TSTP Solution File: FLD052-4 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : FLD052-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat May 4 07:40:04 EDT 2024
% Result : Unsatisfiable 13.22s 2.08s
% Output : CNFRefutation 13.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 36
% Syntax : Number of clauses : 316 ( 178 unt; 9 nHn; 316 RR)
% Number of literals : 573 ( 0 equ; 257 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-1 aty)
% Number of variables : 349 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',associativity_multiplication_1) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',existence_of_identity_multiplication) ).
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/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',existence_of_inverse_multiplication) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',commutativity_multiplication) ).
cnf(product_21,negated_conjecture,
product(b,d,l),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',product_21) ).
cnf(not_sum_14,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',not_sum_14) ).
cnf(product_19,negated_conjecture,
product(b,c,q),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',product_19) ).
cnf(product_16,negated_conjecture,
product(c,multiplicative_inverse(d),t),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',product_16) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',b_is_defined) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',d_is_defined) ).
cnf(product_18,negated_conjecture,
product(a,d,p),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',product_18) ).
cnf(not_sum_13,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',not_sum_13) ).
cnf(product_15,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',product_15) ).
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/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',distributivity_2) ).
cnf(sum_20,negated_conjecture,
sum(p,q,k),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',sum_20) ).
cnf(sum_17,negated_conjecture,
sum(s,t,u),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',sum_17) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',existence_of_identity_addition) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',c_is_defined) ).
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/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',associativity_addition_1) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',well_definedness_of_multiplicative_identity) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',u_is_defined) ).
cnf(l_is_defined,hypothesis,
defined(l),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',l_is_defined) ).
cnf(not_product_22,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',not_product_22) ).
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/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',distributivity_1) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',commutativity_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',a_is_defined) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',existence_of_inverse_addition) ).
cnf(t_is_defined,hypothesis,
defined(t),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',t_is_defined) ).
cnf(p_is_defined,hypothesis,
defined(p),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',p_is_defined) ).
cnf(s_is_defined,hypothesis,
defined(s),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',s_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/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',associativity_addition_2) ).
cnf(q_is_defined,hypothesis,
defined(q),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',q_is_defined) ).
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/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',associativity_multiplication_2) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',well_definedness_of_additive_identity) ).
cnf(k_is_defined,hypothesis,
defined(k),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',k_is_defined) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p',well_definedness_of_additive_inverse) ).
cnf(c_0_36,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_1]) ).
cnf(c_0_37,plain,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_38,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
c_0_36 ).
cnf(c_0_39,plain,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
c_0_37 ).
cnf(c_0_40,plain,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_multiplication]) ).
cnf(c_0_41,plain,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_42,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,X3,X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
c_0_40 ).
cnf(c_0_44,plain,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
c_0_41 ).
cnf(c_0_45,negated_conjecture,
product(b,d,l),
product_21 ).
cnf(c_0_46,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_14]) ).
cnf(c_0_47,negated_conjecture,
product(b,c,q),
product_19 ).
cnf(c_0_48,negated_conjecture,
product(c,multiplicative_inverse(d),t),
product_16 ).
cnf(c_0_49,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_42,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
product(d,b,l),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_52,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_53,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
c_0_46 ).
cnf(c_0_54,negated_conjecture,
product(a,d,p),
product_18 ).
cnf(c_0_55,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_13]) ).
cnf(c_0_56,negated_conjecture,
( product(X1,X2,q)
| ~ product(X3,c,X2)
| ~ product(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_38,c_0_47]) ).
cnf(c_0_57,negated_conjecture,
product(multiplicative_inverse(d),c,t),
inference(spm,[status(thm)],[c_0_44,c_0_48]) ).
cnf(c_0_58,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_49,c_0_50]),c_0_51]),c_0_52])]),c_0_53]) ).
cnf(c_0_59,negated_conjecture,
product(d,a,p),
inference(spm,[status(thm)],[c_0_44,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
product(a,multiplicative_inverse(b),s),
product_15 ).
cnf(c_0_61,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
c_0_55 ).
cnf(c_0_62,plain,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ product(X4,X2,X6)
| ~ product(X5,X2,X7)
| ~ sum(X6,X7,X3) ),
inference(fof_simplification,[status(thm)],[distributivity_2]) ).
cnf(c_0_63,negated_conjecture,
( product(X1,t,q)
| ~ product(X1,multiplicative_inverse(d),b) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
product(l,multiplicative_inverse(d),b),
inference(spm,[status(thm)],[c_0_44,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( product(X1,X2,p)
| ~ product(X3,a,X2)
| ~ product(X1,X3,d) ),
inference(spm,[status(thm)],[c_0_38,c_0_59]) ).
cnf(c_0_66,negated_conjecture,
product(multiplicative_inverse(b),a,s),
inference(spm,[status(thm)],[c_0_44,c_0_60]) ).
cnf(c_0_67,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_49,c_0_45]),c_0_52]),c_0_51])]),c_0_61]) ).
cnf(c_0_68,plain,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ product(X4,X2,X6)
| ~ product(X5,X2,X7)
| ~ sum(X6,X7,X3) ),
c_0_62 ).
cnf(c_0_69,negated_conjecture,
sum(p,q,k),
sum_20 ).
cnf(c_0_70,negated_conjecture,
product(l,t,q),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,negated_conjecture,
( product(X1,s,p)
| ~ product(X1,multiplicative_inverse(b),d) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,negated_conjecture,
product(l,multiplicative_inverse(b),d),
inference(spm,[status(thm)],[c_0_44,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( product(X1,X2,k)
| ~ product(X3,X2,q)
| ~ product(X4,X2,p)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
product(t,l,q),
inference(spm,[status(thm)],[c_0_44,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
product(l,s,p),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( product(X1,l,k)
| ~ product(X2,l,p)
| ~ sum(X2,t,X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
sum(s,t,u),
sum_17 ).
cnf(c_0_78,negated_conjecture,
product(s,l,p),
inference(spm,[status(thm)],[c_0_44,c_0_75]) ).
cnf(c_0_79,plain,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_80,negated_conjecture,
product(u,l,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78])]) ).
cnf(c_0_81,negated_conjecture,
( product(X1,X2,t)
| ~ product(X3,multiplicative_inverse(d),X2)
| ~ product(X1,X3,c) ),
inference(spm,[status(thm)],[c_0_38,c_0_48]) ).
cnf(c_0_82,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_83,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_1]) ).
cnf(c_0_84,plain,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
c_0_79 ).
cnf(c_0_85,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_86,negated_conjecture,
product(l,u,k),
inference(spm,[status(thm)],[c_0_44,c_0_80]) ).
cnf(c_0_87,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_88,hypothesis,
defined(l),
l_is_defined ).
cnf(c_0_89,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
inference(fof_simplification,[status(thm)],[not_product_22]) ).
cnf(c_0_90,plain,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
inference(fof_simplification,[status(thm)],[distributivity_1]) ).
cnf(c_0_91,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_81,c_0_39]),c_0_82])]) ).
cnf(c_0_92,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
c_0_83 ).
cnf(c_0_93,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_94,plain,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_95,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_49,c_0_86]),c_0_87]),c_0_88])]) ).
cnf(c_0_96,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
c_0_89 ).
cnf(c_0_97,negated_conjecture,
( product(X1,X2,s)
| ~ product(X3,multiplicative_inverse(b),X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_38,c_0_60]) ).
cnf(c_0_98,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_99,plain,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
c_0_90 ).
cnf(c_0_100,negated_conjecture,
product(multiplicative_identity,t,t),
inference(spm,[status(thm)],[c_0_91,c_0_48]) ).
cnf(c_0_101,plain,
( sum(X1,X2,multiplicative_identity)
| ~ sum(X3,multiplicative_identity,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_102,plain,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
c_0_94 ).
cnf(c_0_103,negated_conjecture,
sum(additive_identity,l,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_95]),c_0_96]) ).
cnf(c_0_104,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_97,c_0_39]),c_0_98])]) ).
cnf(c_0_105,plain,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_106,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_99,c_0_100]) ).
cnf(c_0_107,plain,
( sum(X1,multiplicative_identity,multiplicative_identity)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_101,c_0_93]) ).
cnf(c_0_108,negated_conjecture,
sum(l,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_109,negated_conjecture,
product(multiplicative_identity,s,s),
inference(spm,[status(thm)],[c_0_104,c_0_60]) ).
cnf(c_0_110,plain,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
c_0_105 ).
cnf(c_0_111,negated_conjecture,
( sum(X1,q,t)
| ~ product(X2,t,X1)
| ~ sum(X2,l,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_106,c_0_70]) ).
cnf(c_0_112,hypothesis,
defined(t),
t_is_defined ).
cnf(c_0_113,negated_conjecture,
sum(l,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_114,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_99,c_0_109]) ).
cnf(c_0_115,hypothesis,
defined(p),
p_is_defined ).
cnf(c_0_116,plain,
( sum(X1,additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_110]) ).
cnf(c_0_117,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_111,c_0_39]),c_0_112])]) ).
cnf(c_0_118,negated_conjecture,
sum(multiplicative_identity,l,multiplicative_identity),
inference(spm,[status(thm)],[c_0_102,c_0_113]) ).
cnf(c_0_119,negated_conjecture,
( sum(X1,p,s)
| ~ product(X2,s,X1)
| ~ sum(X2,l,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_114,c_0_75]) ).
cnf(c_0_120,hypothesis,
defined(s),
s_is_defined ).
cnf(c_0_121,plain,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_2]) ).
cnf(c_0_122,hypothesis,
sum(additive_identity,p,p),
inference(spm,[status(thm)],[c_0_84,c_0_115]) ).
cnf(c_0_123,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_116]) ).
cnf(c_0_124,negated_conjecture,
sum(t,q,t),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118])]) ).
cnf(c_0_125,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_119,c_0_39]),c_0_120])]) ).
cnf(c_0_126,plain,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
c_0_121 ).
cnf(c_0_127,hypothesis,
sum(p,additive_identity,p),
inference(spm,[status(thm)],[c_0_102,c_0_122]) ).
cnf(c_0_128,hypothesis,
( sum(X1,X2,p)
| ~ sum(X3,p,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_92,c_0_122]) ).
cnf(c_0_129,plain,
( sum(X1,additive_identity,additive_identity)
| ~ defined(X2)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_123,c_0_116]) ).
cnf(c_0_130,negated_conjecture,
sum(q,t,t),
inference(spm,[status(thm)],[c_0_102,c_0_124]) ).
cnf(c_0_131,hypothesis,
defined(q),
q_is_defined ).
cnf(c_0_132,hypothesis,
sum(additive_identity,s,s),
inference(spm,[status(thm)],[c_0_84,c_0_120]) ).
cnf(c_0_133,negated_conjecture,
sum(s,p,s),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_118])]) ).
cnf(c_0_134,hypothesis,
( sum(X1,additive_identity,X2)
| ~ sum(X3,p,X2)
| ~ sum(X3,p,X1) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_135,negated_conjecture,
sum(q,p,k),
inference(spm,[status(thm)],[c_0_102,c_0_69]) ).
cnf(c_0_136,hypothesis,
( sum(X1,p,p)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_128,c_0_122]) ).
cnf(c_0_137,negated_conjecture,
sum(q,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_112])]) ).
cnf(c_0_138,hypothesis,
sum(additive_identity,q,q),
inference(spm,[status(thm)],[c_0_84,c_0_131]) ).
cnf(c_0_139,hypothesis,
( sum(X1,s,X2)
| ~ sum(X3,s,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_126,c_0_132]) ).
cnf(c_0_140,negated_conjecture,
sum(p,s,s),
inference(spm,[status(thm)],[c_0_102,c_0_133]) ).
cnf(c_0_141,negated_conjecture,
( sum(X1,additive_identity,k)
| ~ sum(q,p,X1) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_142,hypothesis,
sum(q,p,p),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_143,hypothesis,
( sum(X1,X2,q)
| ~ sum(X3,q,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_92,c_0_138]) ).
cnf(c_0_144,hypothesis,
( sum(X1,s,s)
| ~ sum(p,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_145,negated_conjecture,
sum(p,additive_identity,k),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_146,negated_conjecture,
( sum(X1,k,q)
| ~ sum(X1,p,additive_identity) ),
inference(spm,[status(thm)],[c_0_143,c_0_69]) ).
cnf(c_0_147,negated_conjecture,
sum(k,s,s),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_148,negated_conjecture,
( product(X1,q,q)
| ~ product(X1,b,b) ),
inference(spm,[status(thm)],[c_0_56,c_0_47]) ).
cnf(c_0_149,negated_conjecture,
sum(additive_inverse(p),k,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_110]),c_0_115])]) ).
cnf(c_0_150,negated_conjecture,
sum(k,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_147]),c_0_120])]) ).
cnf(c_0_151,negated_conjecture,
( product(X1,X2,p)
| ~ product(X3,d,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_38,c_0_54]) ).
cnf(c_0_152,negated_conjecture,
( product(X1,X2,l)
| ~ product(X3,d,X2)
| ~ product(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_38,c_0_45]) ).
cnf(c_0_153,negated_conjecture,
product(multiplicative_identity,q,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_39]),c_0_51])]) ).
cnf(c_0_154,negated_conjecture,
sum(k,additive_inverse(p),q),
inference(spm,[status(thm)],[c_0_102,c_0_149]) ).
cnf(c_0_155,hypothesis,
sum(k,p,p),
inference(spm,[status(thm)],[c_0_136,c_0_150]) ).
cnf(c_0_156,negated_conjecture,
( product(X1,p,p)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_151,c_0_54]) ).
cnf(c_0_157,negated_conjecture,
( product(X1,l,l)
| ~ product(X1,b,b) ),
inference(spm,[status(thm)],[c_0_152,c_0_45]) ).
cnf(c_0_158,hypothesis,
( sum(X1,q,q)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_143,c_0_138]) ).
cnf(c_0_159,negated_conjecture,
product(q,multiplicative_identity,q),
inference(spm,[status(thm)],[c_0_44,c_0_153]) ).
cnf(c_0_160,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_123,c_0_154]),c_0_115])]) ).
cnf(c_0_161,hypothesis,
sum(p,k,p),
inference(spm,[status(thm)],[c_0_102,c_0_155]) ).
cnf(c_0_162,negated_conjecture,
product(multiplicative_identity,p,p),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_39]),c_0_98])]) ).
cnf(c_0_163,negated_conjecture,
product(multiplicative_identity,l,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_39]),c_0_51])]) ).
cnf(c_0_164,hypothesis,
sum(additive_identity,l,l),
inference(spm,[status(thm)],[c_0_84,c_0_88]) ).
cnf(c_0_165,hypothesis,
sum(l,q,q),
inference(spm,[status(thm)],[c_0_158,c_0_108]) ).
cnf(c_0_166,negated_conjecture,
( product(X1,multiplicative_identity,k)
| ~ product(X2,multiplicative_identity,p)
| ~ sum(X2,q,X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_159]) ).
cnf(c_0_167,negated_conjecture,
sum(p,q,additive_identity),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_168,negated_conjecture,
product(p,multiplicative_identity,p),
inference(spm,[status(thm)],[c_0_44,c_0_162]) ).
cnf(c_0_169,negated_conjecture,
product(l,multiplicative_identity,l),
inference(spm,[status(thm)],[c_0_44,c_0_163]) ).
cnf(c_0_170,hypothesis,
( sum(X1,X2,l)
| ~ sum(X3,l,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_92,c_0_164]) ).
cnf(c_0_171,hypothesis,
sum(q,l,q),
inference(spm,[status(thm)],[c_0_102,c_0_165]) ).
cnf(c_0_172,negated_conjecture,
product(additive_identity,multiplicative_identity,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_168])]) ).
cnf(c_0_173,plain,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_2]) ).
cnf(c_0_174,negated_conjecture,
( sum(X1,X2,l)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X4,multiplicative_identity,X1)
| ~ sum(X4,X3,l) ),
inference(spm,[status(thm)],[c_0_99,c_0_169]) ).
cnf(c_0_175,hypothesis,
sum(p,q,p),
inference(spm,[status(thm)],[c_0_102,c_0_142]) ).
cnf(c_0_176,hypothesis,
( sum(X1,q,l)
| ~ sum(X1,q,additive_identity) ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_177,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_42,c_0_39]),c_0_85])]) ).
cnf(c_0_178,negated_conjecture,
product(multiplicative_identity,additive_identity,k),
inference(spm,[status(thm)],[c_0_44,c_0_172]) ).
cnf(c_0_179,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_180,plain,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
c_0_173 ).
cnf(c_0_181,hypothesis,
( product(X1,X2,q)
| ~ product(X3,X2,q)
| ~ product(X4,X2,additive_identity)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_138]) ).
cnf(c_0_182,negated_conjecture,
( sum(X1,q,l)
| ~ product(X2,multiplicative_identity,X1)
| ~ sum(X2,q,l) ),
inference(spm,[status(thm)],[c_0_174,c_0_159]) ).
cnf(c_0_183,hypothesis,
product(p,multiplicative_identity,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_175]),c_0_168])]) ).
cnf(c_0_184,hypothesis,
sum(p,q,l),
inference(spm,[status(thm)],[c_0_176,c_0_167]) ).
cnf(c_0_185,negated_conjecture,
product(multiplicative_identity,k,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179])]) ).
cnf(c_0_186,negated_conjecture,
( product(X1,s,X2)
| ~ product(X3,s,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_180,c_0_109]) ).
cnf(c_0_187,negated_conjecture,
( product(X1,multiplicative_identity,q)
| ~ product(X2,multiplicative_identity,additive_identity)
| ~ sum(X2,q,X1) ),
inference(spm,[status(thm)],[c_0_181,c_0_159]) ).
cnf(c_0_188,negated_conjecture,
sum(k,q,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_183]),c_0_184])]) ).
cnf(c_0_189,negated_conjecture,
product(k,multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_44,c_0_185]) ).
cnf(c_0_190,negated_conjecture,
( product(X1,s,p)
| ~ product(l,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_186,c_0_75]) ).
cnf(c_0_191,negated_conjecture,
product(l,multiplicative_identity,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_189])]) ).
cnf(c_0_192,negated_conjecture,
product(q,s,p),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_193,plain,
( product(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_39]) ).
cnf(c_0_194,negated_conjecture,
( product(X1,t,X2)
| ~ product(X3,q,X2)
| ~ product(X3,l,X1) ),
inference(spm,[status(thm)],[c_0_180,c_0_70]) ).
cnf(c_0_195,negated_conjecture,
product(s,q,p),
inference(spm,[status(thm)],[c_0_44,c_0_192]) ).
cnf(c_0_196,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,X4,X2)
| ~ product(X3,X4,X1)
| ~ defined(X4) ),
inference(spm,[status(thm)],[c_0_180,c_0_193]) ).
cnf(c_0_197,negated_conjecture,
( product(X1,t,p)
| ~ product(s,l,X1) ),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_198,negated_conjecture,
( product(X1,multiplicative_identity,l)
| ~ product(l,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_169]),c_0_85])]) ).
cnf(c_0_199,negated_conjecture,
product(l,multiplicative_identity,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_184]),c_0_168])]) ).
cnf(c_0_200,negated_conjecture,
( product(X1,X2,p)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,p) ),
inference(spm,[status(thm)],[c_0_38,c_0_168]) ).
cnf(c_0_201,negated_conjecture,
product(p,t,p),
inference(spm,[status(thm)],[c_0_197,c_0_78]) ).
cnf(c_0_202,negated_conjecture,
product(k,multiplicative_identity,l),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_203,negated_conjecture,
( product(X1,k,p)
| ~ product(X1,p,p) ),
inference(spm,[status(thm)],[c_0_200,c_0_183]) ).
cnf(c_0_204,negated_conjecture,
product(t,p,p),
inference(spm,[status(thm)],[c_0_44,c_0_201]) ).
cnf(c_0_205,plain,
( product(X1,multiplicative_inverse(X1),multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_206,negated_conjecture,
( product(X1,l,p)
| ~ product(X1,k,p) ),
inference(spm,[status(thm)],[c_0_200,c_0_202]) ).
cnf(c_0_207,negated_conjecture,
product(t,k,p),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_208,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_42,c_0_205]) ).
cnf(c_0_209,negated_conjecture,
( product(X1,b,X2)
| ~ product(X3,l,X2)
| ~ product(X3,d,X1) ),
inference(spm,[status(thm)],[c_0_180,c_0_50]) ).
cnf(c_0_210,negated_conjecture,
product(t,l,p),
inference(spm,[status(thm)],[c_0_206,c_0_207]) ).
cnf(c_0_211,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_208,c_0_57]),c_0_82]),c_0_52])]),c_0_53]) ).
cnf(c_0_212,negated_conjecture,
( product(X1,b,p)
| ~ product(t,d,X1) ),
inference(spm,[status(thm)],[c_0_209,c_0_210]) ).
cnf(c_0_213,negated_conjecture,
product(t,d,c),
inference(spm,[status(thm)],[c_0_44,c_0_211]) ).
cnf(c_0_214,negated_conjecture,
product(c,b,p),
inference(spm,[status(thm)],[c_0_212,c_0_213]) ).
cnf(c_0_215,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_208,c_0_66]),c_0_98]),c_0_51])]),c_0_61]) ).
cnf(c_0_216,negated_conjecture,
product(b,c,p),
inference(spm,[status(thm)],[c_0_44,c_0_214]) ).
cnf(c_0_217,negated_conjecture,
product(s,b,a),
inference(spm,[status(thm)],[c_0_44,c_0_215]) ).
cnf(c_0_218,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_49,c_0_59]),c_0_98]),c_0_52])]),c_0_53]) ).
cnf(c_0_219,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_49,c_0_216]),c_0_82]),c_0_51])]),c_0_61]) ).
cnf(c_0_220,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_84,c_0_179]) ).
cnf(c_0_221,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_84,c_0_98]) ).
cnf(c_0_222,negated_conjecture,
( product(X1,X2,a)
| ~ product(X3,b,X2)
| ~ product(X1,X3,s) ),
inference(spm,[status(thm)],[c_0_38,c_0_217]) ).
cnf(c_0_223,negated_conjecture,
product(c,b,q),
inference(spm,[status(thm)],[c_0_44,c_0_47]) ).
cnf(c_0_224,negated_conjecture,
( product(multiplicative_inverse(d),X1,s)
| ~ product(p,multiplicative_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_218]) ).
cnf(c_0_225,negated_conjecture,
product(p,multiplicative_inverse(b),c),
inference(spm,[status(thm)],[c_0_44,c_0_219]) ).
cnf(c_0_226,hypothesis,
sum(additive_identity,d,d),
inference(spm,[status(thm)],[c_0_84,c_0_52]) ).
cnf(c_0_227,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_126,c_0_220]) ).
cnf(c_0_228,plain,
( sum(X1,additive_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_84]) ).
cnf(c_0_229,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,a,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_92,c_0_221]) ).
cnf(c_0_230,negated_conjecture,
( product(X1,q,a)
| ~ product(X1,c,s) ),
inference(spm,[status(thm)],[c_0_222,c_0_223]) ).
cnf(c_0_231,negated_conjecture,
product(multiplicative_inverse(d),c,s),
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_232,hypothesis,
( sum(X1,X2,d)
| ~ sum(X3,d,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_92,c_0_226]) ).
cnf(c_0_233,hypothesis,
( sum(X1,q,X2)
| ~ sum(X3,q,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_126,c_0_138]) ).
cnf(c_0_234,negated_conjecture,
sum(additive_identity,q,additive_identity),
inference(spm,[status(thm)],[c_0_102,c_0_137]) ).
cnf(c_0_235,plain,
( sum(X1,additive_identity,X2)
| ~ defined(X2)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_227,c_0_228]) ).
cnf(c_0_236,hypothesis,
defined(k),
k_is_defined ).
cnf(c_0_237,hypothesis,
( sum(X1,a,a)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_229,c_0_221]) ).
cnf(c_0_238,plain,
( sum(additive_identity,X1,additive_identity)
| sum(X2,X3,multiplicative_identity)
| ~ product(X4,multiplicative_inverse(X1),X3)
| ~ product(X5,multiplicative_inverse(X1),X2)
| ~ defined(X1)
| ~ sum(X5,X4,X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_205]) ).
cnf(c_0_239,negated_conjecture,
product(multiplicative_inverse(d),q,a),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_240,hypothesis,
( sum(X1,d,d)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_232,c_0_226]) ).
cnf(c_0_241,negated_conjecture,
( sum(X1,k,p)
| ~ sum(X1,q,additive_identity) ),
inference(spm,[status(thm)],[c_0_128,c_0_135]) ).
cnf(c_0_242,hypothesis,
( sum(X1,q,additive_identity)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_243,negated_conjecture,
sum(additive_identity,additive_identity,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_150]),c_0_236])]) ).
cnf(c_0_244,hypothesis,
sum(l,a,a),
inference(spm,[status(thm)],[c_0_237,c_0_108]) ).
cnf(c_0_245,plain,
( sum(X1,multiplicative_identity,multiplicative_identity)
| sum(additive_identity,X2,additive_identity)
| ~ product(X3,multiplicative_inverse(X2),X1)
| ~ defined(X2)
| ~ sum(X3,X2,X2) ),
inference(spm,[status(thm)],[c_0_238,c_0_205]) ).
cnf(c_0_246,negated_conjecture,
product(q,multiplicative_inverse(d),a),
inference(spm,[status(thm)],[c_0_44,c_0_239]) ).
cnf(c_0_247,hypothesis,
sum(q,d,d),
inference(spm,[status(thm)],[c_0_240,c_0_137]) ).
cnf(c_0_248,negated_conjecture,
sum(additive_inverse(q),k,p),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_110]),c_0_131])]) ).
cnf(c_0_249,negated_conjecture,
sum(k,q,additive_identity),
inference(spm,[status(thm)],[c_0_242,c_0_243]) ).
cnf(c_0_250,negated_conjecture,
( product(X1,c,X2)
| ~ product(X3,q,X2)
| ~ product(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_180,c_0_47]) ).
cnf(c_0_251,hypothesis,
( sum(X1,l,X2)
| ~ sum(X3,l,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_126,c_0_164]) ).
cnf(c_0_252,hypothesis,
sum(a,l,a),
inference(spm,[status(thm)],[c_0_102,c_0_244]) ).
cnf(c_0_253,negated_conjecture,
sum(a,multiplicative_identity,multiplicative_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_246]),c_0_52]),c_0_247])]),c_0_53]) ).
cnf(c_0_254,negated_conjecture,
( product(X1,additive_identity,p)
| ~ product(X1,k,p) ),
inference(spm,[status(thm)],[c_0_200,c_0_189]) ).
cnf(c_0_255,hypothesis,
sum(l,p,p),
inference(spm,[status(thm)],[c_0_136,c_0_108]) ).
cnf(c_0_256,negated_conjecture,
sum(k,additive_inverse(q),p),
inference(spm,[status(thm)],[c_0_102,c_0_248]) ).
cnf(c_0_257,hypothesis,
sum(k,q,q),
inference(spm,[status(thm)],[c_0_158,c_0_150]) ).
cnf(c_0_258,negated_conjecture,
product(additive_identity,multiplicative_identity,q),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_249]),c_0_189])]) ).
cnf(c_0_259,negated_conjecture,
sum(p,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_140]),c_0_120])]) ).
cnf(c_0_260,negated_conjecture,
( product(X1,c,p)
| ~ product(s,b,X1) ),
inference(spm,[status(thm)],[c_0_250,c_0_195]) ).
cnf(c_0_261,hypothesis,
( sum(X1,l,a)
| ~ sum(a,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_251,c_0_252]) ).
cnf(c_0_262,negated_conjecture,
sum(a,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_253]),c_0_85])]) ).
cnf(c_0_263,negated_conjecture,
product(t,additive_identity,p),
inference(spm,[status(thm)],[c_0_254,c_0_207]) ).
cnf(c_0_264,hypothesis,
sum(p,l,p),
inference(spm,[status(thm)],[c_0_102,c_0_255]) ).
cnf(c_0_265,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_123,c_0_256]),c_0_131])]) ).
cnf(c_0_266,hypothesis,
sum(q,k,q),
inference(spm,[status(thm)],[c_0_102,c_0_257]) ).
cnf(c_0_267,negated_conjecture,
product(multiplicative_identity,additive_identity,q),
inference(spm,[status(thm)],[c_0_44,c_0_258]) ).
cnf(c_0_268,hypothesis,
sum(p,q,q),
inference(spm,[status(thm)],[c_0_158,c_0_259]) ).
cnf(c_0_269,negated_conjecture,
( product(X1,d,X2)
| ~ product(X3,c,X2)
| ~ product(X3,t,X1) ),
inference(spm,[status(thm)],[c_0_180,c_0_213]) ).
cnf(c_0_270,negated_conjecture,
product(a,c,p),
inference(spm,[status(thm)],[c_0_260,c_0_217]) ).
cnf(c_0_271,negated_conjecture,
( product(X1,t,k)
| ~ product(X2,t,p)
| ~ sum(X2,l,X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_70]) ).
cnf(c_0_272,hypothesis,
sum(additive_identity,l,a),
inference(spm,[status(thm)],[c_0_261,c_0_262]) ).
cnf(c_0_273,negated_conjecture,
product(additive_identity,t,p),
inference(spm,[status(thm)],[c_0_44,c_0_263]) ).
cnf(c_0_274,hypothesis,
( product(X1,X2,p)
| ~ product(X3,X2,p)
| ~ product(X4,X2,additive_identity)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_122]) ).
cnf(c_0_275,hypothesis,
( sum(X1,p,l)
| ~ sum(X1,p,additive_identity) ),
inference(spm,[status(thm)],[c_0_170,c_0_264]) ).
cnf(c_0_276,negated_conjecture,
sum(q,p,additive_identity),
inference(spm,[status(thm)],[c_0_265,c_0_266]) ).
cnf(c_0_277,negated_conjecture,
product(multiplicative_identity,q,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_267]),c_0_179])]) ).
cnf(c_0_278,negated_conjecture,
( product(X1,multiplicative_identity,q)
| ~ product(q,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_159]),c_0_85])]) ).
cnf(c_0_279,hypothesis,
product(q,multiplicative_identity,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_268]),c_0_168])]) ).
cnf(c_0_280,negated_conjecture,
( product(X1,d,p)
| ~ product(a,t,X1) ),
inference(spm,[status(thm)],[c_0_269,c_0_270]) ).
cnf(c_0_281,negated_conjecture,
product(a,t,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_271,c_0_272]),c_0_273])]) ).
cnf(c_0_282,negated_conjecture,
( product(X1,multiplicative_identity,p)
| ~ product(X2,multiplicative_identity,additive_identity)
| ~ sum(X2,p,X1) ),
inference(spm,[status(thm)],[c_0_274,c_0_168]) ).
cnf(c_0_283,hypothesis,
sum(q,p,l),
inference(spm,[status(thm)],[c_0_275,c_0_276]) ).
cnf(c_0_284,negated_conjecture,
product(q,multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_44,c_0_277]) ).
cnf(c_0_285,negated_conjecture,
product(k,multiplicative_identity,q),
inference(spm,[status(thm)],[c_0_278,c_0_279]) ).
cnf(c_0_286,negated_conjecture,
product(k,d,p),
inference(spm,[status(thm)],[c_0_280,c_0_281]) ).
cnf(c_0_287,negated_conjecture,
( sum(X1,X2,p)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X4,multiplicative_identity,X1)
| ~ sum(X4,X3,p) ),
inference(spm,[status(thm)],[c_0_99,c_0_168]) ).
cnf(c_0_288,plain,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_additive_inverse]) ).
cnf(c_0_289,hypothesis,
product(l,multiplicative_identity,p),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282,c_0_283]),c_0_284])]) ).
cnf(c_0_290,negated_conjecture,
( product(X1,q,p)
| ~ product(X1,k,p) ),
inference(spm,[status(thm)],[c_0_200,c_0_285]) ).
cnf(c_0_291,negated_conjecture,
product(d,k,p),
inference(spm,[status(thm)],[c_0_44,c_0_286]) ).
cnf(c_0_292,negated_conjecture,
( sum(X1,q,p)
| ~ product(X2,multiplicative_identity,X1)
| ~ sum(X2,q,p) ),
inference(spm,[status(thm)],[c_0_287,c_0_159]) ).
cnf(c_0_293,plain,
( sum(X1,X2,additive_identity)
| ~ defined(X3)
| ~ sum(X1,X4,additive_inverse(X3))
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_110]) ).
cnf(c_0_294,plain,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
c_0_288 ).
cnf(c_0_295,hypothesis,
( sum(X1,l,q)
| ~ sum(q,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_251,c_0_171]) ).
cnf(c_0_296,negated_conjecture,
( product(X1,X2,q)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,q) ),
inference(spm,[status(thm)],[c_0_38,c_0_159]) ).
cnf(c_0_297,negated_conjecture,
product(p,multiplicative_identity,l),
inference(spm,[status(thm)],[c_0_198,c_0_289]) ).
cnf(c_0_298,negated_conjecture,
product(d,q,p),
inference(spm,[status(thm)],[c_0_290,c_0_291]) ).
cnf(c_0_299,negated_conjecture,
sum(k,q,p),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_292,c_0_183]),c_0_175])]) ).
cnf(c_0_300,plain,
( sum(additive_inverse(X1),X2,additive_identity)
| ~ defined(X1)
| ~ sum(additive_identity,X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_293,c_0_228]),c_0_294]) ).
cnf(c_0_301,hypothesis,
sum(additive_identity,l,q),
inference(spm,[status(thm)],[c_0_295,c_0_137]) ).
cnf(c_0_302,negated_conjecture,
( product(X1,l,q)
| ~ product(X1,p,q) ),
inference(spm,[status(thm)],[c_0_296,c_0_297]) ).
cnf(c_0_303,negated_conjecture,
product(multiplicative_inverse(d),p,q),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_298]),c_0_131]),c_0_52])]),c_0_53]) ).
cnf(c_0_304,negated_conjecture,
sum(q,k,p),
inference(spm,[status(thm)],[c_0_102,c_0_299]) ).
cnf(c_0_305,hypothesis,
sum(additive_inverse(l),q,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_301]),c_0_88])]) ).
cnf(c_0_306,negated_conjecture,
( product(X1,multiplicative_identity,b)
| ~ product(multiplicative_inverse(d),l,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_58]),c_0_88])]) ).
cnf(c_0_307,negated_conjecture,
product(multiplicative_inverse(d),l,q),
inference(spm,[status(thm)],[c_0_302,c_0_303]) ).
cnf(c_0_308,negated_conjecture,
sum(q,q,additive_identity),
inference(spm,[status(thm)],[c_0_160,c_0_304]) ).
cnf(c_0_309,hypothesis,
sum(q,additive_inverse(l),additive_identity),
inference(spm,[status(thm)],[c_0_102,c_0_305]) ).
cnf(c_0_310,negated_conjecture,
product(q,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_306,c_0_307]) ).
cnf(c_0_311,hypothesis,
sum(q,q,l),
inference(spm,[status(thm)],[c_0_176,c_0_308]) ).
cnf(c_0_312,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,q,l) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_309]),c_0_88])]) ).
cnf(c_0_313,negated_conjecture,
sum(b,q,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_310]),c_0_311])]) ).
cnf(c_0_314,hypothesis,
sum(b,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_312,c_0_313]) ).
cnf(c_0_315,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_314]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : FLD052-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n010.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 13:25:03 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.17/0.41 Running first-order theorem proving
% 0.17/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.bUhyaQRkru/E---3.1_8864.p
% 13.22/2.08 # Version: 3.1.0
% 13.22/2.08 # Preprocessing class: FSMSSMSMSSSNFFN.
% 13.22/2.08 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.22/2.08 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 13.22/2.08 # Starting new_bool_3 with 300s (1) cores
% 13.22/2.08 # Starting new_bool_1 with 300s (1) cores
% 13.22/2.08 # Starting sh5l with 300s (1) cores
% 13.22/2.08 # sh5l with pid 8945 completed with status 0
% 13.22/2.08 # Result found by sh5l
% 13.22/2.08 # Preprocessing class: FSMSSMSMSSSNFFN.
% 13.22/2.08 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.22/2.08 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 13.22/2.08 # Starting new_bool_3 with 300s (1) cores
% 13.22/2.08 # Starting new_bool_1 with 300s (1) cores
% 13.22/2.08 # Starting sh5l with 300s (1) cores
% 13.22/2.08 # SinE strategy is gf500_gu_R04_F100_L20000
% 13.22/2.08 # Search class: FGUNF-FFMM11-SFFFFFNN
% 13.22/2.08 # partial match(1): FGUNF-FFMM21-SFFFFFNN
% 13.22/2.08 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 13.22/2.08 # Starting G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with 118s (1) cores
% 13.22/2.08 # G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with pid 8952 completed with status 0
% 13.22/2.08 # Result found by G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S
% 13.22/2.08 # Preprocessing class: FSMSSMSMSSSNFFN.
% 13.22/2.08 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.22/2.08 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 13.22/2.08 # Starting new_bool_3 with 300s (1) cores
% 13.22/2.08 # Starting new_bool_1 with 300s (1) cores
% 13.22/2.08 # Starting sh5l with 300s (1) cores
% 13.22/2.08 # SinE strategy is gf500_gu_R04_F100_L20000
% 13.22/2.08 # Search class: FGUNF-FFMM11-SFFFFFNN
% 13.22/2.08 # partial match(1): FGUNF-FFMM21-SFFFFFNN
% 13.22/2.08 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 13.22/2.08 # Starting G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with 118s (1) cores
% 13.22/2.08 # Preprocessing time : 0.001 s
% 13.22/2.08
% 13.22/2.08 # Proof found!
% 13.22/2.08 # SZS status Unsatisfiable
% 13.22/2.08 # SZS output start CNFRefutation
% See solution above
% 13.22/2.08 # Parsed axioms : 48
% 13.22/2.08 # Removed by relevancy pruning/SinE : 5
% 13.22/2.08 # Initial clauses : 43
% 13.22/2.08 # Removed in clause preprocessing : 0
% 13.22/2.08 # Initial clauses in saturation : 43
% 13.22/2.08 # Processed clauses : 14240
% 13.22/2.08 # ...of these trivial : 6255
% 13.22/2.08 # ...subsumed : 1123
% 13.22/2.08 # ...remaining for further processing : 6862
% 13.22/2.08 # Other redundant clauses eliminated : 0
% 13.22/2.08 # Clauses deleted for lack of memory : 0
% 13.22/2.08 # Backward-subsumed : 3
% 13.22/2.08 # Backward-rewritten : 814
% 13.22/2.08 # Generated clauses : 106114
% 13.22/2.08 # ...of the previous two non-redundant : 71192
% 13.22/2.08 # ...aggressively subsumed : 0
% 13.22/2.08 # Contextual simplify-reflections : 26
% 13.22/2.08 # Paramodulations : 106048
% 13.22/2.08 # Factorizations : 66
% 13.22/2.08 # NegExts : 0
% 13.22/2.08 # Equation resolutions : 0
% 13.22/2.08 # Disequality decompositions : 0
% 13.22/2.08 # Total rewrite steps : 80909
% 13.22/2.08 # ...of those cached : 79024
% 13.22/2.08 # Propositional unsat checks : 0
% 13.22/2.08 # Propositional check models : 0
% 13.22/2.08 # Propositional check unsatisfiable : 0
% 13.22/2.08 # Propositional clauses : 0
% 13.22/2.08 # Propositional clauses after purity: 0
% 13.22/2.08 # Propositional unsat core size : 0
% 13.22/2.08 # Propositional preprocessing time : 0.000
% 13.22/2.08 # Propositional encoding time : 0.000
% 13.22/2.08 # Propositional solver time : 0.000
% 13.22/2.08 # Success case prop preproc time : 0.000
% 13.22/2.08 # Success case prop encoding time : 0.000
% 13.22/2.08 # Success case prop solver time : 0.000
% 13.22/2.08 # Current number of processed clauses : 6045
% 13.22/2.08 # Positive orientable unit clauses : 1977
% 13.22/2.08 # Positive unorientable unit clauses: 0
% 13.22/2.08 # Negative unit clauses : 4
% 13.22/2.08 # Non-unit-clauses : 4064
% 13.22/2.08 # Current number of unprocessed clauses: 56977
% 13.22/2.08 # ...number of literals in the above : 141841
% 13.22/2.08 # Current number of archived formulas : 0
% 13.22/2.08 # Current number of archived clauses : 817
% 13.22/2.08 # Clause-clause subsumption calls (NU) : 893762
% 13.22/2.08 # Rec. Clause-clause subsumption calls : 692865
% 13.22/2.08 # Non-unit clause-clause subsumptions : 1150
% 13.22/2.08 # Unit Clause-clause subsumption calls : 359324
% 13.22/2.08 # Rewrite failures with RHS unbound : 0
% 13.22/2.08 # BW rewrite match attempts : 6693
% 13.22/2.08 # BW rewrite match successes : 284
% 13.22/2.08 # Condensation attempts : 0
% 13.22/2.08 # Condensation successes : 0
% 13.22/2.08 # Termbank termtop insertions : 1300499
% 13.22/2.08 # Search garbage collected termcells : 133
% 13.22/2.08
% 13.22/2.08 # -------------------------------------------------
% 13.22/2.08 # User time : 1.576 s
% 13.22/2.08 # System time : 0.043 s
% 13.22/2.08 # Total time : 1.619 s
% 13.22/2.08 # Maximum resident set size: 1868 pages
% 13.22/2.08
% 13.22/2.08 # -------------------------------------------------
% 13.22/2.08 # User time : 1.578 s
% 13.22/2.08 # System time : 0.044 s
% 13.22/2.08 # Total time : 1.623 s
% 13.22/2.08 # Maximum resident set size: 1752 pages
% 13.22/2.08 % E---3.1 exiting
% 13.22/2.08 % E exiting
%------------------------------------------------------------------------------