%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO094-1 : 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 : n003.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 07:17:03 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 47 ( 20 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 120 ( 61 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 63 ( 4 sgn 26 !; 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(c3_37,axiom,
! [VAR_0] : inner_point(ax0_sk8(VAR_0),VAR_0),
file('theBenchmark.p',c3_37) ).
cnf(c_4,plain,
inner_point(ax0_sk8(A),A),
inference(clausify,[status(thm)],[c3_37]) ).
cnf(c_21,plain,
incident_c(ax0_sk8(A),A),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_22,plain,
~ end_point(ax0_sk8(A),A),
inference(resolve,[status(thm)],[c_4,c_2]) ).
fof(proposition_2_14_3_70,axiom,
end_point(sk17,sk14),
file('theBenchmark.p',proposition_2_14_3_70) ).
cnf(c_23,plain,
end_point(sk17,sk14),
inference(clausify,[status(thm)],[proposition_2_14_3_70]) ).
fof(proposition_2_14_3_69,axiom,
part_of(sk16,sk14),
file('theBenchmark.p',proposition_2_14_3_69) ).
cnf(c_24,plain,
part_of(sk16,sk14),
inference(clausify,[status(thm)],[proposition_2_14_3_69]) ).
fof(proposition_2_14_3_68,axiom,
part_of(sk15,sk14),
file('theBenchmark.p',proposition_2_14_3_68) ).
cnf(c_25,plain,
part_of(sk15,sk14),
inference(clausify,[status(thm)],[proposition_2_14_3_68]) ).
fof(proposition_2_14_3_67,axiom,
meet(sk17,sk15,sk16),
file('theBenchmark.p',proposition_2_14_3_67) ).
cnf(c_26,plain,
meet(sk17,sk15,sk16),
inference(clausify,[status(thm)],[proposition_2_14_3_67]) ).
fof(meet_defn_27,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( end_point(VAR_3,VAR_2)
| ~ incident_c(VAR_3,VAR_2)
| ~ incident_c(VAR_3,VAR_1)
| ~ meet(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',meet_defn_27) ).
cnf(c_38,plain,
( end_point(D,C)
| ~ incident_c(D,C)
| ~ incident_c(D,B)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[meet_defn_27]) ).
fof(meet_defn_26,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( end_point(VAR_3,VAR_1)
| ~ incident_c(VAR_3,VAR_2)
| ~ incident_c(VAR_3,VAR_1)
| ~ meet(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',meet_defn_26) ).
cnf(c_39,plain,
( end_point(D,B)
| ~ incident_c(D,C)
| ~ incident_c(D,B)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[meet_defn_26]) ).
fof(meet_defn_25,axiom,
! [VAR_0,VAR_1,VAR_2] :
( incident_c(VAR_0,VAR_2)
| ~ meet(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',meet_defn_25) ).
cnf(c_40,plain,
( incident_c(A,C)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[meet_defn_25]) ).
fof(meet_defn_24,axiom,
! [VAR_0,VAR_1,VAR_2] :
( incident_c(VAR_0,VAR_1)
| ~ meet(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',meet_defn_24) ).
cnf(c_41,plain,
( incident_c(A,B)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[meet_defn_24]) ).
fof(end_point_defn_14,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( part_of(VAR_3,VAR_2)
| part_of(VAR_2,VAR_3)
| ~ incident_c(VAR_0,VAR_3)
| ~ incident_c(VAR_0,VAR_2)
| ~ part_of(VAR_3,VAR_1)
| ~ part_of(VAR_2,VAR_1)
| ~ end_point(VAR_0,VAR_1) ),
file('theBenchmark.p',end_point_defn_14) ).
cnf(c_48,plain,
( part_of(D,C)
| part_of(C,D)
| ~ incident_c(A,D)
| ~ incident_c(A,C)
| ~ part_of(D,B)
| ~ part_of(C,B)
| ~ end_point(A,B) ),
inference(clausify,[status(thm)],[end_point_defn_14]) ).
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_67,plain,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(clausify,[status(thm)],[part_of_defn_1]) ).
cnf(c_428,plain,
( end_point(A,sk16)
| ~ incident_c(A,sk16)
| ~ incident_c(A,sk15) ),
inference(resolve,[status(thm)],[c_38,c_26]) ).
cnf(c_429,plain,
( end_point(ax0_sk8(sk16),sk16)
| ~ incident_c(ax0_sk8(sk16),sk15) ),
inference(resolve,[status(thm)],[c_428,c_21]) ).
cnf(c_117,plain,
~ incident_c(ax0_sk8(sk16),sk15),
inference(resolve,[status(thm)],[c_429,c_22]) ).
cnf(c_430,plain,
( end_point(A,sk15)
| ~ incident_c(A,sk16)
| ~ incident_c(A,sk15) ),
inference(resolve,[status(thm)],[c_39,c_26]) ).
cnf(c_431,plain,
( end_point(ax0_sk8(sk15),sk15)
| ~ incident_c(ax0_sk8(sk15),sk16) ),
inference(resolve,[status(thm)],[c_430,c_21]) ).
cnf(c_123,plain,
~ incident_c(ax0_sk8(sk15),sk16),
inference(resolve,[status(thm)],[c_431,c_22]) ).
cnf(c_125,plain,
incident_c(sk17,sk16),
inference(resolve,[status(thm)],[c_40,c_26]) ).
cnf(c_127,plain,
incident_c(sk17,sk15),
inference(resolve,[status(thm)],[c_41,c_26]) ).
cnf(c_432,plain,
( incident_c(ax0_sk8(A),B)
| ~ part_of(A,B) ),
inference(resolve,[status(thm)],[c_67,c_21]) ).
cnf(c_369,plain,
~ part_of(sk16,sk15),
inference(resolve,[status(thm)],[c_432,c_117]) ).
cnf(c_433,plain,
( incident_c(ax0_sk8(A),B)
| ~ part_of(A,B) ),
inference(resolve,[status(thm)],[c_67,c_21]) ).
cnf(c_381,plain,
~ part_of(sk15,sk16),
inference(resolve,[status(thm)],[c_433,c_123]) ).
cnf(c_434,plain,
( part_of(B,sk16)
| part_of(sk16,B)
| ~ incident_c(A,B)
| ~ incident_c(A,sk16)
| ~ part_of(B,sk14)
| ~ end_point(A,sk14) ),
inference(resolve,[status(thm)],[c_48,c_24]) ).
cnf(c_435,plain,
( part_of(sk15,sk16)
| part_of(sk16,sk15)
| ~ incident_c(A,sk15)
| ~ incident_c(A,sk16)
| ~ end_point(A,sk14) ),
inference(resolve,[status(thm)],[c_434,c_25]) ).
cnf(c_436,plain,
( part_of(sk15,sk16)
| part_of(sk16,sk15)
| ~ incident_c(sk17,sk15)
| ~ end_point(sk17,sk14) ),
inference(resolve,[status(thm)],[c_435,c_125]) ).
cnf(c_437,plain,
( part_of(sk15,sk16)
| part_of(sk16,sk15)
| ~ end_point(sk17,sk14) ),
inference(resolve,[status(thm)],[c_436,c_127]) ).
cnf(c_438,plain,
( part_of(sk15,sk16)
| ~ end_point(sk17,sk14) ),
inference(resolve,[status(thm)],[c_437,c_369]) ).
cnf(c_439,plain,
~ end_point(sk17,sk14),
inference(resolve,[status(thm)],[c_438,c_381]) ).
cnf(c_427,plain,
$false,
inference(resolve,[status(thm)],[c_23,c_439]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO094-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 12:44:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 202140 was started by sandbox2 on n003,
% 0.09/0.36 % Fri Sep 25 12:44:37 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.42
% 0.09/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.42
% 0.09/0.42 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.09/0.42 % Length of proof is 22.
% 0.09/0.42 % Level of proof is 4.
% 0.09/0.42 % Maximum clause weight is 26.000.
% 0.09/0.42 % Given clauses 63.
% 0.09/0.42
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------