%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO067-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 : Sun Sep 27 07:16:58 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 51 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 60 ( 33 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 28 ( 4 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(colinearity1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( colinear(VAR_0,VAR_1,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',colinearity1) ).
cnf(c_19,plain,
( colinear(A,B,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[colinearity1]) ).
fof(colinearity2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( colinear(VAR_2,VAR_0,VAR_1)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',colinearity2) ).
cnf(c_20,plain,
( colinear(C,A,B)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[colinearity2]) ).
fof(colinearity3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( colinear(VAR_1,VAR_2,VAR_0)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',colinearity3) ).
cnf(c_21,plain,
( colinear(B,C,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[colinearity3]) ).
fof(t3,axiom,
! [VAR_0,VAR_1] : between(VAR_0,VAR_1,VAR_1),
file('theBenchmark.p',t3) ).
cnf(c_57,plain,
between(A,B,B),
inference(clausify,[status(thm)],[t3]) ).
fof(part_1,axiom,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
file('theBenchmark.p',part_1) ).
cnf(c_110,plain,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(clausify,[status(thm)],[part_1]) ).
cnf(c_111,plain,
( y = x
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(copy,[status(thm)],[c_110]) ).
fof(part_2,axiom,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
file('theBenchmark.p',part_2) ).
cnf(c_112,plain,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(clausify,[status(thm)],[part_2]) ).
cnf(c_218,plain,
colinear(A,A,B),
inference(resolve,[status(thm)],[c_57,c_21]) ).
cnf(c_219,plain,
colinear(A,B,A),
inference(resolve,[status(thm)],[c_57,c_20]) ).
cnf(c_220,plain,
colinear(A,B,B),
inference(resolve,[status(thm)],[c_57,c_19]) ).
cnf(c_234,plain,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x) ),
inference(resolve,[status(thm)],[c_218,c_112]) ).
cnf(c_235,plain,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x) ),
inference(resolve,[status(thm)],[c_219,c_234]) ).
cnf(c_231,plain,
~ colinear(x,z,y),
inference(resolve,[status(thm)],[c_220,c_235]) ).
cnf(c_236,plain,
( y = x
| ~ colinear(y,x,x)
| ~ colinear(x,y,x) ),
inference(resolve,[status(thm)],[c_218,c_111]) ).
cnf(c_237,plain,
( y = x
| ~ colinear(y,x,x) ),
inference(resolve,[status(thm)],[c_219,c_236]) ).
cnf(c_232,plain,
y = x,
inference(resolve,[status(thm)],[c_220,c_237]) ).
cnf(c_238,plain,
~ colinear(x,z,x),
inference(paramod,[status(thm)],[c_232,c_231]) ).
cnf(c_233,plain,
$false,
inference(resolve,[status(thm)],[c_219,c_238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO067-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 12:40:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1976062 was started by sandbox2 on n018,
% 0.10/0.36 % Fri Sep 25 12:40:05 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.46
% 0.13/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.46
% 0.13/0.46 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.13/0.46 % Length of proof is 13.
% 0.13/0.46 % Level of proof is 3.
% 0.13/0.46 % Maximum clause weight is 16.000.
% 0.13/0.46 % Given clauses 44.
% 0.13/0.46
% 0.13/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------