%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO028-3 : 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 : n008.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 135.36s 23.21s
% Output : CNFRefutation 135.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 21 unt; 0 def)
% Number of atoms : 58 ( 17 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 55 ( 30 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 93 ( 10 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_for_equidistance,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equidistant(VAR_2,VAR_3,VAR_4,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_4,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',transitivity_for_equidistance) ).
cnf(c_2,plain,
( equidistant(C,D,E,F)
| ~ equidistant(A,B,E,F)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[transitivity_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(d1,axiom,
! [VAR_0,VAR_1] : equidistant(VAR_0,VAR_1,VAR_0,VAR_1),
file('theBenchmark.p',d1) ).
cnf(c_20,plain,
equidistant(A,B,A,B),
inference(clausify,[status(thm)],[d1]) ).
fof(d5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equidistant(VAR_0,VAR_1,VAR_4,VAR_5)
| ~ equidistant(VAR_2,VAR_3,VAR_4,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d5) ).
cnf(c_28,plain,
( equidistant(A,B,E,F)
| ~ equidistant(C,D,E,F)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d5]) ).
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(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_43,plain,
equidistant(w,x,y,z),
inference(clausify,[status(thm)],[w_to_x_equals_y_to_z]) ).
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_equal_extensions,axiom,
extension(u,v,w,x) != extension(u,v,y,z),
file('theBenchmark.p',prove_equal_extensions) ).
cnf(c_46,plain,
extension(u,v,w,x) != extension(u,v,y,z),
inference(clausify,[status(thm)],[prove_equal_extensions]) ).
cnf(c_47,plain,
extension(u,v,y,z) != extension(u,v,w,x),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_807,plain,
( equidistant(C,D,E,F)
| ~ equidistant(A,extension(B,A,C,D),E,F) ),
inference(resolve,[status(thm)],[c_2,c_5]) ).
cnf(c_120,plain,
equidistant(A,B,C,extension(D,C,A,B)),
inference(resolve,[status(thm)],[c_807,c_20]) ).
cnf(c_808,plain,
( equidistant(E,extension(F,E,A,B),C,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_28,c_5]) ).
cnf(c_172,plain,
equidistant(A,extension(B,A,w,x),y,z),
inference(resolve,[status(thm)],[c_808,c_43]) ).
cnf(c_809,plain,
( extension(A,B,D,E) = C
| A = B
| ~ equidistant(B,extension(A,B,D,E),B,C)
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_42,c_4]) ).
cnf(c_810,plain,
( extension(B,A,C,D) = extension(B,A,E,F)
| B = A
| ~ equidistant(A,extension(B,A,C,D),A,extension(B,A,E,F)) ),
inference(resolve,[status(thm)],[c_809,c_4]) ).
cnf(c_811,plain,
u != v,
inference(copy,[status(thm)],[c_45]) ).
cnf(c_812,plain,
( extension(u,v,A,B) = extension(u,v,C,D)
| ~ equidistant(v,extension(u,v,A,B),v,extension(u,v,C,D)) ),
inference(resolve,[status(thm)],[c_810,c_811]) ).
cnf(c_813,plain,
extension(u,v,w,x) != extension(u,v,y,z),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_183,plain,
~ equidistant(v,extension(u,v,w,x),v,extension(u,v,y,z)),
inference(resolve,[status(thm)],[c_812,c_813]) ).
cnf(c_814,plain,
( equidistant(C,extension(D,C,w,x),A,B)
| ~ equidistant(y,z,A,B) ),
inference(resolve,[status(thm)],[c_28,c_172]) ).
cnf(c_805,plain,
equidistant(A,extension(B,A,w,x),C,extension(D,C,y,z)),
inference(resolve,[status(thm)],[c_814,c_120]) ).
cnf(c_806,plain,
$false,
inference(resolve,[status(thm)],[c_805,c_183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO028-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/5.45 % Computer : n008.cluster.edu
% 0.19/5.45 % Model : x86_64 x86_64
% 0.19/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.45 % Memory : 8046.5625MB
% 0.19/5.45 % OS : Linux 6.8.0-71-generic
% 0.19/5.45 % CPULimit : 300
% 0.19/5.45 % WCLimit : 300
% 0.19/5.45 % DateTime : Fri Sep 25 12:34:16 UTC 2026
% 0.19/5.45 % CPUTime :
% 0.19/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.46 % Process 1049304 was started by sandbox on n008,
% 0.19/5.46 % Fri Sep 25 12:34:16 2026
% 0.19/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/5.46
% 0.19/5.46 % From the command line: assign(max_seconds, 300).
% 135.36/23.21
% 135.36/23.21 % SZS status Unsatisfiable for theBenchmark
% 135.36/23.21
% 135.36/23.21 % Proof 1 at 1.61 (+ 0.07) seconds.
% 135.36/23.21 % Length of proof is 16.
% 135.36/23.21 % Level of proof is 3.
% 135.36/23.21 % Maximum clause weight is 19.000.
% 135.36/23.21 % Given clauses 82.
% 135.36/23.21
% 135.36/23.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------