%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO034-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:16:50 AM UTC 2026
% Result : Unsatisfiable 18.92s 2.81s
% Output : CNFRefutation 18.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 59 ( 6 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 68 ( 37 ~; 31 |; 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 : 52 ( 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(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(d12,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( equidistant(VAR_1,VAR_6,VAR_3,VAR_7)
| ~ between(VAR_2,VAR_3,VAR_5)
| ~ between(VAR_0,VAR_1,VAR_4)
| ~ equidistant(VAR_4,VAR_6,VAR_5,VAR_7)
| ~ equidistant(VAR_0,VAR_6,VAR_2,VAR_7)
| ~ equidistant(VAR_0,VAR_4,VAR_2,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d12) ).
cnf(c_74,plain,
( equidistant(B,V6,D,V7)
| ~ between(C,D,F)
| ~ between(A,B,E)
| ~ equidistant(E,V6,F,V7)
| ~ equidistant(A,V6,C,V7)
| ~ equidistant(A,E,C,F)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d12]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_77,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(u_to_v_equals_u_to_x,axiom,
equidistant(u,v,u,x),
file('theBenchmark.p',u_to_v_equals_u_to_x) ).
cnf(c_78,plain,
equidistant(u,v,u,x),
inference(clausify,[status(thm)],[u_to_v_equals_u_to_x]) ).
fof(w_to_v_equals_w_to_x,axiom,
equidistant(w,v,w,x),
file('theBenchmark.p',w_to_v_equals_w_to_x) ).
cnf(c_79,plain,
equidistant(w,v,w,x),
inference(clausify,[status(thm)],[w_to_v_equals_w_to_x]) ).
fof(prove_v_is_x,axiom,
v != x,
file('theBenchmark.p',prove_v_is_x) ).
cnf(c_80,plain,
v != x,
inference(clausify,[status(thm)],[prove_v_is_x]) ).
cnf(c_81,plain,
x != v,
inference(copy,[status(thm)],[c_80]) ).
cnf(c_1963,plain,
( equidistant(B,D,B,E)
| ~ between(A,B,C)
| ~ equidistant(C,D,C,E)
| ~ equidistant(A,D,A,E)
| ~ equidistant(A,C,A,C)
| ~ equidistant(A,B,A,B) ),
inference(factor,[status(thm)],[c_74]) ).
cnf(c_1964,plain,
( equidistant(E,C,E,D)
| ~ between(A,E,B)
| ~ equidistant(B,C,B,D)
| ~ equidistant(A,C,A,D)
| ~ equidistant(A,B,A,B) ),
inference(resolve,[status(thm)],[c_20,c_1963]) ).
cnf(c_95,plain,
( equidistant(E,B,E,C)
| ~ between(A,E,D)
| ~ equidistant(D,B,D,C)
| ~ equidistant(A,B,A,C) ),
inference(resolve,[status(thm)],[c_20,c_1964]) ).
cnf(c_566,plain,
equidistant(u,x,u,v),
inference(resolve,[status(thm)],[c_78,c_21]) ).
cnf(c_610,plain,
equidistant(w,x,w,v),
inference(resolve,[status(thm)],[c_79,c_21]) ).
cnf(c_1965,plain,
v != x,
inference(copy,[status(thm)],[c_81]) ).
cnf(c_641,plain,
~ equidistant(v,x,A,A),
inference(resolve,[status(thm)],[c_3,c_1965]) ).
cnf(c_1966,plain,
( equidistant(B,x,B,v)
| ~ between(A,B,w)
| ~ equidistant(A,x,A,v) ),
inference(resolve,[status(thm)],[c_95,c_610]) ).
cnf(c_1967,plain,
( equidistant(v,x,v,v)
| ~ equidistant(u,x,u,v) ),
inference(resolve,[status(thm)],[c_1966,c_77]) ).
cnf(c_1968,plain,
~ equidistant(u,x,u,v),
inference(resolve,[status(thm)],[c_1967,c_641]) ).
cnf(c_1962,plain,
$false,
inference(resolve,[status(thm)],[c_566,c_1968]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO034-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n015.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 12:37:27 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.40 % Process 1353239 was started by sandbox2 on n015,
% 0.12/0.40 % Fri Sep 25 12:37:27 2026
% 0.12/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 18.92/2.81
% 18.92/2.81 % SZS status Unsatisfiable for theBenchmark
% 18.92/2.81
% 18.92/2.81 % Proof 1 at 2.36 (+ 0.03) seconds.
% 18.92/2.81 % Length of proof is 14.
% 18.92/2.81 % Level of proof is 3.
% 18.92/2.81 % Maximum clause weight is 38.000.
% 18.92/2.81 % Given clauses 209.
% 18.92/2.81
% 18.92/2.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------