%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO062-3 : 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 : n014.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 26.26s 3.78s
% Output : CNFRefutation 26.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 18 unt; 0 def)
% Number of atoms : 41 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 53 ( 8 sgn 20 !; 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(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(d10_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = extension(VAR_0,VAR_1,VAR_1,VAR_2)
| VAR_0 = VAR_1
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',d10_1) ).
cnf(c_44,plain,
( C = extension(A,B,B,C)
| A = B
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[d10_1]) ).
cnf(c_45,plain,
( extension(A,B,B,C) = C
| A = B
| ~ between(A,B,C) ),
inference(copy,[status(thm)],[c_44]) ).
fof(t1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( between(VAR_2,VAR_1,VAR_0)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t1) ).
cnf(c_55,plain,
( between(C,B,A)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[t1]) ).
fof(b5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_1,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b5) ).
cnf(c_59,plain,
( between(B,C,D)
| ~ between(A,C,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b5]) ).
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(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_85,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(prove_v_equals_insertion,axiom,
v != insertion(u,w,u,v),
file('theBenchmark.p',prove_v_equals_insertion) ).
cnf(c_86,plain,
v != insertion(u,w,u,v),
inference(clausify,[status(thm)],[prove_v_equals_insertion]) ).
cnf(c_1122,plain,
v != extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),
inference(paramod,[status(thm)],[c_20,c_86]) ).
cnf(c_87,plain,
extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) != v,
inference(copy,[status(thm)],[c_1122]) ).
cnf(c_338,plain,
between(w,v,u),
inference(resolve,[status(thm)],[c_85,c_55]) ).
cnf(c_1123,plain,
( extension(extension(A,B,lower_dimension_point_1,lower_dimension_point_2),B,B,C) = C
| ~ between(extension(A,B,lower_dimension_point_1,lower_dimension_point_2),B,C) ),
inference(resolve,[status(thm)],[c_45,c_71]) ).
cnf(c_363,plain,
~ between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,v),
inference(resolve,[status(thm)],[c_1123,c_87]) ).
cnf(c_453,plain,
( between(v,u,A)
| ~ between(w,u,A) ),
inference(resolve,[status(thm)],[c_338,c_59]) ).
cnf(c_629,plain,
between(v,u,extension(w,u,A,B)),
inference(resolve,[status(thm)],[c_453,c_4]) ).
cnf(c_1120,plain,
between(extension(w,u,A,B),u,v),
inference(resolve,[status(thm)],[c_629,c_55]) ).
cnf(c_1121,plain,
$false,
inference(resolve,[status(thm)],[c_1120,c_363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO062-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 12:37:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 241694 was started by sandbox on n014,
% 0.08/0.35 % Fri Sep 25 12:37:47 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 26.26/3.78
% 26.26/3.78 % SZS status Unsatisfiable for theBenchmark
% 26.26/3.78
% 26.26/3.78 % Proof 1 at 3.29 (+ 0.09) seconds.
% 26.26/3.78 % Length of proof is 17.
% 26.26/3.78 % Level of proof is 5.
% 26.26/3.78 % Maximum clause weight is 21.000.
% 26.26/3.78 % Given clauses 170.
% 26.26/3.78
% 26.26/3.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------