%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO006-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:16:43 AM UTC 2026
% Result : Unsatisfiable 0.94s 0.51s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 32 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(b2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_1
| ~ between(VAR_1,VAR_0,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b2) ).
cnf(c_56,plain,
( A = B
| ~ between(B,A,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b2]) ).
fof(b3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_2
| ~ between(VAR_0,VAR_2,VAR_1)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b3) ).
cnf(c_57,plain,
( B = C
| ~ between(A,C,B)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b3]) ).
fof(a_not_c,axiom,
a != c,
file('theBenchmark.p',a_not_c) ).
cnf(c_58,plain,
a != c,
inference(clausify,[status(thm)],[a_not_c]) ).
cnf(c_59,plain,
c != a,
inference(copy,[status(thm)],[c_58]) ).
fof(c_not_d,axiom,
c != d,
file('theBenchmark.p',c_not_d) ).
cnf(c_62,plain,
c != d,
inference(clausify,[status(thm)],[c_not_d]) ).
cnf(c_63,plain,
d != c,
inference(copy,[status(thm)],[c_62]) ).
fof(c_between_a_and_d,axiom,
between(a,c,d),
file('theBenchmark.p',c_between_a_and_d) ).
cnf(c_64,plain,
between(a,c,d),
inference(clausify,[status(thm)],[c_between_a_and_d]) ).
fof(prove_not_between_others,axiom,
( between(a,d,c)
| between(c,a,d) ),
file('theBenchmark.p',prove_not_between_others) ).
cnf(c_65,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(clausify,[status(thm)],[prove_not_between_others]) ).
cnf(c_337,plain,
( d = c
| ~ between(a,d,c) ),
inference(resolve,[status(thm)],[c_64,c_57]) ).
cnf(c_286,plain,
~ between(a,d,c),
inference(resolve,[status(thm)],[c_63,c_337]) ).
cnf(c_338,plain,
( c = a
| ~ between(c,a,d) ),
inference(resolve,[status(thm)],[c_64,c_56]) ).
cnf(c_287,plain,
~ between(c,a,d),
inference(resolve,[status(thm)],[c_59,c_338]) ).
cnf(c_339,plain,
between(a,d,c),
inference(resolve,[status(thm)],[c_287,c_65]) ).
cnf(c_336,plain,
$false,
inference(resolve,[status(thm)],[c_286,c_339]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 12:32:23 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 170754 was started by sandbox2 on n003,
% 0.10/0.36 % Fri Sep 25 12:32:23 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.94/0.51
% 0.94/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.94/0.51
% 0.94/0.51 % Proof 1 at 0.12 (+ 0.02) seconds.
% 0.94/0.51 % Length of proof is 11.
% 0.94/0.51 % Level of proof is 3.
% 0.94/0.51 % Maximum clause weight is 16.000.
% 0.94/0.51 % Given clauses 48.
% 0.94/0.51
% 0.94/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------