%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO036-2 : 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 : n017.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 0.22s 0.51s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 16 unt; 0 def)
% Number of atoms : 42 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 11 ~; 16 |; 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 : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 30 ( 6 sgn 11 !; 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(lower_dimension1,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('theBenchmark.p',lower_dimension1) ).
cnf(c_10,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(clausify,[status(thm)],[lower_dimension1]) ).
fof(lower_dimension2,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('theBenchmark.p',lower_dimension2) ).
cnf(c_11,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(clausify,[status(thm)],[lower_dimension2]) ).
fof(lower_dimension3,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('theBenchmark.p',lower_dimension3) ).
cnf(c_12,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(clausify,[status(thm)],[lower_dimension3]) ).
fof(prove_axioms_points_are_distinct,axiom,
( lower_dimension_point_1 = lower_dimension_point_3
| lower_dimension_point_2 = lower_dimension_point_3
| lower_dimension_point_1 = lower_dimension_point_2 ),
file('theBenchmark.p',prove_axioms_points_are_distinct) ).
cnf(c_19,plain,
( lower_dimension_point_1 = lower_dimension_point_3
| lower_dimension_point_2 = lower_dimension_point_3
| lower_dimension_point_1 = lower_dimension_point_2 ),
inference(clausify,[status(thm)],[prove_axioms_points_are_distinct]) ).
cnf(c_185,plain,
( lower_dimension_point_1 = lower_dimension_point_3
| lower_dimension_point_2 = lower_dimension_point_3
| lower_dimension_point_2 = lower_dimension_point_1 ),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_186,plain,
( lower_dimension_point_1 = lower_dimension_point_3
| lower_dimension_point_3 = lower_dimension_point_2
| lower_dimension_point_2 = lower_dimension_point_1 ),
inference(copy,[status(thm)],[c_185]) ).
cnf(c_20,plain,
( lower_dimension_point_3 = lower_dimension_point_1
| lower_dimension_point_3 = lower_dimension_point_2
| lower_dimension_point_2 = lower_dimension_point_1 ),
inference(copy,[status(thm)],[c_186]) ).
cnf(c_187,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_40,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_187]) ).
cnf(c_97,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2)
| lower_dimension_point_3 = lower_dimension_point_1
| lower_dimension_point_2 = lower_dimension_point_1 ),
inference(paramod,[status(thm)],[c_20,c_10]) ).
cnf(c_122,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_40,c_4]) ).
cnf(c_130,plain,
( lower_dimension_point_3 = lower_dimension_point_1
| lower_dimension_point_2 = lower_dimension_point_1 ),
inference(resolve,[status(thm)],[c_122,c_97]) ).
cnf(c_188,plain,
( ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1)
| lower_dimension_point_2 = lower_dimension_point_1 ),
inference(paramod,[status(thm)],[c_130,c_11]) ).
cnf(c_183,plain,
lower_dimension_point_2 = lower_dimension_point_1,
inference(resolve,[status(thm)],[c_122,c_188]) ).
cnf(c_189,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1),
inference(paramod,[status(thm)],[c_183,c_12]) ).
cnf(c_184,plain,
$false,
inference(resolve,[status(thm)],[c_122,c_189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO036-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n017.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 12:30:02 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 2269293 was started by sandbox2 on n017,
% 0.19/0.46 % Fri Sep 25 12:30:02 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.22/0.51
% 0.22/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.51
% 0.22/0.51 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.22/0.51 % Length of proof is 14.
% 0.22/0.51 % Level of proof is 5.
% 0.22/0.51 % Maximum clause weight is 19.000.
% 0.22/0.51 % Given clauses 41.
% 0.22/0.51
% 0.22/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------