TSTP Solution File: SWW381+1 by E-SAT---3.1.00
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%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : SWW381+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 06:45:29 EDT 2024
% Result : ContradictoryAxioms 49.09s 7.81s
% Output : CNFRefutation 49.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 41
% Syntax : Number of formulae : 183 ( 128 unt; 0 def)
% Number of atoms : 258 ( 198 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 153 ( 78 ~; 57 |; 8 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 37 ( 37 usr; 10 con; 0-3 aty)
% Number of variables : 246 ( 37 sgn 131 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_vimage__Collect__eq,axiom,
! [X32,X2,X10,X6] : hAPP(c_Set_Ovimage(X6,X10,X2),hAPP(c_Set_OCollect(X10),X32)) = hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBB(X10,tc_HOL_Obool,X6),X32),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
fof(fact_Collect__def,axiom,
! [X32,X6] : hAPP(c_Set_OCollect(X6),X32) = X32,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_not__Some__eq,axiom,
! [X6,X16] :
( ! [X71] : X16 != hAPP(c_Option_Ooption_OSome(X6),X71)
<=> X16 = c_Option_Ooption_ONone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Some__eq) ).
fof(fact_option_Osimps_I2_J,axiom,
! [X148,X6] : c_Option_Ooption_ONone(X6) != hAPP(c_Option_Ooption_OSome(X6),X148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I2_J) ).
fof(fact_vimage__id,axiom,
! [X13,X6] : hAPP(c_Set_Ovimage(X6,X6,c_Fun_Oid(X6)),X13) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__id) ).
fof(fact_option_Oinject,axiom,
! [X192,X39,X6] :
( hAPP(c_Option_Ooption_OSome(X6),X39) = hAPP(c_Option_Ooption_OSome(X6),X192)
<=> X39 = X192 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oinject) ).
fof(help_c__COMBB__1,axiom,
! [X63,X31,X32,X17,X6,X10] : hAPP(hAPP(hAPP(c_COMBB(X10,X6,X17),X32),X31),X63) = hAPP(X32,hAPP(X31,X63)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_number__of__is__id,axiom,
! [X108] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X108) = X108,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(fact_Collect__empty__eq,axiom,
! [X32,X6] :
( hAPP(c_Set_OCollect(X6),X32) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X32,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_Collect__neg__eq,axiom,
! [X32,X6] : hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6),c_fNot),X32)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Set_OCollect(X6),X32)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_add__Pls,axiom,
! [X108] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X108) = X108,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(help_c__COMBK__1,axiom,
! [X324,X38,X10,X6] : hAPP(hAPP(c_COMBK(X6,X10),X38),X324) = X38,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_mult__Pls,axiom,
! [X128] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X128) = c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Pls) ).
fof(fact_rel__simps_I39_J,axiom,
! [X112] : c_Int_OPls != c_Int_OBit1(X112),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
fof(fact_double__complement,axiom,
! [X13,X6] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),X13)) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X32] :
( ~ hBOOL(hAPP(c_fNot,X32))
| ~ hBOOL(X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_not__neg__0,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__0) ).
fof(fact_eq__int__code_I7_J,axiom,
! [X315] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X315))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__int__code_I7_J) ).
fof(fact_eq__equal,axiom,
! [X6] :
( class_HOL_Oequal(X6)
=> c_fequal = c_HOL_Oequal__class_Oequal(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equal) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(arity_Int__Oint__HOL_Oequal,axiom,
class_HOL_Oequal(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__HOL_Oequal) ).
fof(help_c__fequal__2,axiom,
! [X23,X16] :
( X16 != X23
| hBOOL(hAPP(hAPP(c_fequal,X16),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_rel__simps_I51_J,axiom,
! [X131,X113] :
( c_Int_OBit1(X113) = c_Int_OBit1(X131)
<=> X113 = X131 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).
fof(fact_transfer__int__nat__numerals_I2_J,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
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/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(fact_nat__number__of__def,axiom,
! [X118] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X118) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X118)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__def) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__num__one) ).
fof(fact_int__0__neq__1,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(fact_card__UNIV__bool,axiom,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__bool) ).
fof(fact_semiring__norm_I115_J,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(fact_negative__eq__positive,axiom,
! [X96,X111] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X111)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X96)
<=> ( X111 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X96 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__eq__positive) ).
fof(fact_diff__int__def,axiom,
! [X128,X19] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).
fof(fact_Zero__not__Suc,axiom,
! [X99] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X99),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_rel__simps_I44_J,axiom,
! [X113] :
( c_Int_OBit0(X113) = c_Int_OPls
<=> X113 = c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
fof(fact_transfer__int__nat__numerals_I3_J,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I3_J) ).
fof(fact_pred__def,axiom,
! [X108] : c_Int_Opred(X108) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X108),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__def) ).
fof(fact_add__Min,axiom,
! [X108] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X108) = c_Int_Opred(X108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min) ).
fof(fact_add__Min__right,axiom,
! [X108] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X108),c_Int_OMin) = c_Int_Opred(X108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min__right) ).
fof(fact_transfer__int__nat__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
fof(c_0_41,plain,
! [X6805,X6806,X6807,X6808] : hAPP(c_Set_Ovimage(X6808,X6807,X6806),hAPP(c_Set_OCollect(X6807),X6805)) = hAPP(c_Set_OCollect(X6808),hAPP(hAPP(c_COMBB(X6807,tc_HOL_Obool,X6808),X6805),X6806)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_42,plain,
! [X2434,X2435] : hAPP(c_Set_OCollect(X2435),X2434) = X2434,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_43,plain,
! [X6,X16] :
( ! [X71] : X16 != hAPP(c_Option_Ooption_OSome(X6),X71)
<=> X16 = c_Option_Ooption_ONone(X6) ),
inference(fof_simplification,[status(thm)],[fact_not__Some__eq]) ).
fof(c_0_44,plain,
! [X148,X6] : c_Option_Ooption_ONone(X6) != hAPP(c_Option_Ooption_OSome(X6),X148),
inference(fof_simplification,[status(thm)],[fact_option_Osimps_I2_J]) ).
fof(c_0_45,plain,
! [X6877,X6878] : hAPP(c_Set_Ovimage(X6878,X6878,c_Fun_Oid(X6878)),X6877) = X6877,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
cnf(c_0_46,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_OCollect(X2),X4)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_48,plain,
! [X2324,X2325,X2326] :
( ( hAPP(c_Option_Ooption_OSome(X2326),X2325) != hAPP(c_Option_Ooption_OSome(X2326),X2324)
| X2325 = X2324 )
& ( X2325 != X2324
| hAPP(c_Option_Ooption_OSome(X2326),X2325) = hAPP(c_Option_Ooption_OSome(X2326),X2324) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option_Oinject])])]) ).
fof(c_0_49,plain,
! [X2331,X2332,X2334,X2335,X2336] :
( ( X2332 = hAPP(c_Option_Ooption_OSome(X2331),esk52_2(X2331,X2332))
| X2332 = c_Option_Ooption_ONone(X2331) )
& ( X2335 != c_Option_Ooption_ONone(X2334)
| X2335 != hAPP(c_Option_Ooption_OSome(X2334),X2336) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])])])]) ).
fof(c_0_50,plain,
! [X2327,X2328] : c_Option_Ooption_ONone(X2328) != hAPP(c_Option_Ooption_OSome(X2328),X2327),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_44])]) ).
fof(c_0_51,plain,
! [X817,X818,X819,X820,X821,X822] : hAPP(hAPP(hAPP(c_COMBB(X822,X821,X820),X819),X818),X817) = hAPP(X819,hAPP(X818,X817)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_52,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_47]) ).
cnf(c_0_54,plain,
( X2 = X3
| hAPP(c_Option_Ooption_OSome(X1),X2) != hAPP(c_Option_Ooption_OSome(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
( X1 = hAPP(c_Option_Ooption_OSome(X2),esk52_2(X2,X1))
| X1 = c_Option_Ooption_ONone(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
c_Option_Ooption_ONone(X1) != hAPP(c_Option_Ooption_OSome(X1),X2),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_59,plain,
! [X325,X326] :
( hAPP(X326,esk1_2(X325,X326)) != hAPP(X325,esk1_2(X325,X326))
| X326 = X325 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
cnf(c_0_60,plain,
esk52_2(X1,hAPP(c_Option_Ooption_OSome(X1),X2)) = X2,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55])]),c_0_56]) ).
cnf(c_0_61,plain,
hAPP(X1,hAPP(c_Fun_Oid(X2),X3)) = hAPP(X1,X3),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_63,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_60]) ).
fof(c_0_64,plain,
! [X4270] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4270) = X4270,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
fof(c_0_65,plain,
! [X32,X6] :
( hAPP(c_Set_OCollect(X6),X32) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X32,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
cnf(c_0_66,plain,
( X1 = c_Fun_Oid(X2)
| hAPP(X1,esk1_2(c_Fun_Oid(X2),X1)) != esk1_2(c_Fun_Oid(X2),X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_68,plain,
! [X2422,X2423,X2424,X2425,X2427] :
( ( hAPP(c_Set_OCollect(X2423),X2422) != c_Orderings_Obot__class_Obot(tc_fun(X2423,tc_HOL_Obool))
| ~ hBOOL(hAPP(X2422,X2424)) )
& ( hBOOL(hAPP(X2425,esk55_1(X2425)))
| hAPP(c_Set_OCollect(X2427),X2425) = c_Orderings_Obot__class_Obot(tc_fun(X2427,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])])])]) ).
fof(c_0_69,plain,
! [X2093,X2094] : hAPP(c_Set_OCollect(X2094),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2094),c_fNot),X2093)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2094,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2094),X2093)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
cnf(c_0_70,plain,
c_Fun_Oid(X1) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
fof(c_0_71,plain,
! [X6456] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X6456) = X6456,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
fof(c_0_72,plain,
! [X1936,X1937,X1938,X1939] : hAPP(hAPP(c_COMBK(X1939,X1938),X1937),X1936) = X1937,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_73,plain,
( hBOOL(hAPP(X1,esk55_1(X1)))
| hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
fof(c_0_74,plain,
! [X6454] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X6454) = c_Int_OPls,
inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).
fof(c_0_75,plain,
! [X112] : c_Int_OPls != c_Int_OBit1(X112),
inference(fof_simplification,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(c_0_76,plain,
! [X4065,X4066] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4066,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4066,tc_HOL_Obool)),X4065)) = X4065,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_77,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_78,plain,
( X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint)
| hAPP(X1,esk1_2(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) != esk1_2(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_70]),c_0_70]),c_0_70]) ).
cnf(c_0_79,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_80,plain,
! [X32] :
( ~ hBOOL(hAPP(c_fNot,X32))
| ~ hBOOL(X32) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_81,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_82,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk55_1(X1))) ),
inference(rw,[status(thm)],[c_0_73,c_0_47]) ).
cnf(c_0_83,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X1) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_84,plain,
! [X6453] : c_Int_OPls != c_Int_OBit1(X6453),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_75])]) ).
cnf(c_0_85,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_86,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_47]),c_0_47]) ).
cnf(c_0_87,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint) = hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
fof(c_0_88,plain,
! [X2103] :
( ~ hBOOL(hAPP(c_fNot,X2103))
| ~ hBOOL(X2103) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_80])]) ).
cnf(c_0_89,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = X3
| hBOOL(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_81]) ).
cnf(c_0_90,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls)
| hBOOL(c_Int_OPls) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_91,plain,
c_Int_OPls != c_Int_OBit1(X1),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
fof(c_0_92,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(fof_simplification,[status(thm)],[fact_not__neg__0]) ).
cnf(c_0_93,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86]),c_0_86]) ).
cnf(c_0_94,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_70]),c_0_87]) ).
cnf(c_0_95,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_96,plain,
( c_Int_OPls = X1
| hBOOL(c_Int_OPls)
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_83]) ).
cnf(c_0_97,plain,
( hBOOL(c_Int_OBit1(X1))
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X3) != c_Int_OPls ),
inference(spm,[status(thm)],[c_0_91,c_0_89]) ).
fof(c_0_98,plain,
! [X315] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X315))),
inference(fof_simplification,[status(thm)],[fact_eq__int__code_I7_J]) ).
fof(c_0_99,plain,
! [X2182] :
( ~ class_HOL_Oequal(X2182)
| c_fequal = c_HOL_Oequal__class_Oequal(X2182) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equal])])]) ).
fof(c_0_100,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(fof_nnf,[status(thm)],[c_0_92]) ).
cnf(c_0_101,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_fNot) = hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_102,plain,
( hAPP(c_fNot,X1) = c_Int_OPls
| hBOOL(c_Int_OPls)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_103,plain,
( hBOOL(c_Int_OBit1(X1))
| hBOOL(c_Int_OPls) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_90]),c_0_83])]) ).
cnf(c_0_104,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).
cnf(c_0_105,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_106,plain,
! [X5752] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X5752))),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_98])]) ).
cnf(c_0_107,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(X1)
| ~ class_HOL_Oequal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_108,plain,
class_HOL_Oequal(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__HOL_Oequal]) ).
fof(c_0_109,plain,
! [X23,X16] :
( X16 != X23
| hBOOL(hAPP(hAPP(c_fequal,X16),X23)) ),
inference(fof_simplification,[status(thm)],[help_c__fequal__2]) ).
cnf(c_0_110,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
fof(c_0_111,plain,
! [X7793,X7794] :
( ( c_Int_OBit1(X7794) != c_Int_OBit1(X7793)
| X7794 = X7793 )
& ( X7794 != X7793
| c_Int_OBit1(X7794) = c_Int_OBit1(X7793) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])])]) ).
cnf(c_0_112,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_101]),c_0_79]) ).
cnf(c_0_113,plain,
( hAPP(c_fNot,c_Int_OBit1(X1)) = c_Int_OPls
| hBOOL(c_Int_OPls) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_114,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]) ).
cnf(c_0_115,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_116,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_104,c_0_105]) ).
fof(c_0_117,plain,
! [X5598] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5598) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5598)),
inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).
cnf(c_0_118,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1))),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_119,plain,
c_HOL_Oequal__class_Oequal(tc_Int_Oint) = c_fequal,
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
fof(c_0_120,plain,
! [X1974,X1975] :
( X1975 != X1974
| hBOOL(hAPP(hAPP(c_fequal,X1975),X1974)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_109])]) ).
cnf(c_0_121,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)),
inference(rw,[status(thm)],[c_0_110,c_0_105]) ).
cnf(c_0_122,plain,
( X1 = X2
| hBOOL(X1)
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_89,c_0_89]) ).
cnf(c_0_123,plain,
( X1 = X2
| c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_124,plain,
( c_Int_OBit1(X1) = hAPP(c_fNot,c_Int_OPls)
| hBOOL(c_Int_OPls) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_125,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_one__is__num__one]) ).
cnf(c_0_126,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115]),c_0_116]) ).
cnf(c_0_127,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
fof(c_0_128,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(fof_simplification,[status(thm)],[fact_int__0__neq__1]) ).
cnf(c_0_129,plain,
~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OMin),c_Int_OBit0(X1))),
inference(rw,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_130,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_131,plain,
( X1 = hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_132,plain,
( X1 = X2
| hBOOL(c_Int_OPls) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_124]) ).
cnf(c_0_133,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_card__UNIV__bool]) ).
cnf(c_0_134,plain,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_67]),c_0_126]) ).
cnf(c_0_135,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X1),
inference(rw,[status(thm)],[c_0_127,c_0_67]) ).
fof(c_0_136,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[c_0_128]) ).
cnf(c_0_137,plain,
( hBOOL(c_Int_OBit0(X1))
| hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OMin),X2)) ),
inference(spm,[status(thm)],[c_0_129,c_0_122]) ).
cnf(c_0_138,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(er,[status(thm)],[c_0_130]) ).
cnf(c_0_139,plain,
( hAPP(c_fNot,X1) = hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_131]) ).
cnf(c_0_140,plain,
hBOOL(c_Int_OPls),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_132])]) ).
cnf(c_0_141,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).
cnf(c_0_142,plain,
hAPP(c_Int_Onat,c_Int_OBit0(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))))) = hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134]),c_0_135]) ).
cnf(c_0_143,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
fof(c_0_144,plain,
! [X4035,X4036] :
( ( X4036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4036)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4035) )
& ( X4035 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4036)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4035) )
& ( X4036 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4035 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4036)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4035) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__eq__positive])])])]) ).
fof(c_0_145,plain,
! [X4090,X4091] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4091),X4090) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4091),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4090)),
inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).
fof(c_0_146,plain,
! [X99] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X99),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
cnf(c_0_147,plain,
( hBOOL(c_Int_OBit0(X1))
| hBOOL(c_Int_OMin) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_148,plain,
hAPP(c_fNot,c_Int_OPls) = hAPP(c_Nat__Numeral_Oneg,c_Int_OPls),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
fof(c_0_149,plain,
! [X6483] :
( ( c_Int_OBit0(X6483) != c_Int_OPls
| X6483 = c_Int_OPls )
& ( X6483 != c_Int_OPls
| c_Int_OBit0(X6483) = c_Int_OPls ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])])]) ).
cnf(c_0_150,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I3_J]) ).
cnf(c_0_151,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_134]),c_0_135]),c_0_142]),c_0_116]) ).
cnf(c_0_152,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls,
inference(rw,[status(thm)],[c_0_143,c_0_105]) ).
cnf(c_0_153,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_154,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
fof(c_0_155,plain,
! [X5845] : c_Int_Opred(X5845) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5845),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_pred__def]) ).
fof(c_0_156,plain,
! [X5853] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X5853) = c_Int_Opred(X5853),
inference(variable_rename,[status(thm)],[fact_add__Min]) ).
fof(c_0_157,plain,
! [X5854] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5854),c_Int_OMin) = c_Int_Opred(X5854),
inference(variable_rename,[status(thm)],[fact_add__Min__right]) ).
fof(c_0_158,plain,
! [X3671] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3671),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_146])]) ).
cnf(c_0_159,plain,
( hAPP(c_fNot,c_Int_OBit0(X1)) = hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)
| hBOOL(c_Int_OMin) ),
inference(spm,[status(thm)],[c_0_139,c_0_147]) ).
cnf(c_0_160,plain,
hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)) = c_Int_OPls,
inference(spm,[status(thm)],[c_0_112,c_0_148]) ).
cnf(c_0_161,plain,
( X1 = c_Int_OPls
| c_Int_OBit0(X1) != c_Int_OPls ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_162,plain,
c_Int_OBit0(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls)))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_134]),c_0_135]),c_0_142]),c_0_151]),c_0_134]),c_0_67]) ).
cnf(c_0_163,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))) != c_Int_OPls,
inference(rw,[status(thm)],[c_0_152,c_0_126]) ).
cnf(c_0_164,plain,
( X1 = hAPP(c_Int_Onat,c_Int_OPls)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
inference(rw,[status(thm)],[c_0_153,c_0_116]) ).
cnf(c_0_165,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1),
inference(spm,[status(thm)],[c_0_79,c_0_154]) ).
cnf(c_0_166,plain,
c_Int_Opred(X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[c_0_155]) ).
cnf(c_0_167,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1) = c_Int_Opred(X1),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_168,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin) = c_Int_Opred(X1),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_169,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_170,plain,
( c_Int_OBit0(X1) = c_Int_OPls
| hBOOL(c_Int_OMin) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_159]),c_0_160]) ).
cnf(c_0_171,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls)))) != c_Int_OPls,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163]) ).
cnf(c_0_172,plain,
( X1 = hAPP(c_Int_Onat,c_Int_OPls)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
inference(rw,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_173,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_167]),c_0_126]) ).
cnf(c_0_174,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin),
inference(rw,[status(thm)],[c_0_168,c_0_167]) ).
cnf(c_0_175,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_169,c_0_116]) ).
cnf(c_0_176,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I1_J]) ).
cnf(c_0_177,plain,
hBOOL(c_Int_OMin),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_170]),c_0_171]) ).
cnf(c_0_178,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != c_Int_OMin,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_174]),c_0_79]),c_0_175]) ).
cnf(c_0_179,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,c_Int_OPls)) = c_Int_OPls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_176,c_0_116]),c_0_105]) ).
cnf(c_0_180,plain,
hAPP(c_fNot,c_Int_OMin) = hAPP(c_Nat__Numeral_Oneg,c_Int_OPls),
inference(spm,[status(thm)],[c_0_139,c_0_177]) ).
cnf(c_0_181,plain,
c_Int_OMin != c_Int_OPls,
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_182,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_180]),c_0_160]),c_0_181]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW381+1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 20:26:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.51 Running first-order model finding
% 0.21/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.09/7.81 # Version: 3.1.0
% 49.09/7.81 # Preprocessing class: FMLMSLSMSSSNFFN.
% 49.09/7.81 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 49.09/7.81 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 49.09/7.81 # Starting new_bool_3 with 300s (1) cores
% 49.09/7.81 # Starting new_bool_1 with 300s (1) cores
% 49.09/7.81 # Starting sh5l with 300s (1) cores
% 49.09/7.81 # new_bool_1 with pid 27371 completed with status 0
% 49.09/7.81 # Result found by new_bool_1
% 49.09/7.81 # Preprocessing class: FMLMSLSMSSSNFFN.
% 49.09/7.81 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 49.09/7.81 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 49.09/7.81 # Starting new_bool_3 with 300s (1) cores
% 49.09/7.81 # Starting new_bool_1 with 300s (1) cores
% 49.09/7.81 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 49.09/7.81 # Search class: FGHSM-SMLM33-DFFFFFNN
% 49.09/7.81 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 49.09/7.81 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 49.09/7.81 # SAT001_MinMin_p005000_rr with pid 27374 completed with status 0
% 49.09/7.81 # Result found by SAT001_MinMin_p005000_rr
% 49.09/7.81 # Preprocessing class: FMLMSLSMSSSNFFN.
% 49.09/7.81 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 49.09/7.81 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 49.09/7.81 # Starting new_bool_3 with 300s (1) cores
% 49.09/7.81 # Starting new_bool_1 with 300s (1) cores
% 49.09/7.81 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 49.09/7.81 # Search class: FGHSM-SMLM33-DFFFFFNN
% 49.09/7.81 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 49.09/7.81 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 49.09/7.81 # Preprocessing time : 0.075 s
% 49.09/7.81 # Presaturation interreduction done
% 49.09/7.81
% 49.09/7.81 # Proof found!
% 49.09/7.81 # SZS status ContradictoryAxioms
% 49.09/7.81 # SZS output start CNFRefutation
% See solution above
% 49.09/7.81 # Parsed axioms : 5241
% 49.09/7.81 # Removed by relevancy pruning/SinE : 3052
% 49.09/7.81 # Initial clauses : 3335
% 49.09/7.81 # Removed in clause preprocessing : 95
% 49.09/7.81 # Initial clauses in saturation : 3240
% 49.09/7.81 # Processed clauses : 11903
% 49.09/7.81 # ...of these trivial : 284
% 49.09/7.81 # ...subsumed : 4981
% 49.09/7.81 # ...remaining for further processing : 6638
% 49.09/7.81 # Other redundant clauses eliminated : 4917
% 49.09/7.81 # Clauses deleted for lack of memory : 0
% 49.09/7.81 # Backward-subsumed : 288
% 49.09/7.81 # Backward-rewritten : 467
% 49.09/7.81 # Generated clauses : 241303
% 49.09/7.81 # ...of the previous two non-redundant : 225244
% 49.09/7.81 # ...aggressively subsumed : 0
% 49.09/7.81 # Contextual simplify-reflections : 42
% 49.09/7.81 # Paramodulations : 236335
% 49.09/7.81 # Factorizations : 24
% 49.09/7.81 # NegExts : 0
% 49.09/7.81 # Equation resolutions : 4979
% 49.09/7.81 # Disequality decompositions : 0
% 49.09/7.81 # Total rewrite steps : 48307
% 49.09/7.81 # ...of those cached : 42856
% 49.09/7.81 # Propositional unsat checks : 1
% 49.09/7.81 # Propositional check models : 0
% 49.09/7.81 # Propositional check unsatisfiable : 0
% 49.09/7.81 # Propositional clauses : 0
% 49.09/7.81 # Propositional clauses after purity: 0
% 49.09/7.81 # Propositional unsat core size : 0
% 49.09/7.81 # Propositional preprocessing time : 0.000
% 49.09/7.81 # Propositional encoding time : 0.164
% 49.09/7.81 # Propositional solver time : 0.077
% 49.09/7.81 # Success case prop preproc time : 0.000
% 49.09/7.81 # Success case prop encoding time : 0.000
% 49.09/7.81 # Success case prop solver time : 0.000
% 49.09/7.81 # Current number of processed clauses : 3184
% 49.09/7.81 # Positive orientable unit clauses : 691
% 49.09/7.81 # Positive unorientable unit clauses: 62
% 49.09/7.81 # Negative unit clauses : 355
% 49.09/7.81 # Non-unit-clauses : 2076
% 49.09/7.81 # Current number of unprocessed clauses: 191533
% 49.09/7.81 # ...number of literals in the above : 587456
% 49.09/7.81 # Current number of archived formulas : 0
% 49.09/7.81 # Current number of archived clauses : 3196
% 49.09/7.81 # Clause-clause subsumption calls (NU) : 1225924
% 49.09/7.81 # Rec. Clause-clause subsumption calls : 569645
% 49.09/7.81 # Non-unit clause-clause subsumptions : 3647
% 49.09/7.81 # Unit Clause-clause subsumption calls : 65979
% 49.09/7.81 # Rewrite failures with RHS unbound : 215
% 49.09/7.81 # BW rewrite match attempts : 15442
% 49.09/7.81 # BW rewrite match successes : 1032
% 49.09/7.81 # Condensation attempts : 0
% 49.09/7.81 # Condensation successes : 0
% 49.09/7.81 # Termbank termtop insertions : 5260359
% 49.09/7.81 # Search garbage collected termcells : 71093
% 49.09/7.81
% 49.09/7.81 # -------------------------------------------------
% 49.09/7.81 # User time : 6.663 s
% 49.09/7.81 # System time : 0.211 s
% 49.09/7.81 # Total time : 6.874 s
% 49.09/7.81 # Maximum resident set size: 19448 pages
% 49.09/7.81
% 49.09/7.81 # -------------------------------------------------
% 49.09/7.81 # User time : 6.931 s
% 49.09/7.81 # System time : 0.227 s
% 49.09/7.81 # Total time : 7.159 s
% 49.09/7.81 # Maximum resident set size: 9488 pages
% 49.09/7.81 % E---3.1 exiting
%------------------------------------------------------------------------------