%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO112-1 : TPTP v9.3.1. Released v2.4.0.
% 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 07:17:05 AM UTC 2026
% Result : Unsatisfiable 0.02s 0.41s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 63 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 75 ( 40 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 64 ( 2 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(between_c_defn_5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( inner_point(VAR_2,ax1_sk1(VAR_3,VAR_2,VAR_1,VAR_0))
| ~ between_c(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',between_c_defn_5) ).
cnf(c_7,plain,
( inner_point(C,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
inference(clausify,[status(thm)],[between_c_defn_5]) ).
fof(between_c_defn_6,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between_c(VAR_3,VAR_0,VAR_4,VAR_1)
| ~ inner_point(VAR_4,VAR_2)
| ~ end_point(VAR_1,VAR_2)
| ~ end_point(VAR_0,VAR_2)
| ~ part_of(VAR_2,VAR_3)
| VAR_0 = VAR_1 ),
file('theBenchmark.p',between_c_defn_6) ).
cnf(c_8,plain,
( between_c(D,A,E,B)
| ~ inner_point(E,C)
| ~ end_point(B,C)
| ~ end_point(A,C)
| ~ part_of(C,D)
| A = B ),
inference(clausify,[status(thm)],[between_c_defn_6]) ).
cnf(c_19,plain,
( ~ between_c(F,E,D,C)
| between_c(V6,A,D,B)
| ~ end_point(B,ax1_sk1(C,D,E,F))
| ~ end_point(A,ax1_sk1(C,D,E,F))
| ~ part_of(ax1_sk1(C,D,E,F),V6)
| A = B ),
inference(resolve,[status(thm)],[c_8,c_7]) ).
fof(theorem_3_8_2_78,axiom,
~ between_c(sk15,sk18,sk17,sk16),
file('theBenchmark.p',theorem_3_8_2_78) ).
cnf(c_33,plain,
~ between_c(sk15,sk18,sk17,sk16),
inference(clausify,[status(thm)],[theorem_3_8_2_78]) ).
fof(theorem_3_8_2_77,axiom,
between_c(sk15,sk16,sk17,sk18),
file('theBenchmark.p',theorem_3_8_2_77) ).
cnf(c_34,plain,
between_c(sk15,sk16,sk17,sk18),
inference(clausify,[status(thm)],[theorem_3_8_2_77]) ).
fof(between_c_defn_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( end_point(VAR_3,ax1_sk1(VAR_3,VAR_2,VAR_1,VAR_0))
| ~ between_c(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',between_c_defn_4) ).
cnf(c_35,plain,
( end_point(D,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
inference(clausify,[status(thm)],[between_c_defn_4]) ).
fof(between_c_defn_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( end_point(VAR_1,ax1_sk1(VAR_3,VAR_2,VAR_1,VAR_0))
| ~ between_c(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',between_c_defn_3) ).
cnf(c_36,plain,
( end_point(B,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
inference(clausify,[status(thm)],[between_c_defn_3]) ).
fof(between_c_defn_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( part_of(ax1_sk1(VAR_3,VAR_2,VAR_1,VAR_0),VAR_0)
| ~ between_c(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',between_c_defn_2) ).
cnf(c_37,plain,
( part_of(ax1_sk1(D,C,B,A),A)
| ~ between_c(A,B,C,D) ),
inference(clausify,[status(thm)],[between_c_defn_2]) ).
fof(between_c_defn_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 != VAR_3
| ~ between_c(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',between_c_defn_1) ).
cnf(c_38,plain,
( B != D
| ~ between_c(A,B,C,D) ),
inference(clausify,[status(thm)],[between_c_defn_1]) ).
cnf(c_101,plain,
end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[status(thm)],[c_35,c_34]) ).
cnf(c_102,plain,
end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[status(thm)],[c_36,c_34]) ).
cnf(c_103,plain,
part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15),
inference(resolve,[status(thm)],[c_37,c_34]) ).
cnf(c_388,plain,
sk16 != sk18,
inference(resolve,[status(thm)],[c_38,c_34]) ).
cnf(c_104,plain,
sk18 != sk16,
inference(copy,[status(thm)],[c_388]) ).
cnf(c_389,plain,
( ~ between_c(D,C,B,A)
| between_c(E,sk18,B,sk16)
| ~ end_point(sk16,ax1_sk1(A,B,C,D))
| ~ end_point(sk18,ax1_sk1(A,B,C,D))
| ~ part_of(ax1_sk1(A,B,C,D),E) ),
inference(resolve,[status(thm)],[c_19,c_104]) ).
cnf(c_390,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| between_c(A,sk18,sk17,sk16)
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),A) ),
inference(resolve,[status(thm)],[c_389,c_101]) ).
cnf(c_391,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| between_c(A,sk18,sk17,sk16)
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),A) ),
inference(resolve,[status(thm)],[c_390,c_102]) ).
cnf(c_392,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15) ),
inference(resolve,[status(thm)],[c_391,c_33]) ).
cnf(c_393,plain,
~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15),
inference(resolve,[status(thm)],[c_392,c_34]) ).
cnf(c_387,plain,
$false,
inference(resolve,[status(thm)],[c_103,c_393]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO112-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.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 12:48:13 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 2041302 was started by sandbox on n011,
% 0.02/0.36 % Fri Sep 25 12:48:13 2026
% 0.02/0.36 % 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).
% 0.02/0.41
% 0.02/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.02/0.41
% 0.02/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.02/0.41 % Length of proof is 14.
% 0.02/0.41 % Level of proof is 2.
% 0.02/0.41 % Maximum clause weight is 34.000.
% 0.02/0.41 % Given clauses 77.
% 0.02/0.41
% 0.02/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------