TSTP Solution File: FLD048-4 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : FLD048-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n027.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 17:30:08 EDT 2023

% Result   : Unsatisfiable 10.74s 1.89s
% Output   : CNFRefutation 10.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   35
% Syntax   : Number of clauses     :  138 (  63 unt;   8 nHn; 138 RR)
%            Number of literals    :  292 (   0 equ; 152 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;  11 con; 0-2 aty)
%            Number of variables   :  201 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(commutativity_multiplication,axiom,
    ( product(X1,X2,X3)
    | ~ product(X2,X1,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',commutativity_multiplication) ).

cnf(product_14,negated_conjecture,
    product(c,multiplicative_inverse(d),t),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',product_14) ).

cnf(associativity_multiplication_2,axiom,
    ( product(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ product(X5,X2,X6)
    | ~ product(X4,X6,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',associativity_multiplication_2) ).

cnf(associativity_multiplication_1,axiom,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ product(X4,X6,X2)
    | ~ product(X5,X6,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',associativity_multiplication_1) ).

cnf(existence_of_identity_multiplication,axiom,
    ( product(multiplicative_identity,X1,X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',existence_of_identity_multiplication) ).

cnf(totality_of_multiplication,axiom,
    ( product(X1,X2,multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',totality_of_multiplication) ).

cnf(t_is_defined,hypothesis,
    defined(t),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',t_is_defined) ).

cnf(existence_of_inverse_multiplication,axiom,
    ( product(multiplicative_inverse(X1),X1,multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',existence_of_inverse_multiplication) ).

cnf(well_definedness_of_multiplicative_identity,axiom,
    defined(multiplicative_identity),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',well_definedness_of_multiplicative_identity) ).

cnf(d_is_defined,hypothesis,
    defined(d),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',d_is_defined) ).

cnf(not_sum_11,negated_conjecture,
    ~ sum(additive_identity,d,additive_identity),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',not_sum_11) ).

cnf(product_12,negated_conjecture,
    product(s,t,u),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',product_12) ).

cnf(c_is_defined,hypothesis,
    defined(c),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',c_is_defined) ).

cnf(compatibility_of_order_relation_and_addition,axiom,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(X3,X4)
    | ~ sum(X3,X5,X1)
    | ~ sum(X4,X5,X2) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',compatibility_of_order_relation_and_addition) ).

cnf(existence_of_identity_addition,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',existence_of_identity_addition) ).

cnf(totality_of_order_relation,axiom,
    ( less_or_equal(X1,X2)
    | less_or_equal(X2,X1)
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',totality_of_order_relation) ).

cnf(well_definedness_of_additive_identity,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',well_definedness_of_additive_identity) ).

cnf(commutativity_addition,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',commutativity_addition) ).

cnf(u_is_defined,hypothesis,
    defined(u),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',u_is_defined) ).

cnf(antisymmetry_of_order_relation,axiom,
    ( sum(additive_identity,X1,X2)
    | ~ less_or_equal(X1,X2)
    | ~ less_or_equal(X2,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',antisymmetry_of_order_relation) ).

cnf(product_15,negated_conjecture,
    product(a,c,k),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',product_15) ).

cnf(product_13,negated_conjecture,
    product(a,multiplicative_inverse(b),s),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',product_13) ).

cnf(associativity_addition_2,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ sum(X5,X2,X6)
    | ~ sum(X4,X6,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',associativity_addition_2) ).

cnf(a_is_defined,hypothesis,
    defined(a),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',a_is_defined) ).

cnf(b_is_defined,hypothesis,
    defined(b),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',b_is_defined) ).

cnf(not_sum_10,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',not_sum_10) ).

cnf(existence_of_inverse_addition,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',existence_of_inverse_addition) ).

cnf(associativity_addition_1,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',associativity_addition_1) ).

cnf(well_definedness_of_additive_inverse,axiom,
    ( defined(additive_inverse(X1))
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',well_definedness_of_additive_inverse) ).

cnf(distributivity_2,axiom,
    ( product(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ product(X4,X2,X6)
    | ~ product(X5,X2,X7)
    | ~ sum(X6,X7,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',distributivity_2) ).

cnf(product_16,negated_conjecture,
    product(b,d,l),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',product_16) ).

cnf(l_is_defined,hypothesis,
    defined(l),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',l_is_defined) ).

cnf(not_product_17,negated_conjecture,
    ~ product(k,multiplicative_inverse(l),u),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',not_product_17) ).

cnf(distributivity_1,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X6)
    | ~ product(X6,X7,X3)
    | ~ product(X4,X7,X1)
    | ~ product(X5,X7,X2) ),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',distributivity_1) ).

cnf(s_is_defined,hypothesis,
    defined(s),
    file('/export/starexec/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p',s_is_defined) ).

cnf(c_0_35,axiom,
    ( product(X1,X2,X3)
    | ~ product(X2,X1,X3) ),
    commutativity_multiplication ).

cnf(c_0_36,negated_conjecture,
    product(c,multiplicative_inverse(d),t),
    product_14 ).

cnf(c_0_37,axiom,
    ( product(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ product(X5,X2,X6)
    | ~ product(X4,X6,X3) ),
    associativity_multiplication_2 ).

cnf(c_0_38,negated_conjecture,
    product(multiplicative_inverse(d),c,t),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_39,axiom,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ product(X4,X6,X2)
    | ~ product(X5,X6,X3) ),
    associativity_multiplication_1 ).

cnf(c_0_40,axiom,
    ( product(multiplicative_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_multiplication ).

cnf(c_0_41,negated_conjecture,
    ( product(X1,c,X2)
    | ~ product(X3,multiplicative_inverse(d),X1)
    | ~ product(X3,t,X2) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_42,axiom,
    ( product(X1,X2,multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    totality_of_multiplication ).

cnf(c_0_43,hypothesis,
    defined(t),
    t_is_defined ).

cnf(c_0_44,axiom,
    ( product(multiplicative_inverse(X1),X1,multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_multiplication ).

cnf(c_0_45,plain,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,multiplicative_identity)
    | ~ product(X4,X3,X2)
    | ~ defined(X3) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_46,axiom,
    defined(multiplicative_identity),
    well_definedness_of_multiplicative_identity ).

cnf(c_0_47,negated_conjecture,
    ( product(X1,c,multiply(X2,t))
    | ~ product(X2,multiplicative_inverse(d),X1)
    | ~ defined(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).

cnf(c_0_48,plain,
    ( product(X1,multiplicative_inverse(X1),multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_35,c_0_44]) ).

cnf(c_0_49,hypothesis,
    defined(d),
    d_is_defined ).

cnf(c_0_50,negated_conjecture,
    ~ sum(additive_identity,d,additive_identity),
    not_sum_11 ).

cnf(c_0_51,negated_conjecture,
    product(s,t,u),
    product_12 ).

cnf(c_0_52,plain,
    ( product(multiplicative_identity,X1,X2)
    | ~ product(multiplicative_identity,X2,X1)
    | ~ defined(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_40]),c_0_46])]) ).

cnf(c_0_53,negated_conjecture,
    product(multiplicative_identity,c,multiply(d,t)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]),c_0_50]) ).

cnf(c_0_54,hypothesis,
    defined(c),
    c_is_defined ).

cnf(c_0_55,axiom,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(X3,X4)
    | ~ sum(X3,X5,X1)
    | ~ sum(X4,X5,X2) ),
    compatibility_of_order_relation_and_addition ).

cnf(c_0_56,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_addition ).

cnf(c_0_57,axiom,
    ( less_or_equal(X1,X2)
    | less_or_equal(X2,X1)
    | ~ defined(X1)
    | ~ defined(X2) ),
    totality_of_order_relation ).

cnf(c_0_58,negated_conjecture,
    product(t,s,u),
    inference(spm,[status(thm)],[c_0_35,c_0_51]) ).

cnf(c_0_59,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,multiply(X5,X2),X3)
    | ~ product(X4,X5,X1)
    | ~ defined(X2)
    | ~ defined(X5) ),
    inference(spm,[status(thm)],[c_0_37,c_0_42]) ).

cnf(c_0_60,negated_conjecture,
    product(multiplicative_identity,multiply(d,t),c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]) ).

cnf(c_0_61,plain,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(X3,additive_identity)
    | ~ defined(X2)
    | ~ sum(X3,X2,X1) ),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_62,plain,
    ( less_or_equal(X1,X1)
    | ~ defined(X1) ),
    inference(ef,[status(thm)],[c_0_57]) ).

cnf(c_0_63,axiom,
    defined(additive_identity),
    well_definedness_of_additive_identity ).

cnf(c_0_64,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    commutativity_addition ).

cnf(c_0_65,negated_conjecture,
    ( product(X1,s,X2)
    | ~ product(X3,u,X2)
    | ~ product(X3,t,X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_58]) ).

cnf(c_0_66,hypothesis,
    defined(u),
    u_is_defined ).

cnf(c_0_67,negated_conjecture,
    ( product(X1,t,c)
    | ~ product(multiplicative_identity,d,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_43]),c_0_49])]) ).

cnf(c_0_68,plain,
    ( less_or_equal(X1,X2)
    | ~ defined(X2)
    | ~ sum(additive_identity,X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).

cnf(c_0_69,plain,
    ( sum(X1,additive_identity,X1)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_64,c_0_56]) ).

cnf(c_0_70,negated_conjecture,
    ( product(X1,s,multiply(X2,u))
    | ~ product(X2,t,X1)
    | ~ defined(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_42]),c_0_66])]) ).

cnf(c_0_71,negated_conjecture,
    product(d,t,c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_40]),c_0_49])]) ).

cnf(c_0_72,axiom,
    ( sum(additive_identity,X1,X2)
    | ~ less_or_equal(X1,X2)
    | ~ less_or_equal(X2,X1) ),
    antisymmetry_of_order_relation ).

cnf(c_0_73,plain,
    less_or_equal(additive_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_63])]) ).

cnf(c_0_74,negated_conjecture,
    product(a,c,k),
    product_15 ).

cnf(c_0_75,negated_conjecture,
    product(c,s,multiply(d,u)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_49])]) ).

cnf(c_0_76,negated_conjecture,
    product(a,multiplicative_inverse(b),s),
    product_13 ).

cnf(c_0_77,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ sum(X5,X2,X6)
    | ~ sum(X4,X6,X3) ),
    associativity_addition_2 ).

cnf(c_0_78,plain,
    sum(additive_identity,additive_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_73])]) ).

cnf(c_0_79,negated_conjecture,
    ( product(X1,X2,k)
    | ~ product(X3,c,X2)
    | ~ product(X1,X3,a) ),
    inference(spm,[status(thm)],[c_0_39,c_0_74]) ).

cnf(c_0_80,negated_conjecture,
    product(s,c,multiply(d,u)),
    inference(spm,[status(thm)],[c_0_35,c_0_75]) ).

cnf(c_0_81,plain,
    ( product(X1,X2,X3)
    | sum(additive_identity,X1,additive_identity)
    | ~ product(multiplicative_inverse(X1),X3,X2)
    | ~ defined(X3)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_45,c_0_48]) ).

cnf(c_0_82,negated_conjecture,
    product(multiplicative_inverse(b),a,s),
    inference(spm,[status(thm)],[c_0_35,c_0_76]) ).

cnf(c_0_83,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_84,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_85,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    not_sum_10 ).

cnf(c_0_86,plain,
    ( sum(X1,additive_identity,X2)
    | ~ sum(X3,additive_identity,X2)
    | ~ sum(X3,additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_87,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_addition ).

cnf(c_0_88,negated_conjecture,
    ( product(X1,multiply(d,u),k)
    | ~ product(X1,s,a) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_89,negated_conjecture,
    product(b,s,a),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_84])]),c_0_85]) ).

cnf(c_0_90,plain,
    ( sum(X1,additive_identity,additive_identity)
    | ~ sum(additive_inverse(additive_identity),additive_identity,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_63])]) ).

cnf(c_0_91,negated_conjecture,
    product(b,multiply(d,u),k),
    inference(spm,[status(thm)],[c_0_88,c_0_89]) ).

cnf(c_0_92,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    associativity_addition_1 ).

cnf(c_0_93,plain,
    ( sum(additive_inverse(additive_identity),additive_identity,additive_identity)
    | ~ defined(additive_inverse(additive_identity)) ),
    inference(spm,[status(thm)],[c_0_90,c_0_69]) ).

cnf(c_0_94,axiom,
    ( defined(additive_inverse(X1))
    | ~ defined(X1) ),
    well_definedness_of_additive_inverse ).

cnf(c_0_95,axiom,
    ( product(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ product(X4,X2,X6)
    | ~ product(X5,X2,X7)
    | ~ sum(X6,X7,X3) ),
    distributivity_2 ).

cnf(c_0_96,plain,
    ( sum(X1,additive_identity,X2)
    | ~ defined(X2)
    | ~ sum(X2,additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_86,c_0_69]) ).

cnf(c_0_97,negated_conjecture,
    ( product(X1,u,k)
    | ~ product(b,d,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_91]),c_0_66]),c_0_49])]) ).

cnf(c_0_98,negated_conjecture,
    product(b,d,l),
    product_16 ).

cnf(c_0_99,plain,
    ( sum(X1,X2,X3)
    | ~ defined(X3)
    | ~ sum(X1,X4,additive_identity)
    | ~ sum(X4,X3,X2) ),
    inference(spm,[status(thm)],[c_0_92,c_0_56]) ).

cnf(c_0_100,plain,
    sum(additive_inverse(additive_identity),additive_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_63])]) ).

cnf(c_0_101,plain,
    ( product(X1,X2,additive_identity)
    | ~ product(X3,X2,additive_identity)
    | ~ product(X4,X2,additive_identity)
    | ~ sum(X4,X3,X1) ),
    inference(spm,[status(thm)],[c_0_95,c_0_78]) ).

cnf(c_0_102,plain,
    ( product(X1,multiplicative_identity,X1)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_35,c_0_40]) ).

cnf(c_0_103,plain,
    ( sum(additive_identity,additive_identity,additive_inverse(additive_identity))
    | ~ defined(additive_inverse(additive_identity)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_87]),c_0_63])]) ).

cnf(c_0_104,plain,
    ( product(multiplicative_inverse(X1),X2,X3)
    | sum(additive_identity,X1,additive_identity)
    | ~ product(X1,X3,X2)
    | ~ defined(X3)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_45,c_0_44]) ).

cnf(c_0_105,negated_conjecture,
    product(l,u,k),
    inference(spm,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_106,hypothesis,
    defined(l),
    l_is_defined ).

cnf(c_0_107,plain,
    ( sum(additive_inverse(additive_identity),X1,X2)
    | ~ defined(X2)
    | ~ sum(additive_identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_100]) ).

cnf(c_0_108,plain,
    ( product(X1,multiplicative_identity,additive_identity)
    | ~ product(X2,multiplicative_identity,additive_identity)
    | ~ sum(X2,additive_identity,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_63])]) ).

cnf(c_0_109,plain,
    sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_94]),c_0_63])]) ).

cnf(c_0_110,negated_conjecture,
    ( product(multiplicative_inverse(l),k,u)
    | sum(additive_identity,l,additive_identity) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_66]),c_0_106])]) ).

cnf(c_0_111,negated_conjecture,
    ~ product(k,multiplicative_inverse(l),u),
    not_product_17 ).

cnf(c_0_112,plain,
    ( sum(additive_inverse(additive_identity),X1,X1)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_107,c_0_56]) ).

cnf(c_0_113,plain,
    ( product(additive_inverse(additive_identity),multiplicative_identity,additive_identity)
    | ~ product(additive_identity,multiplicative_identity,additive_identity) ),
    inference(spm,[status(thm)],[c_0_108,c_0_109]) ).

cnf(c_0_114,plain,
    ( sum(additive_identity,X1,X2)
    | ~ defined(X2)
    | ~ sum(additive_identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_78]) ).

cnf(c_0_115,negated_conjecture,
    sum(additive_identity,l,additive_identity),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_110]),c_0_111]) ).

cnf(c_0_116,plain,
    ( product(additive_identity,multiplicative_identity,additive_identity)
    | ~ product(additive_inverse(additive_identity),multiplicative_identity,additive_identity) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_112]),c_0_63])]) ).

cnf(c_0_117,plain,
    product(additive_inverse(additive_identity),multiplicative_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_102]),c_0_63])]) ).

cnf(c_0_118,negated_conjecture,
    sum(additive_identity,additive_identity,l),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_106])]) ).

cnf(c_0_119,plain,
    product(additive_identity,multiplicative_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).

cnf(c_0_120,negated_conjecture,
    product(l,multiplicative_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_118]),c_0_119])]) ).

cnf(c_0_121,negated_conjecture,
    ( product(X1,d,X2)
    | ~ product(X3,l,X2)
    | ~ product(X3,b,X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_98]) ).

cnf(c_0_122,negated_conjecture,
    product(multiplicative_identity,l,additive_identity),
    inference(spm,[status(thm)],[c_0_35,c_0_120]) ).

cnf(c_0_123,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X6)
    | ~ product(X6,X7,X3)
    | ~ product(X4,X7,X1)
    | ~ product(X5,X7,X2) ),
    distributivity_1 ).

cnf(c_0_124,negated_conjecture,
    ( product(X1,d,additive_identity)
    | ~ product(multiplicative_identity,b,X1) ),
    inference(spm,[status(thm)],[c_0_121,c_0_122]) ).

cnf(c_0_125,negated_conjecture,
    ( sum(X1,X2,s)
    | ~ product(X3,multiplicative_inverse(b),X2)
    | ~ product(X4,multiplicative_inverse(b),X1)
    | ~ sum(X4,X3,a) ),
    inference(spm,[status(thm)],[c_0_123,c_0_76]) ).

cnf(c_0_126,negated_conjecture,
    product(b,d,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_40]),c_0_84])]) ).

cnf(c_0_127,plain,
    ( sum(X1,additive_inverse(X1),additive_identity)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_64,c_0_87]) ).

cnf(c_0_128,negated_conjecture,
    ( sum(X1,X2,s)
    | ~ product(a,multiplicative_inverse(b),X2)
    | ~ product(additive_identity,multiplicative_inverse(b),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_56]),c_0_83])]) ).

cnf(c_0_129,negated_conjecture,
    product(multiplicative_inverse(b),additive_identity,d),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_126]),c_0_49]),c_0_84])]),c_0_85]) ).

cnf(c_0_130,plain,
    ( sum(X1,X2,additive_identity)
    | ~ defined(X3)
    | ~ sum(X4,additive_inverse(X3),X2)
    | ~ sum(X1,X4,X3) ),
    inference(spm,[status(thm)],[c_0_92,c_0_127]) ).

cnf(c_0_131,negated_conjecture,
    ( sum(X1,s,s)
    | ~ product(additive_identity,multiplicative_inverse(b),X1) ),
    inference(spm,[status(thm)],[c_0_128,c_0_76]) ).

cnf(c_0_132,negated_conjecture,
    product(additive_identity,multiplicative_inverse(b),d),
    inference(spm,[status(thm)],[c_0_35,c_0_129]) ).

cnf(c_0_133,plain,
    ( sum(X1,additive_identity,additive_identity)
    | ~ defined(X2)
    | ~ sum(X1,X2,X2) ),
    inference(spm,[status(thm)],[c_0_130,c_0_127]) ).

cnf(c_0_134,negated_conjecture,
    sum(d,s,s),
    inference(spm,[status(thm)],[c_0_131,c_0_132]) ).

cnf(c_0_135,hypothesis,
    defined(s),
    s_is_defined ).

cnf(c_0_136,negated_conjecture,
    sum(d,additive_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135])]) ).

cnf(c_0_137,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_136]),c_0_50]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem    : FLD048-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.08/0.15  % Command    : run_E %s %d THM
% 0.15/0.37  % Computer : n027.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 2400
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Mon Oct  2 23:28:30 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.22/0.52  Running first-order theorem proving
% 0.22/0.52  Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.KLO79ZdSYc/E---3.1_16657.p
% 10.74/1.89  # Version: 3.1pre001
% 10.74/1.89  # Preprocessing class: FSMSSMSMSSSNFFN.
% 10.74/1.89  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.74/1.89  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 10.74/1.89  # Starting new_bool_3 with 300s (1) cores
% 10.74/1.89  # Starting new_bool_1 with 300s (1) cores
% 10.74/1.89  # Starting sh5l with 300s (1) cores
% 10.74/1.89  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 16735 completed with status 0
% 10.74/1.89  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 10.74/1.89  # Preprocessing class: FSMSSMSMSSSNFFN.
% 10.74/1.89  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.74/1.89  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 10.74/1.89  # No SInE strategy applied
% 10.74/1.89  # Search class: FGUNF-FFMM21-SFFFFFNN
% 10.74/1.89  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 10.74/1.89  # Starting G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with 589s (1) cores
% 10.74/1.89  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 10.74/1.89  # Starting new_bool_3 with 269s (1) cores
% 10.74/1.89  # Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 10.74/1.89  # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 10.74/1.89  # G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with pid 16739 completed with status 0
% 10.74/1.89  # Result found by G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S
% 10.74/1.89  # Preprocessing class: FSMSSMSMSSSNFFN.
% 10.74/1.89  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.74/1.89  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 10.74/1.89  # No SInE strategy applied
% 10.74/1.89  # Search class: FGUNF-FFMM21-SFFFFFNN
% 10.74/1.89  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 10.74/1.89  # Starting G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with 589s (1) cores
% 10.74/1.89  # Preprocessing time       : 0.001 s
% 10.74/1.89  
% 10.74/1.89  # Proof found!
% 10.74/1.89  # SZS status Unsatisfiable
% 10.74/1.89  # SZS output start CNFRefutation
% See solution above
% 10.74/1.90  # Parsed axioms                        : 43
% 10.74/1.90  # Removed by relevancy pruning/SinE    : 0
% 10.74/1.90  # Initial clauses                      : 43
% 10.74/1.90  # Removed in clause preprocessing      : 0
% 10.74/1.90  # Initial clauses in saturation        : 43
% 10.74/1.90  # Processed clauses                    : 7932
% 10.74/1.90  # ...of these trivial                  : 797
% 10.74/1.90  # ...subsumed                          : 1130
% 10.74/1.90  # ...remaining for further processing  : 6005
% 10.74/1.90  # Other redundant clauses eliminated   : 0
% 10.74/1.90  # Clauses deleted for lack of memory   : 0
% 10.74/1.90  # Backward-subsumed                    : 20
% 10.74/1.90  # Backward-rewritten                   : 232
% 10.74/1.90  # Generated clauses                    : 61445
% 10.74/1.90  # ...of the previous two non-redundant : 53543
% 10.74/1.90  # ...aggressively subsumed             : 0
% 10.74/1.90  # Contextual simplify-reflections      : 19
% 10.74/1.90  # Paramodulations                      : 61435
% 10.74/1.90  # Factorizations                       : 10
% 10.74/1.90  # NegExts                              : 0
% 10.74/1.90  # Equation resolutions                 : 0
% 10.74/1.90  # Total rewrite steps                  : 39155
% 10.74/1.90  # Propositional unsat checks           : 0
% 10.74/1.90  #    Propositional check models        : 0
% 10.74/1.90  #    Propositional check unsatisfiable : 0
% 10.74/1.90  #    Propositional clauses             : 0
% 10.74/1.90  #    Propositional clauses after purity: 0
% 10.74/1.90  #    Propositional unsat core size     : 0
% 10.74/1.90  #    Propositional preprocessing time  : 0.000
% 10.74/1.90  #    Propositional encoding time       : 0.000
% 10.74/1.90  #    Propositional solver time         : 0.000
% 10.74/1.90  #    Success case prop preproc time    : 0.000
% 10.74/1.90  #    Success case prop encoding time   : 0.000
% 10.74/1.90  #    Success case prop solver time     : 0.000
% 10.74/1.90  # Current number of processed clauses  : 5753
% 10.74/1.90  #    Positive orientable unit clauses  : 1012
% 10.74/1.90  #    Positive unorientable unit clauses: 0
% 10.74/1.90  #    Negative unit clauses             : 4
% 10.74/1.90  #    Non-unit-clauses                  : 4737
% 10.74/1.90  # Current number of unprocessed clauses: 45651
% 10.74/1.90  # ...number of literals in the above   : 113662
% 10.74/1.90  # Current number of archived formulas  : 0
% 10.74/1.90  # Current number of archived clauses   : 252
% 10.74/1.90  # Clause-clause subsumption calls (NU) : 2279337
% 10.74/1.90  # Rec. Clause-clause subsumption calls : 1615052
% 10.74/1.90  # Non-unit clause-clause subsumptions  : 1169
% 10.74/1.90  # Unit Clause-clause subsumption calls : 275105
% 10.74/1.90  # Rewrite failures with RHS unbound    : 0
% 10.74/1.90  # BW rewrite match attempts            : 1281
% 10.74/1.90  # BW rewrite match successes           : 74
% 10.74/1.90  # Condensation attempts                : 0
% 10.74/1.90  # Condensation successes               : 0
% 10.74/1.90  # Termbank termtop insertions          : 941076
% 10.74/1.90  
% 10.74/1.90  # -------------------------------------------------
% 10.74/1.90  # User time                : 1.289 s
% 10.74/1.90  # System time              : 0.034 s
% 10.74/1.90  # Total time               : 1.323 s
% 10.74/1.90  # Maximum resident set size: 1676 pages
% 10.74/1.90  
% 10.74/1.90  # -------------------------------------------------
% 10.74/1.90  # User time                : 6.493 s
% 10.74/1.90  # System time              : 0.163 s
% 10.74/1.90  # Total time               : 6.656 s
% 10.74/1.90  # Maximum resident set size: 1732 pages
% 10.74/1.90  % E---3.1 exiting
% 10.74/1.90  % E---3.1 exiting
%------------------------------------------------------------------------------