%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO047-3 : 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 : n001.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 07:16:53 AM UTC 2026
% Result : Unsatisfiable 1.25s 0.56s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 11 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 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 : 15 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_54,plain,
( between(C,B,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t1]) ).
fof(b8,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_0,VAR_3,VAR_2)
| ~ between(VAR_1,VAR_3,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b8) ).
cnf(c_61,plain,
( between(A,D,C)
| ~ between(B,D,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b8]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_62,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(w_between_u_and_x,axiom,
between(u,w,x),
file('theBenchmark.p',w_between_u_and_x) ).
cnf(c_63,plain,
between(u,w,x),
inference(clausify,[status(thm)],[w_between_u_and_x]) ).
fof(prove_v_between_u_and_x,axiom,
~ between(u,v,x),
file('theBenchmark.p',prove_v_between_u_and_x) ).
cnf(c_64,plain,
~ between(u,v,x),
inference(clausify,[status(thm)],[prove_v_between_u_and_x]) ).
cnf(c_284,plain,
between(w,v,u),
inference(resolve,[status(thm)],[c_62,c_54]) ).
cnf(c_348,plain,
between(x,w,u),
inference(resolve,[status(thm)],[c_63,c_54]) ).
cnf(c_406,plain,
~ between(x,v,u),
inference(resolve,[status(thm)],[c_54,c_64]) ).
cnf(c_537,plain,
( between(x,A,u)
| ~ between(w,A,u) ),
inference(resolve,[status(thm)],[c_61,c_348]) ).
cnf(c_538,plain,
between(x,v,u),
inference(resolve,[status(thm)],[c_537,c_284]) ).
cnf(c_536,plain,
$false,
inference(resolve,[status(thm)],[c_406,c_538]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO047-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 12:41:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3296334 was started by sandbox on n001,
% 0.11/0.37 % Fri Sep 25 12:41:25 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 1.25/0.56
% 1.25/0.56 % SZS status Unsatisfiable for theBenchmark
% 1.25/0.56
% 1.25/0.56 % Proof 1 at 0.15 (+ 0.02) seconds.
% 1.25/0.56 % Length of proof is 9.
% 1.25/0.56 % Level of proof is 2.
% 1.25/0.56 % Maximum clause weight is 17.000.
% 1.25/0.56 % Given clauses 68.
% 1.25/0.56
% 1.25/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------