%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV909-1 : 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 : 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 09:09:19 AM UTC 2026
% Result : Unsatisfiable 3.98s 0.93s
% Output : CNFRefutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 24 unt; 0 def)
% Number of atoms : 30 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-4 aty)
% Number of variables : 42 ( 8 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Collect__def_0,axiom,
! [VAR_0,VAR_1] : c_Collect(VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Collect__def_0) ).
cnf(c_322,plain,
c_Collect(A,B) = A,
inference(clausify,[status(thm)],[cls_Collect__def_0]) ).
fof(cls_singleton__conv2_0,axiom,
! [VAR_0,VAR_1] : c_Collect(hAPP(c_fequal(VAR_0),VAR_1),VAR_0) = hAPP(c_Set_Oinsert(VAR_1,VAR_0),c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool))),
file('theBenchmark.p',cls_singleton__conv2_0) ).
cnf(c_563,plain,
c_Collect(hAPP(c_fequal(A),B),A) = hAPP(c_Set_Oinsert(B,A),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),
inference(clausify,[status(thm)],[cls_singleton__conv2_0]) ).
cnf(c_3031,plain,
hAPP(c_fequal(A),B) = hAPP(c_Set_Oinsert(B,A),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),
inference(paramod,[status(thm)],[c_322,c_563]) ).
cnf(c_564,plain,
hAPP(c_Set_Oinsert(A,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))) = hAPP(c_fequal(B),A),
inference(copy,[status(thm)],[c_3031]) ).
fof(cls_escape_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( hBOOL(hAPP(hAPP(VAR_1,v_sko__Hoare__Mirabelle__Xescape__1(VAR_0,VAR_1,VAR_3,VAR_2)),v_sko__Hoare__Mirabelle__Xescape__2(VAR_0,VAR_1,VAR_3,VAR_2)))
| c_Hoare__Mirabelle_Ohoare__derivs(VAR_0,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(VAR_1,VAR_2,VAR_3,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('theBenchmark.p',cls_escape_0) ).
cnf(c_648,plain,
( hBOOL(hAPP(hAPP(B,v_sko__Hoare__Mirabelle__Xescape__1(A,B,D,C)),v_sko__Hoare__Mirabelle__Xescape__2(A,B,D,C)))
| c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(B,C,D,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(clausify,[status(thm)],[cls_escape_0]) ).
cnf(c_649,plain,
( hBOOL(hAPP(hAPP(B,v_sko__Hoare__Mirabelle__Xescape__1(A,B,D,C)),v_sko__Hoare__Mirabelle__Xescape__2(A,B,D,C)))
| c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(B,C,D,t_a)),t_a) ),
inference(paramod,[status(thm)],[c_564,c_648]) ).
fof(cls_empty__def_0,axiom,
! [VAR_0] : c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,VAR_0),VAR_0),
file('theBenchmark.p',cls_empty__def_0) ).
cnf(c_653,plain,
c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,A),A),
inference(clausify,[status(thm)],[cls_empty__def_0]) ).
cnf(c_3032,plain,
c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = c_COMBK(c_False,tc_bool,A),
inference(paramod,[status(thm)],[c_322,c_653]) ).
cnf(c_654,plain,
c_COMBK(c_False,tc_bool,A) = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),
inference(copy,[status(thm)],[c_3032]) ).
fof(cls_bot1E_0,axiom,
! [VAR_0,VAR_1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool)),VAR_1)),
file('theBenchmark.p',cls_bot1E_0) ).
cnf(c_677,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B)),
inference(clausify,[status(thm)],[cls_bot1E_0]) ).
fof(cls_COMBK__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : hAPP(c_COMBK(VAR_0,VAR_1,VAR_2),VAR_3) = VAR_0,
file('theBenchmark.p',cls_COMBK__def_0) ).
cnf(c_682,plain,
hAPP(c_COMBK(A,B,C),D) = A,
inference(clausify,[status(thm)],[cls_COMBK__def_0]) ).
fof(cls_conjecture_0,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,v_Q,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_690,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,v_Q,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_3033,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,v_Q,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(paramod,[status(thm)],[c_654,c_690]) ).
cnf(c_691,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,v_Q,t_a)),t_a),
inference(paramod,[status(thm)],[c_564,c_3033]) ).
cnf(c_2949,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B) = c_False,
inference(paramod,[status(thm)],[c_654,c_682]) ).
cnf(c_2951,plain,
~ hBOOL(c_False),
inference(paramod,[status(thm)],[c_2949,c_677]) ).
cnf(c_3034,plain,
hBOOL(hAPP(hAPP(c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xescape__1(v_G,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_Q,v_c)),v_sko__Hoare__Mirabelle__Xescape__2(v_G,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_Q,v_c))),
inference(resolve,[status(thm)],[c_691,c_649]) ).
cnf(c_3035,plain,
hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),v_sko__Hoare__Mirabelle__Xescape__2(v_G,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_Q,v_c))),
inference(paramod,[status(thm)],[c_682,c_3034]) ).
cnf(c_3036,plain,
hBOOL(c_False),
inference(paramod,[status(thm)],[c_2949,c_3035]) ).
cnf(c_3030,plain,
$false,
inference(resolve,[status(thm)],[c_2951,c_3036]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV909-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.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 15:08:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2428310 was started by sandbox on n005,
% 0.10/0.37 % Sat Sep 26 15:08:47 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 3.98/0.93
% 3.98/0.93 % SZS status Unsatisfiable for theBenchmark
% 3.98/0.93
% 3.98/0.93 % Proof 1 at 0.44 (+ 0.07) seconds.
% 3.98/0.93 % Length of proof is 14.
% 3.98/0.93 % Level of proof is 4.
% 3.98/0.93 % Maximum clause weight is 51.000.
% 3.98/0.93 % Given clauses 411.
% 3.98/0.93
% 3.98/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------