%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO006-1 : 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 : 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 07:16:43 AM UTC 2026
% Result : Unsatisfiable 29.42s 4.18s
% Output : CNFRefutation 29.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 30 unt; 0 def)
% Number of atoms : 78 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 35 ~; 27 |; 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 : 83 ( 12 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(identity_for_betweeness,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ between(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',identity_for_betweeness) ).
cnf(c_1,plain,
( A = B
| ~ between(A,B,A) ),
inference(clausify,[status(thm)],[identity_for_betweeness]) ).
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(a_not_c,axiom,
a != c,
file('theBenchmark.p',a_not_c) ).
cnf(c_21,plain,
a != c,
inference(clausify,[status(thm)],[a_not_c]) ).
cnf(c_22,plain,
c != a,
inference(copy,[status(thm)],[c_21]) ).
fof(c_not_d,axiom,
c != d,
file('theBenchmark.p',c_not_d) ).
cnf(c_25,plain,
c != d,
inference(clausify,[status(thm)],[c_not_d]) ).
cnf(c_26,plain,
d != c,
inference(copy,[status(thm)],[c_25]) ).
fof(c_between_a_and_d,axiom,
between(a,c,d),
file('theBenchmark.p',c_between_a_and_d) ).
cnf(c_27,plain,
between(a,c,d),
inference(clausify,[status(thm)],[c_between_a_and_d]) ).
fof(prove_not_between_others,axiom,
( between(a,d,c)
| between(c,a,d) ),
file('theBenchmark.p',prove_not_between_others) ).
cnf(c_28,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(clausify,[status(thm)],[prove_not_between_others]) ).
cnf(c_4640,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_14,c_5]) ).
cnf(c_89,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_4640]) ).
cnf(c_4641,plain,
a != c,
inference(copy,[status(thm)],[c_22]) ).
cnf(c_124,plain,
~ between(a,c,a),
inference(resolve,[status(thm)],[c_1,c_4641]) ).
cnf(c_130,plain,
~ between(d,c,d),
inference(resolve,[status(thm)],[c_1,c_26]) ).
cnf(c_4642,plain,
( between(a,c,A)
| ~ between(c,A,d) ),
inference(resolve,[status(thm)],[c_2,c_27]) ).
cnf(c_4643,plain,
( between(a,d,c)
| between(a,c,a) ),
inference(resolve,[status(thm)],[c_4642,c_28]) ).
cnf(c_185,plain,
between(a,d,c),
inference(resolve,[status(thm)],[c_124,c_4643]) ).
cnf(c_401,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_89,c_13]) ).
cnf(c_430,plain,
( between(C,A,B)
| ~ between(A,B,A) ),
inference(resolve,[status(thm)],[c_401,c_2]) ).
cnf(c_4644,plain,
( between(B,d,outer_pasch(d,a,A,B,c))
| ~ between(A,c,B) ),
inference(resolve,[status(thm)],[c_8,c_185]) ).
cnf(c_471,plain,
between(c,d,outer_pasch(d,a,A,c,c)),
inference(resolve,[status(thm)],[c_4644,c_401]) ).
cnf(c_4645,plain,
( between(B,c,outer_pasch(c,a,A,B,d))
| ~ between(A,d,B) ),
inference(resolve,[status(thm)],[c_8,c_27]) ).
cnf(c_472,plain,
between(d,c,outer_pasch(c,a,A,d,d)),
inference(resolve,[status(thm)],[c_4645,c_401]) ).
cnf(c_4646,plain,
( between(a,outer_pasch(d,a,A,B,c),A)
| ~ between(A,c,B) ),
inference(resolve,[status(thm)],[c_7,c_185]) ).
cnf(c_478,plain,
between(a,outer_pasch(d,a,A,c,c),A),
inference(resolve,[status(thm)],[c_4646,c_401]) ).
cnf(c_4647,plain,
( between(a,outer_pasch(c,a,A,B,d),A)
| ~ between(A,d,B) ),
inference(resolve,[status(thm)],[c_7,c_27]) ).
cnf(c_479,plain,
between(a,outer_pasch(c,a,A,d,d),A),
inference(resolve,[status(thm)],[c_4647,c_401]) ).
cnf(c_4648,plain,
a = outer_pasch(d,a,a,c,c),
inference(resolve,[status(thm)],[c_478,c_1]) ).
cnf(c_4321,plain,
outer_pasch(d,a,a,c,c) = a,
inference(copy,[status(thm)],[c_4648]) ).
cnf(c_4477,plain,
between(c,d,a),
inference(paramod,[status(thm)],[c_4321,c_471]) ).
cnf(c_4649,plain,
( between(A,c,d)
| ~ between(A,c,a) ),
inference(resolve,[status(thm)],[c_2,c_4477]) ).
cnf(c_4616,plain,
~ between(d,c,a),
inference(resolve,[status(thm)],[c_4649,c_130]) ).
cnf(c_4650,plain,
( between(d,c,A)
| ~ between(c,A,outer_pasch(c,a,B,d,d)) ),
inference(resolve,[status(thm)],[c_2,c_472]) ).
cnf(c_4620,plain,
~ between(c,a,outer_pasch(c,a,A,d,d)),
inference(resolve,[status(thm)],[c_4650,c_4616]) ).
cnf(c_4638,plain,
between(A,a,outer_pasch(c,a,a,d,d)),
inference(resolve,[status(thm)],[c_479,c_430]) ).
cnf(c_4639,plain,
$false,
inference(resolve,[status(thm)],[c_4638,c_4620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 12:29:13 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2004144 was started by sandbox2 on n011,
% 0.08/0.36 % Fri Sep 25 12:29:13 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 29.42/4.18
% 29.42/4.18 % SZS status Unsatisfiable for theBenchmark
% 29.42/4.18
% 29.42/4.18 % Proof 1 at 3.35 (+ 0.38) seconds.
% 29.42/4.18 % Length of proof is 29.
% 29.42/4.18 % Level of proof is 9.
% 29.42/4.18 % Maximum clause weight is 27.000.
% 29.42/4.18 % Given clauses 220.
% 29.42/4.18
% 29.42/4.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------