%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO006-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:23:43 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 10 unt; 5 def)
% Number of atoms : 66 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 27 ~; 25 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U,V,W] :
( U = V
| ~ between(V,U,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
between(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( between(a,d,c)
| between(c,a,d) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f110,plain,
! [X0,X1,X2] :
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f112,plain,
! [U,V] :
( U = V
| ! [W] :
( ~ between(V,U,W)
| ~ between(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f113,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f116,plain,
a != c,
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f118,plain,
c != d,
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f119,plain,
between(a,c,d),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f120,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f121,definition,
( sQ0_spl
<=> between(c,a,d) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f124,definition,
( sQ1_spl
<=> between(a,d,c) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ1_spl
| between(a,d,c) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f120,f121,f124]) ).
fof(f135,plain,
between(d,c,a),
inference(resolution,[status(thm)],[f110,f119]) ).
fof(f142,plain,
( c = d
| ~ between(c,d,a) ),
inference(resolution,[status(thm)],[f113,f135]) ).
fof(f143,plain,
( c = a
| ~ between(c,a,d) ),
inference(resolution,[status(thm)],[f113,f119]) ).
fof(f151,definition,
( sQ3_spl
<=> between(c,d,a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( sQ3_spl
| ~ between(c,d,a) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
( sQ4_spl
<=> c = d ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ4_spl
| c = d ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f142,f151,f154]) ).
fof(f158,definition,
( sQ5_spl
<=> c = a ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( ~ sQ5_spl
| c = a ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f143,f121,f158]) ).
fof(f167,plain,
( ~ sQ1_spl
| between(c,d,a) ),
inference(resolution,[status(thm)],[f125,f110]) ).
fof(f172,plain,
( ~ sQ1_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f153]) ).
fof(f173,plain,
( ~ sQ1_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f174,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f116]) ).
fof(f175,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f174]) ).
fof(f176,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f118]) ).
fof(f177,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f176]) ).
fof(f178,plain,
$false,
inference(sat_refutation,[status(thm)],[f127,f157,f161,f173,f175,f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n020.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 20 08:16:16 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.19/0.43 % Drodi V4.1.1
% 0.19/0.46 % Refutation found
% 0.19/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.50 % Elapsed time: 0.075602 seconds
% 0.19/0.50 % CPU time: 0.106082 seconds
% 0.19/0.50 % Total memory used: 3.237 MB
% 0.19/0.50 % Net memory used: 3.235 MB
%------------------------------------------------------------------------------