%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO049-3 : 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 : 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 07:16:54 AM UTC 2026
% Result : Unsatisfiable 55.08s 8.41s
% Output : CNFRefutation 55.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 25 unt; 0 def)
% Number of atoms : 100 ( 19 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 103 ( 50 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 105 ( 15 sgn 38 !; 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(outer_five_segment,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( equidistant(VAR_4,VAR_6,VAR_5,VAR_7)
| VAR_0 = VAR_1
| ~ between(VAR_2,VAR_3,VAR_5)
| ~ between(VAR_0,VAR_1,VAR_4)
| ~ equidistant(VAR_1,VAR_6,VAR_3,VAR_7)
| ~ equidistant(VAR_0,VAR_6,VAR_2,VAR_7)
| ~ equidistant(VAR_1,VAR_4,VAR_3,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',outer_five_segment) ).
cnf(c_6,plain,
( equidistant(E,V6,F,V7)
| A = B
| ~ between(C,D,F)
| ~ between(A,B,E)
| ~ equidistant(B,V6,D,V7)
| ~ equidistant(A,V6,C,V7)
| ~ equidistant(B,E,D,F)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[outer_five_segment]) ).
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(b0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_1,VAR_2,VAR_0)
| VAR_0 != extension(VAR_1,VAR_2,VAR_3,VAR_4) ),
file('theBenchmark.p',b0) ).
cnf(c_32,plain,
( between(B,C,A)
| A != extension(B,C,D,E) ),
inference(clausify,[status(thm)],[b0]) ).
cnf(c_33,plain,
( between(A,B,E)
| extension(A,B,C,D) != E ),
inference(copy,[status(thm)],[c_32]) ).
fof(b1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_3,VAR_1,VAR_2)
| VAR_0 != VAR_2
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b1) ).
cnf(c_54,plain,
( between(D,B,C)
| A != C
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b1]) ).
fof(t2,axiom,
! [VAR_0,VAR_1] : between(VAR_0,VAR_0,VAR_1),
file('theBenchmark.p',t2) ).
cnf(c_56,plain,
between(A,A,B),
inference(clausify,[status(thm)],[t2]) ).
fof(b9,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_0,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b9) ).
cnf(c_63,plain,
( between(A,B,D)
| ~ between(A,C,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b9]) ).
fof(u_to_v_equals_u1_to_v1,axiom,
equidistant(u,v,u1,v1),
file('theBenchmark.p',u_to_v_equals_u1_to_v1) ).
cnf(c_89,plain,
equidistant(u,v,u1,v1),
inference(clausify,[status(thm)],[u_to_v_equals_u1_to_v1]) ).
fof(v_to_w_equals_v1_to_w1,axiom,
equidistant(v,w,v1,w1),
file('theBenchmark.p',v_to_w_equals_v1_to_w1) ).
cnf(c_90,plain,
equidistant(v,w,v1,w1),
inference(clausify,[status(thm)],[v_to_w_equals_v1_to_w1]) ).
fof(u_to_w_equals_u1_to_w1,axiom,
equidistant(u,w,u1,w1),
file('theBenchmark.p',u_to_w_equals_u1_to_w1) ).
cnf(c_91,plain,
equidistant(u,w,u1,w1),
inference(clausify,[status(thm)],[u_to_w_equals_u1_to_w1]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_92,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(prove_v1_between_u1_and_w1,axiom,
~ between(u1,v1,w1),
file('theBenchmark.p',prove_v1_between_u1_and_w1) ).
cnf(c_93,plain,
~ between(u1,v1,w1),
inference(clausify,[status(thm)],[prove_v1_between_u1_and_w1]) ).
cnf(c_568,plain,
equidistant(u1,v1,u,v),
inference(resolve,[status(thm)],[c_89,c_22]) ).
cnf(c_606,plain,
equidistant(v1,w1,v,w),
inference(resolve,[status(thm)],[c_90,c_22]) ).
cnf(c_644,plain,
equidistant(u1,w1,u,w),
inference(resolve,[status(thm)],[c_91,c_22]) ).
cnf(c_3043,plain,
( between(A,B,C)
| ~ between(A,B,A) ),
inference(resolve,[status(thm)],[c_63,c_56]) ).
cnf(c_763,plain,
~ between(u1,v1,u1),
inference(resolve,[status(thm)],[c_3043,c_93]) ).
cnf(c_770,plain,
extension(u1,v1,A,B) != w1,
inference(resolve,[status(thm)],[c_33,c_93]) ).
cnf(c_3044,plain,
( between(C,A,B)
| A != B ),
inference(resolve,[status(thm)],[c_54,c_56]) ).
cnf(c_1162,plain,
v1 != u1,
inference(resolve,[status(thm)],[c_3044,c_763]) ).
cnf(c_3045,plain,
( equidistant(A,C,B,D)
| u1 = v1
| ~ between(u,v,B)
| ~ between(u1,v1,A)
| ~ equidistant(v1,C,v,D)
| ~ equidistant(u1,C,u,D)
| ~ equidistant(v1,A,v,B) ),
inference(resolve,[status(thm)],[c_6,c_568]) ).
cnf(c_3046,plain,
( equidistant(extension(C,v1,v,D),A,D,B)
| u1 = v1
| ~ between(u,v,D)
| ~ between(u1,v1,extension(C,v1,v,D))
| ~ equidistant(v1,A,v,B)
| ~ equidistant(u1,A,u,B) ),
inference(resolve,[status(thm)],[c_3045,c_5]) ).
cnf(c_3047,plain,
( equidistant(extension(A,v1,v,B),w1,B,w)
| u1 = v1
| ~ between(u,v,B)
| ~ between(u1,v1,extension(A,v1,v,B))
| ~ equidistant(v1,w1,v,w) ),
inference(resolve,[status(thm)],[c_3046,c_644]) ).
cnf(c_3048,plain,
( equidistant(extension(A,v1,v,B),w1,B,w)
| u1 = v1
| ~ between(u,v,B)
| ~ between(u1,v1,extension(A,v1,v,B)) ),
inference(resolve,[status(thm)],[c_3047,c_606]) ).
cnf(c_3049,plain,
( equidistant(extension(u1,v1,v,A),w1,A,w)
| u1 = v1
| ~ between(u,v,A) ),
inference(resolve,[status(thm)],[c_3048,c_4]) ).
cnf(c_3050,plain,
( equidistant(extension(u1,v1,v,w),w1,w,w)
| u1 = v1 ),
inference(resolve,[status(thm)],[c_3049,c_92]) ).
cnf(c_3051,plain,
( equidistant(extension(u1,v1,v,w),w1,w,w)
| v1 = u1 ),
inference(copy,[status(thm)],[c_3050]) ).
cnf(c_1831,plain,
equidistant(extension(u1,v1,v,w),w1,w,w),
inference(resolve,[status(thm)],[c_1162,c_3051]) ).
cnf(c_3041,plain,
~ equidistant(extension(u1,v1,A,B),w1,C,C),
inference(resolve,[status(thm)],[c_3,c_770]) ).
cnf(c_3042,plain,
$false,
inference(resolve,[status(thm)],[c_3041,c_1831]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO049-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 12:36:02 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 3497919 was started by sandbox on n005,
% 0.16/0.44 % Fri Sep 25 12:36:02 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 55.08/8.41
% 55.08/8.41 % SZS status Unsatisfiable for theBenchmark
% 55.08/8.41
% 55.08/8.41 % Proof 1 at 7.67 (+ 0.26) seconds.
% 55.08/8.41 % Length of proof is 24.
% 55.08/8.41 % Level of proof is 4.
% 55.08/8.41 % Maximum clause weight is 41.000.
% 55.08/8.41 % Given clauses 323.
% 55.08/8.41
% 55.08/8.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------