%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO002-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 07:16:42 AM UTC 2026
% Result : Unsatisfiable 0.02s 0.42s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 44 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 76 ( 8 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_for_betweeness,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_1,VAR_3,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',transitivity_for_betweeness) ).
cnf(c_2,plain,
( between(A,B,D)
| ~ between(B,D,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[transitivity_for_betweeness]) ).
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_5,plain,
( A = B
| ~ equidistant(A,B,C,C) ),
inference(clausify,[status(thm)],[identity_for_equidistance]) ).
fof(outer_pasch1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_0,outer_pasch(VAR_1,VAR_0,VAR_3,VAR_4,VAR_2),VAR_3)
| ~ between(VAR_3,VAR_2,VAR_4)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',outer_pasch1) ).
cnf(c_7,plain,
( between(A,outer_pasch(B,A,D,E,C),D)
| ~ between(D,C,E)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[outer_pasch1]) ).
fof(outer_pasch2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_4,VAR_1,outer_pasch(VAR_1,VAR_0,VAR_3,VAR_4,VAR_2))
| ~ between(VAR_3,VAR_2,VAR_4)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',outer_pasch2) ).
cnf(c_8,plain,
( between(E,B,outer_pasch(B,A,D,E,C))
| ~ between(D,C,E)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[outer_pasch2]) ).
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_13,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_14,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(clausify,[status(thm)],[segment_construction2]) ).
fof(prove_a_between_a_and_b,axiom,
~ between(a,a,b),
file('theBenchmark.p',prove_a_between_a_and_b) ).
cnf(c_21,plain,
~ between(a,a,b),
inference(clausify,[status(thm)],[prove_a_between_a_and_b]) ).
cnf(c_25,plain,
( between(A,outer_pasch(B,A,A,B,B),A)
| ~ between(A,B,B) ),
inference(factor,[status(thm)],[c_7]) ).
cnf(c_26,plain,
( between(B,B,outer_pasch(B,A,A,B,B))
| ~ between(A,B,B) ),
inference(factor,[status(thm)],[c_8]) ).
cnf(c_238,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_14,c_5]) ).
cnf(c_72,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_238]) ).
cnf(c_161,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_72,c_13]) ).
cnf(c_171,plain,
between(A,A,outer_pasch(A,B,B,A,A)),
inference(resolve,[status(thm)],[c_161,c_26]) ).
cnf(c_172,plain,
between(A,outer_pasch(B,A,A,B,B),A),
inference(resolve,[status(thm)],[c_161,c_25]) ).
cnf(c_190,plain,
( between(C,A,B)
| ~ between(A,B,A) ),
inference(resolve,[status(thm)],[c_161,c_2]) ).
cnf(c_239,plain,
( between(A,A,B)
| ~ between(A,B,outer_pasch(A,C,C,A,A)) ),
inference(resolve,[status(thm)],[c_2,c_171]) ).
cnf(c_228,plain,
~ between(a,b,outer_pasch(a,A,A,a,a)),
inference(resolve,[status(thm)],[c_239,c_21]) ).
cnf(c_236,plain,
between(A,B,outer_pasch(C,B,B,C,C)),
inference(resolve,[status(thm)],[c_172,c_190]) ).
cnf(c_237,plain,
$false,
inference(resolve,[status(thm)],[c_236,c_228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO002-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 12:30:14 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.37 % Process 744039 was started by sandbox on n010,
% 0.02/0.37 % Fri Sep 25 12:30:14 2026
% 0.02/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.37
% 0.02/0.37 % From the command line: assign(max_seconds, 300).
% 0.02/0.42
% 0.02/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.02/0.42
% 0.02/0.42 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.02/0.42 % Length of proof is 17.
% 0.02/0.42 % Level of proof is 5.
% 0.02/0.42 % Maximum clause weight is 17.000.
% 0.02/0.42 % Given clauses 60.
% 0.02/0.42
% 0.02/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------