%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV896-1 : 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 : n026.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 09:09:18 AM UTC 2026
% Result : Unsatisfiable 225.72s 40.46s
% Output : CNFRefutation 225.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 25 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-5 aty)
% Number of variables : 71 ( 16 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
cnf(c_52,plain,
class_Lattices_Oupper__semilattice(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Lattices_Oupper__semilattice]) ).
fof(cls_sup__ge1_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(VAR_0),VAR_1),VAR_2),VAR_0)
| ~ class_Lattices_Oupper__semilattice(VAR_0) ),
file('theBenchmark.p',cls_sup__ge1_0) ).
cnf(c_64,plain,
( c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),A)
| ~ class_Lattices_Oupper__semilattice(A) ),
inference(clausify,[status(thm)],[cls_sup__ge1_0]) ).
fof(cls_le__sup__iff_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(VAR_0),VAR_3),VAR_1),VAR_2,VAR_0)
| c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Lattices_Oupper__semilattice(VAR_0) ),
file('theBenchmark.p',cls_le__sup__iff_1) ).
cnf(c_69,plain,
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A)
| c_lessequals(B,C,A)
| ~ class_Lattices_Oupper__semilattice(A) ),
inference(clausify,[status(thm)],[cls_le__sup__iff_1]) ).
fof(cls_sup__le__fold__sup_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Finite__Set_Ofinite(VAR_3,VAR_0)
| ~ hBOOL(hAPP(hAPP(c_in(VAR_0),VAR_1),VAR_3))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(VAR_0),VAR_1),VAR_2),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(VAR_0),VAR_2,VAR_3,VAR_0,VAR_0),VAR_0)
| ~ class_Lattices_Oupper__semilattice(VAR_0) ),
file('theBenchmark.p',cls_sup__le__fold__sup_0) ).
cnf(c_75,plain,
( ~ c_Finite__Set_Ofinite(D,A)
| ~ hBOOL(hAPP(hAPP(c_in(A),B),D))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),C,D,A,A),A)
| ~ class_Lattices_Oupper__semilattice(A) ),
inference(clausify,[status(thm)],[cls_sup__le__fold__sup_0]) ).
cnf(c_80,plain,
( ~ c_Finite__Set_Ofinite(C,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),A),C))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B,C,tc_nat,tc_nat),tc_nat) ),
inference(resolve,[status(thm)],[c_75,c_52]) ).
cnf(c_92,plain,
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),C),A),B,tc_nat)
| c_lessequals(A,B,tc_nat) ),
inference(resolve,[status(thm)],[c_69,c_52]) ).
cnf(c_104,plain,
c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),tc_nat),
inference(resolve,[status(thm)],[c_64,c_52]) ).
fof(cls_not__less__eq__eq_1,axiom,
! [VAR_0,VAR_1] :
( ~ c_lessequals(c_Suc(VAR_1),VAR_0,tc_nat)
| ~ c_lessequals(VAR_0,VAR_1,tc_nat) ),
file('theBenchmark.p',cls_not__less__eq__eq_1) ).
cnf(c_339,plain,
( ~ c_lessequals(c_Suc(B),A,tc_nat)
| ~ c_lessequals(A,B,tc_nat) ),
inference(clausify,[status(thm)],[cls_not__less__eq__eq_1]) ).
fof(cls_rangeI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : hBOOL(hAPP(hAPP(c_in(VAR_0),hAPP(VAR_1,VAR_2)),hAPP(c_Set_Oimage(VAR_1,VAR_3,VAR_0),c_Orderings_Otop__class_Otop(tc_fun(VAR_3,tc_bool))))),
file('theBenchmark.p',cls_rangeI_0) ).
cnf(c_604,plain,
hBOOL(hAPP(hAPP(c_in(A),hAPP(B,C)),hAPP(c_Set_Oimage(B,D,A),c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool))))),
inference(clausify,[status(thm)],[cls_rangeI_0]) ).
fof(cls_finite_0,axiom,
! [VAR_0,VAR_1] :
( c_Finite__Set_Ofinite(VAR_1,VAR_0)
| ~ class_Finite__Set_Ofinite_Ofinite(VAR_0) ),
file('theBenchmark.p',cls_finite_0) ).
cnf(c_650,plain,
( c_Finite__Set_Ofinite(B,A)
| ~ class_Finite__Set_Ofinite_Ofinite(A) ),
inference(clausify,[status(thm)],[cls_finite_0]) ).
fof(cls_finite__imageI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Finite__Set_Ofinite(VAR_3,VAR_1)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(VAR_0,VAR_1,VAR_2),VAR_3),VAR_2) ),
file('theBenchmark.p',cls_finite__imageI_0) ).
cnf(c_665,plain,
( ~ c_Finite__Set_Ofinite(D,B)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(A,B,C),D),C) ),
inference(clausify,[status(thm)],[cls_finite__imageI_0]) ).
fof(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
cnf(c_896,plain,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(clausify,[status(thm)],[clsarity_bool__Finite__Set_Ofinite_Ofinite]) ).
cnf(c_940,plain,
c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A)),C),tc_nat),
inference(resolve,[status(thm)],[c_104,c_92]) ).
cnf(c_3148,plain,
c_Finite__Set_Ofinite(A,tc_bool),
inference(resolve,[status(thm)],[c_896,c_650]) ).
cnf(c_3445,plain,
c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(A,tc_bool,B),C),B),
inference(resolve,[status(thm)],[c_3148,c_665]) ).
cnf(c_3579,plain,
~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),c_Suc(B))),C),B,tc_nat),
inference(resolve,[status(thm)],[c_940,c_339]) ).
cnf(c_4994,plain,
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(A,D,tc_nat),c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool))),tc_nat)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(A,B)),C),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),C,hAPP(c_Set_Oimage(A,D,tc_nat),c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool))),tc_nat,tc_nat),tc_nat) ),
inference(resolve,[status(thm)],[c_80,c_604]) ).
cnf(c_4992,plain,
c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(A,B)),C),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),C,hAPP(c_Set_Oimage(A,tc_bool,tc_nat),c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool))),tc_nat,tc_nat),tc_nat),
inference(resolve,[status(thm)],[c_4994,c_3445]) ).
cnf(c_4993,plain,
$false,
inference(resolve,[status(thm)],[c_4992,c_3579]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV896-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.57 % Computer : n026.cluster.edu
% 0.10/10.57 % Model : x86_64 x86_64
% 0.10/10.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.57 % Memory : 8046.5625MB
% 0.10/10.57 % OS : Linux 6.8.0-71-generic
% 0.10/10.58 % CPULimit : 300
% 0.10/10.58 % WCLimit : 300
% 0.10/10.58 % DateTime : Sat Sep 26 15:11:06 UTC 2026
% 0.10/10.58 % CPUTime :
% 0.10/10.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.58 % Process 1317429 was started by sandbox on n026,
% 0.10/10.58 % Sat Sep 26 15:11:06 2026
% 0.10/10.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/10.64
% 0.14/10.64 % From the command line: assign(max_seconds, 300).
% 225.72/40.46
% 225.72/40.46 % given #500 (I,wt=192): 697 c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),B,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),C,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),D,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),E),t_b) | -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),F,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),C,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),V6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),E),t_b) | c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(F,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(A,B,F,D,V6,C))),hAPP(C,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(A,B,F,D,V6,C))),hAPP(V6,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(A,B,F,D,V6,C)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b) | -c_Finite__Set_Ofinite(E,t_a) # tptp_name(cls_finite__pointwise_0) # clausal_fof(1). [assumption].
% 225.72/40.46
% 225.72/40.46 % SZS status Unsatisfiable for theBenchmark
% 225.72/40.46
% 225.72/40.46 % Proof 1 at 3.89 (+ 0.99) seconds.
% 225.72/40.46 % Length of proof is 18.
% 225.72/40.46 % Level of proof is 4.
% 225.72/40.46 % Maximum clause weight is 29.000.
% 225.72/40.46 % Given clauses 845.
% 225.72/40.46
% 225.72/40.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------