%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO002-3 : 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 : n026.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 07:16:42 AM UTC 2026
% Result : Unsatisfiable 0.38s 0.50s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 12 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t3,axiom,
! [VAR_0,VAR_1] : between(VAR_0,VAR_1,VAR_1),
file('theBenchmark.p',t3) ).
cnf(c_52,plain,
between(A,B,B),
inference(clausify,[status(thm)],[t3]) ).
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(prove_a_between_a_and_b,axiom,
~ between(a,a,b),
file('theBenchmark.p',prove_a_between_a_and_b) ).
cnf(c_55,plain,
~ between(a,a,b),
inference(clausify,[status(thm)],[prove_a_between_a_and_b]) ).
cnf(c_248,plain,
between(A,A,B),
inference(resolve,[status(thm)],[c_54,c_52]) ).
cnf(c_249,plain,
$false,
inference(resolve,[status(thm)],[c_248,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.44 % Computer : n026.cluster.edu
% 0.12/0.44 % Model : x86_64 x86_64
% 0.12/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.44 % Memory : 8046.5625MB
% 0.12/0.44 % OS : Linux 6.8.0-71-generic
% 0.12/0.44 % CPULimit : 300
% 0.12/0.44 % WCLimit : 300
% 0.12/0.44 % DateTime : Fri Sep 25 12:31:54 UTC 2026
% 0.12/0.44 % CPUTime :
% 0.12/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.44 % Process 2512385 was started by sandbox on n026,
% 0.12/0.44 % Fri Sep 25 12:31:54 2026
% 0.12/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.45
% 0.12/0.45 % From the command line: assign(max_seconds, 300).
% 0.38/0.50
% 0.38/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.38/0.50
% 0.38/0.50 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.38/0.50 % Length of proof is 5.
% 0.38/0.50 % Level of proof is 2.
% 0.38/0.50 % Maximum clause weight is 13.000.
% 0.38/0.50 % Given clauses 45.
% 0.38/0.50
% 0.38/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------