TSTP Solution File: SWW362+1 by E-SAT---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.2.0
% Problem  : SWW362+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d SAT

% Computer : n012.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 18:14:19 EDT 2024

% Result   : Theorem 82.97s 12.95s
% Output   : CNFRefutation 82.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   50 (  29 unt;   0 def)
%            Number of atoms       :  109 (  33 equ)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives :   99 (  40   ~;  40   |;  12   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  10 con; 0-3 aty)
%            Number of variables   :   96 (   8 sgn  53   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_nat__diff__split,axiom,
    ! [X13,X11,X25] :
      ( hBOOL(hAPP(X25,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11),X13)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X13))
         => hBOOL(hAPP(X25,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [X80] :
            ( X11 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),X80)
           => hBOOL(hAPP(X25,X80)) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',fact_nat__diff__split) ).

fof(fact_number__of__is__id,axiom,
    ! [X56] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X56) = X56,
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',fact_number__of__is__id) ).

fof(fact_diff__Suc__1,axiom,
    ! [X48] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X48)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X48,
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',fact_diff__Suc__1) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [X48] : hAPP(c_Nat_OSuc,X48) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X48),
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',fact_Suc__eq__plus1__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/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',fact_One__nat__def) ).

fof(fact_insert__code,axiom,
    ! [X12,X10,X16,X9] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X9),X16),X10),X12))
    <=> ( X16 = X12
        | hBOOL(hAPP(X10,X12)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',fact_insert__code) ).

fof(conj_3,conjecture,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),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)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',conj_3) ).

fof(fact_insert__image,axiom,
    ! [X2,X7,X10,X12,X9] :
      ( hBOOL(hAPP(hAPP(c_member(X9),X12),X10))
     => hAPP(hAPP(c_Set_Oinsert(X7),hAPP(X2,X12)),hAPP(c_Set_Oimage(X9,X7,X2),X10)) = hAPP(c_Set_Oimage(X9,X7,X2),X10) ),
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',fact_insert__image) ).

fof(conj_1,hypothesis,
    v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',conj_1) ).

fof(fact_insert__subset,axiom,
    ! [X15,X10,X12,X9] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X9),X12),X10)),X15))
    <=> ( hBOOL(hAPP(hAPP(c_member(X9),X12),X15))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool)),X10),X15)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',fact_insert__subset) ).

fof(fact_empty__subsetI,axiom,
    ! [X10,X9] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool))),X10)),
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',fact_empty__subsetI) ).

fof(fact_mem__def,axiom,
    ! [X10,X12,X9] :
      ( hBOOL(hAPP(hAPP(c_member(X9),X12),X10))
    <=> hBOOL(hAPP(X10,X12)) ),
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',fact_mem__def) ).

fof(conj_2,hypothesis,
    hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
    file('/export/starexec/sandbox/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p',conj_2) ).

fof(c_0_13,plain,
    ! [X991,X992,X993,X994,X995,X996,X997] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X992),X991))
        | hBOOL(hAPP(X993,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X993,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X992),X991))) )
      & ( X992 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X991),X994)
        | hBOOL(hAPP(X993,X994))
        | ~ hBOOL(hAPP(X993,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X992),X991))) )
      & ( X996 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X995),esk19_3(X995,X996,X997))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X996),X995))
        | hBOOL(hAPP(X997,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X996),X995))) )
      & ( ~ hBOOL(hAPP(X997,esk19_3(X995,X996,X997)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X996),X995))
        | hBOOL(hAPP(X997,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X996),X995))) )
      & ( X996 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X995),esk19_3(X995,X996,X997))
        | ~ hBOOL(hAPP(X997,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X997,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X996),X995))) )
      & ( ~ hBOOL(hAPP(X997,esk19_3(X995,X996,X997)))
        | ~ hBOOL(hAPP(X997,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X997,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X996),X995))) ) ),
    inference(distribute,[status(thm)],[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)],[fact_nat__diff__split])])])])])])]) ).

fof(c_0_14,plain,
    ! [X1920] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1920) = X1920,
    inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).

fof(c_0_15,plain,
    ! [X1787] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1787)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1787,
    inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).

fof(c_0_16,plain,
    ! [X1796] : hAPP(c_Nat_OSuc,X1796) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1796),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).

cnf(c_0_17,plain,
    ( hBOOL(hAPP(X4,X3))
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)
    | ~ hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,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_21,plain,
    hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_22,plain,
    ! [X569,X570,X571,X572] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X572),X571),X570),X569))
        | X571 = X569
        | hBOOL(hAPP(X570,X569)) )
      & ( X571 != X569
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X572),X571),X570),X569)) )
      & ( ~ hBOOL(hAPP(X570,X569))
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X572),X571),X570),X569)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])])]) ).

fof(c_0_23,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),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)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_3])]) ).

cnf(c_0_24,plain,
    ( hBOOL(X1)
    | X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)
    | ~ hBOOL(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).

cnf(c_0_25,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X1,
    inference(rw,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = hAPP(c_Nat_OSuc,X1),
    inference(rw,[status(thm)],[c_0_21,c_0_20]) ).

cnf(c_0_27,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_28,plain,
    ! [X408,X409,X410,X411,X412] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X412),X411),X410))
      | hAPP(hAPP(c_Set_Oinsert(X409),hAPP(X408,X411)),hAPP(c_Set_Oimage(X412,X409,X408),X410)) = hAPP(c_Set_Oimage(X412,X409,X408),X410) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])])]) ).

fof(c_0_29,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),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)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    inference(fof_nnf,[status(thm)],[c_0_23]) ).

cnf(c_0_30,plain,
    ( hBOOL(X1)
    | hAPP(c_Nat_OSuc,X2) != hAPP(c_Nat_OSuc,X1)
    | ~ hBOOL(X2) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

cnf(c_0_31,plain,
    hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
    inference(er,[status(thm)],[c_0_27]) ).

cnf(c_0_32,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)) = hAPP(c_Set_Oimage(X1,X4,X5),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_33,hypothesis,
    v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
    inference(split_conjunct,[status(thm)],[conj_1]) ).

cnf(c_0_34,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),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)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

fof(c_0_35,plain,
    ! [X633,X634,X635,X636] :
      ( ( hBOOL(hAPP(hAPP(c_member(X636),X635),X633))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X636,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X636),X635),X634)),X633)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X636,tc_HOL_Obool)),X634),X633))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X636,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X636),X635),X634)),X633)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X636),X635),X633))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X636,tc_HOL_Obool)),X634),X633))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X636,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X636),X635),X634)),X633)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])])]) ).

fof(c_0_36,plain,
    ! [X508,X509] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X509,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X509,tc_HOL_Obool))),X508)),
    inference(variable_rename,[status(thm)],[fact_empty__subsetI]) ).

cnf(c_0_37,plain,
    ( hBOOL(X1)
    | hAPP(c_Nat_OSuc,hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X3)) != hAPP(c_Nat_OSuc,X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_38,hypothesis,
    ( hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X1)),v_G) = v_G
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X1),v_U)) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),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)],[c_0_34,c_0_33]) ).

cnf(c_0_40,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_41,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

fof(c_0_42,plain,
    ! [X489,X490,X491] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X491),X490),X489))
        | hBOOL(hAPP(X489,X490)) )
      & ( ~ hBOOL(hAPP(X489,X490))
        | hBOOL(hAPP(hAPP(c_member(X491),X490),X489)) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])]) ).

cnf(c_0_43,hypothesis,
    ( hBOOL(X1)
    | hAPP(c_Nat_OSuc,hAPP(v_G,hAPP(v_mgt__call,X2))) != hAPP(c_Nat_OSuc,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X2),v_U)) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_44,hypothesis,
    hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
    inference(split_conjunct,[status(thm)],[conj_2]) ).

cnf(c_0_45,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).

cnf(c_0_46,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_47,hypothesis,
    ( hBOOL(X1)
    | hAPP(c_Nat_OSuc,hAPP(v_G,hAPP(v_mgt__call,v_pn))) != hAPP(c_Nat_OSuc,X1) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_48,negated_conjecture,
    ~ hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_pn))),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_49,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_47]),c_0_48]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWW362+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12  % Command    : run_E %s %d SAT
% 0.13/0.33  % Computer : n012.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Wed Jun 19 05:32:24 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 1.39/1.62  Running first-order model finding
% 1.39/1.62  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/tmp/tmp.YOoWZLpP1T/E---3.1_2444.p
% 82.97/12.95  # Version: 3.2.0
% 82.97/12.95  # Preprocessing class: FMLMSMSMSSSNFFN.
% 82.97/12.95  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 82.97/12.95  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 82.97/12.95  # Starting new_bool_3 with 300s (1) cores
% 82.97/12.95  # Starting new_bool_1 with 300s (1) cores
% 82.97/12.95  # Starting sh5l with 300s (1) cores
% 82.97/12.95  # new_bool_3 with pid 2523 completed with status 0
% 82.97/12.95  # Result found by new_bool_3
% 82.97/12.95  # Preprocessing class: FMLMSMSMSSSNFFN.
% 82.97/12.95  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 82.97/12.95  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 82.97/12.95  # Starting new_bool_3 with 300s (1) cores
% 82.97/12.95  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 82.97/12.95  # Search class: FGHSM-FSLM32-DFFFFFNN
% 82.97/12.95  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 82.97/12.95  # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 23s (1) cores
% 82.97/12.95  # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 2527 completed with status 0
% 82.97/12.95  # Result found by G-E--_301_C18_F1_URBAN_S5PRR_S0Y
% 82.97/12.95  # Preprocessing class: FMLMSMSMSSSNFFN.
% 82.97/12.95  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 82.97/12.95  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 82.97/12.95  # Starting new_bool_3 with 300s (1) cores
% 82.97/12.95  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 82.97/12.95  # Search class: FGHSM-FSLM32-DFFFFFNN
% 82.97/12.95  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 82.97/12.95  # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 23s (1) cores
% 82.97/12.95  # Preprocessing time       : 0.050 s
% 82.97/12.95  
% 82.97/12.95  # Proof found!
% 82.97/12.95  # SZS status Theorem
% 82.97/12.95  # SZS output start CNFRefutation
% See solution above
% 82.97/12.95  # Parsed axioms                        : 5227
% 82.97/12.95  # Removed by relevancy pruning/SinE    : 4589
% 82.97/12.95  # Initial clauses                      : 982
% 82.97/12.95  # Removed in clause preprocessing      : 36
% 82.97/12.95  # Initial clauses in saturation        : 946
% 82.97/12.95  # Processed clauses                    : 7550
% 82.97/12.95  # ...of these trivial                  : 651
% 82.97/12.95  # ...subsumed                          : 3887
% 82.97/12.95  # ...remaining for further processing  : 3012
% 82.97/12.95  # Other redundant clauses eliminated   : 1046
% 82.97/12.95  # Clauses deleted for lack of memory   : 0
% 82.97/12.95  # Backward-subsumed                    : 122
% 82.97/12.95  # Backward-rewritten                   : 262
% 82.97/12.95  # Generated clauses                    : 258398
% 82.97/12.95  # ...of the previous two non-redundant : 243902
% 82.97/12.95  # ...aggressively subsumed             : 0
% 82.97/12.95  # Contextual simplify-reflections      : 21
% 82.97/12.95  # Paramodulations                      : 256998
% 82.97/12.95  # Factorizations                       : 10
% 82.97/12.95  # NegExts                              : 0
% 82.97/12.95  # Equation resolutions                 : 1391
% 82.97/12.95  # Disequality decompositions           : 0
% 82.97/12.95  # Total rewrite steps                  : 73217
% 82.97/12.95  # ...of those cached                   : 65087
% 82.97/12.95  # Propositional unsat checks           : 0
% 82.97/12.95  #    Propositional check models        : 0
% 82.97/12.95  #    Propositional check unsatisfiable : 0
% 82.97/12.95  #    Propositional clauses             : 0
% 82.97/12.95  #    Propositional clauses after purity: 0
% 82.97/12.95  #    Propositional unsat core size     : 0
% 82.97/12.95  #    Propositional preprocessing time  : 0.000
% 82.97/12.95  #    Propositional encoding time       : 0.000
% 82.97/12.95  #    Propositional solver time         : 0.000
% 82.97/12.95  #    Success case prop preproc time    : 0.000
% 82.97/12.95  #    Success case prop encoding time   : 0.000
% 82.97/12.95  #    Success case prop solver time     : 0.000
% 82.97/12.95  # Current number of processed clauses  : 2604
% 82.97/12.95  #    Positive orientable unit clauses  : 325
% 82.97/12.95  #    Positive unorientable unit clauses: 91
% 82.97/12.95  #    Negative unit clauses             : 164
% 82.97/12.95  #    Non-unit-clauses                  : 2024
% 82.97/12.95  # Current number of unprocessed clauses: 235203
% 82.97/12.95  # ...number of literals in the above   : 667612
% 82.97/12.95  # Current number of archived formulas  : 0
% 82.97/12.95  # Current number of archived clauses   : 384
% 82.97/12.95  # Clause-clause subsumption calls (NU) : 419835
% 82.97/12.95  # Rec. Clause-clause subsumption calls : 265196
% 82.97/12.95  # Non-unit clause-clause subsumptions  : 2135
% 82.97/12.95  # Unit Clause-clause subsumption calls : 27166
% 82.97/12.95  # Rewrite failures with RHS unbound    : 268
% 82.97/12.95  # BW rewrite match attempts            : 27363
% 82.97/12.95  # BW rewrite match successes           : 287
% 82.97/12.95  # Condensation attempts                : 0
% 82.97/12.95  # Condensation successes               : 0
% 82.97/12.95  # Termbank termtop insertions          : 8256056
% 82.97/12.95  # Search garbage collected termcells   : 55124
% 82.97/12.95  
% 82.97/12.95  # -------------------------------------------------
% 82.97/12.95  # User time                : 10.588 s
% 82.97/12.95  # System time              : 0.291 s
% 82.97/12.95  # Total time               : 10.879 s
% 82.97/12.95  # Maximum resident set size: 11456 pages
% 82.97/12.95  
% 82.97/12.95  # -------------------------------------------------
% 82.97/12.95  # User time                : 10.832 s
% 82.97/12.95  # System time              : 0.301 s
% 82.97/12.95  # Total time               : 11.133 s
% 82.97/12.95  # Maximum resident set size: 9468 pages
% 82.97/12.95  % E---3.1 exiting
% 82.97/12.96  % E exiting
%------------------------------------------------------------------------------