%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO007-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 07:16:44 AM UTC 2026
% Result : Unsatisfiable 6.68s 6.26s
% Output : CNFRefutation 6.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 17 unt; 0 def)
% Number of atoms : 40 ( 7 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 32 ( 16 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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_55,plain,
( between(C,B,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t1]) ).
fof(b13,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_1,VAR_3,VAR_2)
| between(VAR_1,VAR_2,VAR_3)
| VAR_0 = VAR_1
| ~ between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b13) ).
cnf(c_91,plain,
( between(B,D,C)
| between(B,C,D)
| A = B
| ~ between(A,B,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b13]) ).
fof(a_not_c,axiom,
a != c,
file('theBenchmark.p',a_not_c) ).
cnf(c_92,plain,
a != c,
inference(clausify,[status(thm)],[a_not_c]) ).
cnf(c_93,plain,
c != a,
inference(copy,[status(thm)],[c_92]) ).
fof(a_between_a_and_c,axiom,
between(d,a,c),
file('theBenchmark.p',a_between_a_and_c) ).
cnf(c_94,plain,
between(d,a,c),
inference(clausify,[status(thm)],[a_between_a_and_c]) ).
fof(a_between_a_and_e,axiom,
between(e,a,c),
file('theBenchmark.p',a_between_a_and_e) ).
cnf(c_95,plain,
between(e,a,c),
inference(clausify,[status(thm)],[a_between_a_and_e]) ).
fof(e_not_between_d_and_a,axiom,
~ between(d,e,a),
file('theBenchmark.p',e_not_between_d_and_a) ).
cnf(c_96,plain,
~ between(d,e,a),
inference(clausify,[status(thm)],[e_not_between_d_and_a]) ).
fof(prove_d_between_e_and_a,axiom,
~ between(e,d,a),
file('theBenchmark.p',prove_d_between_e_and_a) ).
cnf(c_97,plain,
~ between(e,d,a),
inference(clausify,[status(thm)],[prove_d_between_e_and_a]) ).
cnf(c_602,plain,
between(c,a,d),
inference(resolve,[status(thm)],[c_94,c_55]) ).
cnf(c_707,plain,
between(c,a,e),
inference(resolve,[status(thm)],[c_95,c_55]) ).
cnf(c_816,plain,
~ between(a,e,d),
inference(resolve,[status(thm)],[c_55,c_96]) ).
cnf(c_852,plain,
~ between(a,d,e),
inference(resolve,[status(thm)],[c_55,c_97]) ).
cnf(c_1109,plain,
( between(a,A,d)
| between(a,d,A)
| c = a
| ~ between(c,a,A) ),
inference(resolve,[status(thm)],[c_91,c_602]) ).
cnf(c_1110,plain,
( between(a,e,d)
| between(a,d,e)
| c = a ),
inference(resolve,[status(thm)],[c_1109,c_707]) ).
cnf(c_1111,plain,
( between(a,e,d)
| between(a,d,e) ),
inference(resolve,[status(thm)],[c_93,c_1110]) ).
cnf(c_1112,plain,
between(a,e,d),
inference(resolve,[status(thm)],[c_852,c_1111]) ).
cnf(c_1108,plain,
$false,
inference(resolve,[status(thm)],[c_816,c_1112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO007-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.35 % Computer : n002.cluster.edu
% 0.08/5.35 % Model : x86_64 x86_64
% 0.08/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.35 % Memory : 8046.5625MB
% 0.08/5.35 % OS : Linux 6.8.0-71-generic
% 0.08/5.35 % CPULimit : 300
% 0.08/5.35 % WCLimit : 300
% 0.08/5.35 % DateTime : Fri Sep 25 12:33:26 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.36 % Process 3259783 was started by sandbox2 on n002,
% 0.08/5.36 % Fri Sep 25 12:33:26 2026
% 0.08/5.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.36
% 0.08/5.36 % From the command line: assign(max_seconds, 300).
% 6.68/6.26
% 6.68/6.26 % SZS status Unsatisfiable for theBenchmark
% 6.68/6.26
% 6.68/6.26 % Proof 1 at 0.80 (+ 0.09) seconds.
% 6.68/6.26 % Length of proof is 13.
% 6.68/6.26 % Level of proof is 2.
% 6.68/6.26 % Maximum clause weight is 24.000.
% 6.68/6.26 % Given clauses 100.
% 6.68/6.26
% 6.68/6.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------