between_on_line(L,A,B,C) )
& ! [L,A,B,C] :
( ( before_on_line(L,B,A)
& before_on_line(L,C,B) )
| ( before_on_line(L,B,C)
& before_on_line(L,A,B) )
| ~ between_on_line(L,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( before_on_line(X0,X3,X2)
| before_on_line(X0,X1,X2)
| ~ between_on_line(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( before_on_line(X0,X2,X1)
| before_on_line(X0,X1,X2)
| ~ between_on_line(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( before_on_line(X0,X3,X2)
| before_on_line(X0,X2,X3)
| ~ between_on_line(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( before_on_line(X0,X2,X1)
| before_on_line(X0,X2,X3)
| ~ between_on_line(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( ~ before_on_line(X0,X2,X3)
| ~ before_on_line(X0,X1,X2)
| between_on_line(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( ~ before_on_line(X0,X2,X1)
| ~ before_on_line(X0,X3,X2)
| between_on_line(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f152,plain,
? [L,A,B,C] :
( ~ between_on_line(L,C,B,A)
& between_on_line(L,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
( ~ between_on_line(sK0_skl,sK3_skl,sK2_skl,sK1_skl)
& between_on_line(sK0_skl,sK1_skl,sK2_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(L,sK0_skl),skolemize(A,sK1_skl),skolemize(B,sK2_skl),skolemize(C,sK3_skl)],[f152]) ).
fof(f154,plain,
between_on_line(sK0_skl,sK1_skl,sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
~ between_on_line(sK0_skl,sK3_skl,sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f161,plain,
( before_on_line(sK0_skl,sK3_skl,sK2_skl)
| before_on_line(sK0_skl,sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f86,f154]) ).
fof(f162,definition,
( sQ0_spl
<=> before_on_line(sK0_skl,sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( ~ sQ0_spl
| before_on_line(sK0_skl,sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,definition,
( sQ1_spl
<=> before_on_line(sK0_skl,sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ1_spl
| before_on_line(sK0_skl,sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f161,f162,f165]) ).
fof(f169,plain,
( before_on_line(sK0_skl,sK2_skl,sK1_skl)
| before_on_line(sK0_skl,sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f87,f154]) ).
fof(f170,definition,
( sQ2_spl
<=> before_on_line(sK0_skl,sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( ~ sQ2_spl
| before_on_line(sK0_skl,sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f169,f162,f170]) ).
fof(f174,plain,
( before_on_line(sK0_skl,sK3_skl,sK2_skl)
| before_on_line(sK0_skl,sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f88,f154]) ).
fof(f175,definition,
( sQ3_spl
<=> before_on_line(sK0_skl,sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ3_spl
| before_on_line(sK0_skl,sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f174,f175,f165]) ).
fof(f179,plain,
( before_on_line(sK0_skl,sK2_skl,sK1_skl)
| before_on_line(sK0_skl,sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f89,f154]) ).
fof(f180,plain,
( sQ2_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f179,f175,f170]) ).
fof(f184,plain,
! [X0] :
( ~ sQ0_spl
| ~ before_on_line(sK0_skl,sK2_skl,X0)
| between_on_line(sK0_skl,X0,sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f91,f163]) ).
fof(f188,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| between_on_line(sK0_skl,sK3_skl,sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f184,f176]) ).
fof(f189,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f155]) ).
fof(f190,plain,
( ~ sQ3_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f194,plain,
! [X0] :
( ~ sQ2_spl
| ~ before_on_line(sK0_skl,X0,sK2_skl)
| between_on_line(sK0_skl,X0,sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f171,f90]) ).
fof(f196,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| between_on_line(sK0_skl,sK3_skl,sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f194,f166]) ).
fof(f197,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f155]) ).
fof(f198,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f199,plain,
$false,
inference(sat_refutation,[status(thm)],[f168,f173,f178,f180,f190,f198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO258+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 14:48:50 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.041863 seconds
% 0.13/0.42 % CPU time: 0.089406 seconds
% 0.13/0.42 % Total memory used: 10.812 MB
% 0.13/0.42 % Net memory used: 10.775 MB
%------------------------------------------------------------------------------