%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWV885-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Thu Sep 24 03:07:04 PM UTC 2026
% Result : Unsatisfiable 6.06s 1.31s
% Output : CNFRefutation 6.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of clauses : 101 ( 68 unt; 9 nHn; 57 RR)
% Number of literals : 150 ( 77 equ; 53 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-4 aty)
% Number of variables : 151 ( 30 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
( ~ class_Lattices_Olattice(X2)
| class_Lattices_Olower__semilattice(tc_fun(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
cnf(cls_le__iff__inf_0,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_le__imp__diff__is__add_0,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
cnf(cls_conjecture_3,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(cls_diff__diff__cancel_0,axiom,
( ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
cnf(cls_Diff__disjoint_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
cnf(cls_Int__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_nat__add__commute_0,axiom,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
cnf(cls_diff__le__self_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
cnf(cls_card__Suc__eq_4,axiom,
( c_Finite__Set_Ocard(X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
| c_in(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_4) ).
cnf(cls_conjecture_6,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_nat__add__assoc_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
cnf(cls_rev__finite__subset_0,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
cnf(cls_set__eq__subset_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_diff__add__inverse_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
cnf(cls_card__Suc__eq_5,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).
cnf(cls_ex__in__conv_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
cnf(cls_card__eq__0__iff_0,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_0) ).
cnf(cls_card__eq__0__iff_2,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_2) ).
cnf(cls_card__empty_0,axiom,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__empty_0) ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
cnf(cls_Diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(c_0_30,plain,
( ~ class_Lattices_Olattice(X2)
| class_Lattices_Olower__semilattice(tc_fun(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clsarity_fun__Lattices_Olower__semilattice]) ).
cnf(c_0_31,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_le__iff__inf_0]) ).
cnf(c_0_32,plain,
( ~ class_Lattices_Olattice(X2)
| class_Lattices_Olower__semilattice(tc_fun(X1,X2)) ),
c_0_30 ).
cnf(c_0_33,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_34,plain,
( ~ c_lessequals(X1,X2,tc_nat)
| X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) ),
inference(fof_simplification,[status(thm)],[cls_le__imp__diff__is__add_0]) ).
cnf(c_0_35,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
cls_conjecture_3 ).
cnf(c_0_36,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
cls_Suc__eq__plus1_0 ).
cnf(c_0_37,plain,
( ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X2 ),
inference(fof_simplification,[status(thm)],[cls_diff__diff__cancel_0]) ).
cnf(c_0_38,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
cls_conjecture_2 ).
cnf(c_0_39,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(fof_simplification,[status(thm)],[cls_Zero__neq__Suc_0]) ).
cnf(c_0_40,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
cls_Diff__disjoint_0 ).
cnf(c_0_41,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
cls_Int__Diff_0 ).
cnf(c_0_42,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2 ),
c_0_31 ).
cnf(c_0_43,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
cls_conjecture_1 ).
cnf(c_0_44,plain,
class_Lattices_Olower__semilattice(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_45,plain,
( ~ c_lessequals(X1,X2,tc_nat)
| X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) ),
c_0_34 ).
cnf(c_0_46,axiom,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
cls_nat__add__commute_0 ).
cnf(c_0_47,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
cls_diff__le__self_0 ).
cnf(c_0_48,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_49,plain,
( ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X2 ),
c_0_37 ).
cnf(c_0_50,negated_conjecture,
c_lessequals(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(rw,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_51,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
c_0_39 ).
cnf(c_0_52,plain,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_53,negated_conjecture,
c_Lattices_Olower__semilattice__class_Oinf(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) = v_G,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_54,axiom,
( c_Finite__Set_Ocard(X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
| c_in(X1,X2,X3) ),
cls_card__Suc__eq_4 ).
cnf(c_0_55,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
inference(fof_simplification,[status(thm)],[cls_conjecture_6]) ).
cnf(c_0_56,plain,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2 ),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_57,negated_conjecture,
c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) = c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_48]) ).
cnf(c_0_59,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
cls_nat__add__assoc_0 ).
cnf(c_0_60,plain,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(X1,X2) ),
inference(fof_simplification,[status(thm)],[cls_rev__finite__subset_0]) ).
cnf(c_0_61,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(rw,[status(thm)],[c_0_51,c_0_36]) ).
cnf(c_0_62,plain,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[cls_set__eq__subset_2]) ).
cnf(c_0_63,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
cls_empty__subsetI_0 ).
cnf(c_0_64,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) = c_HOL_Ominus__class_Ominus(v_G,v_G,tc_fun(t_a,tc_bool)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_65,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(fof_simplification,[status(thm)],[cls_conjecture_5]) ).
cnf(c_0_66,plain,
( c_in(X1,X2,X3)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(X2,X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_Finite__Set_Ocard(X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(rw,[status(thm)],[c_0_54,c_0_36]) ).
cnf(c_0_67,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
c_0_55 ).
cnf(c_0_68,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_46]),c_0_59]) ).
cnf(c_0_69,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
cls_diff__add__inverse_0 ).
cnf(c_0_70,plain,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(X1,X2) ),
c_0_60 ).
cnf(c_0_71,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(spm,[status(thm)],[c_0_61,c_0_59]) ).
cnf(c_0_72,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
cls_card__Suc__eq_5 ).
cnf(c_0_73,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(fof_simplification,[status(thm)],[cls_ex__in__conv_0]) ).
cnf(c_0_74,plain,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| X1 = X2 ),
c_0_62 ).
cnf(c_0_75,negated_conjecture,
c_lessequals(c_HOL_Ominus__class_Ominus(v_G,v_G,tc_fun(t_a,tc_bool)),X1,tc_fun(t_a,tc_bool)),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_76,plain,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_card__eq__0__iff_0]) ).
cnf(c_0_77,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
c_0_65 ).
cnf(c_0_78,plain,
( c_in(X1,X2,X3)
| c_Finite__Set_Ocard(X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(X2,X3),tc_nat) ),
inference(rw,[status(thm)],[c_0_66,c_0_46]) ).
cnf(c_0_79,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68]),c_0_69]) ).
cnf(c_0_80,negated_conjecture,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| c_Finite__Set_Ofinite(v_G,t_a) ),
inference(spm,[status(thm)],[c_0_70,c_0_43]) ).
cnf(c_0_81,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_card__eq__0__iff_2 ).
cnf(c_0_82,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(spm,[status(thm)],[c_0_71,c_0_46]) ).
cnf(c_0_83,plain,
( c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(rw,[status(thm)],[c_0_72,c_0_36]) ).
cnf(c_0_84,axiom,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_card__empty_0 ).
cnf(c_0_85,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
cls_plus__nat_Oadd__0_0 ).
cnf(c_0_86,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
c_0_73 ).
cnf(c_0_87,negated_conjecture,
( ~ c_lessequals(X1,c_HOL_Ominus__class_Ominus(v_G,v_G,tc_fun(t_a,tc_bool)),tc_fun(t_a,tc_bool))
| X1 = c_HOL_Ominus__class_Ominus(v_G,v_G,tc_fun(t_a,tc_bool)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_88,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
cls_Diff__subset_0 ).
cnf(c_0_89,plain,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_76 ).
cnf(c_0_90,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_91,negated_conjecture,
c_Finite__Set_Ofinite(v_G,t_a),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_68]),c_0_82]) ).
cnf(c_0_92,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_HOL_Oone__class_Oone(tc_nat),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84]),c_0_85]),c_0_86]) ).
cnf(c_0_93,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v_G,v_G,tc_fun(t_a,tc_bool)),X1,tc_fun(t_a,tc_bool)) = c_HOL_Ominus__class_Ominus(v_G,v_G,tc_fun(t_a,tc_bool)),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_94,negated_conjecture,
c_HOL_Ominus__class_Ominus(v_G,v_G,tc_fun(t_a,tc_bool)) = v_G,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_64]),c_0_91])]) ).
cnf(c_0_95,axiom,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_natgb_Oadd__r0__iff_1 ).
cnf(c_0_96,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(v_G,v_G,tc_fun(t_a,tc_bool)),t_a),t_a) = c_HOL_Oone__class_Oone(tc_nat),
inference(spm,[status(thm)],[c_0_92,c_0_64]) ).
cnf(c_0_97,negated_conjecture,
c_HOL_Ominus__class_Ominus(v_G,X1,tc_fun(t_a,tc_bool)) = v_G,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_94]) ).
cnf(c_0_98,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Oone__class_Oone(tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_90]),c_0_95]) ).
cnf(c_0_99,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(X1,v_G,t_a),t_a) = c_HOL_Oone__class_Oone(tc_nat),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_100,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV885-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 09:30:04 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.06/1.31 % Version: 3.5.1
% 6.06/1.31 % Preprocessing class: FMLMSMSMSSSNFFN.
% 6.06/1.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.06/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.06/1.31 % Starting new_bool_3 with 300s (1) cores
% 6.06/1.31 % Starting new_bool_1 with 300s (1) cores
% 6.06/1.31 % Starting sh5l with 300s (1) cores
% 6.06/1.31 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2815469 completed with status 0
% 6.06/1.31 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 6.06/1.31 % Preprocessing class: FMLMSMSMSSSNFFN.
% 6.06/1.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.06/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.06/1.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.06/1.31 % No SInE strategy applied
% 6.06/1.31 % Search class: FGHSM-SSLM32-DFFFFFNN
% 6.06/1.31 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 6.06/1.31 % Starting SubtermCWHack with 136s (1) cores
% 6.06/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.06/1.31 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 6.06/1.31 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 6.06/1.31 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 6.06/1.31 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 2815500 completed with status 0
% 6.06/1.31 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 6.06/1.31 % Preprocessing class: FMLMSMSMSSSNFFN.
% 6.06/1.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.06/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.06/1.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.06/1.31 % No SInE strategy applied
% 6.06/1.31 % Search class: FGHSM-SSLM32-DFFFFFNN
% 6.06/1.31 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 6.06/1.31 % Starting SubtermCWHack with 136s (1) cores
% 6.06/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.06/1.31 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 6.06/1.31 % Preprocessing time : 0.025 s
% 6.06/1.31 % Presaturation interreduction done
% 6.06/1.31
% 6.06/1.31 % Proof found!
% 6.06/1.31 % SZS status Unsatisfiable
% 6.06/1.31 % SZS output start CNFRefutation
% See solution above
% 6.06/1.31 % Parsed axioms : 1121
% 6.06/1.31 % Removed by relevancy pruning/SinE : 0
% 6.06/1.31 % Initial clauses : 1121
% 6.06/1.31 % Removed in clause preprocessing : 1
% 6.06/1.31 % Initial clauses in saturation : 1120
% 6.06/1.31 % Processed clauses : 4748
% 6.06/1.31 % ...of these trivial : 148
% 6.06/1.31 % ...subsumed : 2423
% 6.06/1.31 % ...remaining for further processing : 2177
% 6.06/1.31 % Other redundant clauses eliminated : 65
% 6.06/1.31 % Clauses deleted for lack of memory : 0
% 6.06/1.31 % Backward-subsumed : 49
% 6.06/1.31 % Backward-rewritten : 169
% 6.06/1.31 % Generated clauses : 16325
% 6.06/1.31 % ...of the previous two non-redundant : 13375
% 6.06/1.31 % ...aggressively subsumed : 0
% 6.06/1.31 % Contextual simplify-reflections : 11
% 6.06/1.31 % Paramodulations : 16233
% 6.06/1.31 % Factorizations : 5
% 6.06/1.31 % NegExts : 0
% 6.06/1.31 % Equation resolutions : 87
% 6.06/1.31 % Disequality decompositions : 0
% 6.06/1.31 % Total rewrite steps : 12622
% 6.06/1.31 % ...of those cached : 10988
% 6.06/1.31 % Propositional unsat checks : 0
% 6.06/1.31 % Propositional check models : 0
% 6.06/1.31 % Propositional check unsatisfiable : 0
% 6.06/1.31 % Propositional clauses : 0
% 6.06/1.31 % Propositional clauses after purity: 0
% 6.06/1.31 % Propositional unsat core size : 0
% 6.06/1.31 % Propositional preprocessing time : 0.000
% 6.06/1.31 % Propositional encoding time : 0.000
% 6.06/1.31 % Propositional solver time : 0.000
% 6.06/1.31 % Success case prop preproc time : 0.000
% 6.06/1.31 % Success case prop encoding time : 0.000
% 6.06/1.31 % Success case prop solver time : 0.000
% 6.06/1.31 % Current number of processed clauses : 1073
% 6.06/1.31 % Positive orientable unit clauses : 299
% 6.06/1.31 % Positive unorientable unit clauses: 11
% 6.06/1.31 % Negative unit clauses : 216
% 6.06/1.31 % Non-unit-clauses : 547
% 6.06/1.31 % Current number of unprocessed clauses: 10570
% 6.06/1.31 % ...number of literals in the above : 19575
% 6.06/1.31 % Current number of archived formulas : 0
% 6.06/1.31 % Current number of archived clauses : 1105
% 6.06/1.31 % Clause-clause subsumption calls (NU) : 97032
% 6.06/1.31 % Rec. Clause-clause subsumption calls : 69007
% 6.06/1.31 % Non-unit clause-clause subsumptions : 561
% 6.06/1.31 % Unit Clause-clause subsumption calls : 12391
% 6.06/1.31 % Rewrite failures with RHS unbound : 31
% 6.06/1.31 % BW rewrite match attempts : 863
% 6.06/1.31 % BW rewrite match successes : 234
% 6.06/1.31 % Condensation attempts : 0
% 6.06/1.31 % Condensation successes : 0
% 6.06/1.31 % Termbank termtop insertions : 326527
% 6.06/1.31 % Search garbage collected termcells : 2146
% 6.06/1.31
% 6.06/1.31 % -------------------------------------------------
% 6.06/1.31 % User time : 0.806 s
% 6.06/1.31 % System time : 0.032 s
% 6.06/1.31 % Total time : 0.838 s
% 6.06/1.31 % Maximum resident set size: 5440 pages
% 6.06/1.31
% 6.06/1.31 % -------------------------------------------------
% 6.06/1.31 % User time : 3.196 s
% 6.06/1.31 % System time : 0.135 s
% 6.06/1.31 % Total time : 3.331 s
% 6.06/1.31 % Maximum resident set size: 5376 pages
% 6.06/1.31 % E exiting
%------------------------------------------------------------------------------