%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO059-2 : 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 : n006.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 0.13s 15.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 18 unt; 0 def)
% Number of atoms : 36 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 18 ~; 10 |; 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 : 66 ( 7 sgn 14 !; 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(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(prove_congruence,axiom,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('theBenchmark.p',prove_congruence) ).
cnf(c_20,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(clausify,[status(thm)],[prove_congruence]) ).
cnf(c_150,plain,
~ equidistant(v,u,v,reflection(extension(u,v,u,v),v)),
inference(paramod,[status(thm)],[c_19,c_20]) ).
cnf(c_21,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_150]) ).
cnf(c_22,plain,
( equidistant(C,D,C,D)
| ~ equidistant(A,B,C,D) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_39,plain,
( equidistant(B,A,C,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_40,plain,
( equidistant(C,D,B,A)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_151,plain,
( equidistant(C,D,B,A)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_61,plain,
~ equidistant(extension(extension(u,v,u,v),v,extension(u,v,u,v),v),v,v,u),
inference(resolve,[status(thm)],[c_151,c_21]) ).
cnf(c_64,plain,
equidistant(A,B,A,B),
inference(resolve,[status(thm)],[c_22,c_5]) ).
cnf(c_79,plain,
equidistant(extension(A,B,C,D),B,C,D),
inference(resolve,[status(thm)],[c_39,c_5]) ).
cnf(c_81,plain,
~ equidistant(u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v),v),
inference(resolve,[status(thm)],[c_40,c_61]) ).
cnf(c_88,plain,
~ equidistant(v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v),u,v),
inference(resolve,[status(thm)],[c_40,c_81]) ).
cnf(c_102,plain,
( equidistant(C,D,A,B)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_64,c_2]) ).
cnf(c_141,plain,
equidistant(A,B,C,extension(D,C,A,B)),
inference(resolve,[status(thm)],[c_102,c_5]) ).
cnf(c_152,plain,
( equidistant(E,F,C,D)
| ~ equidistant(extension(A,B,C,D),B,E,F) ),
inference(resolve,[status(thm)],[c_2,c_79]) ).
cnf(c_148,plain,
~ equidistant(extension(A,B,u,v),B,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(resolve,[status(thm)],[c_152,c_88]) ).
cnf(c_149,plain,
$false,
inference(resolve,[status(thm)],[c_148,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO059-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/15.38 % Computer : n006.cluster.edu
% 0.09/15.38 % Model : x86_64 x86_64
% 0.09/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.38 % Memory : 8046.5625MB
% 0.09/15.38 % OS : Linux 6.8.0-71-generic
% 0.09/15.38 % CPULimit : 300
% 0.09/15.38 % WCLimit : 300
% 0.09/15.38 % DateTime : Fri Sep 25 12:37:27 UTC 2026
% 0.09/15.38 % CPUTime :
% 0.09/15.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/15.39 % Process 2922716 was started by sandbox on n006,
% 0.09/15.39 % Fri Sep 25 12:37:27 2026
% 0.09/15.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/15.39
% 0.09/15.39 % From the command line: assign(max_seconds, 300).
% 0.13/15.42
% 0.13/15.42 % SZS status Unsatisfiable for theBenchmark
% 0.13/15.42
% 0.13/15.42 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.13/15.42 % Length of proof is 18.
% 0.13/15.42 % Level of proof is 6.
% 0.13/15.42 % Maximum clause weight is 27.000.
% 0.13/15.42 % Given clauses 55.
% 0.13/15.42
% 0.13/15.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------