%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV854-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 09:09:13 AM UTC 2026
% Result : Unsatisfiable 6.03s 1.80s
% Output : CNFRefutation 6.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 12 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_4,axiom,
! [VAR_0] :
( ~ hBOOL(c_in(VAR_0,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,VAR_0),c_Option_Othe(c_Com_Obody(VAR_0),tc_Com_Ocom),hAPP(v_Q,VAR_0),t_a),t_a) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_126,plain,
( ~ hBOOL(c_in(A,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,A),c_Option_Othe(c_Com_Obody(A),tc_Com_Ocom),hAPP(v_Q,A),t_a),t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_1,axiom,
~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_129,plain,
~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
hBOOL(c_in(v_x,v_Procs,tc_Com_Opname)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_130,plain,
hBOOL(c_in(v_x,v_Procs,tc_Com_Opname)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Body__triple__valid__Suc_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_Hoare__Mirabelle_Otriple__valid(VAR_0,c_Hoare__Mirabelle_Otriple_Otriple(VAR_1,c_Option_Othe(c_Com_Obody(VAR_2),tc_Com_Ocom),VAR_3,VAR_4),VAR_4)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,VAR_0),c_Hoare__Mirabelle_Otriple_Otriple(VAR_1,c_Com_Ocom_OBODY(VAR_2),VAR_3,VAR_4),VAR_4) ),
file('theBenchmark.p',cls_Body__triple__valid__Suc_0) ).
cnf(c_133,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(A,c_Hoare__Mirabelle_Otriple_Otriple(B,c_Option_Othe(c_Com_Obody(C),tc_Com_Ocom),D,E),E)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,A),c_Hoare__Mirabelle_Otriple_Otriple(B,c_Com_Ocom_OBODY(C),D,E),E) ),
inference(clausify,[status(thm)],[cls_Body__triple__valid__Suc_0]) ).
cnf(c_747,plain,
c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a),
inference(resolve,[status(thm)],[c_130,c_126]) ).
cnf(c_2657,plain,
c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a),
inference(resolve,[status(thm)],[c_747,c_133]) ).
cnf(c_2656,plain,
$false,
inference(resolve,[status(thm)],[c_129,c_2657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV854-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 15:03:22 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 2999994 was started by sandbox on n013,
% 0.12/0.38 % Sat Sep 26 15:03:22 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 6.03/1.80
% 6.03/1.80 % given #500 (W,wt=13): 1686 -c_lessequals(A,B,tc_bool) | -c_HOL_Oord__class_Oless(B,A,tc_bool). [resolve(577,a,117,a)].
% 6.03/1.80
% 6.03/1.80 % SZS status Unsatisfiable for theBenchmark
% 6.03/1.80
% 6.03/1.80 % Proof 1 at 0.61 (+ 0.11) seconds.
% 6.03/1.80 % Length of proof is 6.
% 6.03/1.80 % Level of proof is 2.
% 6.03/1.80 % Maximum clause weight is 42.000.
% 6.03/1.80 % Given clauses 567.
% 6.03/1.80
% 6.03/1.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------