%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO039-2 : 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 : n010.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 07:16:51 AM UTC 2026
% Result : Unsatisfiable 0.09s 10.56s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 20 unt; 0 def)
% Number of atoms : 28 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 34 ( 6 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(identity_for_equidistance,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_1
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_2) ),
file('theBenchmark.p',identity_for_equidistance) ).
cnf(c_3,plain,
( A = B
| ~ equidistant(A,B,C,C) ),
inference(clausify,[status(thm)],[identity_for_equidistance]) ).
fof(segment_construction1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : between(VAR_0,VAR_1,extension(VAR_0,VAR_1,VAR_2,VAR_3)),
file('theBenchmark.p',segment_construction1) ).
cnf(c_4,plain,
between(A,B,extension(A,B,C,D)),
inference(clausify,[status(thm)],[segment_construction1]) ).
fof(segment_construction2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : equidistant(VAR_0,extension(VAR_1,VAR_0,VAR_2,VAR_3),VAR_2,VAR_3),
file('theBenchmark.p',segment_construction2) ).
cnf(c_5,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(clausify,[status(thm)],[segment_construction2]) ).
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(w_between_u_and_x,axiom,
between(u,w,x),
file('theBenchmark.p',w_between_u_and_x) ).
cnf(c_19,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_20,plain,
u = x,
inference(clausify,[status(thm)],[u_is_x]) ).
cnf(c_21,plain,
x = u,
inference(copy,[status(thm)],[c_20]) ).
fof(prove_corollary,axiom,
~ between(v,w,x),
file('theBenchmark.p',prove_corollary) ).
cnf(c_22,plain,
~ between(v,w,x),
inference(clausify,[status(thm)],[prove_corollary]) ).
cnf(c_162,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_42,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_162]) ).
cnf(c_99,plain,
between(u,w,u),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_100,plain,
~ between(v,w,u),
inference(paramod,[status(thm)],[c_21,c_22]) ).
cnf(c_126,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_42,c_4]) ).
cnf(c_163,plain,
u = w,
inference(resolve,[status(thm)],[c_99,c_7]) ).
cnf(c_158,plain,
w = u,
inference(copy,[status(thm)],[c_163]) ).
cnf(c_164,plain,
~ between(v,u,u),
inference(paramod,[status(thm)],[c_158,c_100]) ).
cnf(c_161,plain,
$false,
inference(resolve,[status(thm)],[c_126,c_164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.53 % Computer : n010.cluster.edu
% 0.09/10.53 % Model : x86_64 x86_64
% 0.09/10.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.53 % Memory : 8046.5625MB
% 0.09/10.53 % OS : Linux 6.8.0-71-generic
% 0.09/10.54 % CPULimit : 300
% 0.09/10.54 % WCLimit : 300
% 0.09/10.54 % DateTime : Fri Sep 25 12:35:41 UTC 2026
% 0.09/10.54 % CPUTime :
% 0.09/10.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.54 % Process 754737 was started by sandbox on n010,
% 0.09/10.54 % Fri Sep 25 12:35:41 2026
% 0.09/10.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/10.54
% 0.09/10.54 % From the command line: assign(max_seconds, 300).
% 0.09/10.56
% 0.09/10.56 % SZS status Unsatisfiable for theBenchmark
% 0.09/10.56
% 0.09/10.56 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/10.56 % Length of proof is 14.
% 0.09/10.56 % Level of proof is 4.
% 0.09/10.56 % Maximum clause weight is 19.000.
% 0.09/10.56 % Given clauses 42.
% 0.09/10.56
% 0.09/10.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------