%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 7.46s 1.43s
% Output : CNFRefutation 7.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 16 unt; 0 def)
% Number of atoms : 51 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 26 ~; 21 |; 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 : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 82 ( 8 sgn 29 !; 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_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(d1,axiom,
! [VAR_0,VAR_1] : equidistant(VAR_0,VAR_1,VAR_0,VAR_1),
file('theBenchmark.p',d1) ).
cnf(c_20,plain,
equidistant(A,B,A,B),
inference(clausify,[status(thm)],[d1]) ).
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(e2_1,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('theBenchmark.p',e2_1) ).
cnf(c_63,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(clausify,[status(thm)],[e2_1]) ).
cnf(c_64,plain,
lower_dimension_point_2 != lower_dimension_point_1,
inference(copy,[status(thm)],[c_63]) ).
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_69,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_618,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_69]) ).
cnf(c_70,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_618]) ).
cnf(c_619,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_136,plain,
equidistant(A,B,C,extension(D,C,A,B)),
inference(resolve,[status(thm)],[c_619,c_20]) ).
cnf(c_290,plain,
~ equidistant(lower_dimension_point_2,lower_dimension_point_1,A,A),
inference(resolve,[status(thm)],[c_3,c_64]) ).
cnf(c_333,plain,
~ equidistant(A,A,lower_dimension_point_1,lower_dimension_point_2),
inference(resolve,[status(thm)],[c_27,c_290]) ).
cnf(c_620,plain,
( equidistant(E,extension(F,E,A,B),C,D)
| ~ equidistant(A,B,C,D) ),
inference(resolve,[status(thm)],[c_28,c_5]) ).
cnf(c_549,plain,
equidistant(A,extension(B,A,C,D),E,extension(F,E,C,D)),
inference(resolve,[status(thm)],[c_620,c_136]) ).
cnf(c_616,plain,
extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v,
inference(resolve,[status(thm)],[c_549,c_70]) ).
cnf(c_621,plain,
equidistant(v,v,lower_dimension_point_1,lower_dimension_point_2),
inference(paramod,[status(thm)],[c_616,c_5]) ).
cnf(c_617,plain,
$false,
inference(resolve,[status(thm)],[c_333,c_621]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n017.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 12:30:18 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 2270648 was started by sandbox2 on n017,
% 0.18/0.45 % Fri Sep 25 12:30:18 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 7.46/1.43
% 7.46/1.43 % SZS status Unsatisfiable for theBenchmark
% 7.46/1.43
% 7.46/1.43 % Proof 1 at 0.87 (+ 0.09) seconds.
% 7.46/1.43 % Length of proof is 17.
% 7.46/1.43 % Level of proof is 4.
% 7.46/1.43 % Maximum clause weight is 30.000.
% 7.46/1.43 % Given clauses 94.
% 7.46/1.43
% 7.46/1.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------