%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO052-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.18s 7.92s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 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(t9,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_0,VAR_3,VAR_1)
| between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_0,VAR_3,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t9) ).
cnf(c_93,plain,
( between(A,D,B)
| between(A,B,D)
| ~ between(A,D,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t9]) ).
fof(v_between_u_and_x,axiom,
between(u,v,x),
file('theBenchmark.p',v_between_u_and_x) ).
cnf(c_94,plain,
between(u,v,x),
inference(clausify,[status(thm)],[v_between_u_and_x]) ).
fof(w_between_u_and_x,axiom,
between(u,w,x),
file('theBenchmark.p',w_between_u_and_x) ).
cnf(c_95,plain,
between(u,w,x),
inference(clausify,[status(thm)],[w_between_u_and_x]) ).
fof(w_not_between_v_and_x,axiom,
~ between(v,w,x),
file('theBenchmark.p',w_not_between_v_and_x) ).
cnf(c_96,plain,
~ between(v,w,x),
inference(clausify,[status(thm)],[w_not_between_v_and_x]) ).
fof(prove_v_between_w_and_x,axiom,
~ between(w,v,x),
file('theBenchmark.p',prove_v_between_w_and_x) ).
cnf(c_97,plain,
~ between(w,v,x),
inference(clausify,[status(thm)],[prove_v_between_w_and_x]) ).
cnf(c_830,plain,
( between(u,A,v)
| between(u,v,A)
| ~ between(u,A,x) ),
inference(resolve,[status(thm)],[c_93,c_94]) ).
cnf(c_716,plain,
( between(u,w,v)
| between(u,v,w) ),
inference(resolve,[status(thm)],[c_830,c_95]) ).
cnf(c_831,plain,
( between(A,w,x)
| ~ between(u,A,w) ),
inference(resolve,[status(thm)],[c_59,c_95]) ).
cnf(c_807,plain,
~ between(u,v,w),
inference(resolve,[status(thm)],[c_831,c_96]) ).
cnf(c_813,plain,
between(u,w,v),
inference(resolve,[status(thm)],[c_807,c_716]) ).
cnf(c_832,plain,
( between(A,v,x)
| ~ between(u,A,v) ),
inference(resolve,[status(thm)],[c_59,c_94]) ).
cnf(c_833,plain,
~ between(u,w,v),
inference(resolve,[status(thm)],[c_832,c_97]) ).
cnf(c_829,plain,
$false,
inference(resolve,[status(thm)],[c_813,c_833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO052-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/7.27 % Computer : n010.cluster.edu
% 0.13/7.27 % Model : x86_64 x86_64
% 0.13/7.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/7.27 % Memory : 8046.5625MB
% 0.13/7.27 % OS : Linux 6.8.0-71-generic
% 0.13/7.27 % CPULimit : 300
% 0.13/7.27 % WCLimit : 300
% 0.13/7.27 % DateTime : Fri Sep 25 12:36:58 UTC 2026
% 0.13/7.28 % CPUTime :
% 0.13/7.28 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/7.28 % Process 756763 was started by sandbox on n010,
% 0.13/7.28 % Fri Sep 25 12:36:58 2026
% 0.13/7.28 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/7.28
% 0.13/7.28 % From the command line: assign(max_seconds, 300).
% 0.18/7.92
% 0.18/7.92 % SZS status Unsatisfiable for theBenchmark
% 0.18/7.92
% 0.18/7.92 % Proof 1 at 0.56 (+ 0.07) seconds.
% 0.18/7.92 % Length of proof is 10.
% 0.18/7.92 % Level of proof is 3.
% 0.18/7.92 % Maximum clause weight is 21.000.
% 0.18/7.92 % Given clauses 74.
% 0.18/7.92
% 0.18/7.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------