TSTP Solution File: SWW247+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SWW247+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n020.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 : Sat May  4 10:00:33 EDT 2024

% Result   : Theorem 4.27s 1.30s
% Output   : CNFRefutation 4.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   66 (  17 unt;   0 def)
%            Number of atoms       :  127 (  79 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  115 (  54   ~;  49   |;   0   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :   69 (   8 sgn  37   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
    hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) = hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
    file('/export/starexec/sandbox2/tmp/tmp.M5PEeiUISA/E---3.1_28048.p',conj_0) ).

fof(clrel_Rings_Oidom__Rings_Ocomm__semiring__1,axiom,
    ! [X91] :
      ( class_Rings_Oidom(X91)
     => class_Rings_Ocomm__semiring__1(X91) ),
    file('/export/starexec/sandbox2/tmp/tmp.M5PEeiUISA/E---3.1_28048.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__1) ).

fof(fact_poly__pCons,axiom,
    ! [X14,X11,X12,X13] :
      ( class_Rings_Ocomm__semiring__0(X13)
     => hAPP(c_Polynomial_Opoly(X13,hAPP(hAPP(c_Polynomial_OpCons(X13),X12),X11)),X14) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X14),hAPP(c_Polynomial_Opoly(X13,X11),X14))) ),
    file('/export/starexec/sandbox2/tmp/tmp.M5PEeiUISA/E---3.1_28048.p',fact_poly__pCons) ).

fof(fact_C,axiom,
    ( class_Rings_Oidom(t_a)
   => ! [X4] :
        ( X4 != c_Groups_Ozero__class_Ozero(t_a)
       => hAPP(c_Polynomial_Opoly(t_a,v_cs____),X4) = c_Groups_Ozero__class_Ozero(t_a) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.M5PEeiUISA/E---3.1_28048.p',fact_C) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X10,X12,X13] :
      ( class_Rings_Ocomm__semiring__1(X13)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X10),X12) ),
    file('/export/starexec/sandbox2/tmp/tmp.M5PEeiUISA/E---3.1_28048.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(tfree_0,hypothesis,
    class_Rings_Oidom(t_a),
    file('/export/starexec/sandbox2/tmp/tmp.M5PEeiUISA/E---3.1_28048.p',tfree_0) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [X12,X13] :
      ( class_Rings_Ocomm__semiring__1(X13)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),c_Groups_Ozero__class_Ozero(X13)) = c_Groups_Ozero__class_Ozero(X13) ),
    file('/export/starexec/sandbox2/tmp/tmp.M5PEeiUISA/E---3.1_28048.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X12,X13] :
      ( class_Rings_Ocomm__semiring__1(X13)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),c_Groups_Ozero__class_Ozero(X13)),X12) = X12 ),
    file('/export/starexec/sandbox2/tmp/tmp.M5PEeiUISA/E---3.1_28048.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(clrel_Rings_Oidom__Rings_Ocomm__semiring__0,axiom,
    ! [X91] :
      ( class_Rings_Oidom(X91)
     => class_Rings_Ocomm__semiring__0(X91) ),
    file('/export/starexec/sandbox2/tmp/tmp.M5PEeiUISA/E---3.1_28048.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__0) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [X12,X13] :
      ( class_Rings_Ocomm__semiring__1(X13)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),c_Groups_Ozero__class_Ozero(X13)),X12) = c_Groups_Ozero__class_Ozero(X13) ),
    file('/export/starexec/sandbox2/tmp/tmp.M5PEeiUISA/E---3.1_28048.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X12,X13] :
      ( class_Rings_Ocomm__semiring__1(X13)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),c_Groups_Ozero__class_Ozero(X13)) = X12 ),
    file('/export/starexec/sandbox2/tmp/tmp.M5PEeiUISA/E---3.1_28048.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(c_0_11,negated_conjecture,
    hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) != hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

fof(c_0_12,plain,
    ! [X170] :
      ( ~ class_Rings_Oidom(X170)
      | class_Rings_Ocomm__semiring__1(X170) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__1])])]) ).

fof(c_0_13,negated_conjecture,
    hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) != hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
    inference(fof_nnf,[status(thm)],[c_0_11]) ).

fof(c_0_14,plain,
    ! [X104,X105,X106,X107] :
      ( ~ class_Rings_Ocomm__semiring__0(X107)
      | hAPP(c_Polynomial_Opoly(X107,hAPP(hAPP(c_Polynomial_OpCons(X107),X106),X105)),X104) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X107),X106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X107),X104),hAPP(c_Polynomial_Opoly(X107,X105),X104))) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])])]) ).

fof(c_0_15,plain,
    ( class_Rings_Oidom(t_a)
   => ! [X4] :
        ( X4 != c_Groups_Ozero__class_Ozero(t_a)
       => hAPP(c_Polynomial_Opoly(t_a,v_cs____),X4) = c_Groups_Ozero__class_Ozero(t_a) ) ),
    inference(fof_simplification,[status(thm)],[fact_C]) ).

fof(c_0_16,plain,
    ! [X590,X591,X592] :
      ( ~ class_Rings_Ocomm__semiring__1(X592)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X592),X591),X590) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X592),X590),X591) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])]) ).

cnf(c_0_17,plain,
    ( class_Rings_Ocomm__semiring__1(X1)
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,hypothesis,
    class_Rings_Oidom(t_a),
    inference(split_conjunct,[status(thm)],[tfree_0]) ).

cnf(c_0_19,negated_conjecture,
    hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) != hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    ( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)))
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_21,plain,
    ! [X134] :
      ( ~ class_Rings_Oidom(t_a)
      | X134 = c_Groups_Ozero__class_Ozero(t_a)
      | hAPP(c_Polynomial_Opoly(t_a,v_cs____),X134) = c_Groups_Ozero__class_Ozero(t_a) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).

fof(c_0_22,plain,
    ! [X593,X594] :
      ( ~ class_Rings_Ocomm__semiring__1(X594)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X594),X593),c_Groups_Ozero__class_Ozero(X594)) = c_Groups_Ozero__class_Ozero(X594) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])])]) ).

fof(c_0_23,plain,
    ! [X599,X600] :
      ( ~ class_Rings_Ocomm__semiring__1(X600)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X600),c_Groups_Ozero__class_Ozero(X600)),X599) = X599 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])]) ).

cnf(c_0_24,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,hypothesis,
    class_Rings_Ocomm__semiring__1(t_a),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_26,negated_conjecture,
    ( hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_x____)))
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_27,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(t_a)
    | hAPP(c_Polynomial_Opoly(t_a,v_cs____),X1) = c_Groups_Ozero__class_Ozero(t_a)
    | ~ class_Rings_Oidom(t_a) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_30,hypothesis,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X2),X1),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_31,negated_conjecture,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_x____))) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____)))
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(spm,[status(thm)],[c_0_26,c_0_20]) ).

cnf(c_0_32,plain,
    ( hAPP(c_Polynomial_Opoly(t_a,v_cs____),X1) = c_Groups_Ozero__class_Ozero(t_a)
    | X1 = c_Groups_Ozero__class_Ozero(t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_18])]) ).

cnf(c_0_33,hypothesis,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),X1),c_Groups_Ozero__class_Ozero(t_a)) = c_Groups_Ozero__class_Ozero(t_a),
    inference(spm,[status(thm)],[c_0_28,c_0_25]) ).

cnf(c_0_34,hypothesis,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),c_Groups_Ozero__class_Ozero(t_a)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_25])]) ).

cnf(c_0_35,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_x____
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____))) != v_c____
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]) ).

fof(c_0_36,plain,
    ! [X171] :
      ( ~ class_Rings_Oidom(X171)
      | class_Rings_Ocomm__semiring__0(X171) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__0])])]) ).

fof(c_0_37,plain,
    ! [X595,X596] :
      ( ~ class_Rings_Ocomm__semiring__1(X596)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X596),c_Groups_Ozero__class_Ozero(X596)),X595) = c_Groups_Ozero__class_Ozero(X596) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])])]) ).

cnf(c_0_38,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_y____
    | c_Groups_Ozero__class_Ozero(t_a) = v_x____
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_32]),c_0_33]),c_0_34])]) ).

cnf(c_0_39,plain,
    ( class_Rings_Ocomm__semiring__0(X1)
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_40,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_41,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_x____
    | c_Groups_Ozero__class_Ozero(t_a) = v_y____ ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_18])]) ).

cnf(c_0_42,hypothesis,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Ozero__class_Ozero(t_a)),X1) = c_Groups_Ozero__class_Ozero(t_a),
    inference(spm,[status(thm)],[c_0_40,c_0_25]) ).

cnf(c_0_43,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_y____
    | v_x____ != v_y____ ),
    inference(ef,[status(thm)],[c_0_41]) ).

cnf(c_0_44,hypothesis,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),X1) = v_y____
    | v_x____ != v_y____ ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

fof(c_0_45,plain,
    ! [X597,X598] :
      ( ~ class_Rings_Ocomm__semiring__1(X598)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X598),X597),c_Groups_Ozero__class_Ozero(X598)) = X597 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])])]) ).

cnf(c_0_46,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_x____
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) != v_c____
    | v_x____ != v_y____
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(spm,[status(thm)],[c_0_35,c_0_44]) ).

cnf(c_0_47,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_48,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_x____
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) != v_c____
    | v_x____ != v_y____ ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_39]),c_0_18])]) ).

cnf(c_0_49,negated_conjecture,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_y____) = X1
    | v_x____ != v_y____ ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_43]),c_0_25])]) ).

cnf(c_0_50,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_x____
    | v_x____ != v_y____ ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_51,hypothesis,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),X1) = v_x____
    | v_x____ != v_y____ ),
    inference(spm,[status(thm)],[c_0_42,c_0_50]) ).

cnf(c_0_52,hypothesis,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),X1) = v_x____
    | c_Groups_Ozero__class_Ozero(t_a) = v_y____ ),
    inference(spm,[status(thm)],[c_0_42,c_0_41]) ).

cnf(c_0_53,negated_conjecture,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____))) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____)
    | v_x____ != v_y____
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(spm,[status(thm)],[c_0_31,c_0_51]) ).

cnf(c_0_54,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_y____
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____))) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____)
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(spm,[status(thm)],[c_0_31,c_0_52]) ).

cnf(c_0_55,negated_conjecture,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_x____) = X1
    | c_Groups_Ozero__class_Ozero(t_a) = v_y____ ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_41]),c_0_25])]) ).

cnf(c_0_56,hypothesis,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____)
    | v_x____ != v_y____
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(spm,[status(thm)],[c_0_53,c_0_44]) ).

cnf(c_0_57,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_y____
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_32]),c_0_33]),c_0_34]),c_0_55]) ).

cnf(c_0_58,hypothesis,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____)
    | v_x____ != v_y____ ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_39]),c_0_18])]) ).

cnf(c_0_59,negated_conjecture,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_x____) = X1
    | v_x____ != v_y____ ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_50]),c_0_25])]) ).

cnf(c_0_60,negated_conjecture,
    c_Groups_Ozero__class_Ozero(t_a) = v_y____,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_39]),c_0_18])]) ).

cnf(c_0_61,negated_conjecture,
    v_x____ != v_y____,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_49]) ).

cnf(c_0_62,hypothesis,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),X1) = v_y____,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_60]),c_0_60]) ).

cnf(c_0_63,hypothesis,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_y____) = X1,
    inference(rw,[status(thm)],[c_0_34,c_0_60]) ).

cnf(c_0_64,negated_conjecture,
    ~ class_Rings_Ocomm__semiring__0(t_a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_60]),c_0_61]),c_0_62]),c_0_63])]) ).

cnf(c_0_65,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_39]),c_0_18])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.25  % Problem    : SWW247+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.26  % Command    : run_E %s %d THM
% 0.27/0.47  % Computer : n020.cluster.edu
% 0.27/0.47  % Model    : x86_64 x86_64
% 0.27/0.47  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.47  % Memory   : 8042.1875MB
% 0.27/0.47  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.27/0.47  % CPULimit   : 300
% 0.27/0.47  % WCLimit    : 300
% 0.27/0.47  % DateTime   : Fri May  3 13:23:16 EDT 2024
% 0.33/0.48  % CPUTime    : 
% 0.41/0.69  Running first-order theorem proving
% 0.41/0.69  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.M5PEeiUISA/E---3.1_28048.p
% 4.27/1.30  # Version: 3.1.0
% 4.27/1.30  # Preprocessing class: FMLMSMSMSSSNFFN.
% 4.27/1.30  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.27/1.30  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.27/1.30  # Starting new_bool_3 with 300s (1) cores
% 4.27/1.30  # Starting new_bool_1 with 300s (1) cores
% 4.27/1.30  # Starting sh5l with 300s (1) cores
% 4.27/1.30  # new_bool_1 with pid 28128 completed with status 0
% 4.27/1.30  # Result found by new_bool_1
% 4.27/1.30  # Preprocessing class: FMLMSMSMSSSNFFN.
% 4.27/1.30  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.27/1.30  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.27/1.30  # Starting new_bool_3 with 300s (1) cores
% 4.27/1.30  # Starting new_bool_1 with 300s (1) cores
% 4.27/1.30  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.27/1.30  # Search class: FGHSM-FSLM31-DFFFFFNN
% 4.27/1.30  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 4.27/1.30  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 4.27/1.30  # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 28130 completed with status 0
% 4.27/1.30  # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 4.27/1.30  # Preprocessing class: FMLMSMSMSSSNFFN.
% 4.27/1.30  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.27/1.30  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.27/1.30  # Starting new_bool_3 with 300s (1) cores
% 4.27/1.30  # Starting new_bool_1 with 300s (1) cores
% 4.27/1.30  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.27/1.30  # Search class: FGHSM-FSLM31-DFFFFFNN
% 4.27/1.30  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 4.27/1.30  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 4.27/1.30  # Preprocessing time       : 0.011 s
% 4.27/1.30  # Presaturation interreduction done
% 4.27/1.30  
% 4.27/1.30  # Proof found!
% 4.27/1.30  # SZS status Theorem
% 4.27/1.30  # SZS output start CNFRefutation
% See solution above
% 4.27/1.30  # Parsed axioms                        : 1214
% 4.27/1.30  # Removed by relevancy pruning/SinE    : 724
% 4.27/1.30  # Initial clauses                      : 695
% 4.27/1.30  # Removed in clause preprocessing      : 43
% 4.27/1.30  # Initial clauses in saturation        : 652
% 4.27/1.30  # Processed clauses                    : 4284
% 4.27/1.30  # ...of these trivial                  : 114
% 4.27/1.30  # ...subsumed                          : 2529
% 4.27/1.30  # ...remaining for further processing  : 1641
% 4.27/1.30  # Other redundant clauses eliminated   : 443
% 4.27/1.30  # Clauses deleted for lack of memory   : 0
% 4.27/1.30  # Backward-subsumed                    : 73
% 4.27/1.30  # Backward-rewritten                   : 161
% 4.27/1.30  # Generated clauses                    : 24957
% 4.27/1.30  # ...of the previous two non-redundant : 21886
% 4.27/1.30  # ...aggressively subsumed             : 0
% 4.27/1.30  # Contextual simplify-reflections      : 8
% 4.27/1.30  # Paramodulations                      : 24493
% 4.27/1.30  # Factorizations                       : 13
% 4.27/1.30  # NegExts                              : 0
% 4.27/1.30  # Equation resolutions                 : 462
% 4.27/1.30  # Disequality decompositions           : 0
% 4.27/1.30  # Total rewrite steps                  : 17961
% 4.27/1.30  # ...of those cached                   : 16454
% 4.27/1.30  # Propositional unsat checks           : 0
% 4.27/1.30  #    Propositional check models        : 0
% 4.27/1.30  #    Propositional check unsatisfiable : 0
% 4.27/1.30  #    Propositional clauses             : 0
% 4.27/1.30  #    Propositional clauses after purity: 0
% 4.27/1.30  #    Propositional unsat core size     : 0
% 4.27/1.30  #    Propositional preprocessing time  : 0.000
% 4.27/1.30  #    Propositional encoding time       : 0.000
% 4.27/1.30  #    Propositional solver time         : 0.000
% 4.27/1.30  #    Success case prop preproc time    : 0.000
% 4.27/1.30  #    Success case prop encoding time   : 0.000
% 4.27/1.30  #    Success case prop solver time     : 0.000
% 4.27/1.30  # Current number of processed clauses  : 876
% 4.27/1.30  #    Positive orientable unit clauses  : 143
% 4.27/1.30  #    Positive unorientable unit clauses: 8
% 4.27/1.30  #    Negative unit clauses             : 135
% 4.27/1.30  #    Non-unit-clauses                  : 590
% 4.27/1.30  # Current number of unprocessed clauses: 18399
% 4.27/1.30  # ...number of literals in the above   : 47760
% 4.27/1.30  # Current number of archived formulas  : 0
% 4.27/1.30  # Current number of archived clauses   : 692
% 4.27/1.30  # Clause-clause subsumption calls (NU) : 47251
% 4.27/1.30  # Rec. Clause-clause subsumption calls : 41447
% 4.27/1.30  # Non-unit clause-clause subsumptions  : 1064
% 4.27/1.30  # Unit Clause-clause subsumption calls : 2634
% 4.27/1.30  # Rewrite failures with RHS unbound    : 0
% 4.27/1.30  # BW rewrite match attempts            : 1272
% 4.27/1.30  # BW rewrite match successes           : 141
% 4.27/1.30  # Condensation attempts                : 0
% 4.27/1.30  # Condensation successes               : 0
% 4.27/1.30  # Termbank termtop insertions          : 623922
% 4.27/1.30  # Search garbage collected termcells   : 13214
% 4.27/1.30  
% 4.27/1.30  # -------------------------------------------------
% 4.27/1.30  # User time                : 0.534 s
% 4.27/1.30  # System time              : 0.026 s
% 4.27/1.30  # Total time               : 0.560 s
% 4.27/1.30  # Maximum resident set size: 5016 pages
% 4.27/1.30  
% 4.27/1.30  # -------------------------------------------------
% 4.27/1.30  # User time                : 0.560 s
% 4.27/1.30  # System time              : 0.029 s
% 4.27/1.30  # Total time               : 0.588 s
% 4.27/1.30  # Maximum resident set size: 3252 pages
% 4.27/1.30  % E---3.1 exiting
% 4.27/1.30  % E exiting
%------------------------------------------------------------------------------