%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO063-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 07:16:57 AM UTC 2026
% Result : Unsatisfiable 3.89s 1.06s
% Output : CNFRefutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 15 unt; 0 def)
% Number of atoms : 27 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 14 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 34 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(insertion,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : insertion(VAR_0,VAR_1,VAR_2,VAR_3) = extension(extension(VAR_1,VAR_0,lower_dimension_point_1,lower_dimension_point_2),VAR_0,VAR_2,VAR_3),
file('theBenchmark.p',insertion) ).
cnf(c_20,plain,
insertion(A,B,C,D) = extension(extension(B,A,lower_dimension_point_1,lower_dimension_point_2),A,C,D),
inference(clausify,[status(thm)],[insertion]) ).
fof(d2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equidistant(VAR_2,VAR_3,VAR_0,VAR_1)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d2) ).
cnf(c_22,plain,
( equidistant(C,D,A,B)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d2]) ).
fof(d10_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( VAR_4 = VAR_5
| extension(VAR_4,VAR_5,VAR_0,VAR_1) = extension(VAR_4,VAR_5,VAR_2,VAR_3)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d10_2) ).
cnf(c_46,plain,
( E = F
| extension(E,F,A,B) = extension(E,F,C,D)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d10_2]) ).
fof(e3_1,axiom,
! [VAR_0,VAR_1] : VAR_0 != extension(VAR_1,VAR_0,lower_dimension_point_1,lower_dimension_point_2),
file('theBenchmark.p',e3_1) ).
cnf(c_70,plain,
A != extension(B,A,lower_dimension_point_1,lower_dimension_point_2),
inference(clausify,[status(thm)],[e3_1]) ).
cnf(c_71,plain,
extension(A,B,lower_dimension_point_1,lower_dimension_point_2) != B,
inference(copy,[status(thm)],[c_70]) ).
fof(w_to_x_equals_y_to_z,axiom,
equidistant(w,x,y,z),
file('theBenchmark.p',w_to_x_equals_y_to_z) ).
cnf(c_87,plain,
equidistant(w,x,y,z),
inference(clausify,[status(thm)],[w_to_x_equals_y_to_z]) ).
fof(prove_equality_of_insertions,axiom,
insertion(u,v,w,x) != insertion(u,v,y,z),
file('theBenchmark.p',prove_equality_of_insertions) ).
cnf(c_88,plain,
insertion(u,v,w,x) != insertion(u,v,y,z),
inference(clausify,[status(thm)],[prove_equality_of_insertions]) ).
cnf(c_353,plain,
extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) != insertion(u,v,y,z),
inference(paramod,[status(thm)],[c_20,c_88]) ).
cnf(c_354,plain,
extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) != extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z),
inference(paramod,[status(thm)],[c_20,c_353]) ).
cnf(c_89,plain,
extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) != extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x),
inference(copy,[status(thm)],[c_354]) ).
cnf(c_347,plain,
equidistant(y,z,w,x),
inference(resolve,[status(thm)],[c_87,c_22]) ).
cnf(c_355,plain,
( extension(v,u,lower_dimension_point_1,lower_dimension_point_2) = u
| ~ equidistant(y,z,w,x) ),
inference(resolve,[status(thm)],[c_46,c_89]) ).
cnf(c_356,plain,
~ equidistant(y,z,w,x),
inference(resolve,[status(thm)],[c_355,c_71]) ).
cnf(c_352,plain,
$false,
inference(resolve,[status(thm)],[c_347,c_356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO063-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 12:38:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2941387 was started by sandbox on n020,
% 0.10/0.37 % Fri Sep 25 12:38:48 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 3.89/1.06
% 3.89/1.06 % SZS status Unsatisfiable for theBenchmark
% 3.89/1.06
% 3.89/1.06 % Proof 1 at 0.61 (+ 0.02) seconds.
% 3.89/1.06 % Length of proof is 10.
% 3.89/1.06 % Level of proof is 2.
% 3.89/1.06 % Maximum clause weight is 25.000.
% 3.89/1.06 % Given clauses 66.
% 3.89/1.06
% 3.89/1.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------