%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO058-2 : 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 : n010.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 07:16:56 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 16 unt; 0 def)
% Number of atoms : 28 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 40 ( 1 sgn 17 !; 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_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(reflection,axiom,
! [VAR_0,VAR_1] : reflection(VAR_0,VAR_1) = extension(VAR_0,VAR_1,VAR_0,VAR_1),
file('theBenchmark.p',reflection) ).
cnf(c_19,plain,
reflection(A,B) = extension(A,B,A,B),
inference(clausify,[status(thm)],[reflection]) ).
fof(v_equals_reflection,axiom,
v = reflection(u,v),
file('theBenchmark.p',v_equals_reflection) ).
cnf(c_20,plain,
v = reflection(u,v),
inference(clausify,[status(thm)],[v_equals_reflection]) ).
cnf(c_150,plain,
v = extension(u,v,u,v),
inference(paramod,[status(thm)],[c_19,c_20]) ).
cnf(c_21,plain,
extension(u,v,u,v) = v,
inference(copy,[status(thm)],[c_150]) ).
fof(prove_u_equals_v,axiom,
u != v,
file('theBenchmark.p',prove_u_equals_v) ).
cnf(c_22,plain,
u != v,
inference(clausify,[status(thm)],[prove_u_equals_v]) ).
cnf(c_41,plain,
( equidistant(C,D,B,A)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_100,plain,
equidistant(v,v,u,v),
inference(paramod,[status(thm)],[c_21,c_5]) ).
cnf(c_102,plain,
~ equidistant(u,v,A,A),
inference(resolve,[status(thm)],[c_3,c_22]) ).
cnf(c_148,plain,
~ equidistant(A,A,u,v),
inference(resolve,[status(thm)],[c_41,c_102]) ).
cnf(c_149,plain,
$false,
inference(resolve,[status(thm)],[c_148,c_100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO058-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n010.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 12:38:09 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 760054 was started by sandbox on n010,
% 0.09/5.38 % Fri Sep 25 12:38:09 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.14/5.40
% 0.14/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.40
% 0.14/5.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/5.40 % Length of proof is 13.
% 0.14/5.40 % Level of proof is 3.
% 0.14/5.40 % Maximum clause weight is 20.000.
% 0.14/5.40 % Given clauses 42.
% 0.14/5.40
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------