TSTP Solution File: SWW369+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW369+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n025.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 : 600s
% DateTime : Thu Jul 21 00:10:40 EDT 2022
% Result : Theorem 0.94s 5.13s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 27
% Syntax : Number of formulae : 99 ( 66 unt; 0 def)
% Number of atoms : 138 ( 81 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 35 ~; 26 |; 3 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-3 aty)
% Number of variables : 160 ( 8 sgn 101 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_less__eq__Suc__le__raw,axiom,
! [X27] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_Suc__mono,axiom,
! [X14,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X14))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X13)),hAPP(c_Nat_OSuc,X14))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Suc__mono) ).
fof(conj_1,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,v_n)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_1) ).
fof(fact_not__less__eq,axiom,
! [X27,X26] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X27))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),hAPP(c_Nat_OSuc,X26))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_not__less__eq) ).
fof(fact_nat__add__left__cancel,axiom,
! [X27,X26,X28] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X27)
<=> X26 = X27 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_add__Suc__right,axiom,
! [X14,X13] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),hAPP(c_Nat_OSuc,X14)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),X14)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_add__diff__inverse,axiom,
! [X14,X13] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X14))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13),X14)) = X13 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_add__Suc__shift,axiom,
! [X14,X13] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X13)),X14) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),hAPP(c_Nat_OSuc,X14)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_nat__add__commute,axiom,
! [X14,X13] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),X14) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X13),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_diff__le__self,axiom,
! [X14,X13] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13),X14)),X13)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_diff__le__self) ).
fof(conj_6,conjecture,
hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_6) ).
fof(fact_card__insert,axiom,
! [X8,X9,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X9))
=> hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Set_Oinsert(X7),X8),X9)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X9),hAPP(hAPP(c_Set_Oinsert(X7),X8),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_card__insert) ).
fof(conj_4,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_4) ).
fof(fact_Diff__insert__absorb,axiom,
! [X9,X8,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X8),X9))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X8),X9)),hAPP(hAPP(c_Set_Oinsert(X7),X8),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X9 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Diff__insert__absorb) ).
fof(fact_Un__insert__right,axiom,
! [X12,X10,X9,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X9),hAPP(hAPP(c_Set_Oinsert(X7),X10),X12)) = hAPP(hAPP(c_Set_Oinsert(X7),X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X9),X12)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Un__insert__right) ).
fof(fact_Un__empty__right,axiom,
! [X9,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X9),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = X9,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Un__empty__right) ).
fof(fact_Suc__eq__plus1,axiom,
! [X14] : hAPP(c_Nat_OSuc,X14) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(conj_2,hypothesis,
hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Nat_OSuc,v_n)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_2) ).
fof(fact_le__add__diff__inverse,axiom,
! [X13,X14] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),X13))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13),X14)) = X13 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(conj_5,hypothesis,
hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_G)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_5) ).
fof(fact_Un__Diff,axiom,
! [X37,X12,X9,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X9),X12)),X37) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X9),X37)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X12),X37)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Un__Diff) ).
fof(fact_Diff__cancel,axiom,
! [X9,X7] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X9),X9) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Diff__cancel) ).
fof(fact_Suc__pred_H,axiom,
! [X14] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))
=> X14 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Suc__pred_H) ).
fof(fact_zero__less__diff,axiom,
! [X26,X27] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27),X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X27)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_diff__diff__left,axiom,
! [X21,X22,X23] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23),X22)),X21) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X21)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_One__nat__def) ).
fof(fact_diff__diff__cancel,axiom,
! [X14,X23] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23),X14))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),X23)) = X23 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_diff__diff__cancel) ).
fof(c_0_27,plain,
! [X28] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(c_0_28,plain,
! [X15,X16] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X15))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X16)),hAPP(c_Nat_OSuc,X15))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
cnf(c_0_29,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,v_n)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))),
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_30,plain,
hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_31,plain,
! [X28,X29,X28,X29] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29),X28))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(c_Nat_OSuc,X29))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(c_Nat_OSuc,X29)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29),X28)) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__eq])])])])]) ).
cnf(c_0_32,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),v_n),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_34,plain,
! [X29,X30,X31,X29,X30,X31] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X30) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X29)
| X30 = X29 )
& ( X30 != X29
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X30) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X29) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])])])]) ).
fof(c_0_35,plain,
! [X15,X16] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),hAPP(c_Nat_OSuc,X15)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),X15)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_36,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,v_n)),hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_38,plain,
! [X15,X16] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X15))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16),X15)) = X16 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__diff__inverse])])]) ).
fof(c_0_39,plain,
! [X15,X16] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X16)),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),hAPP(c_Nat_OSuc,X15)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(c_0_40,plain,
! [X15,X16] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X16),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(c_0_41,plain,
! [X15,X16] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16),X15)),X16)),
inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).
fof(c_0_42,negated_conjecture,
hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n),
inference(assume_negation,[status(cth)],[conj_6]) ).
fof(c_0_43,plain,
! [X10,X11,X12] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))
| hAPP(c_Finite__Set_Ocard(X12),hAPP(hAPP(c_Set_Oinsert(X12),X10),X11)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X12),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X12),X10),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert])]) ).
fof(c_0_44,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
inference(fof_simplification,[status(thm)],[conj_4]) ).
fof(c_0_45,plain,
! [X10,X11,X12] :
( hBOOL(hAPP(hAPP(c_member(X12),X11),X10))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X12),X11),X10)),hAPP(hAPP(c_Set_Oinsert(X12),X11),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))) = X10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Diff__insert__absorb])])]) ).
fof(c_0_46,plain,
! [X13,X14,X15,X16] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X15),hAPP(hAPP(c_Set_Oinsert(X16),X14),X13)) = hAPP(hAPP(c_Set_Oinsert(X16),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X15),X13)),
inference(variable_rename,[status(thm)],[fact_Un__insert__right]) ).
fof(c_0_47,plain,
! [X10,X11] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11,tc_HOL_Obool)),X10),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_HOL_Obool))) = X10,
inference(variable_rename,[status(thm)],[fact_Un__empty__right]) ).
fof(c_0_48,plain,
! [X15] : hAPP(c_Nat_OSuc,X15) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
cnf(c_0_49,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_50,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_51,hypothesis,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Nat_OSuc,v_n))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_52,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_53,hypothesis,
hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Nat_OSuc,v_n)),
inference(split_conjunct,[status(thm)],[conj_2]) ).
cnf(c_0_54,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_55,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_56,plain,
! [X15,X16] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16),X15))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15),X16)) = X15 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).
cnf(c_0_57,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_58,negated_conjecture,
hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
cnf(c_0_59,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_60,hypothesis,
hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_G)),
inference(split_conjunct,[status(thm)],[conj_5]) ).
cnf(c_0_61,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_62,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_63,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_64,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X2,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_65,plain,
! [X38,X39,X40,X41] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X41,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X41,tc_HOL_Obool)),X40),X39)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X41,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X41,tc_HOL_Obool)),X40),X38)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X41,tc_HOL_Obool)),X39),X38)),
inference(variable_rename,[status(thm)],[fact_Un__Diff]) ).
fof(c_0_66,plain,
! [X10,X11] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11,tc_HOL_Obool)),X10),X10) = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).
fof(c_0_67,plain,
! [X15] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15))
| X15 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred_H])]) ).
fof(c_0_68,plain,
! [X28,X29,X28,X29] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X29),X28)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X29)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X29))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X29),X28))) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])])])]) ).
fof(c_0_69,plain,
! [X24,X25,X26] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26),X25)),X24) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
cnf(c_0_70,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_71,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_One__nat__def]) ).
cnf(c_0_72,plain,
( X1 = hAPP(c_Nat_OSuc,X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1) != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_73,hypothesis,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),v_n)) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54]),c_0_50]),c_0_55]) ).
cnf(c_0_74,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_75,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))),
inference(spm,[status(thm)],[c_0_57,c_0_53]) ).
fof(c_0_76,plain,
! [X24,X25] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)) = X25 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).
cnf(c_0_77,negated_conjecture,
hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_78,hypothesis,
hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Set_Oinsert(t_a),X1),v_G)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(hAPP(c_Set_Oinsert(t_a),X1),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))))),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_79,hypothesis,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) = v_G,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_80,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X1),X3),X2),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_81,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_82,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_83,plain,
( X1 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_84,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_85,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_86,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rw,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_87,hypothesis,
( X1 = hAPP(c_Nat_OSuc,v_n)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),X1) != hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_88,hypothesis,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G))) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_89,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_90,negated_conjecture,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n) != hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))))),
inference(rw,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_91,hypothesis,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) = v_G,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_82]),c_0_64]) ).
cnf(c_0_92,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(rw,[status(thm)],[c_0_83,c_0_71]) ).
cnf(c_0_93,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n))),
inference(spm,[status(thm)],[c_0_84,c_0_33]) ).
cnf(c_0_94,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_95,hypothesis,
hAPP(c_Nat_OSuc,v_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G)),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,hypothesis,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G))) = hAPP(c_Finite__Set_Ocard(t_a),v_G),
inference(spm,[status(thm)],[c_0_89,c_0_75]) ).
cnf(c_0_97,negated_conjecture,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n) != hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(t_a),v_G)),
inference(rw,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_98,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]),c_0_95]),c_0_96]),c_0_97]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW369+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 5 12:53:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.94/5.13 # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.94/5.13 # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.94/5.13 # Preprocessing time : 0.285 s
% 0.94/5.13
% 0.94/5.13 # Proof found!
% 0.94/5.13 # SZS status Theorem
% 0.94/5.13 # SZS output start CNFRefutation
% See solution above
% 0.94/5.13 # Proof object total steps : 99
% 0.94/5.13 # Proof object clause steps : 48
% 0.94/5.13 # Proof object formula steps : 51
% 0.94/5.13 # Proof object conjectures : 6
% 0.94/5.13 # Proof object clause conjectures : 3
% 0.94/5.13 # Proof object formula conjectures : 3
% 0.94/5.13 # Proof object initial clauses used : 27
% 0.94/5.13 # Proof object initial formulas used : 27
% 0.94/5.13 # Proof object generating inferences : 15
% 0.94/5.13 # Proof object simplifying inferences : 17
% 0.94/5.13 # Training examples: 0 positive, 0 negative
% 0.94/5.13 # Parsed axioms : 5230
% 0.94/5.13 # Removed by relevancy pruning/SinE : 4729
% 0.94/5.13 # Initial clauses : 744
% 0.94/5.13 # Removed in clause preprocessing : 27
% 0.94/5.13 # Initial clauses in saturation : 717
% 0.94/5.13 # Processed clauses : 5069
% 0.94/5.13 # ...of these trivial : 227
% 0.94/5.13 # ...subsumed : 2376
% 0.94/5.13 # ...remaining for further processing : 2465
% 0.94/5.13 # Other redundant clauses eliminated : 145
% 0.94/5.13 # Clauses deleted for lack of memory : 59761
% 0.94/5.13 # Backward-subsumed : 16
% 0.94/5.13 # Backward-rewritten : 260
% 0.94/5.13 # Generated clauses : 140450
% 0.94/5.13 # ...of the previous two non-trivial : 133906
% 0.94/5.13 # Contextual simplify-reflections : 26
% 0.94/5.13 # Paramodulations : 140163
% 0.94/5.13 # Factorizations : 4
% 0.94/5.13 # Equation resolutions : 284
% 0.94/5.13 # Current number of processed clauses : 2163
% 0.94/5.13 # Positive orientable unit clauses : 335
% 0.94/5.13 # Positive unorientable unit clauses: 211
% 0.94/5.13 # Negative unit clauses : 406
% 0.94/5.13 # Non-unit-clauses : 1211
% 0.94/5.13 # Current number of unprocessed clauses: 60484
% 0.94/5.13 # ...number of literals in the above : 115762
% 0.94/5.13 # Current number of archived formulas : 0
% 0.94/5.13 # Current number of archived clauses : 276
% 0.94/5.13 # Clause-clause subsumption calls (NU) : 176092
% 0.94/5.13 # Rec. Clause-clause subsumption calls : 161949
% 0.94/5.13 # Non-unit clause-clause subsumptions : 798
% 0.94/5.13 # Unit Clause-clause subsumption calls : 45885
% 0.94/5.13 # Rewrite failures with RHS unbound : 723
% 0.94/5.13 # BW rewrite match attempts : 50721
% 0.94/5.13 # BW rewrite match successes : 810
% 0.94/5.13 # Condensation attempts : 0
% 0.94/5.13 # Condensation successes : 0
% 0.94/5.13 # Termbank termtop insertions : 5711736
% 0.94/5.13
% 0.94/5.13 # -------------------------------------------------
% 0.94/5.13 # User time : 3.178 s
% 0.94/5.13 # System time : 0.093 s
% 0.94/5.13 # Total time : 3.271 s
% 0.94/5.13 # Maximum resident set size: 138216 pages
% 0.94/24.10 eprover: CPU time limit exceeded, terminating
% 0.94/24.10 eprover: CPU time limit exceeded, terminating
% 0.94/24.11 eprover: CPU time limit exceeded, terminating
% 0.94/24.12 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.12 eprover: No such file or directory
% 0.94/24.13 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.13 eprover: No such file or directory
% 0.94/24.13 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.13 eprover: No such file or directory
% 0.94/24.13 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.13 eprover: No such file or directory
% 0.94/24.13 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.94/24.13 eprover: No such file or directory
% 0.94/24.13 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.13 eprover: No such file or directory
% 0.94/24.14 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.94/24.14 eprover: No such file or directory
% 0.94/24.14 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.14 eprover: No such file or directory
% 0.94/24.14 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.14 eprover: No such file or directory
% 0.94/24.14 eprover: eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.14 eprover: No such file or directory
% 0.94/24.14 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.94/24.14 eprover: No such file or directory
% 0.94/24.14 Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.14 eprover: No such file or directory
% 0.94/24.15 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.94/24.15 eprover: No such file or directory
% 0.94/24.15 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.15 eprover: eprover: No such file or directory
% 0.94/24.15 Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.15 eprover: No such file or directory
% 0.94/24.15 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.peprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.15
% 0.94/24.15 eprover: No such file or directory
% 0.94/24.15 eprover: No such file or directory
% 0.94/24.15 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.15 eprover: No such file or directory
% 0.94/24.16 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.16 eprover: No such file or directory
% 0.94/24.16 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.16 eprover: No such file or directory
% 0.94/24.16 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.94/24.16 eprover: No such file or directory
% 0.94/24.16 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.16 eprover: No such file or directory
% 0.94/24.16 eprover: eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.inCannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.94/24.16
% 0.94/24.16 eprover: No such file or directory
% 0.94/24.16 eprover: No such file or directory
% 0.94/24.16 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.16 eprover: No such file or directory
% 0.94/24.16 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.17 eprover: eprover: No such file or directory
% 0.94/24.17 Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.94/24.17 eprover: No such file or directory
% 0.94/24.17 eprover: eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.94/24.17 eprover: eprover: No such file or directory
% 0.94/24.17 Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.17 eprover: No such file or directory
% 0.94/24.17 Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.17 eprover: No such file or directory
% 0.94/24.17 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.94/24.17 eprover: No such file or directory
% 0.94/24.18 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.94/24.18 eprover: No such file or directory
% 0.94/24.18 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.94/24.18 eprover: No such file or directory
%------------------------------------------------------------------------------