%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO027-3 : 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 : n005.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 07:16:49 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 15 unt; 0 def)
% Number of atoms : 34 ( 16 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 32 ( 18 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 27 ( 3 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(d9,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| VAR_0 = VAR_1
| ~ equidistant(VAR_1,VAR_2,VAR_1,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',d9) ).
cnf(c_42,plain,
( C = D
| A = B
| ~ equidistant(B,C,B,D)
| ~ between(A,B,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[d9]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_43,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(u_not_v,axiom,
u != v,
file('theBenchmark.p',u_not_v) ).
cnf(c_44,plain,
u != v,
inference(clausify,[status(thm)],[u_not_v]) ).
cnf(c_45,plain,
v != u,
inference(copy,[status(thm)],[c_44]) ).
fof(prove_w_is_an_extension,axiom,
w != extension(u,v,v,w),
file('theBenchmark.p',prove_w_is_an_extension) ).
cnf(c_46,plain,
w != extension(u,v,v,w),
inference(clausify,[status(thm)],[prove_w_is_an_extension]) ).
cnf(c_47,plain,
extension(u,v,v,w) != w,
inference(copy,[status(thm)],[c_46]) ).
cnf(c_157,plain,
( A = w
| u = v
| ~ equidistant(v,A,v,w)
| ~ between(u,v,A) ),
inference(resolve,[status(thm)],[c_42,c_43]) ).
cnf(c_158,plain,
( extension(A,v,v,w) = w
| u = v
| ~ between(u,v,extension(A,v,v,w)) ),
inference(resolve,[status(thm)],[c_157,c_5]) ).
cnf(c_159,plain,
u != v,
inference(copy,[status(thm)],[c_45]) ).
cnf(c_160,plain,
( extension(A,v,v,w) = w
| ~ between(u,v,extension(A,v,v,w)) ),
inference(resolve,[status(thm)],[c_158,c_159]) ).
cnf(c_161,plain,
~ between(u,v,extension(u,v,v,w)),
inference(resolve,[status(thm)],[c_160,c_47]) ).
cnf(c_156,plain,
$false,
inference(resolve,[status(thm)],[c_4,c_161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO027-3 : 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 : n005.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 12:33:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3492869 was started by sandbox on n005,
% 0.09/0.36 % Fri Sep 25 12:33:17 2026
% 0.09/0.36 % 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).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 9.
% 0.09/0.39 % Level of proof is 2.
% 0.09/0.39 % Maximum clause weight is 19.000.
% 0.09/0.39 % Given clauses 38.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------