%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO010-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:23:45 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 20
% Syntax : Number of formulae : 83 ( 3 unt; 11 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 183 ( 79 ~; 93 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 12 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X,Y,Z] :
( colinear(X,Y,Z)
| ~ between(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [Y,Z,X] :
( colinear(X,Y,Z)
| ~ between(Y,Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( colinear(X,Y,Z)
| ~ between(Z,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,Z] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f88,axiom,
! [W,V,U] :
( colinear(U,V,W)
| ~ between(W,V,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f89,axiom,
! [U,W,V] :
( colinear(U,V,W)
| ~ between(U,W,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,axiom,
! [V,U,W] :
( colinear(U,V,W)
| ~ between(V,U,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,hypothesis,
colinear(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,plain,
! [X0,X1,X2] :
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f116,plain,
! [X0,X1,X2] :
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f117,plain,
! [X0,X1,X2] :
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f118,plain,
! [X0,X1,X2] :
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f215,plain,
! [X0,X1,X2] :
( colinear(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f216,plain,
! [X0,X1,X2] :
( colinear(X0,X2,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f217,plain,
! [X0,X1,X2] :
( colinear(X1,X0,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f218,plain,
colinear(a,b,c),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f219,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f220,definition,
( sQ0_spl
<=> colinear(a,c,b) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ0_spl
| ~ colinear(a,c,b) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
( sQ1_spl
<=> colinear(b,a,c) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ1_spl
| ~ colinear(b,a,c) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
( sQ2_spl
<=> colinear(b,c,a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f229,definition,
( sQ3_spl
<=> colinear(c,a,b) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( sQ3_spl
| ~ colinear(c,a,b) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f232,definition,
( sQ4_spl
<=> colinear(c,b,a) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( ~ sQ4_spl
| colinear(c,b,a) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f234,plain,
( sQ4_spl
| ~ colinear(c,b,a) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f219,f220,f223,f226,f229,f232]) ).
fof(f239,plain,
( between(c,a,b)
| between(b,c,a)
| between(a,b,c) ),
inference(resolution,[status(thm)],[f118,f218]) ).
fof(f240,definition,
( sQ5_spl
<=> between(a,b,c) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( ~ sQ5_spl
| between(a,b,c) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,definition,
( sQ6_spl
<=> between(b,c,a) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( ~ sQ6_spl
| between(b,c,a) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,definition,
( sQ7_spl
<=> between(c,a,b) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( ~ sQ7_spl
| between(c,a,b) ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f239,f240,f243,f246]) ).
fof(f251,plain,
( ~ sQ7_spl
| colinear(b,c,a) ),
inference(resolution,[status(thm)],[f247,f116]) ).
fof(f252,plain,
( ~ sQ7_spl
| colinear(c,a,b) ),
inference(resolution,[status(thm)],[f247,f115]) ).
fof(f253,plain,
( ~ sQ6_spl
| colinear(c,a,b) ),
inference(resolution,[status(thm)],[f244,f117]) ).
fof(f255,plain,
( ~ sQ6_spl
| colinear(b,c,a) ),
inference(resolution,[status(thm)],[f244,f115]) ).
fof(f263,plain,
( ~ sQ5_spl
| colinear(c,b,a) ),
inference(resolution,[status(thm)],[f215,f241]) ).
fof(f266,plain,
( ~ sQ5_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f234]) ).
fof(f267,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f268,plain,
( sQ3_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f252]) ).
fof(f269,plain,
( sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f271,plain,
( ~ sQ6_spl
| colinear(c,b,a) ),
inference(resolution,[status(thm)],[f217,f244]) ).
fof(f289,plain,
( ~ sQ4_spl
| between(a,c,b)
| between(b,a,c)
| between(c,b,a) ),
inference(resolution,[status(thm)],[f233,f118]) ).
fof(f290,definition,
( sQ8_spl
<=> between(c,b,a) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( ~ sQ8_spl
| between(c,b,a) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,definition,
( sQ9_spl
<=> between(b,a,c) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( ~ sQ9_spl
| between(b,a,c) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,definition,
( sQ10_spl
<=> between(a,c,b) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ10_spl
| between(a,c,b) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,plain,
( ~ sQ4_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f289,f290,f293,f296,f232]) ).
fof(f304,plain,
( ~ sQ10_spl
| colinear(b,a,c) ),
inference(resolution,[status(thm)],[f297,f116]) ).
fof(f311,plain,
( ~ sQ9_spl
| colinear(a,c,b) ),
inference(resolution,[status(thm)],[f294,f117]) ).
fof(f313,plain,
( ~ sQ9_spl
| colinear(b,a,c) ),
inference(resolution,[status(thm)],[f294,f115]) ).
fof(f318,plain,
( ~ sQ8_spl
| colinear(a,c,b) ),
inference(resolution,[status(thm)],[f291,f116]) ).
fof(f328,plain,
( ~ sQ9_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f225]) ).
fof(f329,plain,
( ~ sQ9_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f328]) ).
fof(f357,plain,
( ~ sQ8_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f222]) ).
fof(f358,plain,
( ~ sQ8_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f362,plain,
( ~ sQ5_spl
| colinear(b,c,a) ),
inference(resolution,[status(thm)],[f241,f117]) ).
fof(f363,plain,
( ~ sQ5_spl
| colinear(c,a,b) ),
inference(resolution,[status(thm)],[f241,f116]) ).
fof(f402,plain,
( ~ sQ10_spl
| colinear(a,c,b) ),
inference(resolution,[status(thm)],[f297,f115]) ).
fof(f429,plain,
( sQ1_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f304]) ).
fof(f430,plain,
( sQ1_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f429]) ).
fof(f431,plain,
( ~ sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f311,f220,f293]) ).
fof(f433,plain,
( ~ sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f271,f232,f243]) ).
fof(f434,plain,
( ~ sQ6_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f255,f226,f243]) ).
fof(f449,plain,
( ~ sQ8_spl
| colinear(b,a,c) ),
inference(resolution,[status(thm)],[f291,f117]) ).
fof(f452,plain,
( ~ sQ8_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f449,f223,f290]) ).
fof(f453,plain,
( ~ sQ10_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f402,f220,f296]) ).
fof(f456,plain,
( ~ sQ5_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f362,f226,f240]) ).
fof(f458,plain,
( ~ sQ6_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f253,f229,f243]) ).
fof(f459,plain,
( ~ sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f363,f229,f240]) ).
fof(f461,plain,
( ~ sQ7_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f251,f226,f246]) ).
fof(f464,plain,
( ~ sQ7_spl
| colinear(a,c,b) ),
inference(resolution,[status(thm)],[f247,f217]) ).
fof(f465,plain,
( ~ sQ7_spl
| colinear(c,b,a) ),
inference(resolution,[status(thm)],[f247,f216]) ).
fof(f470,plain,
( ~ sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f464,f220,f246]) ).
fof(f471,plain,
( ~ sQ7_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f465,f232,f246]) ).
fof(f472,plain,
$false,
inference(sat_refutation,[status(thm)],[f235,f249,f267,f269,f299,f329,f358,f430,f431,f433,f434,f452,f453,f456,f458,f459,f461,f470,f471]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO010-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 08:16:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.40 % Refutation found
% 0.08/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.054689 seconds
% 0.08/0.42 % CPU time: 0.177140 seconds
% 0.08/0.42 % Total memory used: 98.571 MB
% 0.08/0.42 % Net memory used: 98.453 MB
%------------------------------------------------------------------------------