%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 06:59:26 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 20 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 20 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 20 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(direct_success,axiom,
! [VAR_0,VAR_1] :
( ~ follows(VAR_0,VAR_1)
| succeeds(VAR_0,VAR_1) ),
file('theBenchmark.p',direct_success) ).
cnf(c_2,plain,
( ~ follows(A,B)
| succeeds(A,B) ),
inference(clausify,[status(thm)],[direct_success]) ).
fof(transition_3_to_6,axiom,
follows(p6,p3),
file('theBenchmark.p',transition_3_to_6) ).
cnf(c_5,plain,
follows(p6,p3),
inference(clausify,[status(thm)],[transition_3_to_6]) ).
fof(transition_6_to_7,axiom,
follows(p7,p6),
file('theBenchmark.p',transition_6_to_7) ).
cnf(c_6,plain,
follows(p7,p6),
inference(clausify,[status(thm)],[transition_6_to_7]) ).
fof(transition_7_to_8,axiom,
follows(p8,p7),
file('theBenchmark.p',transition_7_to_8) ).
cnf(c_7,plain,
follows(p8,p7),
inference(clausify,[status(thm)],[transition_7_to_8]) ).
fof(state_8,axiom,
has(p8,goto(loop)),
file('theBenchmark.p',state_8) ).
cnf(c_15,plain,
has(p8,goto(loop)),
inference(clausify,[status(thm)],[state_8]) ).
fof(goto_success,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ labels(VAR_2,VAR_0)
| ~ has(VAR_1,goto(VAR_2))
| succeeds(VAR_0,VAR_1) ),
file('theBenchmark.p',goto_success) ).
cnf(c_16,plain,
( ~ labels(C,A)
| ~ has(B,goto(C))
| succeeds(A,B) ),
inference(clausify,[status(thm)],[goto_success]) ).
fof(label_state_3,axiom,
labels(loop,p3),
file('theBenchmark.p',label_state_3) ).
cnf(c_17,plain,
labels(loop,p3),
inference(clausify,[status(thm)],[label_state_3]) ).
cnf(c_19,plain,
( ~ labels(loop,A)
| succeeds(A,p8) ),
inference(resolve,[status(thm)],[c_16,c_15]) ).
cnf(c_20,plain,
succeeds(p3,p8),
inference(resolve,[status(thm)],[c_17,c_19]) ).
cnf(c_21,plain,
succeeds(p8,p7),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_22,plain,
succeeds(p7,p6),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_23,plain,
succeeds(p6,p3),
inference(resolve,[status(thm)],[c_5,c_2]) ).
fof(prove_there_is_a_loop_through_p3,axiom,
~ succeeds(p3,p3),
file('theBenchmark.p',prove_there_is_a_loop_through_p3) ).
cnf(c_27,plain,
~ succeeds(p3,p3),
inference(clausify,[status(thm)],[prove_there_is_a_loop_through_p3]) ).
fof(transitivity_of_success,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ succeeds(VAR_2,VAR_1)
| ~ succeeds(VAR_0,VAR_2)
| succeeds(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_success) ).
cnf(c_28,plain,
( ~ succeeds(C,B)
| ~ succeeds(A,C)
| succeeds(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_success]) ).
cnf(c_48,plain,
( ~ succeeds(p8,A)
| succeeds(p3,A) ),
inference(resolve,[status(thm)],[c_28,c_20]) ).
cnf(c_36,plain,
succeeds(p3,p7),
inference(resolve,[status(thm)],[c_48,c_21]) ).
cnf(c_49,plain,
( ~ succeeds(A,p3)
| ~ succeeds(p3,A) ),
inference(resolve,[status(thm)],[c_28,c_27]) ).
cnf(c_37,plain,
~ succeeds(p3,p6),
inference(resolve,[status(thm)],[c_49,c_23]) ).
cnf(c_50,plain,
( ~ succeeds(A,p6)
| ~ succeeds(p3,A) ),
inference(resolve,[status(thm)],[c_28,c_37]) ).
cnf(c_46,plain,
~ succeeds(p3,p7),
inference(resolve,[status(thm)],[c_50,c_22]) ).
cnf(c_47,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 23:20:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 4061986 was started by sandbox on n003,
% 0.10/0.36 % Sat Sep 26 23:20:39 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 18.
% 0.10/0.38 % Level of proof is 4.
% 0.10/0.38 % Maximum clause weight is 9.000.
% 0.10/0.38 % Given clauses 12.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------