%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV834-1 : 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 : n016.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 09:09:11 AM UTC 2026
% Result : Unsatisfiable 4.49s 1.83s
% Output : CNFRefutation 4.49s
% 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 : 12 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 10 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_128,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(hAPP(c_Set_Oinsert(VAR_0),VAR_1),c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool))),
file('theBenchmark.p',cls_singleton__conv2_0) ).
cnf(c_513,plain,
c_Collect(hAPP(c_fequal(A),B),A) = hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),
inference(clausify,[status(thm)],[cls_singleton__conv2_0]) ).
cnf(c_2226,plain,
hAPP(c_fequal(A),B) = hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),
inference(paramod,[status(thm)],[c_128,c_513]) ).
cnf(c_514,plain,
hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))) = hAPP(c_fequal(A),B),
inference(copy,[status(thm)],[c_2226]) ).
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(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(VAR_1,VAR_2,VAR_3,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_604,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(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(B,C,D,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_605,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_514,c_604]) ).
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_613,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_2227,plain,
c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = c_COMBK(c_False,tc_bool,A),
inference(paramod,[status(thm)],[c_128,c_613]) ).
cnf(c_614,plain,
c_COMBK(c_False,tc_bool,A) = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),
inference(copy,[status(thm)],[c_2227]) ).
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_640,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_647,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(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),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_654,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),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_2228,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(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,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(paramod,[status(thm)],[c_614,c_654]) ).
cnf(c_655,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,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),t_a),
inference(paramod,[status(thm)],[c_514,c_2228]) ).
cnf(c_1985,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B) = c_False,
inference(paramod,[status(thm)],[c_614,c_647]) ).
cnf(c_1987,plain,
~ hBOOL(c_False),
inference(paramod,[status(thm)],[c_1985,c_640]) ).
cnf(c_2229,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),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),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),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c))),
inference(resolve,[status(thm)],[c_655,c_605]) ).
cnf(c_2230,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),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c))),
inference(paramod,[status(thm)],[c_647,c_2229]) ).
cnf(c_2231,plain,
hBOOL(c_False),
inference(paramod,[status(thm)],[c_1985,c_2230]) ).
cnf(c_2225,plain,
$false,
inference(resolve,[status(thm)],[c_1987,c_2231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV834-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n016.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 26 15:07:16 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.36 % Process 1156718 was started by sandbox on n016,
% 0.07/0.36 % Sat Sep 26 15:07:16 2026
% 0.07/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 4.49/1.83
% 4.49/1.83 % SZS status Unsatisfiable for theBenchmark
% 4.49/1.83
% 4.49/1.83 % Proof 1 at 0.58 (+ 0.09) seconds.
% 4.49/1.83 % Length of proof is 14.
% 4.49/1.83 % Level of proof is 4.
% 4.49/1.83 % Maximum clause weight is 152.000.
% 4.49/1.83 % Given clauses 385.
% 4.49/1.83
% 4.49/1.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------