%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO008-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : Tue May 5 04:11:04 PM UTC 2026
% Result : Unsatisfiable 131.77s 96.46s
% Output : CNFRefutation 137.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 36
% Syntax : Number of clauses : 555 ( 460 unt; 0 nHn; 141 RR)
% Number of literals : 763 ( 42 equ; 215 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 844 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity2,axiom,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity2) ).
cnf(distributivity5,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ sum(X1,X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity5) ).
cnf(distributivity7,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ sum(X6,X2,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity7) ).
cnf(distributivity4,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
cnf(distributivity6,axiom,
( sum(X1,X6,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
cnf(distributivity3,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity3) ).
cnf(distributivity1,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity1) ).
cnf(distributivity8,axiom,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity8) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(commutativity_of_multiplication,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
cnf(x_plus_y__plus_z,hypothesis,
sum(x_plus_y,z,x_plus_y__plus_z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y__plus_z) ).
cnf(x_plus__y_plus_z,hypothesis,
sum(x,y_plus_z,x__plus_y_plus_z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus__y_plus_z) ).
cnf(x_plus_y,hypothesis,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).
cnf(y_plus_z,hypothesis,
sum(y,z,y_plus_z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',y_plus_z) ).
cnf(prove_equality,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equality) ).
cnf(i_0_27,axiom,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity2,
[final] ).
cnf(i_0_28,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ sum(X1,X6,X7) ),
distributivity5,
[final] ).
cnf(i_0_29,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ sum(X6,X2,X7) ),
distributivity7,
[final] ).
cnf(i_0_30,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity4,
[final] ).
cnf(i_0_31,axiom,
( sum(X1,X6,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X3,X5,X7) ),
distributivity6,
[final] ).
cnf(i_0_32,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
distributivity3,
[final] ).
cnf(i_0_33,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
distributivity1,
[final] ).
cnf(i_0_34,axiom,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
distributivity8,
[final] ).
cnf(i_0_35,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined,
[final] ).
cnf(i_0_36,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined,
[final] ).
cnf(i_0_37,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity_of_multiplication,
[final] ).
cnf(i_0_38,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition,
[final] ).
cnf(i_0_39,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication,
[final] ).
cnf(i_0_40,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition,
[final] ).
cnf(i_0_41,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1,
[final] ).
cnf(i_0_42,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1,
[final] ).
cnf(i_0_43,axiom,
product(X1,inverse(X1),additive_identity),
multiplicative_inverse2,
[final] ).
cnf(i_0_44,axiom,
sum(X1,inverse(X1),multiplicative_identity),
additive_inverse2,
[final] ).
cnf(i_0_45,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1,
[final] ).
cnf(i_0_46,axiom,
sum(additive_identity,X1,X1),
additive_identity1,
[final] ).
cnf(i_0_47,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2,
[final] ).
cnf(i_0_48,axiom,
sum(X1,additive_identity,X1),
additive_identity2,
[final] ).
cnf(i_0_49,hypothesis,
sum(x_plus_y,z,x_plus_y__plus_z),
x_plus_y__plus_z,
[final] ).
cnf(i_0_50,hypothesis,
sum(x,y_plus_z,x__plus_y_plus_z),
x_plus__y_plus_z,
[final] ).
cnf(i_0_51,hypothesis,
sum(x,y,x_plus_y),
x_plus_y,
[final] ).
cnf(i_0_52,hypothesis,
sum(y,z,y_plus_z),
y_plus_z,
[final] ).
cnf(i_0_53,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
prove_equality,
[final] ).
cnf(i_0_54,axiom,
X1 = X1 ).
cnf(i_0_55,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_56,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_57,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_58,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_59,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_60,axiom,
( X1 != X2
| ~ sum(X1,X3,X4)
| sum(X2,X3,X4) ) ).
cnf(i_0_61,axiom,
( X1 != X2
| ~ sum(X3,X1,X4)
| sum(X3,X2,X4) ) ).
cnf(i_0_62,axiom,
( X1 != X2
| ~ sum(X3,X4,X1)
| sum(X3,X4,X2) ) ).
cnf(i_0_63,plain,
product(X1,X2,multiply(X2,X1)),
inference(scs_inference,[],[i_0_39,i_0_37]) ).
cnf(i_0_65,plain,
sum(X1,X2,add(X2,X1)),
inference(scs_inference,[],[i_0_39,i_0_40,i_0_37,i_0_38]) ).
cnf(i_0_67,plain,
~ product(multiplicative_identity,x_plus_y__plus_z,x__plus_y_plus_z),
inference(scs_inference,[],[i_0_53,i_0_45,i_0_39,i_0_40,i_0_37,i_0_38,i_0_35]) ).
cnf(i_0_68,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_70,plain,
~ sum(additive_identity,x_plus_y__plus_z,x__plus_y_plus_z),
inference(scs_inference,[],[i_0_53,i_0_45,i_0_46,i_0_39,i_0_40,i_0_37,i_0_38,i_0_35,i_0_36]) ).
cnf(i_0_71,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_74,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_76,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_77,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_78,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_79,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_82,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_83,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_84,plain,
product(inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_87,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_88,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_91,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_92,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_93,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_94,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_97,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_98,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_99,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_100,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_103,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_104,plain,
product(inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_105,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_108,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_109,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_110,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_111,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_114,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_115,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_116,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_117,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_121,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_147,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_153,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_163,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_181,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_195,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_204,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_205,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_206,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_209,plain,
product(inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_211,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_214,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_215,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_216,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_221,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_225,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_226,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_228,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_229,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_245,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_247,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_278,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_283,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_286,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_289,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_290,plain,
product(inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_291,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_295,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_296,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_300,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_301,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_304,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_305,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_306,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_337,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_341,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_342,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_348,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_351,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_365,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_368,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_370,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_371,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_372,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_378,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_380,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_381,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_382,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_383,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_384,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_398,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_403,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_405,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_412,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_413,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_417,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_420,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_426,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_427,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_428,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_432,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_447,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_459,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_460,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_461,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_462,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_463,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_464,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_476,plain,
product(inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_477,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_482,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_488,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_489,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_492,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_493,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_501,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_507,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_508,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_516,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_524,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_525,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_528,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_529,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_532,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_533,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_537,plain,
sum(z,x_plus_y,x_plus_y__plus_z),
inference(scs_inference,[],[i_0_49,i_0_38]) ).
cnf(i_0_545,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_553,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_557,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_560,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_564,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_568,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_572,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_586,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_591,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_592,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_593,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_594,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_595,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_596,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_605,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_614,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_618,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_631,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_634,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_635,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_644,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_645,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_648,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_649,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_664,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_667,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_672,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_673,plain,
product(inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_677,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_680,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_681,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_692,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_696,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_697,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_698,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_710,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_723,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_729,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_753,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_754,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_757,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_758,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_761,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_762,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_769,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_776,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_781,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_782,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_785,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_786,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_789,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_790,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_806,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_809,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_810,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_815,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_816,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_832,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_835,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_837,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_838,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_839,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_840,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_841,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_842,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_843,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_844,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_845,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_846,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_853,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_858,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_863,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_870,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_871,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_889,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_910,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_920,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_928,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_929,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_943,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_947,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_953,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_957,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_958,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_960,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_961,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_962,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_963,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_978,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_988,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_989,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_991,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_992,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_993,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1002,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1006,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1016,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1017,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1020,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1021,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1025,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1029,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1032,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1039,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1045,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_1046,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1057,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1065,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1071,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1075,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1084,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1088,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1096,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1097,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1101,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1102,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1107,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1130,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1138,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1148,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1153,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1154,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1156,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1157,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1158,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1159,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1160,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1161,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1162,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1165,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1167,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1177,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1181,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1183,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1184,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1185,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1186,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_1187,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1188,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1189,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1190,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1191,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1192,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1196,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1205,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1209,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1216,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_1218,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_1219,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1220,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1224,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_1227,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_1228,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1229,plain,
product(inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1234,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1235,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1238,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1239,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1246,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_1247,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1248,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1253,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1254,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1257,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1258,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1261,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_1265,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1267,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1268,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1269,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1270,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1271,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1272,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1273,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1287,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1291,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1293,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1294,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_1295,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1296,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1311,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1315,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1319,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1327,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1331,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1332,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1333,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1334,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1335,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1336,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1337,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1338,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1339,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1347,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1351,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1352,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1353,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1356,plain,
product(inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1357,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1358,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_1362,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1363,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1364,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1367,plain,
product(inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1368,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1369,plain,
sum(inverse(X1),X1,multiplicative_identity),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_1378,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1389,plain,
product(X1,inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1390,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1391,plain,
sum(X1,inverse(X1),multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_1395,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1396,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1397,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1401,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1402,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1403,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1412,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1413,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1414,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1419,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1420,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1423,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1424,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1427,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1428,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1443,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1447,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1453,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1454,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1457,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1460,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1470,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1473,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1477,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1486,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1494,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1497,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1498,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1500,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1501,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1511,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1512,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_1515,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1519,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_1530,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1534,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1537,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1538,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1542,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(c_0_563,axiom,
( product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ product(X6,X2,X7)
| ~ sum(X4,X6,X1)
| ~ sum(X5,X7,X3) ),
i_0_30 ).
cnf(c_0_564,axiom,
sum(additive_identity,X1,X1),
i_0_46 ).
cnf(c_0_565,plain,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ product(X4,X2,additive_identity)
| ~ product(X5,X2,X3) ),
inference(spm,[status(thm)],[c_0_563,c_0_564]) ).
cnf(c_0_566,axiom,
product(inverse(X1),X1,additive_identity),
i_0_41 ).
cnf(c_0_567,axiom,
( X1 = X2
| ~ product(X3,X4,X1)
| ~ product(X3,X4,X2) ),
i_0_35 ).
cnf(c_0_568,plain,
product(X1,X2,multiply(X2,X1)),
i_0_63 ).
cnf(c_0_569,plain,
( product(X1,X2,X3)
| ~ sum(inverse(X2),X4,X1)
| ~ product(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_565,c_0_566]) ).
cnf(c_0_570,axiom,
sum(X1,additive_identity,X1),
i_0_48 ).
cnf(c_0_571,plain,
( X1 = additive_identity
| ~ product(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_567,c_0_566]) ).
cnf(c_0_572,plain,
( X1 = multiply(X2,X3)
| ~ product(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_567,c_0_568]) ).
cnf(c_0_573,plain,
( product(inverse(X1),X1,X2)
| ~ product(additive_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_569,c_0_570]) ).
cnf(c_0_574,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_571,c_0_568]) ).
cnf(c_0_575,plain,
( X1 = additive_identity
| ~ product(additive_identity,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_572,c_0_573]),c_0_574]) ).
cnf(c_0_576,axiom,
product(X1,X2,multiply(X1,X2)),
i_0_39 ).
cnf(c_0_577,axiom,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X4,X6,X2)
| ~ product(X5,X6,X7)
| ~ sum(X4,X7,X3) ),
i_0_28 ).
cnf(c_0_578,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_575,c_0_576]) ).
cnf(c_0_579,axiom,
( X1 = X2
| ~ sum(X3,X4,X1)
| ~ sum(X3,X4,X2) ),
i_0_36 ).
cnf(c_0_580,plain,
( product(X1,X2,X3)
| ~ sum(X3,X4,X2)
| ~ sum(X3,X5,X1)
| ~ product(X5,X4,additive_identity) ),
inference(spm,[status(thm)],[c_0_577,c_0_570]) ).
cnf(c_0_581,plain,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_568,c_0_578]) ).
cnf(c_0_582,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_579,c_0_564]) ).
cnf(c_0_583,plain,
sum(X1,X2,add(X2,X1)),
i_0_65 ).
cnf(c_0_584,plain,
( product(X1,X2,X3)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_580,c_0_581]) ).
cnf(c_0_585,axiom,
sum(X1,X2,add(X1,X2)),
i_0_40 ).
cnf(c_0_586,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_582,c_0_583]) ).
cnf(c_0_587,axiom,
sum(inverse(X1),X1,multiplicative_identity),
i_0_42 ).
cnf(c_0_588,axiom,
product(multiplicative_identity,X1,X1),
i_0_45 ).
cnf(c_0_589,axiom,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X6,X5,X2)
| ~ sum(X4,X6,X7)
| ~ product(X7,X5,X3) ),
i_0_32 ).
cnf(c_0_590,plain,
( product(X1,X2,X2)
| ~ sum(X2,X3,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_584,c_0_585]),c_0_586]) ).
cnf(c_0_591,plain,
( product(multiplicative_identity,X1,X2)
| ~ product(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_569,c_0_587]) ).
cnf(c_0_592,plain,
( X1 = X2
| ~ product(multiplicative_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_567,c_0_588]) ).
cnf(c_0_593,plain,
product(additive_identity,X1,additive_identity),
inference(spm,[status(thm)],[c_0_576,c_0_578]) ).
cnf(c_0_594,plain,
( sum(X1,X2,X3)
| ~ product(add(X4,X5),X6,X3)
| ~ product(X5,X6,X2)
| ~ product(X4,X6,X1) ),
inference(spm,[status(thm)],[c_0_589,c_0_585]) ).
cnf(c_0_595,plain,
product(add(X1,X2),X2,X2),
inference(spm,[status(thm)],[c_0_590,c_0_583]) ).
cnf(c_0_596,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_567,c_0_576]) ).
cnf(c_0_597,plain,
product(multiplicative_identity,X1,multiply(X1,X1)),
inference(spm,[status(thm)],[c_0_591,c_0_576]) ).
cnf(c_0_598,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_592,c_0_576]) ).
cnf(c_0_599,hypothesis,
sum(x,y,x_plus_y),
i_0_51 ).
cnf(c_0_600,plain,
( product(X1,X2,X3)
| ~ sum(X3,additive_identity,X1)
| ~ sum(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_580,c_0_593]) ).
cnf(c_0_601,plain,
( sum(X1,X2,X3)
| ~ product(X3,X3,X2)
| ~ product(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_594,c_0_595]) ).
cnf(c_0_602,plain,
multiply(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_596,c_0_597]),c_0_598]) ).
cnf(c_0_603,hypothesis,
( product(X1,X2,x_plus_y)
| ~ sum(x,X3,X2)
| ~ sum(x,X4,X1)
| ~ product(X4,X3,y) ),
inference(spm,[status(thm)],[c_0_577,c_0_599]) ).
cnf(c_0_604,hypothesis,
sum(x,y_plus_z,x__plus_y_plus_z),
i_0_50 ).
cnf(c_0_605,plain,
( product(X1,X2,X1)
| ~ sum(X1,X3,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_600,c_0_585]),c_0_586]) ).
cnf(c_0_606,hypothesis,
sum(y,z,y_plus_z),
i_0_52 ).
cnf(c_0_607,plain,
product(add(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_590,c_0_585]) ).
cnf(c_0_608,hypothesis,
sum(x_plus_y,z,x_plus_y__plus_z),
i_0_49 ).
cnf(c_0_609,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
i_0_38 ).
cnf(c_0_610,plain,
( sum(X1,X2,X2)
| ~ product(X3,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_601,c_0_576]),c_0_602]) ).
cnf(c_0_611,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_579,c_0_585]) ).
cnf(c_0_612,hypothesis,
( product(X1,x__plus_y_plus_z,x_plus_y)
| ~ sum(x,X2,X1)
| ~ product(X2,y_plus_z,y) ),
inference(spm,[status(thm)],[c_0_603,c_0_604]) ).
cnf(c_0_613,hypothesis,
product(y,y_plus_z,y),
inference(spm,[status(thm)],[c_0_605,c_0_606]) ).
cnf(c_0_614,plain,
sum(z,x_plus_y,x_plus_y__plus_z),
i_0_537 ).
cnf(c_0_615,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X1,X6,X7)
| ~ product(X4,X6,X2)
| ~ product(X5,X7,X3) ),
i_0_31 ).
cnf(c_0_616,plain,
( sum(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X3,X3,X1) ),
inference(spm,[status(thm)],[c_0_594,c_0_607]) ).
cnf(c_0_617,hypothesis,
product(x_plus_y,x_plus_y__plus_z,x_plus_y),
inference(spm,[status(thm)],[c_0_605,c_0_608]) ).
cnf(c_0_618,hypothesis,
sum(y_plus_z,x,x__plus_y_plus_z),
inference(spm,[status(thm)],[c_0_609,c_0_604]) ).
cnf(c_0_619,plain,
sum(multiply(X1,X2),X2,X2),
inference(spm,[status(thm)],[c_0_610,c_0_576]) ).
cnf(c_0_620,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_611,c_0_583]) ).
cnf(c_0_621,hypothesis,
( product(X1,x__plus_y_plus_z,x_plus_y)
| ~ sum(x,y,X1) ),
inference(spm,[status(thm)],[c_0_612,c_0_613]) ).
cnf(c_0_622,hypothesis,
( product(X1,X2,y_plus_z)
| ~ sum(y,X3,X2)
| ~ sum(y,X4,X1)
| ~ product(X4,X3,z) ),
inference(spm,[status(thm)],[c_0_577,c_0_606]) ).
cnf(c_0_623,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
i_0_37 ).
cnf(c_0_624,plain,
product(z,x_plus_y__plus_z,z),
inference(spm,[status(thm)],[c_0_605,c_0_614]) ).
cnf(c_0_625,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X5,add(X1,X6),X3)
| ~ product(X4,X6,X2) ),
inference(spm,[status(thm)],[c_0_615,c_0_585]) ).
cnf(c_0_626,plain,
product(X1,add(X1,X2),X1),
inference(spm,[status(thm)],[c_0_605,c_0_585]) ).
cnf(c_0_627,hypothesis,
( sum(X1,x_plus_y,x_plus_y__plus_z)
| ~ product(x_plus_y__plus_z,x_plus_y__plus_z,X1) ),
inference(spm,[status(thm)],[c_0_616,c_0_617]) ).
cnf(c_0_628,hypothesis,
sum(y,x,x_plus_y),
inference(spm,[status(thm)],[c_0_609,c_0_599]) ).
cnf(c_0_629,hypothesis,
( product(X1,X2,x__plus_y_plus_z)
| ~ sum(X3,X4,X1)
| ~ product(X4,X2,x)
| ~ product(X3,X2,y_plus_z) ),
inference(spm,[status(thm)],[c_0_563,c_0_618]) ).
cnf(c_0_630,axiom,
product(X1,multiplicative_identity,X1),
i_0_47 ).
cnf(c_0_631,plain,
add(X1,multiply(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_611,c_0_619]),c_0_620]) ).
cnf(c_0_632,hypothesis,
( multiply(X1,x__plus_y_plus_z) = x_plus_y
| ~ sum(x,y,X1) ),
inference(spm,[status(thm)],[c_0_596,c_0_621]) ).
cnf(c_0_633,hypothesis,
( product(X1,y_plus_z,y_plus_z)
| ~ sum(y,X2,X1)
| ~ product(X2,z,z) ),
inference(spm,[status(thm)],[c_0_622,c_0_606]) ).
cnf(c_0_634,plain,
product(x_plus_y__plus_z,z,z),
inference(spm,[status(thm)],[c_0_623,c_0_624]) ).
cnf(c_0_635,plain,
( sum(X1,X2,X1)
| ~ sum(X1,X3,X1)
| ~ product(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_625,c_0_626]) ).
cnf(c_0_636,hypothesis,
sum(x_plus_y__plus_z,x_plus_y,x_plus_y__plus_z),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_627,c_0_576]),c_0_602]) ).
cnf(c_0_637,hypothesis,
product(y,x_plus_y,y),
inference(spm,[status(thm)],[c_0_605,c_0_628]) ).
cnf(c_0_638,hypothesis,
product(y_plus_z,x__plus_y_plus_z,y_plus_z),
inference(spm,[status(thm)],[c_0_605,c_0_618]) ).
cnf(c_0_639,hypothesis,
( product(X1,multiplicative_identity,x__plus_y_plus_z)
| ~ sum(X2,x,X1)
| ~ product(X2,multiplicative_identity,y_plus_z) ),
inference(spm,[status(thm)],[c_0_629,c_0_630]) ).
cnf(c_0_640,plain,
( product(X1,X2,x_plus_y__plus_z)
| ~ sum(X3,X4,X1)
| ~ product(X4,X2,x_plus_y)
| ~ product(X3,X2,z) ),
inference(spm,[status(thm)],[c_0_563,c_0_614]) ).
cnf(c_0_641,plain,
( add(x__plus_y_plus_z,x_plus_y) = x__plus_y_plus_z
| ~ sum(x,y,X1) ),
inference(spm,[status(thm)],[c_0_631,c_0_632]) ).
cnf(c_0_642,axiom,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X6,X5,X2)
| ~ product(X4,X6,X7)
| ~ sum(X7,X5,X3) ),
i_0_29 ).
cnf(c_0_643,plain,
( product(X1,y_plus_z,y_plus_z)
| ~ sum(y,x_plus_y__plus_z,X1) ),
inference(spm,[status(thm)],[c_0_633,c_0_634]) ).
cnf(c_0_644,hypothesis,
( sum(x_plus_y__plus_z,X1,x_plus_y__plus_z)
| ~ product(x_plus_y,X2,X1) ),
inference(spm,[status(thm)],[c_0_635,c_0_636]) ).
cnf(c_0_645,hypothesis,
product(x_plus_y,y,y),
inference(spm,[status(thm)],[c_0_623,c_0_637]) ).
cnf(c_0_646,hypothesis,
( sum(X1,y_plus_z,x__plus_y_plus_z)
| ~ product(x__plus_y_plus_z,x__plus_y_plus_z,X1) ),
inference(spm,[status(thm)],[c_0_616,c_0_638]) ).
cnf(c_0_647,hypothesis,
sum(z,y,y_plus_z),
inference(spm,[status(thm)],[c_0_609,c_0_606]) ).
cnf(c_0_648,hypothesis,
( product(X1,multiplicative_identity,x__plus_y_plus_z)
| ~ sum(y_plus_z,x,X1) ),
inference(spm,[status(thm)],[c_0_639,c_0_630]) ).
cnf(c_0_649,plain,
( product(X1,multiplicative_identity,x_plus_y__plus_z)
| ~ sum(X2,x_plus_y,X1)
| ~ product(X2,multiplicative_identity,z) ),
inference(spm,[status(thm)],[c_0_640,c_0_630]) ).
cnf(c_0_650,plain,
( product(X1,X2,x_plus_y__plus_z)
| ~ sum(z,X3,X2)
| ~ sum(z,X4,X1)
| ~ product(X4,X3,x_plus_y) ),
inference(spm,[status(thm)],[c_0_577,c_0_614]) ).
cnf(c_0_651,plain,
add(x__plus_y_plus_z,x_plus_y) = x__plus_y_plus_z,
inference(spm,[status(thm)],[c_0_641,c_0_585]) ).
cnf(c_0_652,plain,
( product(X1,X2,X3)
| ~ sum(X4,X3,X2)
| ~ sum(X5,X3,X1)
| ~ product(X5,X4,additive_identity) ),
inference(spm,[status(thm)],[c_0_642,c_0_564]) ).
cnf(c_0_653,hypothesis,
product(x,x_plus_y,x),
inference(spm,[status(thm)],[c_0_605,c_0_599]) ).
cnf(c_0_654,plain,
sum(multiply(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_610,c_0_568]) ).
cnf(c_0_655,plain,
( multiply(X1,y_plus_z) = y_plus_z
| ~ sum(y,x_plus_y__plus_z,X1) ),
inference(spm,[status(thm)],[c_0_596,c_0_643]) ).
cnf(c_0_656,hypothesis,
sum(x_plus_y__plus_z,y,x_plus_y__plus_z),
inference(spm,[status(thm)],[c_0_644,c_0_645]) ).
cnf(c_0_657,hypothesis,
sum(x__plus_y_plus_z,y_plus_z,x__plus_y_plus_z),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_646,c_0_576]),c_0_602]) ).
cnf(c_0_658,hypothesis,
product(z,y_plus_z,z),
inference(spm,[status(thm)],[c_0_605,c_0_647]) ).
cnf(c_0_659,hypothesis,
( X1 = x__plus_y_plus_z
| ~ sum(y_plus_z,x,X2)
| ~ product(X2,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_567,c_0_648]) ).
cnf(c_0_660,plain,
( product(X1,multiplicative_identity,x_plus_y__plus_z)
| ~ sum(z,x_plus_y,X1) ),
inference(spm,[status(thm)],[c_0_649,c_0_630]) ).
cnf(c_0_661,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
i_0_53 ).
cnf(c_0_662,hypothesis,
( sum(X1,X2,X3)
| ~ product(x__plus_y_plus_z,X4,X3)
| ~ product(x,X4,X2)
| ~ product(y_plus_z,X4,X1) ),
inference(spm,[status(thm)],[c_0_589,c_0_618]) ).
cnf(c_0_663,plain,
( product(X1,x_plus_y__plus_z,x_plus_y__plus_z)
| ~ sum(z,X2,X1)
| ~ product(X2,x_plus_y,x_plus_y) ),
inference(spm,[status(thm)],[c_0_650,c_0_614]) ).
cnf(c_0_664,plain,
product(x__plus_y_plus_z,x_plus_y,x_plus_y),
inference(spm,[status(thm)],[c_0_595,c_0_651]) ).
cnf(c_0_665,plain,
( product(X1,X2,X3)
| ~ sum(additive_identity,X3,X1)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_652,c_0_593]) ).
cnf(c_0_666,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_582,c_0_585]) ).
cnf(c_0_667,hypothesis,
product(x_plus_y,x,x),
inference(spm,[status(thm)],[c_0_623,c_0_653]) ).
cnf(c_0_668,plain,
( sum(y_plus_z,X1,X1)
| ~ sum(y,x_plus_y__plus_z,X1) ),
inference(spm,[status(thm)],[c_0_654,c_0_655]) ).
cnf(c_0_669,hypothesis,
sum(y,x_plus_y__plus_z,x_plus_y__plus_z),
inference(spm,[status(thm)],[c_0_609,c_0_656]) ).
cnf(c_0_670,hypothesis,
( sum(x__plus_y_plus_z,X1,x__plus_y_plus_z)
| ~ product(y_plus_z,X2,X1) ),
inference(spm,[status(thm)],[c_0_635,c_0_657]) ).
cnf(c_0_671,hypothesis,
product(y_plus_z,z,z),
inference(spm,[status(thm)],[c_0_623,c_0_658]) ).
cnf(c_0_672,hypothesis,
( ~ sum(y_plus_z,x,X1)
| ~ sum(z,x_plus_y,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_659,c_0_660]),c_0_661]) ).
cnf(c_0_673,hypothesis,
( sum(X1,X2,multiply(x__plus_y_plus_z,X3))
| ~ product(x,X3,X2)
| ~ product(y_plus_z,X3,X1) ),
inference(spm,[status(thm)],[c_0_662,c_0_576]) ).
cnf(c_0_674,plain,
( product(X1,x_plus_y__plus_z,x_plus_y__plus_z)
| ~ sum(z,x__plus_y_plus_z,X1) ),
inference(spm,[status(thm)],[c_0_663,c_0_664]) ).
cnf(c_0_675,plain,
( product(X1,X2,X1)
| ~ sum(X3,X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_665,c_0_585]),c_0_666]) ).
cnf(c_0_676,hypothesis,
sum(x_plus_y__plus_z,x,x_plus_y__plus_z),
inference(spm,[status(thm)],[c_0_644,c_0_667]) ).
cnf(c_0_677,plain,
sum(y_plus_z,x_plus_y__plus_z,x_plus_y__plus_z),
inference(spm,[status(thm)],[c_0_668,c_0_669]) ).
cnf(c_0_678,hypothesis,
sum(x__plus_y_plus_z,z,x__plus_y_plus_z),
inference(spm,[status(thm)],[c_0_670,c_0_671]) ).
cnf(c_0_679,hypothesis,
( ~ sum(z,x_plus_y,multiply(x__plus_y_plus_z,X1))
| ~ product(x,X1,x)
| ~ product(y_plus_z,X1,y_plus_z) ),
inference(spm,[status(thm)],[c_0_672,c_0_673]) ).
cnf(c_0_680,plain,
( multiply(X1,x_plus_y__plus_z) = x_plus_y__plus_z
| ~ sum(z,x__plus_y_plus_z,X1) ),
inference(spm,[status(thm)],[c_0_596,c_0_674]) ).
cnf(c_0_681,plain,
product(x,x_plus_y__plus_z,x),
inference(spm,[status(thm)],[c_0_675,c_0_676]) ).
cnf(c_0_682,plain,
product(y_plus_z,x_plus_y__plus_z,y_plus_z),
inference(spm,[status(thm)],[c_0_605,c_0_677]) ).
cnf(c_0_683,hypothesis,
sum(z,x__plus_y_plus_z,x__plus_y_plus_z),
inference(spm,[status(thm)],[c_0_609,c_0_678]) ).
cnf(c_0_684,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_679,c_0_680]),c_0_614]),c_0_681]),c_0_682]),c_0_683])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO008-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n007.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:43:54 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 131.77/96.46 % Version : CSE_E---1.7
% 131.77/96.46 % Problem : theBenchmark.p
% 131.77/96.46 % SZS status Unsatisfiable for theBenchmark.p
% 131.77/96.46 % SZS output start CNFRefutation
% See solution above
% 137.40/102.08 % Total time : 95.757s
%------------------------------------------------------------------------------