%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO051-3 : 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 : n020.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 07:16:54 AM UTC 2026
% Result : Unsatisfiable 0.15s 6.04s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 15 unt; 0 def)
% Number of atoms : 47 ( 8 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 42 ( 20 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 19 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(b5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_1,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b5) ).
cnf(c_59,plain,
( between(B,C,D)
| ~ between(A,C,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b5]) ).
fof(b12,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_0,VAR_3,VAR_2)
| between(VAR_0,VAR_2,VAR_3)
| VAR_0 = VAR_1
| ~ between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b12) ).
cnf(c_90,plain,
( between(A,D,C)
| between(A,C,D)
| A = B
| ~ between(A,B,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b12]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_91,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(v_between_u_and_x,axiom,
between(u,v,x),
file('theBenchmark.p',v_between_u_and_x) ).
cnf(c_92,plain,
between(u,v,x),
inference(clausify,[status(thm)],[v_between_u_and_x]) ).
fof(u_not_v,axiom,
u != v,
file('theBenchmark.p',u_not_v) ).
cnf(c_93,plain,
u != v,
inference(clausify,[status(thm)],[u_not_v]) ).
cnf(c_94,plain,
v != u,
inference(copy,[status(thm)],[c_93]) ).
fof(w_not_between_v_and_x,axiom,
~ between(v,w,x),
file('theBenchmark.p',w_not_between_v_and_x) ).
cnf(c_95,plain,
~ between(v,w,x),
inference(clausify,[status(thm)],[w_not_between_v_and_x]) ).
fof(prove_x_between_v_and_w,axiom,
~ between(v,x,w),
file('theBenchmark.p',prove_x_between_v_and_w) ).
cnf(c_96,plain,
~ between(v,x,w),
inference(clausify,[status(thm)],[prove_x_between_v_and_w]) ).
cnf(c_808,plain,
( between(u,A,w)
| between(u,w,A)
| u = v
| ~ between(u,v,A) ),
inference(resolve,[status(thm)],[c_90,c_91]) ).
cnf(c_809,plain,
( between(u,x,w)
| between(u,w,x)
| u = v ),
inference(resolve,[status(thm)],[c_808,c_92]) ).
cnf(c_810,plain,
( between(u,x,w)
| between(u,w,x)
| v = u ),
inference(copy,[status(thm)],[c_809]) ).
cnf(c_699,plain,
( between(u,x,w)
| between(u,w,x) ),
inference(resolve,[status(thm)],[c_94,c_810]) ).
cnf(c_811,plain,
( between(v,w,A)
| ~ between(u,w,A) ),
inference(resolve,[status(thm)],[c_59,c_91]) ).
cnf(c_794,plain,
~ between(u,w,x),
inference(resolve,[status(thm)],[c_811,c_95]) ).
cnf(c_798,plain,
between(u,x,w),
inference(resolve,[status(thm)],[c_794,c_699]) ).
cnf(c_812,plain,
( between(v,x,A)
| ~ between(u,x,A) ),
inference(resolve,[status(thm)],[c_59,c_92]) ).
cnf(c_813,plain,
~ between(u,x,w),
inference(resolve,[status(thm)],[c_812,c_96]) ).
cnf(c_807,plain,
$false,
inference(resolve,[status(thm)],[c_798,c_813]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO051-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n020.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Fri Sep 25 12:37:40 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 2939541 was started by sandbox2 on n020,
% 0.11/5.38 % Fri Sep 25 12:37:40 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/6.04
% 0.15/6.04 % SZS status Unsatisfiable for theBenchmark
% 0.15/6.04
% 0.15/6.04 % Proof 1 at 0.57 (+ 0.08) seconds.
% 0.15/6.04 % Length of proof is 12.
% 0.15/6.04 % Level of proof is 4.
% 0.15/6.04 % Maximum clause weight is 24.000.
% 0.15/6.04 % Given clauses 72.
% 0.15/6.04
% 0.15/6.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------