%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO039-3 : 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 : n007.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 07:16:52 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 17 unt; 0 def)
% Number of atoms : 27 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 32 ( 10 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(identity_for_betweeness,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ between(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',identity_for_betweeness) ).
cnf(c_7,plain,
( A = B
| ~ between(A,B,A) ),
inference(clausify,[status(thm)],[identity_for_betweeness]) ).
fof(e1,axiom,
! [VAR_0,VAR_1,VAR_2] : VAR_0 = extension(VAR_1,VAR_0,VAR_2,VAR_2),
file('theBenchmark.p',e1) ).
cnf(c_29,plain,
A = extension(B,A,C,C),
inference(clausify,[status(thm)],[e1]) ).
cnf(c_30,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_29]) ).
fof(b0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_1,VAR_2,VAR_0)
| VAR_0 != extension(VAR_1,VAR_2,VAR_3,VAR_4) ),
file('theBenchmark.p',b0) ).
cnf(c_31,plain,
( between(B,C,A)
| A != extension(B,C,D,E) ),
inference(clausify,[status(thm)],[b0]) ).
cnf(c_32,plain,
( between(A,B,E)
| extension(A,B,C,D) != E ),
inference(copy,[status(thm)],[c_31]) ).
fof(w_between_u_and_x,axiom,
between(u,w,x),
file('theBenchmark.p',w_between_u_and_x) ).
cnf(c_53,plain,
between(u,w,x),
inference(clausify,[status(thm)],[w_between_u_and_x]) ).
fof(u_is_x,axiom,
u = x,
file('theBenchmark.p',u_is_x) ).
cnf(c_54,plain,
u = x,
inference(clausify,[status(thm)],[u_is_x]) ).
cnf(c_55,plain,
x = u,
inference(copy,[status(thm)],[c_54]) ).
fof(prove_corollary,axiom,
~ between(v,w,x),
file('theBenchmark.p',prove_corollary) ).
cnf(c_56,plain,
~ between(v,w,x),
inference(clausify,[status(thm)],[prove_corollary]) ).
cnf(c_57,plain,
~ between(v,w,u),
inference(paramod,[status(thm)],[c_55,c_56]) ).
cnf(c_67,plain,
between(u,w,u),
inference(paramod,[status(thm)],[c_55,c_53]) ).
cnf(c_177,plain,
extension(v,w,A,B) != u,
inference(resolve,[status(thm)],[c_32,c_57]) ).
cnf(c_230,plain,
u = w,
inference(resolve,[status(thm)],[c_67,c_7]) ).
cnf(c_222,plain,
w = u,
inference(copy,[status(thm)],[c_230]) ).
cnf(c_228,plain,
extension(v,u,A,B) != u,
inference(paramod,[status(thm)],[c_222,c_177]) ).
cnf(c_229,plain,
$false,
inference(resolve,[status(thm)],[c_228,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO039-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 12:33:08 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 999685 was started by sandbox on n007,
% 0.09/0.37 % Fri Sep 25 12:33:08 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.42
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.42
% 0.14/0.42 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.14/0.42 % Length of proof is 15.
% 0.14/0.42 % Level of proof is 5.
% 0.14/0.42 % Maximum clause weight is 21.000.
% 0.14/0.42 % Given clauses 51.
% 0.14/0.42
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------