%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO058-3 : 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 : n005.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 0.16s 0.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 18 unt; 0 def)
% Number of atoms : 30 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 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 : 50 ( 5 sgn 18 !; 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(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(e1,axiom,
! [VAR_0,VAR_1,VAR_2] : VAR_0 = extension(VAR_1,VAR_0,VAR_2,VAR_2),
file('theBenchmark.p',e1) ).
cnf(c_29,plain,
A = extension(B,A,C,C),
inference(clausify,[status(thm)],[e1]) ).
cnf(c_30,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_29]) ).
fof(v_equals_reflection,axiom,
v = reflection(u,v),
file('theBenchmark.p',v_equals_reflection) ).
cnf(c_38,plain,
v = reflection(u,v),
inference(clausify,[status(thm)],[v_equals_reflection]) ).
cnf(c_146,plain,
v = extension(u,v,u,v),
inference(paramod,[status(thm)],[c_19,c_38]) ).
cnf(c_39,plain,
extension(u,v,u,v) = v,
inference(copy,[status(thm)],[c_146]) ).
fof(prove_u_equals_v,axiom,
u != v,
file('theBenchmark.p',prove_u_equals_v) ).
cnf(c_40,plain,
u != v,
inference(clausify,[status(thm)],[prove_u_equals_v]) ).
cnf(c_55,plain,
( equidistant(E,F,C,D)
| ~ equidistant(A,extension(B,A,C,D),E,F) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_129,plain,
equidistant(v,v,u,v),
inference(paramod,[status(thm)],[c_39,c_5]) ).
cnf(c_131,plain,
~ equidistant(u,v,A,A),
inference(resolve,[status(thm)],[c_3,c_40]) ).
cnf(c_147,plain,
~ equidistant(A,extension(B,A,C,C),u,v),
inference(resolve,[status(thm)],[c_55,c_131]) ).
cnf(c_144,plain,
~ equidistant(A,A,u,v),
inference(paramod,[status(thm)],[c_30,c_147]) ).
cnf(c_145,plain,
$false,
inference(resolve,[status(thm)],[c_144,c_129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO058-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 12:37:18 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 3499110 was started by sandbox on n005,
% 0.16/0.42 % Fri Sep 25 12:37:18 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.48
% 0.16/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.48
% 0.16/0.48 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.16/0.48 % Length of proof is 14.
% 0.16/0.48 % Level of proof is 3.
% 0.16/0.48 % Maximum clause weight is 15.000.
% 0.16/0.48 % Given clauses 44.
% 0.16/0.48
% 0.16/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------