%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO045-3 : 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 : n008.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 0.16s 10.82s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 31 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 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 : 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(b6,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = VAR_2
| between(VAR_0,VAR_2,VAR_3)
| ~ between(VAR_1,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b6) ).
cnf(c_59,plain,
( B = C
| between(A,C,D)
| ~ between(B,C,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b6]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_60,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(w_between_v_and_x,axiom,
between(v,w,x),
file('theBenchmark.p',w_between_v_and_x) ).
cnf(c_61,plain,
between(v,w,x),
inference(clausify,[status(thm)],[w_between_v_and_x]) ).
fof(v_not_w,axiom,
v != w,
file('theBenchmark.p',v_not_w) ).
cnf(c_62,plain,
v != w,
inference(clausify,[status(thm)],[v_not_w]) ).
cnf(c_63,plain,
w != v,
inference(copy,[status(thm)],[c_62]) ).
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_274,plain,
between(w,v,u),
inference(resolve,[status(thm)],[c_60,c_54]) ).
cnf(c_333,plain,
between(x,w,v),
inference(resolve,[status(thm)],[c_61,c_54]) ).
cnf(c_393,plain,
~ between(x,v,u),
inference(resolve,[status(thm)],[c_54,c_64]) ).
cnf(c_512,plain,
( w = v
| between(x,v,A)
| ~ between(w,v,A) ),
inference(resolve,[status(thm)],[c_59,c_333]) ).
cnf(c_513,plain,
( w = v
| between(x,v,u) ),
inference(resolve,[status(thm)],[c_512,c_274]) ).
cnf(c_514,plain,
w = v,
inference(resolve,[status(thm)],[c_393,c_513]) ).
cnf(c_511,plain,
$false,
inference(resolve,[status(thm)],[c_63,c_514]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO045-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.39 % Computer : n008.cluster.edu
% 0.09/10.39 % Model : x86_64 x86_64
% 0.09/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.39 % Memory : 8046.5625MB
% 0.09/10.39 % OS : Linux 6.8.0-71-generic
% 0.09/10.39 % CPULimit : 300
% 0.09/10.39 % WCLimit : 300
% 0.09/10.39 % DateTime : Fri Sep 25 12:36:54 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.39 % Process 1054108 was started by sandbox on n008,
% 0.09/10.39 % Fri Sep 25 12:36:54 2026
% 0.09/10.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/10.40
% 0.16/10.40 % From the command line: assign(max_seconds, 300).
% 0.16/10.82
% 0.16/10.82 % SZS status Unsatisfiable for theBenchmark
% 0.16/10.82
% 0.16/10.82 % Proof 1 at 0.35 (+ 0.06) seconds.
% 0.16/10.82 % Length of proof is 11.
% 0.16/10.82 % Level of proof is 2.
% 0.16/10.82 % Maximum clause weight is 20.000.
% 0.16/10.82 % Given clauses 67.
% 0.16/10.82
% 0.16/10.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------