%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO026-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 0.88s 0.56s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 68 ( 14 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 78 ( 39 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 55 ( 0 sgn 17 !; 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(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(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(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_21,plain,
( equidistant(C,D,A,B)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d2]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_42,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(v_between_u_and_x,axiom,
between(u,v,x),
file('theBenchmark.p',v_between_u_and_x) ).
cnf(c_43,plain,
between(u,v,x),
inference(clausify,[status(thm)],[v_between_u_and_x]) ).
fof(v_to_w_equals_v_to_x,axiom,
equidistant(v,w,v,x),
file('theBenchmark.p',v_to_w_equals_v_to_x) ).
cnf(c_44,plain,
equidistant(v,w,v,x),
inference(clausify,[status(thm)],[v_to_w_equals_v_to_x]) ).
fof(u_not_v,axiom,
u != v,
file('theBenchmark.p',u_not_v) ).
cnf(c_45,plain,
u != v,
inference(clausify,[status(thm)],[u_not_v]) ).
fof(prove_w_is_x,axiom,
w != x,
file('theBenchmark.p',prove_w_is_x) ).
cnf(c_46,plain,
w != x,
inference(clausify,[status(thm)],[prove_w_is_x]) ).
cnf(c_47,plain,
x != w,
inference(copy,[status(thm)],[c_46]) ).
cnf(c_154,plain,
equidistant(v,x,v,w),
inference(resolve,[status(thm)],[c_44,c_21]) ).
cnf(c_172,plain,
~ equidistant(x,w,A,A),
inference(resolve,[status(thm)],[c_3,c_47]) ).
cnf(c_257,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_20]) ).
cnf(c_258,plain,
( equidistant(B,D,C,D)
| E = A
| ~ between(E,A,C)
| ~ between(E,A,B)
| ~ equidistant(A,D,A,D)
| ~ equidistant(A,B,A,C) ),
inference(resolve,[status(thm)],[c_257,c_20]) ).
cnf(c_259,plain,
( equidistant(B,E,C,E)
| D = A
| ~ between(D,A,C)
| ~ between(D,A,B)
| ~ equidistant(A,B,A,C) ),
inference(resolve,[status(thm)],[c_258,c_20]) ).
cnf(c_260,plain,
( equidistant(x,B,A,B)
| u = v
| ~ between(u,v,A)
| ~ equidistant(v,x,v,A) ),
inference(resolve,[status(thm)],[c_259,c_43]) ).
cnf(c_261,plain,
( equidistant(x,A,w,A)
| u = v
| ~ equidistant(v,x,v,w) ),
inference(resolve,[status(thm)],[c_260,c_42]) ).
cnf(c_262,plain,
( equidistant(x,A,w,A)
| ~ equidistant(v,x,v,w) ),
inference(resolve,[status(thm)],[c_261,c_45]) ).
cnf(c_263,plain,
~ equidistant(v,x,v,w),
inference(resolve,[status(thm)],[c_262,c_172]) ).
cnf(c_256,plain,
$false,
inference(resolve,[status(thm)],[c_154,c_263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO026-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.43 % Computer : n017.cluster.edu
% 0.14/0.43 % Model : x86_64 x86_64
% 0.14/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.43 % Memory : 8046.5625MB
% 0.14/0.43 % OS : Linux 6.8.0-71-generic
% 0.14/0.43 % CPULimit : 300
% 0.14/0.43 % WCLimit : 300
% 0.14/0.43 % DateTime : Fri Sep 25 12:28:49 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.43 % Process 2266003 was started by sandbox2 on n017,
% 0.14/0.43 % Fri Sep 25 12:28:49 2026
% 0.14/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.44
% 0.14/0.44 % From the command line: assign(max_seconds, 300).
% 0.88/0.56
% 0.88/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.88/0.56
% 0.88/0.56 % Proof 1 at 0.11 (+ 0.01) seconds.
% 0.88/0.56 % Length of proof is 13.
% 0.88/0.56 % Level of proof is 3.
% 0.88/0.56 % Maximum clause weight is 38.000.
% 0.88/0.56 % Given clauses 62.
% 0.88/0.56
% 0.88/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------