%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO037-2 : 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 : n011.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 07:16:51 AM UTC 2026
% Result : Unsatisfiable 0.83s 0.54s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 22 unt; 0 def)
% Number of atoms : 51 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 81 ( 11 sgn 19 !; 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_construction1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : between(VAR_0,VAR_1,extension(VAR_0,VAR_1,VAR_2,VAR_3)),
file('theBenchmark.p',segment_construction1) ).
cnf(c_4,plain,
between(A,B,extension(A,B,C,D)),
inference(clausify,[status(thm)],[segment_construction1]) ).
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(lower_dimension3,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('theBenchmark.p',lower_dimension3) ).
cnf(c_12,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(clausify,[status(thm)],[lower_dimension3]) ).
fof(prove_lengthen,axiom,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
file('theBenchmark.p',prove_lengthen) ).
cnf(c_19,plain,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
inference(clausify,[status(thm)],[prove_lengthen]) ).
cnf(c_338,plain,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v ),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_20,plain,
( ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v ),
inference(resolve,[status(thm)],[c_4,c_338]) ).
cnf(c_339,plain,
( equidistant(B,A,C,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_40,plain,
equidistant(A,B,A,B),
inference(resolve,[status(thm)],[c_339,c_1]) ).
cnf(c_340,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_42,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_340]) ).
cnf(c_341,plain,
( equidistant(C,D,E,F)
| ~ equidistant(A,extension(B,A,C,D),E,F) ),
inference(resolve,[status(thm)],[c_2,c_5]) ).
cnf(c_126,plain,
equidistant(A,B,C,extension(D,C,A,B)),
inference(resolve,[status(thm)],[c_341,c_40]) ).
cnf(c_127,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_42,c_4]) ).
cnf(c_128,plain,
equidistant(A,A,B,B),
inference(paramod,[status(thm)],[c_42,c_5]) ).
cnf(c_189,plain,
( equidistant(B,C,D,D)
| ~ equidistant(A,A,B,C) ),
inference(resolve,[status(thm)],[c_128,c_2]) ).
cnf(c_342,plain,
( equidistant(E,extension(F,E,A,B),C,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2,c_126]) ).
cnf(c_266,plain,
equidistant(A,extension(B,A,C,D),E,extension(F,E,C,D)),
inference(resolve,[status(thm)],[c_342,c_126]) ).
cnf(c_273,plain,
extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v,
inference(resolve,[status(thm)],[c_266,c_20]) ).
cnf(c_274,plain,
equidistant(v,v,lower_dimension_point_1,lower_dimension_point_2),
inference(paramod,[status(thm)],[c_273,c_5]) ).
cnf(c_278,plain,
equidistant(lower_dimension_point_1,lower_dimension_point_2,A,A),
inference(resolve,[status(thm)],[c_274,c_189]) ).
cnf(c_343,plain,
lower_dimension_point_1 = lower_dimension_point_2,
inference(resolve,[status(thm)],[c_278,c_3]) ).
cnf(c_334,plain,
lower_dimension_point_2 = lower_dimension_point_1,
inference(copy,[status(thm)],[c_343]) ).
cnf(c_344,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1),
inference(paramod,[status(thm)],[c_334,c_12]) ).
cnf(c_337,plain,
$false,
inference(resolve,[status(thm)],[c_127,c_344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO037-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 12:34:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2013273 was started by sandbox on n011,
% 0.09/0.37 % Fri Sep 25 12:34:44 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.83/0.54
% 0.83/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.83/0.54
% 0.83/0.54 % Proof 1 at 0.14 (+ 0.02) seconds.
% 0.83/0.54 % Length of proof is 20.
% 0.83/0.54 % Level of proof is 8.
% 0.83/0.54 % Maximum clause weight is 30.000.
% 0.83/0.54 % Given clauses 51.
% 0.83/0.54
% 0.83/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------