%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO001-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 07:16:41 AM UTC 2026
% Result : Unsatisfiable 5.28s 1.15s
% Output : CNFRefutation 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 16 unt; 0 def)
% Number of atoms : 46 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 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 : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 71 ( 11 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(b_between_a_and_c,axiom,
between(a,b,c),
file('theBenchmark.p',b_between_a_and_c) ).
cnf(c_21,plain,
between(a,b,c),
inference(clausify,[status(thm)],[b_between_a_and_c]) ).
fof(prove_b_between_c_and_a,axiom,
~ between(c,b,a),
file('theBenchmark.p',prove_b_between_c_and_a) ).
cnf(c_22,plain,
~ between(c,b,a),
inference(clausify,[status(thm)],[prove_b_between_c_and_a]) ).
cnf(c_1167,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_14,c_5]) ).
cnf(c_59,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_1167]) ).
cnf(c_84,plain,
( between(c,B,outer_pasch(B,A,a,c,b))
| ~ between(A,B,b) ),
inference(resolve,[status(thm)],[c_21,c_8]) ).
cnf(c_86,plain,
( between(A,outer_pasch(B,A,a,c,b),a)
| ~ between(A,B,b) ),
inference(resolve,[status(thm)],[c_21,c_7]) ).
cnf(c_264,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_59,c_13]) ).
cnf(c_317,plain,
( between(C,A,B)
| ~ between(A,B,A) ),
inference(resolve,[status(thm)],[c_264,c_2]) ).
cnf(c_843,plain,
between(c,b,outer_pasch(b,A,a,c,b)),
inference(resolve,[status(thm)],[c_84,c_264]) ).
cnf(c_1168,plain,
( between(c,b,A)
| ~ between(b,A,outer_pasch(b,B,a,c,b)) ),
inference(resolve,[status(thm)],[c_2,c_843]) ).
cnf(c_952,plain,
~ between(b,a,outer_pasch(b,A,a,c,b)),
inference(resolve,[status(thm)],[c_1168,c_22]) ).
cnf(c_1091,plain,
between(A,outer_pasch(b,A,a,c,b),a),
inference(resolve,[status(thm)],[c_86,c_264]) ).
cnf(c_1165,plain,
~ between(a,outer_pasch(b,A,a,c,b),a),
inference(resolve,[status(thm)],[c_317,c_952]) ).
cnf(c_1166,plain,
$false,
inference(resolve,[status(thm)],[c_1165,c_1091]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO001-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n013.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 12:29:36 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 425268 was started by sandbox2 on n013,
% 0.17/0.44 % Fri Sep 25 12:29:36 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 5.28/1.15
% 5.28/1.15 % SZS status Unsatisfiable for theBenchmark
% 5.28/1.15
% 5.28/1.15 % Proof 1 at 0.67 (+ 0.03) seconds.
% 5.28/1.15 % Length of proof is 18.
% 5.28/1.15 % Level of proof is 6.
% 5.28/1.15 % Maximum clause weight is 21.000.
% 5.28/1.15 % Given clauses 151.
% 5.28/1.15
% 5.28/1.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------