%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO067-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /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 : Sun Sep 27 07:16:58 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 60 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 35 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 54 ( 9 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(identity_for_equidistance,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_1
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_2) ),
file('theBenchmark.p',identity_for_equidistance) ).
cnf(c_3,plain,
( A = B
| ~ equidistant(A,B,C,C) ),
inference(clausify,[status(thm)],[identity_for_equidistance]) ).
fof(segment_construction1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : between(VAR_0,VAR_1,extension(VAR_0,VAR_1,VAR_2,VAR_3)),
file('theBenchmark.p',segment_construction1) ).
cnf(c_4,plain,
between(A,B,extension(A,B,C,D)),
inference(clausify,[status(thm)],[segment_construction1]) ).
fof(segment_construction2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : equidistant(VAR_0,extension(VAR_1,VAR_0,VAR_2,VAR_3),VAR_2,VAR_3),
file('theBenchmark.p',segment_construction2) ).
cnf(c_5,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(clausify,[status(thm)],[segment_construction2]) ).
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(part_1,axiom,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
file('theBenchmark.p',part_1) ).
cnf(c_23,plain,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(clausify,[status(thm)],[part_1]) ).
cnf(c_24,plain,
( y = x
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(copy,[status(thm)],[c_23]) ).
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_25,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_183,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_46,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_183]) ).
cnf(c_132,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_46,c_4]) ).
cnf(c_158,plain,
colinear(A,A,B),
inference(resolve,[status(thm)],[c_132,c_21]) ).
cnf(c_159,plain,
colinear(A,B,A),
inference(resolve,[status(thm)],[c_132,c_20]) ).
cnf(c_160,plain,
colinear(A,B,B),
inference(resolve,[status(thm)],[c_132,c_19]) ).
cnf(c_184,plain,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x) ),
inference(resolve,[status(thm)],[c_158,c_25]) ).
cnf(c_185,plain,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x) ),
inference(resolve,[status(thm)],[c_159,c_184]) ).
cnf(c_177,plain,
~ colinear(x,z,y),
inference(resolve,[status(thm)],[c_160,c_185]) ).
cnf(c_186,plain,
( y = x
| ~ colinear(y,x,x)
| ~ colinear(x,y,x) ),
inference(resolve,[status(thm)],[c_158,c_24]) ).
cnf(c_187,plain,
( y = x
| ~ colinear(y,x,x) ),
inference(resolve,[status(thm)],[c_159,c_186]) ).
cnf(c_178,plain,
y = x,
inference(resolve,[status(thm)],[c_160,c_187]) ).
cnf(c_188,plain,
~ colinear(x,z,x),
inference(paramod,[status(thm)],[c_178,c_177]) ).
cnf(c_182,plain,
$false,
inference(resolve,[status(thm)],[c_159,c_188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO067-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 12:41:27 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1362914 was started by sandbox on n015,
% 0.18/0.45 % Fri Sep 25 12:41:27 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.48
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.48
% 0.18/0.48 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.18/0.48 % Length of proof is 17.
% 0.18/0.48 % Level of proof is 5.
% 0.18/0.48 % Maximum clause weight is 21.000.
% 0.18/0.48 % Given clauses 47.
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------