%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO111-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.10s 0.36s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 17 unt; 0 def)
% Number of atoms : 107 ( 29 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 53 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 67 ( 2 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(inner_point_defn_22,axiom,
! [VAR_0,VAR_1] :
( ~ end_point(VAR_0,VAR_1)
| ~ inner_point(VAR_0,VAR_1) ),
file('theBenchmark.p',inner_point_defn_22) ).
cnf(c_2,plain,
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
inference(clausify,[status(thm)],[inner_point_defn_22]) ).
fof(inner_point_defn_21,axiom,
! [VAR_0,VAR_1] :
( incident_c(VAR_0,VAR_1)
| ~ inner_point(VAR_0,VAR_1) ),
file('theBenchmark.p',inner_point_defn_21) ).
cnf(c_3,plain,
( incident_c(A,B)
| ~ inner_point(A,B) ),
inference(clausify,[status(thm)],[inner_point_defn_21]) ).
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]) ).
cnf(c_20,plain,
( incident_c(C,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_21,plain,
( ~ end_point(C,ax1_sk1(D,C,B,A))
| ~ between_c(A,B,C,D) ),
inference(resolve,[status(thm)],[c_7,c_2]) ).
fof(theorem_3_8_1_78,axiom,
( sk16 = sk18
| sk17 = sk18
| sk16 = sk17
| ~ incident_c(sk18,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk16,sk15) ),
file('theBenchmark.p',theorem_3_8_1_78) ).
cnf(c_33,plain,
( sk16 = sk18
| sk17 = sk18
| sk16 = sk17
| ~ incident_c(sk18,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk16,sk15) ),
inference(clausify,[status(thm)],[theorem_3_8_1_78]) ).
cnf(c_611,plain,
( sk16 = sk18
| sk17 = sk18
| sk17 = sk16
| ~ incident_c(sk18,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk16,sk15) ),
inference(copy,[status(thm)],[c_33]) ).
cnf(c_612,plain,
( sk16 = sk18
| sk18 = sk17
| sk17 = sk16
| ~ incident_c(sk18,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk16,sk15) ),
inference(copy,[status(thm)],[c_611]) ).
cnf(c_34,plain,
( sk18 = sk16
| sk18 = sk17
| sk17 = sk16
| ~ incident_c(sk18,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk16,sk15) ),
inference(copy,[status(thm)],[c_612]) ).
fof(theorem_3_8_1_77,axiom,
between_c(sk15,sk16,sk17,sk18),
file('theBenchmark.p',theorem_3_8_1_77) ).
cnf(c_35,plain,
between_c(sk15,sk16,sk17,sk18),
inference(clausify,[status(thm)],[theorem_3_8_1_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_36,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_37,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_38,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_39,plain,
( B != D
| ~ between_c(A,B,C,D) ),
inference(clausify,[status(thm)],[between_c_defn_1]) ).
fof(end_point_defn_13,axiom,
! [VAR_0,VAR_1] :
( incident_c(VAR_0,VAR_1)
| ~ end_point(VAR_0,VAR_1) ),
file('theBenchmark.p',end_point_defn_13) ).
cnf(c_62,plain,
( incident_c(A,B)
| ~ end_point(A,B) ),
inference(clausify,[status(thm)],[end_point_defn_13]) ).
fof(part_of_defn_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( incident_c(VAR_2,VAR_1)
| ~ incident_c(VAR_2,VAR_0)
| ~ part_of(VAR_0,VAR_1) ),
file('theBenchmark.p',part_of_defn_1) ).
cnf(c_80,plain,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(clausify,[status(thm)],[part_of_defn_1]) ).
cnf(c_99,plain,
~ end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[status(thm)],[c_35,c_21]) ).
cnf(c_100,plain,
incident_c(sk17,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[status(thm)],[c_35,c_20]) ).
cnf(c_102,plain,
end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_103,plain,
end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[status(thm)],[c_37,c_35]) ).
cnf(c_104,plain,
part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15),
inference(resolve,[status(thm)],[c_38,c_35]) ).
cnf(c_613,plain,
sk16 != sk18,
inference(resolve,[status(thm)],[c_39,c_35]) ).
cnf(c_105,plain,
sk18 != sk16,
inference(copy,[status(thm)],[c_613]) ).
cnf(c_109,plain,
( sk18 = sk17
| sk17 = sk16
| ~ incident_c(sk18,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk16,sk15) ),
inference(resolve,[status(thm)],[c_105,c_34]) ).
cnf(c_364,plain,
incident_c(sk18,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[status(thm)],[c_102,c_62]) ).
cnf(c_369,plain,
incident_c(sk16,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[status(thm)],[c_103,c_62]) ).
cnf(c_375,plain,
( incident_c(A,sk15)
| ~ incident_c(A,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(resolve,[status(thm)],[c_104,c_80]) ).
cnf(c_490,plain,
incident_c(sk16,sk15),
inference(resolve,[status(thm)],[c_375,c_369]) ).
cnf(c_491,plain,
incident_c(sk18,sk15),
inference(resolve,[status(thm)],[c_375,c_364]) ).
cnf(c_492,plain,
incident_c(sk17,sk15),
inference(resolve,[status(thm)],[c_375,c_100]) ).
cnf(c_614,plain,
( sk18 = sk17
| sk17 = sk16
| ~ incident_c(sk18,sk15)
| ~ incident_c(sk17,sk15) ),
inference(resolve,[status(thm)],[c_490,c_109]) ).
cnf(c_615,plain,
( sk18 = sk17
| sk17 = sk16
| ~ incident_c(sk18,sk15) ),
inference(resolve,[status(thm)],[c_492,c_614]) ).
cnf(c_501,plain,
( sk18 = sk17
| sk17 = sk16 ),
inference(resolve,[status(thm)],[c_491,c_615]) ).
cnf(c_616,plain,
( end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| sk17 = sk16 ),
inference(paramod,[status(thm)],[c_501,c_102]) ).
cnf(c_596,plain,
sk17 = sk16,
inference(resolve,[status(thm)],[c_99,c_616]) ).
cnf(c_617,plain,
~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(paramod,[status(thm)],[c_596,c_99]) ).
cnf(c_610,plain,
$false,
inference(resolve,[status(thm)],[c_103,c_617]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO111-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 12:47:51 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 2130715 was started by sandbox2 on n012,
% 0.03/0.31 % Fri Sep 25 12:47:51 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 0.10/0.36
% 0.10/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.36
% 0.10/0.36 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.10/0.36 % Length of proof is 30.
% 0.10/0.36 % Level of proof is 6.
% 0.10/0.36 % Maximum clause weight is 23.000.
% 0.10/0.36 % Given clauses 110.
% 0.10/0.36
% 0.10/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------