%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO081-1 : 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 : n002.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 07:17:00 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(part_of_transitivity_69,axiom,
~ part_of(sk14,sk16),
file('theBenchmark.p',part_of_transitivity_69) ).
cnf(c_23,plain,
~ part_of(sk14,sk16),
inference(clausify,[status(thm)],[part_of_transitivity_69]) ).
fof(part_of_transitivity_68,axiom,
part_of(sk15,sk16),
file('theBenchmark.p',part_of_transitivity_68) ).
cnf(c_24,plain,
part_of(sk15,sk16),
inference(clausify,[status(thm)],[part_of_transitivity_68]) ).
fof(part_of_transitivity_67,axiom,
part_of(sk14,sk15),
file('theBenchmark.p',part_of_transitivity_67) ).
cnf(c_25,plain,
part_of(sk14,sk15),
inference(clausify,[status(thm)],[part_of_transitivity_67]) ).
fof(part_of_defn_3,axiom,
! [VAR_0,VAR_1] :
( part_of(VAR_0,VAR_1)
| ~ incident_c(ax0_sk1(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',part_of_defn_3) ).
cnf(c_64,plain,
( part_of(A,B)
| ~ incident_c(ax0_sk1(A,B),B) ),
inference(clausify,[status(thm)],[part_of_defn_3]) ).
fof(part_of_defn_2,axiom,
! [VAR_0,VAR_1] :
( part_of(VAR_0,VAR_1)
| incident_c(ax0_sk1(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',part_of_defn_2) ).
cnf(c_65,plain,
( part_of(A,B)
| incident_c(ax0_sk1(A,B),A) ),
inference(clausify,[status(thm)],[part_of_defn_2]) ).
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_66,plain,
( incident_c(C,B)
| ~ incident_c(C,A)
| ~ part_of(A,B) ),
inference(clausify,[status(thm)],[part_of_defn_1]) ).
cnf(c_290,plain,
~ incident_c(ax0_sk1(sk14,sk16),sk16),
inference(resolve,[status(thm)],[c_64,c_23]) ).
cnf(c_309,plain,
incident_c(ax0_sk1(sk14,sk16),sk14),
inference(resolve,[status(thm)],[c_65,c_23]) ).
cnf(c_386,plain,
( incident_c(A,sk16)
| ~ incident_c(A,sk15) ),
inference(resolve,[status(thm)],[c_66,c_24]) ).
cnf(c_377,plain,
~ incident_c(ax0_sk1(sk14,sk16),sk15),
inference(resolve,[status(thm)],[c_386,c_290]) ).
cnf(c_387,plain,
( incident_c(A,sk15)
| ~ incident_c(A,sk14) ),
inference(resolve,[status(thm)],[c_66,c_25]) ).
cnf(c_388,plain,
~ incident_c(ax0_sk1(sk14,sk16),sk14),
inference(resolve,[status(thm)],[c_387,c_377]) ).
cnf(c_385,plain,
$false,
inference(resolve,[status(thm)],[c_309,c_388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO081-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n002.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Fri Sep 25 12:43:41 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 3284881 was started by sandbox2 on n002,
% 0.11/5.38 % Fri Sep 25 12:43:41 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.38
% 0.11/5.38 % From the command line: assign(max_seconds, 300).
% 0.15/5.42
% 0.15/5.42 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.42
% 0.15/5.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/5.42 % Length of proof is 10.
% 0.15/5.42 % Level of proof is 3.
% 0.15/5.42 % Maximum clause weight is 18.000.
% 0.15/5.42 % Given clauses 56.
% 0.15/5.42
% 0.15/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------