TSTP Solution File: FLD052-4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD052-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n007.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 : Wed Aug 30 22:27:39 EDT 2023
% Result : Unsatisfiable 2.55s 2.71s
% Output : CNFRefutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 63
% Syntax : Number of formulae : 494 ( 258 unt; 22 typ; 0 def)
% Number of atoms : 855 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 760 ( 377 ~; 383 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-2 aty)
% Number of variables : 473 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_23,type,
additive_identity: $i ).
tff(decl_24,type,
defined: $i > $o ).
tff(decl_25,type,
additive_inverse: $i > $i ).
tff(decl_26,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
multiplicative_identity: $i ).
tff(decl_28,type,
multiplicative_inverse: $i > $i ).
tff(decl_29,type,
add: ( $i * $i ) > $i ).
tff(decl_30,type,
multiply: ( $i * $i ) > $i ).
tff(decl_31,type,
less_or_equal: ( $i * $i ) > $o ).
tff(decl_32,type,
a: $i ).
tff(decl_33,type,
b: $i ).
tff(decl_34,type,
c: $i ).
tff(decl_35,type,
d: $i ).
tff(decl_36,type,
u: $i ).
tff(decl_37,type,
v: $i ).
tff(decl_38,type,
k: $i ).
tff(decl_39,type,
l: $i ).
tff(decl_40,type,
p: $i ).
tff(decl_41,type,
q: $i ).
tff(decl_42,type,
s: $i ).
tff(decl_43,type,
t: $i ).
cnf(associativity_multiplication_1,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(product_19,negated_conjecture,
product(b,c,q),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_19) ).
cnf(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(product_21,negated_conjecture,
product(b,d,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_21) ).
cnf(totality_of_multiplication,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(l_is_defined,hypothesis,
defined(l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_is_defined) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
cnf(product_18,negated_conjecture,
product(a,d,p),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_18) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_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/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
cnf(not_sum_14,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_14) ).
cnf(product_16,negated_conjecture,
product(c,multiplicative_inverse(d),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_16) ).
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/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(sum_20,negated_conjecture,
sum(p,q,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_20) ).
cnf(not_sum_13,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_13) ).
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/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',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/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(product_15,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_15) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(sum_17,negated_conjecture,
sum(s,t,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_17) ).
cnf(associativity_addition_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(antisymmetry_of_order_relation,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
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/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(q_is_defined,hypothesis,
defined(q),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_is_defined) ).
cnf(p_is_defined,hypothesis,
defined(p),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_is_defined) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
cnf(associativity_addition_2,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(totality_of_addition,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
cnf(not_product_22,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_22) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(s_is_defined,hypothesis,
defined(s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_is_defined) ).
cnf(t_is_defined,hypothesis,
defined(t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_is_defined) ).
cnf(k_is_defined,hypothesis,
defined(k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_is_defined) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(c_0_41,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_42,negated_conjecture,
product(b,c,q),
product_19 ).
cnf(c_0_43,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_44,negated_conjecture,
product(b,d,l),
product_21 ).
cnf(c_0_45,negated_conjecture,
( product(X1,X2,q)
| ~ product(X3,c,X2)
| ~ product(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( product(X1,d,X2)
| ~ product(X3,l,X2)
| ~ product(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_48,hypothesis,
defined(l),
l_is_defined ).
cnf(c_0_49,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_50,negated_conjecture,
( product(X1,q,q)
| ~ product(X1,b,b) ),
inference(spm,[status(thm)],[c_0_45,c_0_42]) ).
cnf(c_0_51,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_52,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_53,negated_conjecture,
( product(X1,d,multiply(X2,l))
| ~ product(X2,b,X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_54,negated_conjecture,
product(c,b,q),
inference(spm,[status(thm)],[c_0_49,c_0_42]) ).
cnf(c_0_55,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_56,negated_conjecture,
product(a,d,p),
product_18 ).
cnf(c_0_57,negated_conjecture,
product(d,b,l),
inference(spm,[status(thm)],[c_0_49,c_0_44]) ).
cnf(c_0_58,negated_conjecture,
product(multiplicative_identity,q,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_59,negated_conjecture,
product(q,d,multiply(c,l)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
cnf(c_0_60,negated_conjecture,
( product(X1,X2,p)
| ~ product(X3,d,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_41,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
( product(X1,b,X2)
| ~ product(X3,l,X2)
| ~ product(X3,d,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
( product(X1,X2,q)
| ~ product(X3,q,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_41,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
product(d,q,multiply(c,l)),
inference(spm,[status(thm)],[c_0_49,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
( product(X1,p,p)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_60,c_0_56]) ).
cnf(c_0_65,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_66,negated_conjecture,
( product(X1,b,multiply(X2,l))
| ~ product(X2,d,X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_47]),c_0_48])]) ).
cnf(c_0_67,negated_conjecture,
( product(X1,multiply(c,l),q)
| ~ product(X1,d,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_69,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_70,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
not_sum_14 ).
cnf(c_0_71,negated_conjecture,
product(multiplicative_identity,p,p),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_51]),c_0_65])]) ).
cnf(c_0_72,negated_conjecture,
product(p,b,multiply(a,l)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_56]),c_0_65])]) ).
cnf(c_0_73,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_43,c_0_47]) ).
cnf(c_0_74,negated_conjecture,
product(multiplicative_inverse(d),multiply(c,l),q),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]),c_0_70]) ).
cnf(c_0_75,negated_conjecture,
product(c,multiplicative_inverse(d),t),
product_16 ).
cnf(c_0_76,negated_conjecture,
( product(X1,X2,p)
| ~ product(X3,p,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_41,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
product(b,p,multiply(a,l)),
inference(spm,[status(thm)],[c_0_49,c_0_72]) ).
cnf(c_0_78,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_79,negated_conjecture,
sum(p,q,k),
sum_20 ).
cnf(c_0_80,negated_conjecture,
( product(X1,l,q)
| ~ product(multiplicative_inverse(d),c,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_48]),c_0_55])]) ).
cnf(c_0_81,negated_conjecture,
product(multiplicative_inverse(d),c,t),
inference(spm,[status(thm)],[c_0_49,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
( product(X1,multiply(a,l),p)
| ~ product(X1,b,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
not_sum_13 ).
cnf(c_0_84,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_85,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_86,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_87,negated_conjecture,
( product(X1,X2,k)
| ~ product(X3,X2,q)
| ~ product(X4,X2,p)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_88,negated_conjecture,
product(t,l,q),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
product(multiplicative_inverse(b),multiply(a,l),p),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_68]),c_0_52])]),c_0_83]) ).
cnf(c_0_90,negated_conjecture,
product(a,multiplicative_inverse(b),s),
product_15 ).
cnf(c_0_91,plain,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,additive_identity)
| ~ defined(X2)
| ~ sum(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_92,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_86]) ).
cnf(c_0_93,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_94,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_95,negated_conjecture,
( product(X1,l,k)
| ~ product(X2,l,p)
| ~ sum(X2,t,X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,negated_conjecture,
sum(s,t,u),
sum_17 ).
cnf(c_0_97,negated_conjecture,
( product(X1,l,p)
| ~ product(multiplicative_inverse(b),a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_89]),c_0_48]),c_0_65])]) ).
cnf(c_0_98,negated_conjecture,
product(multiplicative_inverse(b),a,s),
inference(spm,[status(thm)],[c_0_49,c_0_90]) ).
cnf(c_0_99,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_100,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_91,c_0_92]),c_0_93])]) ).
cnf(c_0_101,plain,
( sum(X1,additive_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_85]) ).
cnf(c_0_102,negated_conjecture,
( product(u,l,k)
| ~ product(s,l,p) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
product(s,l,p),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_104,plain,
( sum(X1,X2,X3)
| ~ defined(X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_99,c_0_85]) ).
cnf(c_0_105,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_106,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_107,plain,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_93])]) ).
cnf(c_0_108,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,X3,X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_51]) ).
cnf(c_0_109,negated_conjecture,
product(u,l,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_103])]) ).
cnf(c_0_110,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_111,plain,
( sum(additive_inverse(X1),X2,X3)
| ~ defined(X3)
| ~ defined(X1)
| ~ sum(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,hypothesis,
defined(q),
q_is_defined ).
cnf(c_0_113,hypothesis,
defined(p),
p_is_defined ).
cnf(c_0_114,negated_conjecture,
( product(X1,X2,s)
| ~ product(X3,multiplicative_inverse(b),X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_41,c_0_90]) ).
cnf(c_0_115,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_107])]) ).
cnf(c_0_116,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_108,c_0_68]) ).
cnf(c_0_117,negated_conjecture,
product(l,u,k),
inference(spm,[status(thm)],[c_0_49,c_0_109]) ).
cnf(c_0_118,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_119,negated_conjecture,
( sum(X1,X2,t)
| ~ product(X3,multiplicative_inverse(d),X2)
| ~ product(X4,multiplicative_inverse(d),X1)
| ~ sum(X4,X3,c) ),
inference(spm,[status(thm)],[c_0_110,c_0_75]) ).
cnf(c_0_120,plain,
( sum(X1,additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_105]) ).
cnf(c_0_121,negated_conjecture,
sum(additive_inverse(p),k,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_79]),c_0_112]),c_0_113])]) ).
cnf(c_0_122,negated_conjecture,
( product(multiplicative_identity,X1,s)
| ~ product(a,multiplicative_inverse(b),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_51]),c_0_65])]) ).
cnf(c_0_123,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_124,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_addition ).
cnf(c_0_125,plain,
( sum(additive_identity,X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_115]) ).
cnf(c_0_126,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_116,c_0_117]),c_0_118]),c_0_48])]) ).
cnf(c_0_127,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
not_product_22 ).
cnf(c_0_128,negated_conjecture,
( product(X1,X2,t)
| ~ product(X3,multiplicative_inverse(d),X2)
| ~ product(X1,X3,c) ),
inference(spm,[status(thm)],[c_0_41,c_0_75]) ).
cnf(c_0_129,negated_conjecture,
( sum(X1,X2,t)
| ~ product(c,multiplicative_inverse(d),X2)
| ~ product(additive_identity,multiplicative_inverse(d),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_85]),c_0_55])]) ).
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_99,c_0_120]) ).
cnf(c_0_131,negated_conjecture,
sum(k,additive_inverse(p),q),
inference(spm,[status(thm)],[c_0_94,c_0_121]) ).
cnf(c_0_132,negated_conjecture,
sum(q,p,k),
inference(spm,[status(thm)],[c_0_94,c_0_79]) ).
cnf(c_0_133,negated_conjecture,
product(multiplicative_identity,s,s),
inference(spm,[status(thm)],[c_0_122,c_0_90]) ).
cnf(c_0_134,plain,
( sum(X1,X2,X3)
| ~ defined(X2)
| ~ defined(X4)
| ~ sum(X5,add(X4,X2),X3)
| ~ sum(X5,X4,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_135,plain,
( sum(additive_identity,add(additive_identity,X1),X1)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_124]),c_0_93])]) ).
cnf(c_0_136,negated_conjecture,
sum(additive_identity,l,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_126]),c_0_127]) ).
cnf(c_0_137,negated_conjecture,
( product(multiplicative_identity,X1,t)
| ~ product(c,multiplicative_inverse(d),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_51]),c_0_55])]) ).
cnf(c_0_138,negated_conjecture,
( sum(X1,t,t)
| ~ product(additive_identity,multiplicative_inverse(d),X1) ),
inference(spm,[status(thm)],[c_0_129,c_0_75]) ).
cnf(c_0_139,negated_conjecture,
( sum(X1,q,additive_identity)
| ~ sum(X1,k,p) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_113])]) ).
cnf(c_0_140,negated_conjecture,
sum(additive_inverse(q),k,p),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_132]),c_0_113]),c_0_112])]) ).
cnf(c_0_141,negated_conjecture,
( sum(X1,X2,s)
| ~ product(X3,s,X2)
| ~ product(X4,s,X1)
| ~ sum(X4,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_110,c_0_133]) ).
cnf(c_0_142,negated_conjecture,
product(l,s,p),
inference(spm,[status(thm)],[c_0_49,c_0_103]) ).
cnf(c_0_143,plain,
( sum(X1,X2,X2)
| ~ defined(X2)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_93])]) ).
cnf(c_0_144,negated_conjecture,
sum(additive_identity,additive_identity,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_136]),c_0_48])]) ).
cnf(c_0_145,negated_conjecture,
product(multiplicative_identity,t,t),
inference(spm,[status(thm)],[c_0_137,c_0_75]) ).
cnf(c_0_146,negated_conjecture,
( sum(multiply(additive_identity,multiplicative_inverse(d)),t,t)
| ~ defined(multiplicative_inverse(d)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_47]),c_0_93])]) ).
cnf(c_0_147,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_148,plain,
( sum(X1,X2,X3)
| ~ defined(X3)
| ~ defined(X1)
| ~ sum(additive_inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_104,c_0_120]) ).
cnf(c_0_149,negated_conjecture,
sum(additive_inverse(q),q,additive_identity),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_150,negated_conjecture,
( sum(X1,p,s)
| ~ product(X2,s,X1)
| ~ sum(X2,l,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_151,hypothesis,
defined(s),
s_is_defined ).
cnf(c_0_152,negated_conjecture,
( sum(l,X1,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_153,negated_conjecture,
( sum(X1,X2,t)
| ~ product(X3,t,X2)
| ~ product(X4,t,X1)
| ~ sum(X4,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_110,c_0_145]) ).
cnf(c_0_154,negated_conjecture,
product(l,t,q),
inference(spm,[status(thm)],[c_0_49,c_0_88]) ).
cnf(c_0_155,plain,
( sum(X1,additive_identity,X2)
| ~ defined(X3)
| ~ sum(X4,X3,X2)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_101]) ).
cnf(c_0_156,negated_conjecture,
sum(multiply(additive_identity,multiplicative_inverse(d)),t,t),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_69])]),c_0_70]) ).
cnf(c_0_157,hypothesis,
defined(t),
t_is_defined ).
cnf(c_0_158,negated_conjecture,
( sum(X1,p,X2)
| ~ sum(X3,k,X2)
| ~ sum(X3,q,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_132]) ).
cnf(c_0_159,hypothesis,
defined(k),
k_is_defined ).
cnf(c_0_160,negated_conjecture,
sum(q,additive_identity,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_112])]) ).
cnf(c_0_161,negated_conjecture,
( sum(s,p,s)
| ~ sum(multiplicative_identity,l,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_51]),c_0_151])]) ).
cnf(c_0_162,negated_conjecture,
( sum(X1,l,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_152]) ).
cnf(c_0_163,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_164,negated_conjecture,
( sum(X1,q,t)
| ~ product(X2,t,X1)
| ~ sum(X2,l,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_165,negated_conjecture,
sum(k,additive_inverse(q),p),
inference(spm,[status(thm)],[c_0_94,c_0_140]) ).
cnf(c_0_166,negated_conjecture,
( sum(X1,additive_identity,t)
| ~ sum(multiply(additive_identity,multiplicative_inverse(d)),t,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157])]) ).
cnf(c_0_167,negated_conjecture,
( sum(X1,p,k)
| ~ sum(additive_identity,q,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_85]),c_0_159])]) ).
cnf(c_0_168,plain,
( sum(X1,X2,add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_124]) ).
cnf(c_0_169,negated_conjecture,
sum(additive_identity,q,q),
inference(spm,[status(thm)],[c_0_94,c_0_160]) ).
cnf(c_0_170,negated_conjecture,
sum(s,p,s),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163])]) ).
cnf(c_0_171,negated_conjecture,
( sum(t,q,t)
| ~ sum(multiplicative_identity,l,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_51]),c_0_157])]) ).
cnf(c_0_172,negated_conjecture,
( sum(X1,p,additive_identity)
| ~ sum(X1,k,q) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_165]),c_0_112])]) ).
cnf(c_0_173,negated_conjecture,
sum(t,additive_identity,t),
inference(spm,[status(thm)],[c_0_166,c_0_156]) ).
cnf(c_0_174,negated_conjecture,
sum(add(q,additive_identity),p,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_93]),c_0_112])]) ).
cnf(c_0_175,negated_conjecture,
( sum(X1,X2,q)
| ~ sum(X3,q,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_99,c_0_169]) ).
cnf(c_0_176,plain,
( sum(X1,additive_identity,additive_identity)
| ~ defined(X2)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_130,c_0_120]) ).
cnf(c_0_177,negated_conjecture,
sum(p,s,s),
inference(spm,[status(thm)],[c_0_94,c_0_170]) ).
cnf(c_0_178,negated_conjecture,
sum(t,q,t),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_162]),c_0_163])]) ).
cnf(c_0_179,negated_conjecture,
sum(additive_inverse(p),p,additive_identity),
inference(spm,[status(thm)],[c_0_172,c_0_121]) ).
cnf(c_0_180,negated_conjecture,
sum(additive_identity,t,t),
inference(spm,[status(thm)],[c_0_94,c_0_173]) ).
cnf(c_0_181,negated_conjecture,
sum(p,add(q,additive_identity),k),
inference(spm,[status(thm)],[c_0_94,c_0_174]) ).
cnf(c_0_182,negated_conjecture,
( sum(X1,q,q)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_85]),c_0_112])]) ).
cnf(c_0_183,negated_conjecture,
sum(p,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_151])]) ).
cnf(c_0_184,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_115]) ).
cnf(c_0_185,negated_conjecture,
sum(q,t,t),
inference(spm,[status(thm)],[c_0_94,c_0_178]) ).
cnf(c_0_186,negated_conjecture,
sum(p,additive_identity,p),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_179]),c_0_113])]) ).
cnf(c_0_187,negated_conjecture,
( sum(X1,t,X2)
| ~ sum(X3,t,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_180]) ).
cnf(c_0_188,negated_conjecture,
( sum(X1,additive_identity,k)
| ~ sum(p,q,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_181]),c_0_93]),c_0_112])]) ).
cnf(c_0_189,negated_conjecture,
sum(p,q,q),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_190,negated_conjecture,
( sum(X1,X2,q)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,q) ),
inference(spm,[status(thm)],[c_0_99,c_0_160]) ).
cnf(c_0_191,plain,
( sum(X1,additive_identity,X2)
| ~ defined(X2)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_184,c_0_101]) ).
cnf(c_0_192,negated_conjecture,
sum(q,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_185]),c_0_157])]) ).
cnf(c_0_193,negated_conjecture,
sum(additive_identity,p,p),
inference(spm,[status(thm)],[c_0_94,c_0_186]) ).
cnf(c_0_194,negated_conjecture,
( sum(X1,t,t)
| ~ sum(q,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_187,c_0_185]) ).
cnf(c_0_195,negated_conjecture,
sum(q,additive_identity,k),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
cnf(c_0_196,negated_conjecture,
( sum(X1,l,q)
| ~ sum(X1,additive_identity,q) ),
inference(spm,[status(thm)],[c_0_190,c_0_144]) ).
cnf(c_0_197,negated_conjecture,
sum(additive_identity,additive_identity,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_112])]) ).
cnf(c_0_198,negated_conjecture,
( sum(X1,X2,p)
| ~ sum(X3,p,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_99,c_0_193]) ).
cnf(c_0_199,negated_conjecture,
sum(k,t,t),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_200,negated_conjecture,
sum(additive_identity,l,q),
inference(spm,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_201,negated_conjecture,
( sum(X1,p,p)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_85]),c_0_113])]) ).
cnf(c_0_202,negated_conjecture,
sum(k,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_199]),c_0_157])]) ).
cnf(c_0_203,negated_conjecture,
( product(X1,X2,l)
| ~ product(X3,d,X2)
| ~ product(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_41,c_0_44]) ).
cnf(c_0_204,negated_conjecture,
( sum(X1,q,X2)
| ~ sum(X3,q,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_169]) ).
cnf(c_0_205,negated_conjecture,
sum(additive_identity,q,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_200]),c_0_48])]) ).
cnf(c_0_206,negated_conjecture,
sum(k,p,p),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_207,negated_conjecture,
( product(X1,l,l)
| ~ product(X1,b,b) ),
inference(spm,[status(thm)],[c_0_203,c_0_44]) ).
cnf(c_0_208,plain,
( product(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_51]) ).
cnf(c_0_209,negated_conjecture,
product(q,multiplicative_identity,q),
inference(spm,[status(thm)],[c_0_49,c_0_58]) ).
cnf(c_0_210,negated_conjecture,
sum(additive_identity,additive_identity,p),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_183]),c_0_113])]) ).
cnf(c_0_211,negated_conjecture,
( sum(X1,q,l)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_204,c_0_205]) ).
cnf(c_0_212,negated_conjecture,
sum(p,k,p),
inference(spm,[status(thm)],[c_0_94,c_0_206]) ).
cnf(c_0_213,negated_conjecture,
product(multiplicative_identity,l,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_51]),c_0_52])]) ).
cnf(c_0_214,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,X4,X2)
| ~ product(X3,X4,X1)
| ~ defined(X4) ),
inference(spm,[status(thm)],[c_0_43,c_0_208]) ).
cnf(c_0_215,negated_conjecture,
( product(X1,multiplicative_identity,k)
| ~ product(X2,multiplicative_identity,p)
| ~ sum(X2,q,X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_209]) ).
cnf(c_0_216,negated_conjecture,
( sum(p,X1,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_143,c_0_210]) ).
cnf(c_0_217,negated_conjecture,
product(p,multiplicative_identity,p),
inference(spm,[status(thm)],[c_0_49,c_0_71]) ).
cnf(c_0_218,negated_conjecture,
sum(p,q,l),
inference(spm,[status(thm)],[c_0_211,c_0_210]) ).
cnf(c_0_219,negated_conjecture,
sum(p,q,additive_identity),
inference(spm,[status(thm)],[c_0_139,c_0_212]) ).
cnf(c_0_220,negated_conjecture,
product(l,multiplicative_identity,l),
inference(spm,[status(thm)],[c_0_49,c_0_213]) ).
cnf(c_0_221,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X2,multiplicative_identity,X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_208]),c_0_163])]) ).
cnf(c_0_222,negated_conjecture,
product(q,multiplicative_identity,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_217]),c_0_112])]) ).
cnf(c_0_223,negated_conjecture,
product(l,multiplicative_identity,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_218]),c_0_217])]) ).
cnf(c_0_224,negated_conjecture,
product(additive_identity,multiplicative_identity,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_219]),c_0_217])]) ).
cnf(c_0_225,negated_conjecture,
( product(X1,X2,l)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,l) ),
inference(spm,[status(thm)],[c_0_41,c_0_220]) ).
cnf(c_0_226,negated_conjecture,
product(k,multiplicative_identity,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_112])]) ).
cnf(c_0_227,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_108,c_0_51]),c_0_163])]) ).
cnf(c_0_228,negated_conjecture,
product(multiplicative_identity,l,k),
inference(spm,[status(thm)],[c_0_49,c_0_223]) ).
cnf(c_0_229,negated_conjecture,
product(multiplicative_identity,additive_identity,k),
inference(spm,[status(thm)],[c_0_49,c_0_224]) ).
cnf(c_0_230,negated_conjecture,
( product(X1,q,l)
| ~ product(X1,k,l) ),
inference(spm,[status(thm)],[c_0_225,c_0_226]) ).
cnf(c_0_231,negated_conjecture,
product(multiplicative_identity,k,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_48])]) ).
cnf(c_0_232,negated_conjecture,
( product(X1,u,X2)
| ~ product(X3,k,X2)
| ~ product(X3,l,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_117]) ).
cnf(c_0_233,negated_conjecture,
product(multiplicative_identity,k,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_229]),c_0_93])]) ).
cnf(c_0_234,negated_conjecture,
product(multiplicative_identity,q,l),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_235,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(multiplicative_identity,X2,X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_214,c_0_51]) ).
cnf(c_0_236,negated_conjecture,
( product(X1,l,X2)
| ~ product(X3,k,X2)
| ~ product(X3,u,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_109]) ).
cnf(c_0_237,negated_conjecture,
( product(X1,u,additive_identity)
| ~ product(multiplicative_identity,l,X1) ),
inference(spm,[status(thm)],[c_0_232,c_0_233]) ).
cnf(c_0_238,negated_conjecture,
product(multiplicative_identity,l,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_234]),c_0_112])]) ).
cnf(c_0_239,negated_conjecture,
( sum(X1,X2,p)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,p) ),
inference(spm,[status(thm)],[c_0_99,c_0_186]) ).
cnf(c_0_240,negated_conjecture,
product(l,multiplicative_identity,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_234]),c_0_112])]) ).
cnf(c_0_241,negated_conjecture,
( product(X1,l,l)
| ~ product(multiplicative_identity,u,X1) ),
inference(spm,[status(thm)],[c_0_236,c_0_231]) ).
cnf(c_0_242,plain,
( product(X1,multiplicative_inverse(X1),multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_68]) ).
cnf(c_0_243,negated_conjecture,
product(q,u,additive_identity),
inference(spm,[status(thm)],[c_0_237,c_0_238]) ).
cnf(c_0_244,negated_conjecture,
sum(q,p,p),
inference(spm,[status(thm)],[c_0_201,c_0_192]) ).
cnf(c_0_245,negated_conjecture,
( sum(X1,l,p)
| ~ sum(X1,additive_identity,p) ),
inference(spm,[status(thm)],[c_0_239,c_0_144]) ).
cnf(c_0_246,negated_conjecture,
( product(X1,X2,p)
| ~ product(X3,s,X2)
| ~ product(X1,X3,l) ),
inference(spm,[status(thm)],[c_0_41,c_0_142]) ).
cnf(c_0_247,negated_conjecture,
( product(X1,q,l)
| ~ product(X1,l,l) ),
inference(spm,[status(thm)],[c_0_225,c_0_240]) ).
cnf(c_0_248,negated_conjecture,
product(u,l,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_51]),c_0_118])]) ).
cnf(c_0_249,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_108,c_0_242]) ).
cnf(c_0_250,negated_conjecture,
( product(X1,t,X2)
| ~ product(X3,q,X2)
| ~ product(X3,l,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_154]) ).
cnf(c_0_251,negated_conjecture,
product(u,q,additive_identity),
inference(spm,[status(thm)],[c_0_49,c_0_243]) ).
cnf(c_0_252,negated_conjecture,
sum(p,q,p),
inference(spm,[status(thm)],[c_0_94,c_0_244]) ).
cnf(c_0_253,negated_conjecture,
sum(additive_identity,l,p),
inference(spm,[status(thm)],[c_0_245,c_0_210]) ).
cnf(c_0_254,negated_conjecture,
( product(X1,s,p)
| ~ product(X1,multiplicative_identity,l) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_51]),c_0_151])]) ).
cnf(c_0_255,negated_conjecture,
product(q,multiplicative_identity,l),
inference(spm,[status(thm)],[c_0_49,c_0_234]) ).
cnf(c_0_256,negated_conjecture,
product(u,q,l),
inference(spm,[status(thm)],[c_0_247,c_0_248]) ).
cnf(c_0_257,negated_conjecture,
product(d,t,c),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_81]),c_0_55]),c_0_69])]),c_0_70]) ).
cnf(c_0_258,negated_conjecture,
( product(X1,t,additive_identity)
| ~ product(u,l,X1) ),
inference(spm,[status(thm)],[c_0_250,c_0_251]) ).
cnf(c_0_259,negated_conjecture,
( product(X1,d,k)
| ~ product(multiplicative_identity,b,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_228]) ).
cnf(c_0_260,negated_conjecture,
product(p,multiplicative_identity,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_252]),c_0_217])]) ).
cnf(c_0_261,negated_conjecture,
( sum(X1,p,X2)
| ~ sum(X3,p,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_193]) ).
cnf(c_0_262,negated_conjecture,
sum(additive_identity,p,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_253]),c_0_48])]) ).
cnf(c_0_263,negated_conjecture,
product(q,s,p),
inference(spm,[status(thm)],[c_0_254,c_0_255]) ).
cnf(c_0_264,negated_conjecture,
( product(X1,t,l)
| ~ product(u,l,X1) ),
inference(spm,[status(thm)],[c_0_250,c_0_256]) ).
cnf(c_0_265,negated_conjecture,
( product(X1,X2,c)
| ~ product(X3,t,X2)
| ~ product(X1,X3,d) ),
inference(spm,[status(thm)],[c_0_41,c_0_257]) ).
cnf(c_0_266,negated_conjecture,
product(k,t,additive_identity),
inference(spm,[status(thm)],[c_0_258,c_0_109]) ).
cnf(c_0_267,negated_conjecture,
product(b,d,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_51]),c_0_52])]) ).
cnf(c_0_268,negated_conjecture,
( product(X1,X2,p)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,p) ),
inference(spm,[status(thm)],[c_0_41,c_0_217]) ).
cnf(c_0_269,negated_conjecture,
product(k,multiplicative_identity,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_223]),c_0_48])]) ).
cnf(c_0_270,negated_conjecture,
product(multiplicative_identity,p,k),
inference(spm,[status(thm)],[c_0_49,c_0_260]) ).
cnf(c_0_271,negated_conjecture,
( sum(X1,p,l)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_261,c_0_262]) ).
cnf(c_0_272,negated_conjecture,
product(s,q,p),
inference(spm,[status(thm)],[c_0_49,c_0_263]) ).
cnf(c_0_273,negated_conjecture,
product(multiplicative_inverse(b),l,d),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_44]),c_0_69]),c_0_52])]),c_0_83]) ).
cnf(c_0_274,negated_conjecture,
product(k,t,l),
inference(spm,[status(thm)],[c_0_264,c_0_109]) ).
cnf(c_0_275,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_110,c_0_90]) ).
cnf(c_0_276,negated_conjecture,
( product(X1,additive_identity,c)
| ~ product(X1,k,d) ),
inference(spm,[status(thm)],[c_0_265,c_0_266]) ).
cnf(c_0_277,negated_conjecture,
product(multiplicative_inverse(b),k,d),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_267]),c_0_69]),c_0_52])]),c_0_83]) ).
cnf(c_0_278,negated_conjecture,
( product(X1,l,p)
| ~ product(X1,k,p) ),
inference(spm,[status(thm)],[c_0_268,c_0_269]) ).
cnf(c_0_279,negated_conjecture,
product(multiplicative_identity,k,p),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_270]),c_0_113])]) ).
cnf(c_0_280,negated_conjecture,
sum(l,p,l),
inference(spm,[status(thm)],[c_0_271,c_0_144]) ).
cnf(c_0_281,negated_conjecture,
( product(X1,t,p)
| ~ product(s,l,X1) ),
inference(spm,[status(thm)],[c_0_250,c_0_272]) ).
cnf(c_0_282,negated_conjecture,
product(l,multiplicative_inverse(b),d),
inference(spm,[status(thm)],[c_0_49,c_0_273]) ).
cnf(c_0_283,negated_conjecture,
( product(X1,l,c)
| ~ product(X1,k,d) ),
inference(spm,[status(thm)],[c_0_265,c_0_274]) ).
cnf(c_0_284,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_275,c_0_85]),c_0_65])]) ).
cnf(c_0_285,negated_conjecture,
product(multiplicative_inverse(b),additive_identity,c),
inference(spm,[status(thm)],[c_0_276,c_0_277]) ).
cnf(c_0_286,negated_conjecture,
( product(X1,t,q)
| ~ product(multiplicative_identity,l,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_51]),c_0_112])]) ).
cnf(c_0_287,negated_conjecture,
product(multiplicative_identity,l,p),
inference(spm,[status(thm)],[c_0_278,c_0_279]) ).
cnf(c_0_288,negated_conjecture,
( product(X1,t,k)
| ~ product(X2,t,p)
| ~ sum(X2,l,X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_154]) ).
cnf(c_0_289,negated_conjecture,
sum(p,l,l),
inference(spm,[status(thm)],[c_0_94,c_0_280]) ).
cnf(c_0_290,negated_conjecture,
product(p,t,p),
inference(spm,[status(thm)],[c_0_281,c_0_103]) ).
cnf(c_0_291,negated_conjecture,
( product(X1,X2,d)
| ~ product(X3,multiplicative_inverse(b),X2)
| ~ product(X1,X3,l) ),
inference(spm,[status(thm)],[c_0_41,c_0_282]) ).
cnf(c_0_292,negated_conjecture,
product(multiplicative_inverse(b),l,c),
inference(spm,[status(thm)],[c_0_283,c_0_277]) ).
cnf(c_0_293,negated_conjecture,
( sum(X1,s,s)
| ~ product(additive_identity,multiplicative_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_284,c_0_90]) ).
cnf(c_0_294,negated_conjecture,
product(additive_identity,multiplicative_inverse(b),c),
inference(spm,[status(thm)],[c_0_49,c_0_285]) ).
cnf(c_0_295,negated_conjecture,
product(p,t,q),
inference(spm,[status(thm)],[c_0_286,c_0_287]) ).
cnf(c_0_296,negated_conjecture,
( product(l,t,k)
| ~ product(p,t,p) ),
inference(spm,[status(thm)],[c_0_288,c_0_289]) ).
cnf(c_0_297,negated_conjecture,
( product(X1,k,p)
| ~ product(X1,p,p) ),
inference(spm,[status(thm)],[c_0_268,c_0_260]) ).
cnf(c_0_298,negated_conjecture,
product(t,p,p),
inference(spm,[status(thm)],[c_0_49,c_0_290]) ).
cnf(c_0_299,negated_conjecture,
( product(X1,multiplicative_inverse(d),X2)
| ~ product(X3,t,X2)
| ~ product(X3,c,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_75]) ).
cnf(c_0_300,negated_conjecture,
( product(multiplicative_identity,X1,d)
| ~ product(l,multiplicative_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_291,c_0_213]) ).
cnf(c_0_301,negated_conjecture,
product(l,multiplicative_inverse(b),c),
inference(spm,[status(thm)],[c_0_49,c_0_292]) ).
cnf(c_0_302,negated_conjecture,
sum(c,s,s),
inference(spm,[status(thm)],[c_0_293,c_0_294]) ).
cnf(c_0_303,negated_conjecture,
( product(X1,s,X2)
| ~ product(X3,p,X2)
| ~ product(X3,l,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_142]) ).
cnf(c_0_304,negated_conjecture,
product(t,p,q),
inference(spm,[status(thm)],[c_0_49,c_0_295]) ).
cnf(c_0_305,negated_conjecture,
product(l,t,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_296,c_0_290])]) ).
cnf(c_0_306,negated_conjecture,
product(t,k,p),
inference(spm,[status(thm)],[c_0_297,c_0_298]) ).
cnf(c_0_307,plain,
( product(X1,X2,X3)
| sum(additive_identity,X2,additive_identity)
| ~ product(X4,multiplicative_inverse(X2),X1)
| ~ product(X4,multiplicative_identity,X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_68]) ).
cnf(c_0_308,negated_conjecture,
( product(X1,multiplicative_inverse(d),t)
| ~ product(multiplicative_identity,c,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_299,c_0_51]),c_0_157])]) ).
cnf(c_0_309,negated_conjecture,
product(multiplicative_identity,c,d),
inference(spm,[status(thm)],[c_0_300,c_0_301]) ).
cnf(c_0_310,negated_conjecture,
sum(c,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_302]),c_0_151])]) ).
cnf(c_0_311,negated_conjecture,
( product(X1,s,q)
| ~ product(t,l,X1) ),
inference(spm,[status(thm)],[c_0_303,c_0_304]) ).
cnf(c_0_312,negated_conjecture,
product(t,l,k),
inference(spm,[status(thm)],[c_0_49,c_0_305]) ).
cnf(c_0_313,negated_conjecture,
product(t,l,p),
inference(spm,[status(thm)],[c_0_278,c_0_306]) ).
cnf(c_0_314,plain,
( product(X1,X2,X3)
| sum(additive_identity,X2,additive_identity)
| ~ product(X3,multiplicative_inverse(X2),X1)
| ~ defined(X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_307,c_0_208]) ).
cnf(c_0_315,negated_conjecture,
product(d,multiplicative_inverse(d),t),
inference(spm,[status(thm)],[c_0_308,c_0_309]) ).
cnf(c_0_316,negated_conjecture,
( product(X1,c,X2)
| ~ product(X3,q,X2)
| ~ product(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_317,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_249,c_0_98]),c_0_65]),c_0_52])]),c_0_83]) ).
cnf(c_0_318,negated_conjecture,
( sum(X1,additive_identity,l)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_144]),c_0_93])]) ).
cnf(c_0_319,negated_conjecture,
sum(additive_identity,additive_identity,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_310]),c_0_55])]) ).
cnf(c_0_320,negated_conjecture,
( product(X1,X2,q)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,q) ),
inference(spm,[status(thm)],[c_0_41,c_0_209]) ).
cnf(c_0_321,negated_conjecture,
product(k,multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_224]),c_0_93])]) ).
cnf(c_0_322,negated_conjecture,
product(k,s,q),
inference(spm,[status(thm)],[c_0_311,c_0_312]) ).
cnf(c_0_323,negated_conjecture,
product(d,a,p),
inference(spm,[status(thm)],[c_0_49,c_0_56]) ).
cnf(c_0_324,negated_conjecture,
( product(X1,b,p)
| ~ product(t,d,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_313]) ).
cnf(c_0_325,negated_conjecture,
product(t,d,d),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_314,c_0_315]),c_0_69])]),c_0_70]) ).
cnf(c_0_326,negated_conjecture,
( product(X1,c,p)
| ~ product(s,b,X1) ),
inference(spm,[status(thm)],[c_0_316,c_0_272]) ).
cnf(c_0_327,negated_conjecture,
product(s,b,a),
inference(spm,[status(thm)],[c_0_49,c_0_317]) ).
cnf(c_0_328,negated_conjecture,
sum(c,additive_identity,l),
inference(spm,[status(thm)],[c_0_318,c_0_319]) ).
cnf(c_0_329,negated_conjecture,
( product(X1,additive_identity,q)
| ~ product(X1,k,q) ),
inference(spm,[status(thm)],[c_0_320,c_0_321]) ).
cnf(c_0_330,negated_conjecture,
product(s,k,q),
inference(spm,[status(thm)],[c_0_49,c_0_322]) ).
cnf(c_0_331,negated_conjecture,
product(multiplicative_inverse(d),p,a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_323]),c_0_65]),c_0_69])]),c_0_70]) ).
cnf(c_0_332,negated_conjecture,
product(d,b,p),
inference(spm,[status(thm)],[c_0_324,c_0_325]) ).
cnf(c_0_333,negated_conjecture,
product(a,c,p),
inference(spm,[status(thm)],[c_0_326,c_0_327]) ).
cnf(c_0_334,negated_conjecture,
( product(X1,X2,k)
| ~ product(X3,X2,p)
| ~ product(X4,X2,q)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_132]) ).
cnf(c_0_335,negated_conjecture,
sum(additive_identity,c,l),
inference(spm,[status(thm)],[c_0_94,c_0_328]) ).
cnf(c_0_336,negated_conjecture,
product(s,additive_identity,q),
inference(spm,[status(thm)],[c_0_329,c_0_330]) ).
cnf(c_0_337,negated_conjecture,
( product(X1,s,X2)
| ~ product(X3,s,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_133]) ).
cnf(c_0_338,negated_conjecture,
( product(X1,multiplicative_identity,a)
| ~ product(multiplicative_inverse(d),p,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_331]),c_0_113])]) ).
cnf(c_0_339,negated_conjecture,
product(multiplicative_inverse(d),p,b),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_332]),c_0_52]),c_0_69])]),c_0_70]) ).
cnf(c_0_340,negated_conjecture,
( product(X1,b,X2)
| ~ product(X3,a,X2)
| ~ product(X3,s,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_327]) ).
cnf(c_0_341,negated_conjecture,
product(c,a,p),
inference(spm,[status(thm)],[c_0_49,c_0_333]) ).
cnf(c_0_342,negated_conjecture,
( product(X1,s,k)
| ~ product(X2,s,q)
| ~ sum(X2,l,X1) ),
inference(spm,[status(thm)],[c_0_334,c_0_142]) ).
cnf(c_0_343,negated_conjecture,
sum(additive_identity,l,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_335]),c_0_55])]) ).
cnf(c_0_344,negated_conjecture,
product(additive_identity,s,q),
inference(spm,[status(thm)],[c_0_49,c_0_336]) ).
cnf(c_0_345,negated_conjecture,
sum(t,s,u),
inference(spm,[status(thm)],[c_0_94,c_0_96]) ).
cnf(c_0_346,negated_conjecture,
( product(X1,s,p)
| ~ product(l,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_337,c_0_142]) ).
cnf(c_0_347,negated_conjecture,
product(b,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_338,c_0_339]) ).
cnf(c_0_348,negated_conjecture,
( product(X1,b,p)
| ~ product(c,s,X1) ),
inference(spm,[status(thm)],[c_0_340,c_0_341]) ).
cnf(c_0_349,negated_conjecture,
product(c,s,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_342,c_0_343]),c_0_344])]) ).
cnf(c_0_350,negated_conjecture,
sum(additive_inverse(t),u,s),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_345]),c_0_151]),c_0_157])]) ).
cnf(c_0_351,negated_conjecture,
( sum(X1,X2,t)
| ~ sum(X3,t,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_99,c_0_180]) ).
cnf(c_0_352,negated_conjecture,
( product(X1,additive_identity,p)
| ~ product(X1,k,p) ),
inference(spm,[status(thm)],[c_0_268,c_0_321]) ).
cnf(c_0_353,negated_conjecture,
( product(X1,multiplicative_inverse(b),X2)
| ~ product(X3,s,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_90]) ).
cnf(c_0_354,negated_conjecture,
product(k,s,p),
inference(spm,[status(thm)],[c_0_346,c_0_223]) ).
cnf(c_0_355,negated_conjecture,
( product(X1,a,p)
| ~ product(X1,b,p) ),
inference(spm,[status(thm)],[c_0_268,c_0_347]) ).
cnf(c_0_356,negated_conjecture,
product(k,b,p),
inference(spm,[status(thm)],[c_0_348,c_0_349]) ).
cnf(c_0_357,negated_conjecture,
sum(u,additive_inverse(t),s),
inference(spm,[status(thm)],[c_0_94,c_0_350]) ).
cnf(c_0_358,negated_conjecture,
( sum(X1,u,t)
| ~ sum(X1,s,additive_identity) ),
inference(spm,[status(thm)],[c_0_351,c_0_96]) ).
cnf(c_0_359,negated_conjecture,
product(s,multiplicative_identity,s),
inference(spm,[status(thm)],[c_0_49,c_0_133]) ).
cnf(c_0_360,negated_conjecture,
product(multiplicative_identity,additive_identity,p),
inference(spm,[status(thm)],[c_0_352,c_0_279]) ).
cnf(c_0_361,negated_conjecture,
( product(X1,multiplicative_inverse(b),p)
| ~ product(k,a,X1) ),
inference(spm,[status(thm)],[c_0_353,c_0_354]) ).
cnf(c_0_362,negated_conjecture,
product(k,a,p),
inference(spm,[status(thm)],[c_0_355,c_0_356]) ).
cnf(c_0_363,negated_conjecture,
( sum(X1,s,additive_identity)
| ~ sum(X1,u,t) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_357]),c_0_157])]) ).
cnf(c_0_364,negated_conjecture,
sum(additive_inverse(s),u,t),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_358,c_0_105]),c_0_151])]) ).
cnf(c_0_365,negated_conjecture,
( product(X1,X2,s)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,s) ),
inference(spm,[status(thm)],[c_0_41,c_0_359]) ).
cnf(c_0_366,negated_conjecture,
product(p,multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_360]),c_0_93])]) ).
cnf(c_0_367,negated_conjecture,
( product(multiplicative_inverse(d),X1,s)
| ~ product(p,multiplicative_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_331]) ).
cnf(c_0_368,negated_conjecture,
product(p,multiplicative_inverse(b),p),
inference(spm,[status(thm)],[c_0_361,c_0_362]) ).
cnf(c_0_369,negated_conjecture,
product(t,d,c),
inference(spm,[status(thm)],[c_0_49,c_0_257]) ).
cnf(c_0_370,negated_conjecture,
sum(additive_inverse(s),s,additive_identity),
inference(spm,[status(thm)],[c_0_363,c_0_364]) ).
cnf(c_0_371,negated_conjecture,
( product(X1,additive_identity,s)
| ~ product(X1,p,s) ),
inference(spm,[status(thm)],[c_0_365,c_0_366]) ).
cnf(c_0_372,negated_conjecture,
product(multiplicative_inverse(d),p,s),
inference(spm,[status(thm)],[c_0_367,c_0_368]) ).
cnf(c_0_373,negated_conjecture,
product(c,b,p),
inference(spm,[status(thm)],[c_0_324,c_0_369]) ).
cnf(c_0_374,negated_conjecture,
sum(s,additive_identity,s),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_370]),c_0_151])]) ).
cnf(c_0_375,negated_conjecture,
product(multiplicative_inverse(d),additive_identity,s),
inference(spm,[status(thm)],[c_0_371,c_0_372]) ).
cnf(c_0_376,negated_conjecture,
product(b,c,p),
inference(spm,[status(thm)],[c_0_49,c_0_373]) ).
cnf(c_0_377,negated_conjecture,
sum(additive_identity,s,s),
inference(spm,[status(thm)],[c_0_94,c_0_374]) ).
cnf(c_0_378,negated_conjecture,
product(additive_identity,multiplicative_inverse(d),s),
inference(spm,[status(thm)],[c_0_49,c_0_375]) ).
cnf(c_0_379,negated_conjecture,
product(multiplicative_inverse(b),p,c),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_376]),c_0_55]),c_0_52])]),c_0_83]) ).
cnf(c_0_380,negated_conjecture,
( product(X1,s,a)
| ~ product(b,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_337,c_0_317]) ).
cnf(c_0_381,negated_conjecture,
( sum(X1,X2,s)
| ~ sum(X3,s,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_99,c_0_377]) ).
cnf(c_0_382,negated_conjecture,
sum(s,t,t),
inference(spm,[status(thm)],[c_0_138,c_0_378]) ).
cnf(c_0_383,negated_conjecture,
product(p,multiplicative_inverse(b),c),
inference(spm,[status(thm)],[c_0_49,c_0_379]) ).
cnf(c_0_384,plain,
( product(X1,X2,multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_47]) ).
cnf(c_0_385,negated_conjecture,
product(multiply(b,multiplicative_identity),s,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_380,c_0_47]),c_0_163]),c_0_52])]) ).
cnf(c_0_386,negated_conjecture,
( product(X1,X2,u)
| ~ product(X3,X2,s)
| ~ product(X4,X2,t)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_345]) ).
cnf(c_0_387,negated_conjecture,
( sum(X1,s,s)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_381,c_0_85]),c_0_151])]) ).
cnf(c_0_388,negated_conjecture,
sum(s,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_382]),c_0_157])]) ).
cnf(c_0_389,negated_conjecture,
( product(X1,multiplicative_identity,t)
| ~ product(multiplicative_inverse(d),c,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_81]),c_0_55])]) ).
cnf(c_0_390,negated_conjecture,
product(multiplicative_inverse(d),c,s),
inference(spm,[status(thm)],[c_0_367,c_0_383]) ).
cnf(c_0_391,negated_conjecture,
( product(X1,l,additive_identity)
| ~ product(multiplicative_identity,u,X1) ),
inference(spm,[status(thm)],[c_0_236,c_0_233]) ).
cnf(c_0_392,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X2,X5),X3)
| ~ product(X4,X5,X1)
| ~ defined(X5)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_384]) ).
cnf(c_0_393,negated_conjecture,
product(s,multiply(b,multiplicative_identity),a),
inference(spm,[status(thm)],[c_0_49,c_0_385]) ).
cnf(c_0_394,negated_conjecture,
( product(X1,multiplicative_identity,u)
| ~ product(X2,multiplicative_identity,t)
| ~ sum(X2,s,X1) ),
inference(spm,[status(thm)],[c_0_386,c_0_359]) ).
cnf(c_0_395,negated_conjecture,
sum(s,s,s),
inference(spm,[status(thm)],[c_0_387,c_0_388]) ).
cnf(c_0_396,negated_conjecture,
product(s,multiplicative_identity,t),
inference(spm,[status(thm)],[c_0_389,c_0_390]) ).
cnf(c_0_397,negated_conjecture,
product(u,l,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_391,c_0_51]),c_0_118])]) ).
cnf(c_0_398,negated_conjecture,
( product(X1,b,a)
| ~ product(s,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_392,c_0_393]),c_0_163]),c_0_52])]) ).
cnf(c_0_399,negated_conjecture,
product(s,multiplicative_identity,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_394,c_0_395]),c_0_396])]) ).
cnf(c_0_400,negated_conjecture,
( product(X1,d,additive_identity)
| ~ product(u,b,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_397]) ).
cnf(c_0_401,negated_conjecture,
product(u,b,a),
inference(spm,[status(thm)],[c_0_398,c_0_399]) ).
cnf(c_0_402,negated_conjecture,
product(a,d,additive_identity),
inference(spm,[status(thm)],[c_0_400,c_0_401]) ).
cnf(c_0_403,negated_conjecture,
product(d,a,additive_identity),
inference(spm,[status(thm)],[c_0_49,c_0_402]) ).
cnf(c_0_404,negated_conjecture,
product(multiplicative_inverse(d),additive_identity,a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_403]),c_0_65]),c_0_69])]),c_0_70]) ).
cnf(c_0_405,negated_conjecture,
product(additive_identity,multiplicative_inverse(d),a),
inference(spm,[status(thm)],[c_0_49,c_0_404]) ).
cnf(c_0_406,negated_conjecture,
product(t,multiplicative_identity,t),
inference(spm,[status(thm)],[c_0_49,c_0_145]) ).
cnf(c_0_407,negated_conjecture,
product(multiplicative_identity,q,k),
inference(spm,[status(thm)],[c_0_49,c_0_222]) ).
cnf(c_0_408,negated_conjecture,
sum(a,t,t),
inference(spm,[status(thm)],[c_0_138,c_0_405]) ).
cnf(c_0_409,negated_conjecture,
( product(X1,X2,t)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,t) ),
inference(spm,[status(thm)],[c_0_41,c_0_406]) ).
cnf(c_0_410,negated_conjecture,
product(t,multiplicative_identity,s),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_396]),c_0_151])]) ).
cnf(c_0_411,negated_conjecture,
( product(t,X1,t)
| ~ product(d,multiplicative_inverse(d),X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_369]) ).
cnf(c_0_412,negated_conjecture,
product(multiplicative_identity,k,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_407]),c_0_112])]) ).
cnf(c_0_413,negated_conjecture,
sum(a,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_408]),c_0_157])]) ).
cnf(c_0_414,negated_conjecture,
( product(X1,s,t)
| ~ product(X1,t,t) ),
inference(spm,[status(thm)],[c_0_409,c_0_410]) ).
cnf(c_0_415,negated_conjecture,
product(t,t,t),
inference(spm,[status(thm)],[c_0_411,c_0_315]) ).
cnf(c_0_416,negated_conjecture,
( product(X1,t,X2)
| ~ product(X3,t,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_145]) ).
cnf(c_0_417,negated_conjecture,
( sum(X1,p,s)
| ~ sum(s,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_261,c_0_170]) ).
cnf(c_0_418,negated_conjecture,
product(multiplicative_identity,additive_identity,q),
inference(spm,[status(thm)],[c_0_329,c_0_412]) ).
cnf(c_0_419,negated_conjecture,
( product(X1,a,X2)
| ~ product(X3,p,X2)
| ~ product(X3,d,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_323]) ).
cnf(c_0_420,negated_conjecture,
sum(additive_identity,additive_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_413]),c_0_65])]) ).
cnf(c_0_421,negated_conjecture,
( product(X1,X2,c)
| ~ product(X3,d,X2)
| ~ product(X1,X3,t) ),
inference(spm,[status(thm)],[c_0_41,c_0_369]) ).
cnf(c_0_422,negated_conjecture,
product(t,s,t),
inference(spm,[status(thm)],[c_0_414,c_0_415]) ).
cnf(c_0_423,negated_conjecture,
( product(X1,t,q)
| ~ product(l,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_416,c_0_154]) ).
cnf(c_0_424,negated_conjecture,
( product(X1,multiplicative_identity,k)
| ~ product(X2,multiplicative_identity,q)
| ~ sum(X2,p,X1) ),
inference(spm,[status(thm)],[c_0_334,c_0_217]) ).
cnf(c_0_425,negated_conjecture,
sum(additive_identity,p,s),
inference(spm,[status(thm)],[c_0_417,c_0_388]) ).
cnf(c_0_426,negated_conjecture,
product(additive_identity,multiplicative_identity,q),
inference(spm,[status(thm)],[c_0_49,c_0_418]) ).
cnf(c_0_427,negated_conjecture,
( product(X1,a,q)
| ~ product(t,d,X1) ),
inference(spm,[status(thm)],[c_0_419,c_0_304]) ).
cnf(c_0_428,negated_conjecture,
sum(a,additive_identity,l),
inference(spm,[status(thm)],[c_0_318,c_0_420]) ).
cnf(c_0_429,negated_conjecture,
( product(X1,c,c)
| ~ product(X1,t,t) ),
inference(spm,[status(thm)],[c_0_421,c_0_369]) ).
cnf(c_0_430,negated_conjecture,
product(s,t,t),
inference(spm,[status(thm)],[c_0_49,c_0_422]) ).
cnf(c_0_431,negated_conjecture,
product(k,t,q),
inference(spm,[status(thm)],[c_0_423,c_0_223]) ).
cnf(c_0_432,negated_conjecture,
product(s,multiplicative_identity,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_424,c_0_425]),c_0_426])]) ).
cnf(c_0_433,negated_conjecture,
product(c,a,q),
inference(spm,[status(thm)],[c_0_427,c_0_369]) ).
cnf(c_0_434,negated_conjecture,
sum(additive_identity,a,l),
inference(spm,[status(thm)],[c_0_94,c_0_428]) ).
cnf(c_0_435,negated_conjecture,
product(t,additive_identity,p),
inference(spm,[status(thm)],[c_0_352,c_0_306]) ).
cnf(c_0_436,negated_conjecture,
( product(X1,d,X2)
| ~ product(X3,c,X2)
| ~ product(X3,t,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_369]) ).
cnf(c_0_437,negated_conjecture,
product(s,c,c),
inference(spm,[status(thm)],[c_0_429,c_0_430]) ).
cnf(c_0_438,negated_conjecture,
( product(X1,t,q)
| ~ product(k,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_416,c_0_431]) ).
cnf(c_0_439,negated_conjecture,
product(k,multiplicative_identity,s),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_432]),c_0_151])]) ).
cnf(c_0_440,negated_conjecture,
product(a,c,q),
inference(spm,[status(thm)],[c_0_49,c_0_433]) ).
cnf(c_0_441,negated_conjecture,
sum(additive_identity,l,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_434]),c_0_65])]) ).
cnf(c_0_442,negated_conjecture,
product(additive_identity,t,p),
inference(spm,[status(thm)],[c_0_49,c_0_435]) ).
cnf(c_0_443,negated_conjecture,
( product(X1,d,c)
| ~ product(s,t,X1) ),
inference(spm,[status(thm)],[c_0_436,c_0_437]) ).
cnf(c_0_444,negated_conjecture,
product(s,t,q),
inference(spm,[status(thm)],[c_0_438,c_0_439]) ).
cnf(c_0_445,negated_conjecture,
( product(X1,d,q)
| ~ product(a,t,X1) ),
inference(spm,[status(thm)],[c_0_436,c_0_440]) ).
cnf(c_0_446,negated_conjecture,
product(a,t,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_288,c_0_441]),c_0_442])]) ).
cnf(c_0_447,negated_conjecture,
( product(X1,multiplicative_identity,d)
| ~ product(multiplicative_inverse(b),l,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_273]),c_0_48])]) ).
cnf(c_0_448,negated_conjecture,
product(q,d,c),
inference(spm,[status(thm)],[c_0_443,c_0_444]) ).
cnf(c_0_449,negated_conjecture,
product(k,d,q),
inference(spm,[status(thm)],[c_0_445,c_0_446]) ).
cnf(c_0_450,negated_conjecture,
product(c,multiplicative_identity,d),
inference(spm,[status(thm)],[c_0_447,c_0_292]) ).
cnf(c_0_451,negated_conjecture,
product(d,q,c),
inference(spm,[status(thm)],[c_0_49,c_0_448]) ).
cnf(c_0_452,plain,
( sum(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X5,X3,X1)
| ~ defined(X3)
| ~ sum(X5,X4,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_110,c_0_51]) ).
cnf(c_0_453,negated_conjecture,
( product(X1,d,d)
| ~ product(multiplicative_inverse(b),b,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_273]) ).
cnf(c_0_454,negated_conjecture,
product(d,k,q),
inference(spm,[status(thm)],[c_0_49,c_0_449]) ).
cnf(c_0_455,negated_conjecture,
product(multiplicative_inverse(d),l,b),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_57]),c_0_52]),c_0_69])]),c_0_70]) ).
cnf(c_0_456,negated_conjecture,
( product(X1,d,q)
| ~ product(X1,c,q) ),
inference(spm,[status(thm)],[c_0_320,c_0_450]) ).
cnf(c_0_457,negated_conjecture,
product(multiplicative_inverse(d),c,q),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_451]),c_0_112]),c_0_69])]),c_0_70]) ).
cnf(c_0_458,plain,
( sum(X1,X2,X3)
| ~ product(multiplicative_identity,X3,X2)
| ~ product(additive_identity,X3,X1)
| ~ defined(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_452,c_0_85]),c_0_163])]) ).
cnf(c_0_459,negated_conjecture,
product(multiplicative_identity,d,d),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_453,c_0_68]),c_0_52])]),c_0_83]) ).
cnf(c_0_460,negated_conjecture,
product(d,additive_identity,q),
inference(spm,[status(thm)],[c_0_329,c_0_454]) ).
cnf(c_0_461,negated_conjecture,
( sum(X1,X2,l)
| ~ product(X3,b,X2)
| ~ product(X4,b,X1)
| ~ sum(X4,X3,d) ),
inference(spm,[status(thm)],[c_0_110,c_0_57]) ).
cnf(c_0_462,negated_conjecture,
( product(X1,b,b)
| ~ product(multiplicative_inverse(d),d,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_455]) ).
cnf(c_0_463,negated_conjecture,
product(multiplicative_inverse(d),d,q),
inference(spm,[status(thm)],[c_0_456,c_0_457]) ).
cnf(c_0_464,negated_conjecture,
( sum(X1,d,d)
| ~ product(additive_identity,d,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_458,c_0_459]),c_0_69])]) ).
cnf(c_0_465,negated_conjecture,
product(additive_identity,d,q),
inference(spm,[status(thm)],[c_0_49,c_0_460]) ).
cnf(c_0_466,negated_conjecture,
( sum(X1,l,l)
| ~ product(X2,b,X1)
| ~ sum(X2,d,d) ),
inference(spm,[status(thm)],[c_0_461,c_0_57]) ).
cnf(c_0_467,negated_conjecture,
product(q,b,b),
inference(spm,[status(thm)],[c_0_462,c_0_463]) ).
cnf(c_0_468,negated_conjecture,
sum(q,d,d),
inference(spm,[status(thm)],[c_0_464,c_0_465]) ).
cnf(c_0_469,negated_conjecture,
sum(b,l,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_466,c_0_467]),c_0_468])]) ).
cnf(c_0_470,negated_conjecture,
sum(b,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_469]),c_0_48])]) ).
cnf(c_0_471,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_470]),c_0_83]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : FLD052-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.09/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.37 % Computer : n007.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Mon Aug 28 00:38:12 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.22/0.60 start to proof: theBenchmark
% 2.55/2.71 % Version : CSE_E---1.5
% 2.55/2.71 % Problem : theBenchmark.p
% 2.55/2.71 % Proof found
% 2.55/2.71 % SZS status Theorem for theBenchmark.p
% 2.55/2.71 % SZS output start Proof
% See solution above
% 2.55/2.73 % Total time : 2.101000 s
% 2.55/2.73 % SZS output end Proof
% 2.55/2.73 % Total time : 2.105000 s
%------------------------------------------------------------------------------