%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT016-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:05:50 PM UTC 2026
% Result : Unsatisfiable 17.21s 10.78s
% Output : CNFRefutation 17.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 36
% Syntax : Number of clauses : 144 ( 85 unt; 19 nHn; 60 RR)
% Number of literals : 209 ( 131 equ; 58 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 4 con; 0-4 aty)
% Number of variables : 269 ( 88 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Collect__neg__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
cnf(cls_Collect__def_0,axiom,
hAPP(c_Collect(X1),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_vimage__Collect__eq_0,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Collect(X3),X4)) = hAPP(c_Collect(X2),hAPP(hAPP(c_COMBB(X3,tc_bool,X2),X4),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).
cnf(cls_Collect__mem__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(cls_vimage__Compl_0,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X4)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
cnf(cls_vimage__const_0,axiom,
( hAPP(c_Set_Ovimage(c_COMBK(X1,X2,X3),X3,X2),X4) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_COMBI__def_0,axiom,
hAPP(c_COMBI(X1),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
cnf(cls_Compl__empty__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
cnf(cls_top__fun__eq_0,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(cls_fun__Compl__def_0,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
cnf(clsarity_bool__HOL_Ouminus,axiom,
class_HOL_Ouminus(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
cnf(cls_bot__fun__eq_0,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(cls_compl__bot__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_vimage__ident_0,axiom,
hAPP(c_Set_Ovimage(c_COMBI(X1),X1,X1),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__ident_0) ).
cnf(cls_Compl__eq__Compl__iff_0,axiom,
( X2 = X3
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
cnf(cls_insert__image_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),X5)) = hAPP(c_Set_Oimage(X2,X4,X1),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X3),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
cnf(cls_sup__top__left_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
cnf(cls_image__ident_0,axiom,
hAPP(c_Set_Oimage(c_COMBI(X1),X1,X1),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__ident_0) ).
cnf(cls_exE__some_0,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exE__some_0) ).
cnf(cls_RangeP_Ointros_0,axiom,
( hBOOL(c_Predicate_ORangeP(X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(X1,X5),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeP_Ointros_0) ).
cnf(cls_UNIV__not__empty_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_sup__bot__right_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
cnf(cls_sup__top__right_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(c_0_36,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
cls_Collect__neg__eq_0 ).
cnf(c_0_37,axiom,
hAPP(c_Collect(X1),X2) = X2,
cls_Collect__def_0 ).
cnf(c_0_38,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Collect(X3),X4)) = hAPP(c_Collect(X2),hAPP(hAPP(c_COMBB(X3,tc_bool,X2),X4),X1)),
cls_vimage__Collect__eq_0 ).
cnf(c_0_39,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_40,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
cls_double__complement_0 ).
cnf(c_0_41,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37]) ).
cnf(c_0_42,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X4)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),
cls_vimage__Compl_0 ).
cnf(c_0_43,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_COMBB(X3,tc_bool,X2),X4),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_37]),c_0_37]) ).
cnf(c_0_44,axiom,
( hAPP(c_Set_Ovimage(c_COMBK(X1,X2,X3),X3,X2),X4) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
cls_vimage__const_0 ).
cnf(c_0_45,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_46,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_47,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
cls_COMBB__def_0 ).
cnf(c_0_48,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_41]) ).
cnf(c_0_49,plain,
hAPP(hAPP(c_COMBB(X1,tc_bool,X2),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X3)),X4) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X2),c_Not),hAPP(hAPP(c_COMBB(X1,tc_bool,X2),X3),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_41]),c_0_43]),c_0_43]),c_0_41]) ).
cnf(c_0_50,plain,
( hAPP(hAPP(c_COMBB(X1,tc_bool,X2),X3),c_COMBK(X4,X1,X2)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(rw,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_51,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
hAPP(c_Not,hAPP(c_Not,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_47]) ).
cnf(c_0_53,axiom,
hAPP(c_COMBI(X1),X2) = X2,
cls_COMBI__def_0 ).
cnf(c_0_54,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Compl__empty__eq_0 ).
cnf(c_0_55,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__fun__eq_0 ).
cnf(c_0_56,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_57,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
cls_fun__Compl__def_0 ).
cnf(c_0_58,axiom,
class_HOL_Ouminus(tc_bool),
clsarity_bool__HOL_Ouminus ).
cnf(c_0_59,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__fun__eq_0 ).
cnf(c_0_60,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_61,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__bot__eq_0 ).
cnf(c_0_62,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_63,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)),X2) = X2,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_64,plain,
( hAPP(hAPP(c_COMBB(X1,tc_bool,X2),X3),c_COMBK(X4,X1,X2)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X3,X4)) ),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_65,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_66,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_54,c_0_41]) ).
cnf(c_0_67,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_68,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_69,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x)) = hAPP(c_Not,hAPP(X1,v_x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_41]),c_0_47]) ).
cnf(c_0_70,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_71,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_72,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_73,plain,
( c_COMBK(X1,tc_bool,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_47]),c_0_65]) ).
cnf(c_0_74,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(spm,[status(thm)],[c_0_47,c_0_66]) ).
cnf(c_0_75,plain,
hBOOL(c_Orderings_Otop__class_Otop(tc_bool)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_76,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_77,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_ComplI_0 ).
cnf(c_0_78,plain,
( hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)) = X3
| ~ hBOOL(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_79,plain,
hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(rw,[status(thm)],[c_0_77,c_0_41]) ).
cnf(c_0_81,axiom,
hAPP(c_Set_Ovimage(c_COMBI(X1),X1,X1),X2) = X2,
cls_vimage__ident_0 ).
cnf(c_0_82,plain,
hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_83,plain,
( hBOOL(hAPP(c_Not,hAPP(X1,X2)))
| hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_51]),c_0_47]),c_0_51]) ).
cnf(c_0_84,axiom,
( X2 = X3
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3) ),
cls_Compl__eq__Compl__iff_0 ).
cnf(c_0_85,plain,
hAPP(hAPP(c_COMBB(X1,tc_bool,X1),X2),c_COMBI(X1)) = X2,
inference(rw,[status(thm)],[c_0_81,c_0_43]) ).
cnf(c_0_86,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_78,c_0_82]) ).
cnf(c_0_87,plain,
( hBOOL(hAPP(c_Not,X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_53]) ).
cnf(c_0_88,plain,
( X1 = X2
| hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X3),c_Not),X1) != hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X3),c_Not),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_41]),c_0_41]) ).
cnf(c_0_89,plain,
c_COMBI(tc_bool) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not),
inference(spm,[status(thm)],[c_0_48,c_0_85]) ).
cnf(c_0_90,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(c_Not,X1)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),X5)) = hAPP(c_Set_Oimage(X2,X4,X1),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X3),X5)) ),
cls_insert__image_0 ).
cnf(c_0_92,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__left_0 ).
cnf(c_0_93,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_94,plain,
( X1 = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),X1) != c_Not ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_85]),c_0_89]) ).
cnf(c_0_95,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_90]),c_0_65]) ).
cnf(c_0_96,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
cls_empty__not__insert_0 ).
cnf(c_0_97,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),X5)) = hAPP(c_Set_Oimage(X2,X4,X1),X5)
| ~ hBOOL(hAPP(X5,X3)) ),
inference(rw,[status(thm)],[c_0_91,c_0_51]) ).
cnf(c_0_98,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_99,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)) != c_Not ),
inference(spm,[status(thm)],[c_0_94,c_0_66]) ).
cnf(c_0_100,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_86,c_0_95]) ).
cnf(c_0_101,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X4,X5)) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_102,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),X1) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_76]),c_0_76]) ).
cnf(c_0_103,axiom,
hAPP(c_Set_Oimage(c_COMBI(X1),X1,X1),X2) = X2,
cls_image__ident_0 ).
cnf(c_0_104,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
cls_exE__some_0 ).
cnf(c_0_105,axiom,
( hBOOL(c_Predicate_ORangeP(X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(X1,X5),X2)) ),
cls_RangeP_Ointros_0 ).
cnf(c_0_106,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) != c_Not ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_107,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_79])]) ).
cnf(c_0_108,plain,
hAPP(c_Set_Oimage(hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not),tc_bool,tc_bool),X1) = X1,
inference(spm,[status(thm)],[c_0_103,c_0_89]) ).
cnf(c_0_109,plain,
( hBOOL(hAPP(c_Not,c_Hilbert__Choice_OEps(c_Not,X1)))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_104,c_0_65]) ).
cnf(c_0_110,plain,
hBOOL(c_Predicate_ORangeP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1,X2,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_98]),c_0_75])]) ).
cnf(c_0_111,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_UNIV__not__empty_0 ).
cnf(c_0_112,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Not ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_100])]) ).
cnf(c_0_113,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_114,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) != c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_115,plain,
hBOOL(hAPP(c_Not,c_Hilbert__Choice_OEps(c_Not,X1))),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_116,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Not
| c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_117,plain,
( X1 = X2
| hBOOL(X1)
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_95]) ).
cnf(c_0_118,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_113,c_0_70]) ).
cnf(c_0_119,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__right_0 ).
cnf(c_0_120,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) != hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(spm,[status(thm)],[c_0_114,c_0_100]) ).
cnf(c_0_121,plain,
hAPP(c_Set_Oimage(X1,X2,X3),c_Not) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_101,c_0_115]) ).
cnf(c_0_122,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Not
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117])]),c_0_118]) ).
cnf(c_0_123,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),c_COMBI(X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(X5) ),
inference(spm,[status(thm)],[c_0_101,c_0_53]) ).
cnf(c_0_124,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),c_Orderings_Obot__class_Obot(tc_bool)) = X1,
inference(spm,[status(thm)],[c_0_119,c_0_93]) ).
cnf(c_0_125,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_100])]) ).
cnf(c_0_126,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Not,
inference(spm,[status(thm)],[c_0_121,c_0_103]) ).
cnf(c_0_127,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))
| c_Orderings_Obot__class_Obot(tc_bool) = c_Not ),
inference(spm,[status(thm)],[c_0_86,c_0_122]) ).
cnf(c_0_128,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__right_0 ).
cnf(c_0_129,plain,
( c_COMBI(X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_123,c_0_103]) ).
cnf(c_0_130,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_131,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Not ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_100]) ).
cnf(c_0_132,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_128,c_0_93]) ).
cnf(c_0_133,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_129,c_0_89]) ).
cnf(c_0_134,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Not ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_47]),c_0_65])]) ).
cnf(c_0_135,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0 ).
cnf(c_0_136,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_76]),c_0_76]) ).
cnf(c_0_137,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Not
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_138,plain,
hBOOL(c_Predicate_ORangeP(c_fequal(X1),X2,X3,X4)),
inference(spm,[status(thm)],[c_0_105,c_0_135]) ).
cnf(c_0_139,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_136,c_0_125]) ).
cnf(c_0_140,plain,
c_Orderings_Obot__class_Obot(tc_bool) = c_Not,
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_141,plain,
hAPP(c_Not,c_Not) = c_Not,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140]),c_0_140]),c_0_65]),c_0_140]),c_0_140]),c_0_126]) ).
cnf(c_0_142,plain,
~ hBOOL(c_Not),
inference(rw,[status(thm)],[c_0_118,c_0_140]) ).
cnf(c_0_143,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_141]),c_0_142]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT016-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:53:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 17.21/10.78 % Version : CSE_E---1.7
% 17.21/10.78 % Problem : theBenchmark.p
% 17.21/10.78 % SZS status Unsatisfiable for theBenchmark.p
% 17.21/10.78 % SZS output start CNFRefutation
% See solution above
% 17.31/10.85 % Total time : 7.447s
%------------------------------------------------------------------------------