%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO064-3 : 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 : 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 : Sun Sep 27 07:16:57 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.71s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 6 !; 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(t1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( between(VAR_2,VAR_1,VAR_0)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t1) ).
cnf(c_59,plain,
( between(C,B,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t1]) ).
fof(v_between_w_and_u,axiom,
between(w,v,u),
file('theBenchmark.p',v_between_w_and_u) ).
cnf(c_101,plain,
between(w,v,u),
inference(clausify,[status(thm)],[v_between_w_and_u]) ).
fof(prove_uvw_colinear,axiom,
~ colinear(u,v,w),
file('theBenchmark.p',prove_uvw_colinear) ).
cnf(c_102,plain,
~ colinear(u,v,w),
inference(clausify,[status(thm)],[prove_uvw_colinear]) ).
cnf(c_636,plain,
between(u,v,w),
inference(resolve,[status(thm)],[c_101,c_59]) ).
cnf(c_730,plain,
~ between(u,v,w),
inference(resolve,[status(thm)],[c_19,c_102]) ).
cnf(c_729,plain,
$false,
inference(resolve,[status(thm)],[c_636,c_730]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO064-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n004.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 12:38:27 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3186379 was started by sandbox2 on n004,
% 0.10/5.38 % Fri Sep 25 12:38:27 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.71
% 0.15/5.71 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.71
% 0.15/5.71 % Proof 1 at 0.27 (+ 0.04) seconds.
% 0.15/5.71 % Length of proof is 6.
% 0.15/5.71 % Level of proof is 2.
% 0.15/5.71 % Maximum clause weight is 13.000.
% 0.15/5.71 % Given clauses 79.
% 0.15/5.71
% 0.15/5.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------