%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO059-3 : 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 : n008.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 0.21s 10.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 28 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 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 : 54 ( 4 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(d4_5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equidistant(VAR_3,VAR_2,VAR_1,VAR_0)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d4_5) ).
cnf(c_27,plain,
( equidistant(D,C,B,A)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d4_5]) ).
fof(d5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equidistant(VAR_0,VAR_1,VAR_4,VAR_5)
| ~ equidistant(VAR_2,VAR_3,VAR_4,VAR_5)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d5) ).
cnf(c_28,plain,
( equidistant(A,B,E,F)
| ~ equidistant(C,D,E,F)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d5]) ).
fof(prove_congruence,axiom,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('theBenchmark.p',prove_congruence) ).
cnf(c_48,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(clausify,[status(thm)],[prove_congruence]) ).
cnf(c_255,plain,
~ equidistant(v,u,v,reflection(extension(u,v,u,v),v)),
inference(paramod,[status(thm)],[c_19,c_48]) ).
cnf(c_49,plain,
~ equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(paramod,[status(thm)],[c_19,c_255]) ).
cnf(c_119,plain,
equidistant(A,B,C,extension(D,C,A,B)),
inference(resolve,[status(thm)],[c_21,c_5]) ).
cnf(c_125,plain,
equidistant(A,B,extension(C,D,B,A),D),
inference(resolve,[status(thm)],[c_27,c_5]) ).
cnf(c_256,plain,
( equidistant(A,B,E,extension(F,E,C,D))
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_28,c_119]) ).
cnf(c_257,plain,
~ equidistant(v,u,extension(u,v,u,v),v),
inference(resolve,[status(thm)],[c_256,c_49]) ).
cnf(c_254,plain,
$false,
inference(resolve,[status(thm)],[c_125,c_257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/10.45 % Computer : n008.cluster.edu
% 0.17/10.45 % Model : x86_64 x86_64
% 0.17/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.45 % Memory : 8046.5625MB
% 0.17/10.45 % OS : Linux 6.8.0-71-generic
% 0.17/10.45 % CPULimit : 300
% 0.17/10.45 % WCLimit : 300
% 0.17/10.45 % DateTime : Fri Sep 25 12:38:20 UTC 2026
% 0.17/10.45 % CPUTime :
% 0.17/10.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/10.45 % Process 1055757 was started by sandbox on n008,
% 0.17/10.45 % Fri Sep 25 12:38:20 2026
% 0.17/10.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/10.46
% 0.17/10.46 % From the command line: assign(max_seconds, 300).
% 0.21/10.60
% 0.21/10.60 % SZS status Unsatisfiable for theBenchmark
% 0.21/10.60
% 0.21/10.60 % Proof 1 at 0.12 (+ 0.01) seconds.
% 0.21/10.60 % Length of proof is 10.
% 0.21/10.60 % Level of proof is 2.
% 0.21/10.60 % Maximum clause weight is 32.000.
% 0.21/10.60 % Given clauses 62.
% 0.21/10.60
% 0.21/10.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------