%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO046-3 : 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 : 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 07:16:53 AM UTC 2026
% Result : Unsatisfiable 2.04s 0.92s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 38 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 16 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 24 ( 0 sgn 11 !; 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(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_58,plain,
( between(B,C,D)
| ~ between(A,C,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b5]) ).
fof(b7,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = VAR_2
| between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_1,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b7) ).
cnf(c_60,plain,
( B = C
| between(A,B,D)
| ~ between(B,C,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b7]) ).
fof(v_between_u_and_x,axiom,
between(u,v,x),
file('theBenchmark.p',v_between_u_and_x) ).
cnf(c_61,plain,
between(u,v,x),
inference(clausify,[status(thm)],[v_between_u_and_x]) ).
fof(w_between_v_and_x,axiom,
between(v,w,x),
file('theBenchmark.p',w_between_v_and_x) ).
cnf(c_62,plain,
between(v,w,x),
inference(clausify,[status(thm)],[w_between_v_and_x]) ).
fof(prove_w_between_u_and_x,axiom,
~ between(u,w,x),
file('theBenchmark.p',prove_w_between_u_and_x) ).
cnf(c_63,plain,
~ between(u,w,x),
inference(clausify,[status(thm)],[prove_w_between_u_and_x]) ).
cnf(c_278,plain,
between(x,v,u),
inference(resolve,[status(thm)],[c_61,c_54]) ).
cnf(c_340,plain,
between(x,w,v),
inference(resolve,[status(thm)],[c_62,c_54]) ).
cnf(c_402,plain,
~ between(x,w,u),
inference(resolve,[status(thm)],[c_54,c_63]) ).
cnf(c_635,plain,
( between(w,v,A)
| ~ between(x,v,A) ),
inference(resolve,[status(thm)],[c_58,c_340]) ).
cnf(c_539,plain,
between(w,v,u),
inference(resolve,[status(thm)],[c_635,c_278]) ).
cnf(c_636,plain,
( w = v
| between(x,w,A)
| ~ between(w,v,A) ),
inference(resolve,[status(thm)],[c_60,c_340]) ).
cnf(c_637,plain,
( w = v
| between(x,w,u) ),
inference(resolve,[status(thm)],[c_636,c_539]) ).
cnf(c_601,plain,
w = v,
inference(resolve,[status(thm)],[c_402,c_637]) ).
cnf(c_638,plain,
~ between(x,v,u),
inference(paramod,[status(thm)],[c_601,c_402]) ).
cnf(c_634,plain,
$false,
inference(resolve,[status(thm)],[c_278,c_638]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO046-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n015.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Fri Sep 25 12:39:13 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 1356087 was started by sandbox on n015,
% 0.08/0.37 % Fri Sep 25 12:39:13 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 2.04/0.92
% 2.04/0.92 % SZS status Unsatisfiable for theBenchmark
% 2.04/0.92
% 2.04/0.92 % Proof 1 at 0.23 (+ 0.05) seconds.
% 2.04/0.92 % Length of proof is 12.
% 2.04/0.92 % Level of proof is 4.
% 2.04/0.92 % Maximum clause weight is 20.000.
% 2.04/0.92 % Given clauses 68.
% 2.04/0.92
% 2.04/0.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------