%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO087-1 : 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 : n005.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 07:17:02 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.49s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 23 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 29 ( 1 sgn 12 !; 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(corollary_2_9_68,axiom,
meet(sk16,sk14,sk15),
file('theBenchmark.p',corollary_2_9_68) ).
cnf(c_23,plain,
meet(sk16,sk14,sk15),
inference(clausify,[status(thm)],[corollary_2_9_68]) ).
fof(corollary_2_9_67,axiom,
part_of(sk14,sk15),
file('theBenchmark.p',corollary_2_9_67) ).
cnf(c_24,plain,
part_of(sk14,sk15),
inference(clausify,[status(thm)],[corollary_2_9_67]) ).
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_37,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(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_65,plain,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(clausify,[status(thm)],[part_of_defn_1]) ).
cnf(c_357,plain,
( end_point(A,sk14)
| ~ incident_c(A,sk15)
| ~ incident_c(A,sk14) ),
inference(resolve,[status(thm)],[c_37,c_23]) ).
cnf(c_358,plain,
( end_point(ax0_sk8(sk14),sk14)
| ~ incident_c(ax0_sk8(sk14),sk15) ),
inference(resolve,[status(thm)],[c_357,c_21]) ).
cnf(c_113,plain,
~ incident_c(ax0_sk8(sk14),sk15),
inference(resolve,[status(thm)],[c_358,c_22]) ).
cnf(c_359,plain,
( incident_c(ax0_sk8(A),B)
| ~ part_of(A,B) ),
inference(resolve,[status(thm)],[c_65,c_21]) ).
cnf(c_360,plain,
~ part_of(sk14,sk15),
inference(resolve,[status(thm)],[c_359,c_113]) ).
cnf(c_356,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_360]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO087-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.43 % Computer : n005.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Fri Sep 25 12:41:37 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.44 % Process 3510242 was started by sandbox2 on n005,
% 0.16/5.44 % Fri Sep 25 12:41:37 2026
% 0.16/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.44
% 0.16/5.44 % From the command line: assign(max_seconds, 300).
% 0.16/5.49
% 0.16/5.49 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.49
% 0.16/5.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.16/5.49 % Length of proof is 11.
% 0.16/5.49 % Level of proof is 3.
% 0.16/5.49 % Maximum clause weight is 18.000.
% 0.16/5.49 % Given clauses 58.
% 0.16/5.49
% 0.16/5.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------