%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO027-2 : 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 : 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 07:16:49 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 18 unt; 0 def)
% Number of atoms : 75 ( 17 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 84 ( 41 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 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 : 90 ( 3 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_for_equidistance,axiom,
! [VAR_0,VAR_1] : equidistant(VAR_0,VAR_1,VAR_1,VAR_0),
file('theBenchmark.p',reflexivity_for_equidistance) ).
cnf(c_1,plain,
equidistant(A,B,B,A),
inference(clausify,[status(thm)],[reflexivity_for_equidistance]) ).
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(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(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_19,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(u_not_v,axiom,
u != v,
file('theBenchmark.p',u_not_v) ).
cnf(c_20,plain,
u != v,
inference(clausify,[status(thm)],[u_not_v]) ).
cnf(c_21,plain,
v != u,
inference(copy,[status(thm)],[c_20]) ).
fof(prove_w_is_an_extension,axiom,
w != extension(u,v,v,w),
file('theBenchmark.p',prove_w_is_an_extension) ).
cnf(c_22,plain,
w != extension(u,v,v,w),
inference(clausify,[status(thm)],[prove_w_is_an_extension]) ).
cnf(c_23,plain,
extension(u,v,v,w) != w,
inference(copy,[status(thm)],[c_22]) ).
cnf(c_163,plain,
( equidistant(B,A,C,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_43,plain,
equidistant(A,B,A,B),
inference(resolve,[status(thm)],[c_163,c_1]) ).
cnf(c_124,plain,
~ equidistant(extension(u,v,v,w),w,A,A),
inference(resolve,[status(thm)],[c_3,c_23]) ).
cnf(c_164,plain,
( equidistant(B,E,C,F)
| D = A
| ~ between(D,A,C)
| ~ between(D,A,B)
| ~ equidistant(A,E,A,F)
| ~ equidistant(D,E,D,F)
| ~ equidistant(A,B,A,C) ),
inference(resolve,[status(thm)],[c_6,c_43]) ).
cnf(c_165,plain,
( equidistant(extension(E,D,D,F),B,F,C)
| A = D
| ~ between(A,D,F)
| ~ between(A,D,extension(E,D,D,F))
| ~ equidistant(D,B,D,C)
| ~ equidistant(A,B,A,C) ),
inference(resolve,[status(thm)],[c_164,c_5]) ).
cnf(c_166,plain,
( equidistant(extension(D,A,A,E),B,E,B)
| C = A
| ~ between(C,A,E)
| ~ between(C,A,extension(D,A,A,E))
| ~ equidistant(A,B,A,B) ),
inference(resolve,[status(thm)],[c_165,c_43]) ).
cnf(c_167,plain,
( equidistant(extension(C,B,B,D),E,D,E)
| A = B
| ~ between(A,B,D)
| ~ between(A,B,extension(C,B,B,D)) ),
inference(resolve,[status(thm)],[c_166,c_43]) ).
cnf(c_168,plain,
( equidistant(extension(A,B,B,C),D,C,D)
| A = B
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_167,c_4]) ).
cnf(c_169,plain,
( equidistant(extension(u,v,v,w),A,w,A)
| u = v ),
inference(resolve,[status(thm)],[c_168,c_19]) ).
cnf(c_170,plain,
( equidistant(extension(u,v,v,w),A,w,A)
| v = u ),
inference(copy,[status(thm)],[c_169]) ).
cnf(c_161,plain,
equidistant(extension(u,v,v,w),A,w,A),
inference(resolve,[status(thm)],[c_21,c_170]) ).
cnf(c_162,plain,
$false,
inference(resolve,[status(thm)],[c_161,c_124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO027-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n014.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 12:33:17 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.41 % Process 229151 was started by sandbox on n014,
% 0.14/0.41 % Fri Sep 25 12:33:17 2026
% 0.14/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.42
% 0.14/0.42 % From the command line: assign(max_seconds, 300).
% 0.14/0.46
% 0.14/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.46
% 0.14/0.46 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.46 % Length of proof is 15.
% 0.14/0.46 % Level of proof is 3.
% 0.14/0.46 % Maximum clause weight is 41.000.
% 0.14/0.46 % Given clauses 41.
% 0.14/0.46
% 0.14/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------