%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV858-1 : 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 : n004.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 09:09:14 AM UTC 2026
% Result : Unsatisfiable 86.09s 12.44s
% Output : CNFRefutation 86.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 20 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 4 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_6,axiom,
! [VAR_0,VAR_1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(VAR_0,v_n(VAR_0),t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),VAR_1),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(VAR_0,VAR_1,t_a) ),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_215,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(A,v_n(A),t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),B),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(A,B,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
fof(cls_conjecture_5,axiom,
! [VAR_0,VAR_1] :
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(VAR_0)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),VAR_1),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(VAR_0,VAR_1,t_a) ),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_216,plain,
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(A)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),B),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(A,B,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_4,axiom,
! [VAR_0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),VAR_0),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,VAR_0,t_a) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_217,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),A),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,A,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_3,axiom,
~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_218,plain,
~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_2,axiom,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_219,plain,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_220,plain,
c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_mem__def_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(hAPP(c_in(VAR_2),VAR_1),VAR_0))
| hBOOL(hAPP(VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_mem__def_0) ).
cnf(c_224,plain,
( ~ hBOOL(hAPP(hAPP(c_in(C),B),A))
| hBOOL(hAPP(A,B)) ),
inference(clausify,[status(thm)],[cls_mem__def_0]) ).
fof(cls_mem__def_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(VAR_2,VAR_1))
| hBOOL(hAPP(hAPP(c_in(VAR_0),VAR_1),VAR_2)) ),
file('theBenchmark.p',cls_mem__def_1) ).
cnf(c_225,plain,
( ~ hBOOL(hAPP(C,B))
| hBOOL(hAPP(hAPP(c_in(A),B),C)) ),
inference(clausify,[status(thm)],[cls_mem__def_1]) ).
fof(cls_predicate1D_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_lessequals(VAR_2,VAR_0,tc_fun(VAR_3,tc_bool))
| ~ hBOOL(hAPP(VAR_2,VAR_1))
| hBOOL(hAPP(VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_predicate1D_0) ).
cnf(c_235,plain,
( ~ c_lessequals(C,A,tc_fun(D,tc_bool))
| ~ hBOOL(hAPP(C,B))
| hBOOL(hAPP(A,B)) ),
inference(clausify,[status(thm)],[cls_predicate1D_0]) ).
cnf(c_897,plain,
hBOOL(hAPP(v_tsa,v_xa)),
inference(resolve,[status(thm)],[c_224,c_219]) ).
cnf(c_914,plain,
( ~ hBOOL(hAPP(v_tsa,A))
| hBOOL(hAPP(v_ts_H,A)) ),
inference(resolve,[status(thm)],[c_235,c_220]) ).
cnf(c_4215,plain,
hBOOL(hAPP(v_ts_H,v_xa)),
inference(resolve,[status(thm)],[c_914,c_897]) ).
cnf(c_4219,plain,
hBOOL(hAPP(hAPP(c_in(A),v_xa),v_ts_H)),
inference(resolve,[status(thm)],[c_4215,c_225]) ).
cnf(c_4252,plain,
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(A)),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(A,v_xa,t_a) ),
inference(resolve,[status(thm)],[c_4219,c_216]) ).
cnf(c_33233,plain,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_x)),v_Ga)),
inference(resolve,[status(thm)],[c_4252,c_218]) ).
cnf(c_33258,plain,
c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a),
inference(resolve,[status(thm)],[c_33233,c_217]) ).
cnf(c_33272,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),A),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(v_x,A,t_a) ),
inference(resolve,[status(thm)],[c_33258,c_215]) ).
cnf(c_34012,plain,
c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
inference(resolve,[status(thm)],[c_33272,c_4219]) ).
cnf(c_34011,plain,
$false,
inference(resolve,[status(thm)],[c_218,c_34012]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV858-1 : 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 : n004.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 15:04:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1994749 was started by sandbox on n004,
% 0.10/0.37 % Sat Sep 26 15:04:06 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).
% 86.09/12.44
% 86.09/12.44 % given #500 (I,wt=29): 732 c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(A,B,C),c_Set_Oinsert(A,D,C),tc_fun(C,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(A,B,C),D,tc_fun(C,tc_bool)) | -hBOOL(hAPP(hAPP(c_in(C),A),D)). [back_rewrite(366),rewrite([486(4)])].
% 86.09/12.44
% 86.09/12.44 % given #1000 (T,wt=10): 4482 class_Orderings_Oorder(tc_fun(A,tc_fun(B,tc_fun(C,tc_fun(D,tc_bool))))). [resolve(3752,a,208,b)].
% 86.09/12.44
% 86.09/12.44 % given #1500 (F,wt=19): 10834 c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatLeast(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),tc_fun(A,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(v_tsa,c_SetInterval_Oord__class_OatMost(v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_x,v_tsa),tc_nat),tc_fun(B,tc_bool)). [back_rewrite(10130),rewrite([10781(12)]),flip(a)].
% 86.09/12.44
% 86.09/12.44 % given #2000 (T,wt=12): 13488 hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(A,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool))). [para(704(a,1),13476(a,1,2))].
% 86.09/12.44
% 86.09/12.44 % given #2500 (F,wt=18): 19427 c_SetInterval_Oord__class_OatLeastAtMost(c_Complete__Lattice_OInf__class_OInf(v_tsa,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(v_xa,A,tc_bool),tc_bool) != c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatLeast(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),tc_fun(tc_bool,tc_bool)). [resolve(18301,a,12274,c),unit_del(a,190)].
% 86.09/12.44
% 86.09/12.44 % given #3000 (A,wt=19): 1216 c_lessequals(c_SetInterval_Oord__class_OatMost(A,tc_fun(B,tc_bool)),c_SetInterval_Oord__class_OatMost(c_Set_Oinsert(C,A,B),tc_fun(B,tc_bool)),tc_fun(tc_fun(B,tc_bool),tc_bool)). [resolve(300,a,242,c),unit_del(a,879)].
% 86.09/12.44
% 86.09/12.44 % given #3500 (T,wt=12): 18897 hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_OInf__class_OInf(c_SetInterval_Oord__class_OatMost(A,tc_bool),tc_bool),tc_bool),tc_bool),B)). [para(18787(a,2),13477(a,1,1,1,1))].
% 86.09/12.44
% 86.09/12.44 % given #4000 (F,wt=20): 23858 c_SetInterval_Oord__class_OatLeastAtMost(c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(A,v_tsa,B),tc_bool),c_Complete__Lattice_OSup__class_OSup(v_tsa,tc_bool),tc_bool) != c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatLeast(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),tc_fun(tc_bool,tc_bool)). [resolve(20083,a,12274,c),unit_del(a,190)].
% 86.09/12.44
% 86.09/12.44 % given #4500 (T,wt=13): 2850 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat). [resolve(694,a,227,d),unit_del(a,200)].
% 86.09/12.44
% 86.09/12.44 % given #5000 (F,wt=17): 33634 -hBOOL(hAPP(hAPP(c_in(A),c_Complete__Lattice_OInf__class_OInf(v_Ga,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatMost(c_Complete__Lattice_OSup__class_OSup(v_Ga,tc_bool),tc_bool),tc_fun(A,tc_bool)))). [para(33320(a,1),33415(a,1,2,1,1))].
% 86.09/12.44
% 86.09/12.44 % SZS status Unsatisfiable for theBenchmark
% 86.09/12.44
% 86.09/12.44 % Proof 1 at 9.48 (+ 2.31) seconds.
% 86.09/12.44 % Length of proof is 18.
% 86.09/12.44 % Level of proof is 8.
% 86.09/12.44 % Maximum clause weight is 21.000.
% 86.09/12.44 % Given clauses 5096.
% 86.09/12.44
% 86.09/12.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------