TSTP Solution File: SWW305+1 by E---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.2.0
% Problem  : SWW305+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.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 : Mon Jun 24 18:11:34 EDT 2024

% Result   : ContradictoryAxioms 70.71s 11.34s
% Output   : CNFRefutation 70.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   79 (  62 unt;   0 def)
%            Number of atoms       :   98 (  78 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   48 (  29   ~;  15   |;   1   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   22 (  22 usr;  10 con; 0-3 aty)
%            Number of variables   :  125 (  14 sgn  70   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
    ! [X18,X5] :
      ( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_Collect__empty__eq) ).

fof(fact_empty__def,axiom,
    ! [X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse)),
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_empty__def) ).

fof(fact_Collect__def,axiom,
    ! [X18,X5] : hAPP(c_Set_OCollect(X5),X18) = X18,
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_Collect__def) ).

fof(fact_Collect__neg__eq,axiom,
    ! [X18,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X18)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X18)),
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_Collect__neg__eq) ).

fof(help_c__COMBK__1,axiom,
    ! [X325,X54,X5,X35] : hAPP(hAPP(c_COMBK(X35,X5),X54),X325) = X54,
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',help_c__COMBK__1) ).

fof(fact_double__complement,axiom,
    ! [X22,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X22)) = X22,
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_double__complement) ).

fof(help_c__fNot__1,axiom,
    ! [X18] :
      ( ~ hBOOL(hAPP(c_fNot,X18))
      | ~ hBOOL(X18) ),
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',help_c__fNot__1) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X100] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X100),
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_Zero__not__Suc) ).

fof(help_c__COMBB__1,axiom,
    ! [X30,X17,X18,X39,X5,X21] : hAPP(hAPP(hAPP(c_COMBB(X21,X5,X39),X18),X17),X30) = hAPP(X18,hAPP(X17,X30)),
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',help_c__COMBB__1) ).

fof(fact_number__of__is__id,axiom,
    ! [X107] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X107) = X107,
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_number__of__is__id) ).

fof(fact_add__eq__self__zero,axiom,
    ! [X76,X100] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X76) = X100
     => X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_add__eq__self__zero) ).

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/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.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/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_Pls__def) ).

fof(fact_rev__rev__ident,axiom,
    ! [X249,X35] : hAPP(c_List_Orev(X35),hAPP(c_List_Orev(X35),X249)) = X249,
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_rev__rev__ident) ).

fof(fact_neg__number__of__Min,axiom,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_neg__number__of__Min) ).

fof(fact_add__Suc__right,axiom,
    ! [X76,X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),hAPP(c_Nat_OSuc,X76)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X76)),
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_add__Suc__right) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X100,
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_Nat_Oadd__0__right) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X76] : X76 != hAPP(c_Nat_OSuc,X76),
    file('/export/starexec/sandbox2/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p',fact_n__not__Suc__n) ).

fof(c_0_18,plain,
    ! [X18,X5] :
      ( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).

fof(c_0_19,plain,
    ! [X15416] : c_Orderings_Obot__class_Obot(tc_fun(X15416,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X15416),hAPP(c_COMBK(tc_HOL_Obool,X15416),c_fFalse)),
    inference(variable_rename,[status(thm)],[fact_empty__def]) ).

fof(c_0_20,plain,
    ! [X4333,X4334] : hAPP(c_Set_OCollect(X4334),X4333) = X4333,
    inference(variable_rename,[status(thm)],[fact_Collect__def]) ).

fof(c_0_21,plain,
    ! [X4344,X4345] : hAPP(c_Set_OCollect(X4345),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4345),c_fNot),X4344)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4345,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4345),X4344)),
    inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).

fof(c_0_22,plain,
    ! [X597,X598,X599,X600,X602] :
      ( ( hAPP(c_Set_OCollect(X598),X597) != c_Orderings_Obot__class_Obot(tc_fun(X598,tc_HOL_Obool))
        | ~ hBOOL(hAPP(X597,X599)) )
      & ( hBOOL(hAPP(X600,esk12_1(X600)))
        | hAPP(c_Set_OCollect(X602),X600) = c_Orderings_Obot__class_Obot(tc_fun(X602,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_18])])])])])]) ).

fof(c_0_23,plain,
    ! [X5767,X5768,X5769,X5770] : hAPP(hAPP(c_COMBK(X5770,X5769),X5768),X5767) = X5768,
    inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).

cnf(c_0_24,plain,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,plain,
    hAPP(c_Set_OCollect(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_26,plain,
    ! [X3988,X3989] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3989,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3989,tc_HOL_Obool)),X3988)) = X3988,
    inference(variable_rename,[status(thm)],[fact_double__complement]) ).

cnf(c_0_27,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_21]) ).

fof(c_0_28,plain,
    ! [X18] :
      ( ~ hBOOL(hAPP(c_fNot,X18))
      | ~ hBOOL(X18) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).

cnf(c_0_29,plain,
    ( hBOOL(hAPP(X1,esk12_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_22]) ).

cnf(c_0_30,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_31,plain,
    hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(rw,[status(thm)],[c_0_24,c_0_25]) ).

fof(c_0_32,plain,
    ! [X100] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X100),
    inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).

fof(c_0_33,plain,
    ! [X2012,X2013,X2014,X2015,X2016,X2017] : hAPP(hAPP(hAPP(c_COMBB(X2017,X2016,X2015),X2014),X2013),X2012) = hAPP(X2014,hAPP(X2013,X2012)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

cnf(c_0_34,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_26]) ).

cnf(c_0_35,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_27,c_0_25]),c_0_25]) ).

fof(c_0_36,plain,
    ! [X8332] :
      ( ~ hBOOL(hAPP(c_fNot,X8332))
      | ~ hBOOL(X8332) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).

cnf(c_0_37,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(X1,esk12_1(X1))) ),
    inference(rw,[status(thm)],[c_0_29,c_0_25]) ).

cnf(c_0_38,plain,
    hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

fof(c_0_39,plain,
    ! [X4747] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4747) = X4747,
    inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).

fof(c_0_40,plain,
    ! [X2967,X2968] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2968),X2967) != X2968
      | X2967 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).

cnf(c_0_41,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_42,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).

fof(c_0_43,plain,
    ! [X2937] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2937),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_32])]) ).

cnf(c_0_44,plain,
    hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_45,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_34,c_0_35]),c_0_35]) ).

fof(c_0_46,plain,
    ! [X10087,X10088] : hAPP(c_List_Orev(X10088),hAPP(c_List_Orev(X10088),X10087)) = X10087,
    inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).

cnf(c_0_47,plain,
    ( ~ hBOOL(hAPP(c_fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_48,plain,
    ( c_fFalse = X1
    | hBOOL(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_37]),c_0_38]),c_0_30]) ).

cnf(c_0_49,plain,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    inference(split_conjunct,[status(thm)],[fact_neg__number__of__Min]) ).

cnf(c_0_50,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_51,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_52,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
    inference(rw,[status(thm)],[c_0_41,c_0_42]) ).

fof(c_0_53,plain,
    ! [X3120,X3121] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3121),hAPP(c_Nat_OSuc,X3120)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3121),X3120)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

cnf(c_0_54,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_55,plain,
    hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_44]) ).

cnf(c_0_56,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_57,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | ~ hBOOL(X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_58,plain,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)),
    inference(rw,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_59,plain,
    ( X1 = hAPP(c_Int_Onat,c_Int_OPls)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != X2 ),
    inference(rw,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_60,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_53]) ).

cnf(c_0_61,plain,
    hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
    inference(rw,[status(thm)],[c_0_54,c_0_52]) ).

fof(c_0_62,plain,
    ! [X2971] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2971),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2971,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(c_0_63,plain,
    ! [X76] : X76 != hAPP(c_Nat_OSuc,X76),
    inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).

cnf(c_0_64,plain,
    hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_65,plain,
    hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)) = c_fFalse,
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_66,plain,
    hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).

cnf(c_0_67,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

fof(c_0_68,plain,
    ! [X5841] : X5841 != hAPP(c_Nat_OSuc,X5841),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_63])]) ).

cnf(c_0_69,plain,
    ( hAPP(c_fNot,X1) = c_fFalse
    | c_fFalse = X1 ),
    inference(spm,[status(thm)],[c_0_57,c_0_48]) ).

cnf(c_0_70,plain,
    hAPP(c_fNot,c_fFalse) = hAPP(c_Nat__Numeral_Oneg,c_Int_OMin),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_71,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) != X1,
    inference(spm,[status(thm)],[c_0_66,c_0_60]) ).

cnf(c_0_72,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onat,c_Int_OPls)) = X1,
    inference(rw,[status(thm)],[c_0_67,c_0_52]) ).

cnf(c_0_73,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_74,plain,
    ( hAPP(c_Nat__Numeral_Oneg,c_Int_OMin) = X1
    | c_fFalse = X1 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_69]),c_0_70]) ).

cnf(c_0_75,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_76,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)) = c_fFalse,
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74])]) ).

cnf(c_0_77,plain,
    hAPP(c_Nat__Numeral_Oneg,c_Int_OMin) != hAPP(c_Nat_OSuc,c_fFalse),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_78,plain,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_74])]),c_0_73]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SWW305+1 : TPTP v8.2.0. Released v5.2.0.
% 0.04/0.13  % Command    : run_E %s %d THM
% 0.12/0.35  % Computer : n004.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit   : 300
% 0.12/0.35  % WCLimit    : 300
% 0.12/0.35  % DateTime   : Wed Jun 19 06:49:09 EDT 2024
% 0.12/0.36  % CPUTime    : 
% 1.38/1.58  Running first-order theorem proving
% 1.38/1.58  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/tmp/tmp.WdOyrgIx8c/E---3.1_1572.p
% 70.71/11.34  # Version: 3.2.0
% 70.71/11.34  # Preprocessing class: FMLMSMSMSSSNFFN.
% 70.71/11.34  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 70.71/11.34  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 70.71/11.34  # Starting new_bool_3 with 300s (1) cores
% 70.71/11.34  # Starting new_bool_1 with 300s (1) cores
% 70.71/11.34  # Starting sh5l with 300s (1) cores
% 70.71/11.34  # sh5l with pid 1655 completed with status 0
% 70.71/11.34  # Result found by sh5l
% 70.71/11.34  # Preprocessing class: FMLMSMSMSSSNFFN.
% 70.71/11.34  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 70.71/11.34  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 70.71/11.34  # Starting new_bool_3 with 300s (1) cores
% 70.71/11.34  # Starting new_bool_1 with 300s (1) cores
% 70.71/11.34  # Starting sh5l with 300s (1) cores
% 70.71/11.34  # SinE strategy is gf500_gu_R04_F100_L20000
% 70.71/11.34  # Search class: FGHSM-SMLM33-DFFFFFNN
% 70.71/11.34  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 70.71/11.34  # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 70.71/11.34  # SAT001_MinMin_p005000_rr with pid 1658 completed with status 0
% 70.71/11.34  # Result found by SAT001_MinMin_p005000_rr
% 70.71/11.34  # Preprocessing class: FMLMSMSMSSSNFFN.
% 70.71/11.34  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 70.71/11.34  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 70.71/11.34  # Starting new_bool_3 with 300s (1) cores
% 70.71/11.34  # Starting new_bool_1 with 300s (1) cores
% 70.71/11.34  # Starting sh5l with 300s (1) cores
% 70.71/11.34  # SinE strategy is gf500_gu_R04_F100_L20000
% 70.71/11.34  # Search class: FGHSM-SMLM33-DFFFFFNN
% 70.71/11.34  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 70.71/11.34  # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 70.71/11.34  # Preprocessing time       : 0.152 s
% 70.71/11.34  # Presaturation interreduction done
% 70.71/11.34  
% 70.71/11.34  # Proof found!
% 70.71/11.34  # SZS status ContradictoryAxioms
% 70.71/11.34  # SZS output start CNFRefutation
% See solution above
% 70.71/11.34  # Parsed axioms                        : 5225
% 70.71/11.34  # Removed by relevancy pruning/SinE    : 643
% 70.71/11.34  # Initial clauses                      : 6710
% 70.71/11.34  # Removed in clause preprocessing      : 174
% 70.71/11.34  # Initial clauses in saturation        : 6536
% 70.71/11.34  # Processed clauses                    : 19888
% 70.71/11.34  # ...of these trivial                  : 369
% 70.71/11.34  # ...subsumed                          : 6888
% 70.71/11.34  # ...remaining for further processing  : 12631
% 70.71/11.34  # Other redundant clauses eliminated   : 1376
% 70.71/11.34  # Clauses deleted for lack of memory   : 0
% 70.71/11.34  # Backward-subsumed                    : 385
% 70.71/11.34  # Backward-rewritten                   : 489
% 70.71/11.34  # Generated clauses                    : 169054
% 70.71/11.34  # ...of the previous two non-redundant : 160819
% 70.71/11.34  # ...aggressively subsumed             : 0
% 70.71/11.34  # Contextual simplify-reflections      : 33
% 70.71/11.34  # Paramodulations                      : 167685
% 70.71/11.34  # Factorizations                       : 2
% 70.71/11.34  # NegExts                              : 0
% 70.71/11.34  # Equation resolutions                 : 1424
% 70.71/11.34  # Disequality decompositions           : 0
% 70.71/11.34  # Total rewrite steps                  : 56325
% 70.71/11.34  # ...of those cached                   : 40208
% 70.71/11.34  # Propositional unsat checks           : 3
% 70.71/11.34  #    Propositional check models        : 2
% 70.71/11.34  #    Propositional check unsatisfiable : 0
% 70.71/11.34  #    Propositional clauses             : 0
% 70.71/11.34  #    Propositional clauses after purity: 0
% 70.71/11.34  #    Propositional unsat core size     : 0
% 70.71/11.34  #    Propositional preprocessing time  : 0.000
% 70.71/11.34  #    Propositional encoding time       : 0.204
% 70.71/11.34  #    Propositional solver time         : 0.097
% 70.71/11.34  #    Success case prop preproc time    : 0.000
% 70.71/11.34  #    Success case prop encoding time   : 0.000
% 70.71/11.34  #    Success case prop solver time     : 0.000
% 70.71/11.34  # Current number of processed clauses  : 6094
% 70.71/11.34  #    Positive orientable unit clauses  : 1400
% 70.71/11.34  #    Positive unorientable unit clauses: 112
% 70.71/11.34  #    Negative unit clauses             : 929
% 70.71/11.34  #    Non-unit-clauses                  : 3653
% 70.71/11.34  # Current number of unprocessed clauses: 143889
% 70.71/11.34  # ...number of literals in the above   : 298081
% 70.71/11.34  # Current number of archived formulas  : 0
% 70.71/11.34  # Current number of archived clauses   : 6112
% 70.71/11.34  # Clause-clause subsumption calls (NU) : 4259360
% 70.71/11.34  # Rec. Clause-clause subsumption calls : 2010280
% 70.71/11.34  # Non-unit clause-clause subsumptions  : 4007
% 70.71/11.34  # Unit Clause-clause subsumption calls : 306724
% 70.71/11.34  # Rewrite failures with RHS unbound    : 609
% 70.71/11.34  # BW rewrite match attempts            : 31029
% 70.71/11.34  # BW rewrite match successes           : 1353
% 70.71/11.34  # Condensation attempts                : 0
% 70.71/11.34  # Condensation successes               : 0
% 70.71/11.34  # Termbank termtop insertions          : 5530544
% 70.71/11.34  # Search garbage collected termcells   : 96995
% 70.71/11.34  
% 70.71/11.34  # -------------------------------------------------
% 70.71/11.34  # User time                : 9.097 s
% 70.71/11.34  # System time              : 0.237 s
% 70.71/11.34  # Total time               : 9.334 s
% 70.71/11.34  # Maximum resident set size: 37816 pages
% 70.71/11.34  
% 70.71/11.34  # -------------------------------------------------
% 70.71/11.34  # User time                : 9.338 s
% 70.71/11.34  # System time              : 0.248 s
% 70.71/11.34  # Total time               : 9.586 s
% 70.71/11.34  # Maximum resident set size: 9504 pages
% 70.71/11.34  % E---3.1 exiting
% 70.71/11.34  % E exiting
%------------------------------------------------------------------------------