%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO010-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.10s 0.57s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 26
% Syntax : Number of formulae : 111 ( 12 unt; 14 def)
% Number of atoms : 254 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 259 ( 116 ~; 129 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 90 ( 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f23,hypothesis,
colinear(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,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(f28,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f47,plain,
! [X0,X1,X2] :
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
! [X0,X1,X2] :
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f49,plain,
! [X0,X1,X2] :
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f50,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(f51,plain,
colinear(a,b,c),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f52,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)],[f24]) ).
fof(f53,definition,
( sQ0_spl
<=> colinear(a,c,b) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ0_spl
| ~ colinear(a,c,b) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ1_spl
<=> colinear(b,a,c) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f59,definition,
( sQ2_spl
<=> colinear(b,c,a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( sQ2_spl
| ~ colinear(b,c,a) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,definition,
( sQ3_spl
<=> colinear(c,a,b) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( sQ3_spl
| ~ colinear(c,a,b) ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,definition,
( sQ4_spl
<=> colinear(c,b,a) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( sQ4_spl
| ~ colinear(c,b,a) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f53,f56,f59,f62,f65]) ).
fof(f69,plain,
( between(c,a,b)
| between(b,c,a)
| between(a,b,c) ),
inference(resolution,[status(thm)],[f50,f51]) ).
fof(f70,definition,
( sQ5_spl
<=> between(a,b,c) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ5_spl
| between(a,b,c) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ6_spl
<=> between(b,c,a) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ6_spl
| between(b,c,a) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,definition,
( sQ7_spl
<=> between(c,a,b) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ7_spl
| between(c,a,b) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f69,f70,f73,f76]) ).
fof(f81,plain,
( ~ sQ7_spl
| colinear(b,c,a) ),
inference(resolution,[status(thm)],[f77,f48]) ).
fof(f82,plain,
( ~ sQ7_spl
| colinear(c,a,b) ),
inference(resolution,[status(thm)],[f77,f47]) ).
fof(f83,plain,
( ~ sQ6_spl
| colinear(c,a,b) ),
inference(resolution,[status(thm)],[f74,f49]) ).
fof(f85,plain,
( ~ sQ6_spl
| colinear(b,c,a) ),
inference(resolution,[status(thm)],[f74,f47]) ).
fof(f86,plain,
( ~ sQ5_spl
| colinear(b,c,a) ),
inference(resolution,[status(thm)],[f71,f49]) ).
fof(f100,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f31,f29]) ).
fof(f105,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f100,f30]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( X1 = inner_pasch(X0,X1,X2,X3,X1)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f35,f34]) ).
fof(f146,plain,
! [X0,X1,X2,X3,X4] :
( colinear(inner_pasch(X0,X1,X2,X4,X3),X0,X4)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f36,f49]) ).
fof(f160,plain,
! [X0,X1,X2] :
( X1 = inner_pasch(X0,X1,X2,X2,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f108,f105]) ).
fof(f161,plain,
( ~ sQ5_spl
| b = inner_pasch(a,b,c,c,b) ),
inference(resolution,[status(thm)],[f160,f71]) ).
fof(f162,plain,
( ~ sQ6_spl
| c = inner_pasch(b,c,a,a,c) ),
inference(resolution,[status(thm)],[f160,f74]) ).
fof(f163,plain,
( ~ sQ7_spl
| a = inner_pasch(c,a,b,b,a) ),
inference(resolution,[status(thm)],[f160,f77]) ).
fof(f223,plain,
( ~ sQ5_spl
| colinear(b,a,c)
| ~ between(b,c,c)
| ~ between(a,b,c) ),
inference(paramodulation,[status(thm)],[f161,f146]) ).
fof(f224,plain,
( ~ sQ5_spl
| between(c,b,a)
| ~ between(b,c,c)
| ~ between(a,b,c) ),
inference(paramodulation,[status(thm)],[f161,f36]) ).
fof(f229,definition,
( sQ8_spl
<=> between(b,c,c) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( sQ8_spl
| ~ between(b,c,c) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f232,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f223,f70,f229,f56]) ).
fof(f233,definition,
( sQ9_spl
<=> between(c,b,a) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f234,plain,
( ~ sQ9_spl
| between(c,b,a) ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f236,plain,
( sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f224,f70,f229,f233]) ).
fof(f247,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f105]) ).
fof(f248,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f281,plain,
( ~ sQ9_spl
| colinear(c,b,a) ),
inference(resolution,[status(thm)],[f234,f47]) ).
fof(f282,plain,
( ~ sQ9_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f67]) ).
fof(f283,plain,
( ~ sQ9_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f282]) ).
fof(f284,plain,
( sQ3_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f64,f82]) ).
fof(f285,plain,
( sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f284]) ).
fof(f287,definition,
( sQ12_spl
<=> between(b,a,c) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( ~ sQ12_spl
| between(b,a,c) ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f290,definition,
( sQ13_spl
<=> between(a,c,b) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( ~ sQ13_spl
| between(a,c,b) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f298,plain,
( ~ sQ13_spl
| colinear(b,a,c) ),
inference(resolution,[status(thm)],[f291,f48]) ).
fof(f299,plain,
( ~ sQ13_spl
| colinear(a,c,b) ),
inference(resolution,[status(thm)],[f291,f47]) ).
fof(f304,plain,
( ~ sQ12_spl
| colinear(c,b,a) ),
inference(resolution,[status(thm)],[f288,f48]) ).
fof(f305,plain,
( ~ sQ12_spl
| colinear(b,a,c) ),
inference(resolution,[status(thm)],[f288,f47]) ).
fof(f306,plain,
( ~ sQ6_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f61]) ).
fof(f307,plain,
( ~ sQ6_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f314,plain,
( sQ0_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f299]) ).
fof(f315,plain,
( sQ0_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f314]) ).
fof(f322,plain,
( ~ sQ9_spl
| colinear(a,c,b) ),
inference(resolution,[status(thm)],[f234,f48]) ).
fof(f333,plain,
( ~ sQ12_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f304,f65,f287]) ).
fof(f334,plain,
( ~ sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f322,f53,f233]) ).
fof(f336,plain,
( ~ sQ13_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f298,f56,f290]) ).
fof(f337,plain,
( sQ3_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f64,f83]) ).
fof(f338,plain,
( sQ3_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f348,plain,
( ~ sQ12_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f305,f56,f287]) ).
fof(f366,plain,
( ~ sQ6_spl
| colinear(c,b,a)
| ~ between(c,a,a)
| ~ between(b,c,a) ),
inference(paramodulation,[status(thm)],[f162,f146]) ).
fof(f367,plain,
( ~ sQ6_spl
| between(a,c,b)
| ~ between(c,a,a)
| ~ between(b,c,a) ),
inference(paramodulation,[status(thm)],[f162,f36]) ).
fof(f372,definition,
( sQ14_spl
<=> between(c,a,a) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( sQ14_spl
| ~ between(c,a,a) ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f375,plain,
( sQ4_spl
| ~ sQ14_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f366,f73,f372,f65]) ).
fof(f376,plain,
( sQ13_spl
| ~ sQ14_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f367,f73,f372,f290]) ).
fof(f387,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f374,f105]) ).
fof(f388,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f387]) ).
fof(f389,plain,
( ~ sQ7_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f81,f59,f76]) ).
fof(f400,plain,
( ~ sQ7_spl
| colinear(a,c,b)
| ~ between(a,b,b)
| ~ between(c,a,b) ),
inference(paramodulation,[status(thm)],[f163,f146]) ).
fof(f401,plain,
( ~ sQ7_spl
| between(b,a,c)
| ~ between(a,b,b)
| ~ between(c,a,b) ),
inference(paramodulation,[status(thm)],[f163,f36]) ).
fof(f406,definition,
( sQ17_spl
<=> between(a,b,b) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f408,plain,
( sQ17_spl
| ~ between(a,b,b) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,plain,
( sQ0_spl
| ~ sQ17_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f400,f76,f406,f53]) ).
fof(f410,plain,
( sQ12_spl
| ~ sQ17_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f401,f76,f406,f287]) ).
fof(f421,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f408,f105]) ).
fof(f422,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f421]) ).
fof(f423,plain,
( ~ sQ5_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f86,f59,f70]) ).
fof(f428,plain,
( ~ sQ5_spl
| colinear(c,a,b) ),
inference(resolution,[status(thm)],[f71,f48]) ).
fof(f430,plain,
( ~ sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f428,f62,f70]) ).
fof(f431,plain,
$false,
inference(sat_refutation,[status(thm)],[f68,f79,f232,f236,f248,f283,f285,f307,f315,f333,f334,f336,f338,f348,f375,f376,f388,f389,f409,f410,f422,f423,f430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.49 % Computer : n018.cluster.edu
% 0.10/0.49 % Model : x86_64 x86_64
% 0.10/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.49 % Memory : 8046.5625MB
% 0.10/0.49 % OS : Linux 6.8.0-71-generic
% 0.10/0.49 % CPULimit : 300
% 0.10/0.49 % WCLimit : 300
% 0.10/0.49 % DateTime : Sun Sep 20 08:17:13 UTC 2026
% 0.10/0.49 % CPUTime :
% 0.10/0.50 % Drodi V4.1.1
% 0.10/0.57 % Refutation found
% 0.10/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.59 % Elapsed time: 0.086797 seconds
% 0.10/0.59 % CPU time: 0.372946 seconds
% 0.10/0.59 % Total memory used: 84.599 MB
% 0.10/0.59 % Net memory used: 83.847 MB
%------------------------------------------------------------------------------