%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV885-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 03:00:07 PM UTC 2026
% Result : Unsatisfiable 3.60s 1.01s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of clauses : 83 ( 55 unt; 11 nHn; 49 RR)
% Number of literals : 125 ( 57 equ; 48 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 : 20 ( 20 usr; 9 con; 0-4 aty)
% Number of variables : 110 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(cls_diff__le__self_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
cnf(cls_not__less__eq__eq_1,axiom,
( ~ c_lessequals(c_Suc(X2),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_add__diff__inverse_0,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_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/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__eq_4) ).
cnf(cls_ex__in__conv_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_card__eq__0__iff_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
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/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_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/sandbox2/benchmark/theBenchmark.p',cls_card__eq__0__iff_2) ).
cnf(cls_le0_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_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/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).
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/sandbox2/benchmark/theBenchmark.p',cls_card__empty_0) ).
cnf(cls_Diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_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/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(c_0_26,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_27,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_28,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_29,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_30,plain,
( ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1) ),
inference(fof_simplification,[status(thm)],[cls_less__le__not__le_1]) ).
cnf(c_0_31,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
cls_diff__le__self_0 ).
cnf(c_0_32,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_26,c_0_27]) ).
cnf(c_0_33,plain,
( ~ c_lessequals(c_Suc(X2),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[cls_not__less__eq__eq_1]) ).
cnf(c_0_34,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_28 ).
cnf(c_0_35,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_29,c_0_27]) ).
cnf(c_0_36,plain,
( ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1) ),
c_0_30 ).
cnf(c_0_37,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_31,c_0_32]) ).
cnf(c_0_38,axiom,
class_Orderings_Opreorder(tc_nat),
clsarity_nat__Orderings_Opreorder ).
cnf(c_0_39,plain,
( ~ c_lessequals(c_Suc(X2),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_33 ).
cnf(c_0_40,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_41,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2 ),
cls_add__diff__inverse_0 ).
cnf(c_0_42,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_35])]) ).
cnf(c_0_43,negated_conjecture,
~ c_HOL_Oord__class_Oless(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),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_44,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_45,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_46,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_47,plain,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_48,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_49,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_50,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_40 ).
cnf(c_0_51,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(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_52,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_53,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_46,c_0_27]) ).
cnf(c_0_54,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_55,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_56,negated_conjecture,
~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
inference(spm,[status(thm)],[c_0_47,c_0_35]) ).
cnf(c_0_57,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_58,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
cls_le0_0 ).
cnf(c_0_59,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_60,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_61,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Diff__cancel_0 ).
cnf(c_0_62,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
c_0_48 ).
cnf(c_0_63,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_49 ).
cnf(c_0_64,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_50,c_0_51]),c_0_52]) ).
cnf(c_0_65,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_53,c_0_44]) ).
cnf(c_0_66,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
c_0_54 ).
cnf(c_0_67,plain,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| c_Finite__Set_Ofinite(X1,X2) ),
c_0_55 ).
cnf(c_0_68,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_69,negated_conjecture,
c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
cnf(c_0_70,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_59,c_0_27]) ).
cnf(c_0_71,plain,
c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,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_73,plain,
~ c_in(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(X2,tc_bool)),X2),
inference(rw,[status(thm)],[c_0_62,c_0_61]) ).
cnf(c_0_74,plain,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(X2,tc_bool)) ),
inference(rw,[status(thm)],[c_0_63,c_0_61]) ).
cnf(c_0_75,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_64,c_0_65]),c_0_66]) ).
cnf(c_0_76,negated_conjecture,
c_Finite__Set_Ofinite(v_G,t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]) ).
cnf(c_0_77,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_78,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_61]),c_0_61]),c_0_71]),c_0_72]),c_0_61]),c_0_73]) ).
cnf(c_0_79,negated_conjecture,
c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(t_a,tc_bool)) = v_G,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76])]) ).
cnf(c_0_80,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_64,c_0_75]),c_0_77]) ).
cnf(c_0_81,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_78,c_0_79]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]),
[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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n006.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 09:29:57 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 3.60/1.01 % Version: 3.5.1
% 3.60/1.01 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.60/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.60/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.60/1.01 % Starting new_bool_3 with 300s (1) cores
% 3.60/1.01 % Starting new_bool_1 with 300s (1) cores
% 3.60/1.01 % Starting sh5l with 300s (1) cores
% 3.60/1.01 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2523523 completed with status 0
% 3.60/1.01 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.60/1.01 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.60/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.60/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.60/1.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.60/1.01 % No SInE strategy applied
% 3.60/1.01 % Search class: FGHSM-SSLM32-DFFFFFNN
% 3.60/1.01 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 3.60/1.01 % Starting SubtermCWHack with 136s (1) cores
% 3.60/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.60/1.01 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 3.60/1.01 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 3.60/1.01 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 3.60/1.01 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2523531 completed with status 0
% 3.60/1.01 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.60/1.01 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.60/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.60/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.60/1.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.60/1.01 % No SInE strategy applied
% 3.60/1.01 % Search class: FGHSM-SSLM32-DFFFFFNN
% 3.60/1.01 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 3.60/1.01 % Starting SubtermCWHack with 136s (1) cores
% 3.60/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.60/1.01 % Preprocessing time : 0.011 s
% 3.60/1.01 % Presaturation interreduction done
% 3.60/1.01
% 3.60/1.01 % Proof found!
% 3.60/1.01 % SZS status Unsatisfiable
% 3.60/1.01 % SZS output start CNFRefutation
% See solution above
% 3.60/1.01 % Parsed axioms : 1121
% 3.60/1.01 % Removed by relevancy pruning/SinE : 0
% 3.60/1.01 % Initial clauses : 1121
% 3.60/1.01 % Removed in clause preprocessing : 1
% 3.60/1.01 % Initial clauses in saturation : 1120
% 3.60/1.01 % Processed clauses : 2636
% 3.60/1.01 % ...of these trivial : 60
% 3.60/1.01 % ...subsumed : 551
% 3.60/1.01 % ...remaining for further processing : 2025
% 3.60/1.01 % Other redundant clauses eliminated : 105
% 3.60/1.01 % Clauses deleted for lack of memory : 0
% 3.60/1.01 % Backward-subsumed : 41
% 3.60/1.01 % Backward-rewritten : 134
% 3.60/1.01 % Generated clauses : 18528
% 3.60/1.01 % ...of the previous two non-redundant : 15441
% 3.60/1.01 % ...aggressively subsumed : 0
% 3.60/1.01 % Contextual simplify-reflections : 6
% 3.60/1.01 % Paramodulations : 18401
% 3.60/1.01 % Factorizations : 4
% 3.60/1.01 % NegExts : 0
% 3.60/1.01 % Equation resolutions : 122
% 3.60/1.01 % Disequality decompositions : 0
% 3.60/1.01 % Total rewrite steps : 12213
% 3.60/1.01 % ...of those cached : 10866
% 3.60/1.01 % Propositional unsat checks : 0
% 3.60/1.01 % Propositional check models : 0
% 3.60/1.01 % Propositional check unsatisfiable : 0
% 3.60/1.01 % Propositional clauses : 0
% 3.60/1.01 % Propositional clauses after purity: 0
% 3.60/1.01 % Propositional unsat core size : 0
% 3.60/1.01 % Propositional preprocessing time : 0.000
% 3.60/1.01 % Propositional encoding time : 0.000
% 3.60/1.01 % Propositional solver time : 0.000
% 3.60/1.01 % Success case prop preproc time : 0.000
% 3.60/1.01 % Success case prop encoding time : 0.000
% 3.60/1.01 % Success case prop solver time : 0.000
% 3.60/1.01 % Current number of processed clauses : 964
% 3.60/1.01 % Positive orientable unit clauses : 185
% 3.60/1.01 % Positive unorientable unit clauses: 11
% 3.60/1.01 % Negative unit clauses : 34
% 3.60/1.01 % Non-unit-clauses : 734
% 3.60/1.01 % Current number of unprocessed clauses: 14799
% 3.60/1.01 % ...number of literals in the above : 41372
% 3.60/1.01 % Current number of archived formulas : 0
% 3.60/1.01 % Current number of archived clauses : 1062
% 3.60/1.01 % Clause-clause subsumption calls (NU) : 136748
% 3.60/1.01 % Rec. Clause-clause subsumption calls : 89877
% 3.60/1.01 % Non-unit clause-clause subsumptions : 389
% 3.60/1.01 % Unit Clause-clause subsumption calls : 2758
% 3.60/1.01 % Rewrite failures with RHS unbound : 0
% 3.60/1.01 % BW rewrite match attempts : 445
% 3.60/1.01 % BW rewrite match successes : 188
% 3.60/1.01 % Condensation attempts : 0
% 3.60/1.01 % Condensation successes : 0
% 3.60/1.01 % Termbank termtop insertions : 377761
% 3.60/1.01 % Search garbage collected termcells : 2146
% 3.60/1.01
% 3.60/1.01 % -------------------------------------------------
% 3.60/1.01 % User time : 0.475 s
% 3.60/1.01 % System time : 0.027 s
% 3.60/1.01 % Total time : 0.502 s
% 3.60/1.01 % Maximum resident set size: 5440 pages
% 3.60/1.01
% 3.60/1.01 % -------------------------------------------------
% 3.60/1.01 % User time : 2.430 s
% 3.60/1.01 % System time : 0.120 s
% 3.60/1.01 % Total time : 2.549 s
% 3.60/1.01 % Maximum resident set size: 5376 pages
% 3.60/1.01 % E exiting
%------------------------------------------------------------------------------