%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG005-2 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 05:04:57 PM UTC 2026
% Result : Unsatisfiable 5.49s 5.63s
% Output : CNFRefutation 6.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 31
% Syntax : Number of clauses : 268 ( 163 unt; 0 nHn; 135 RR)
% Number of literals : 525 ( 0 equ; 291 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 685 ( 38 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/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
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/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
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/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
cnf(associativity_of_multiplication1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
cnf(associativity_of_multiplication2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
cnf(associativity_of_addition1,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).
cnf(associativity_of_addition2,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
cnf(multiplication_is_well_defined,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(addition_is_well_defined,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(product_substitution1,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).
cnf(product_substitution2,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
cnf(sum_substitution1,axiom,
( sum(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ sum(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution1) ).
cnf(sum_substitution2,axiom,
( sum(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ sum(X3,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution2) ).
cnf(sum_substitution3,axiom,
( sum(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ sum(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution3) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(multiply_substitution1,axiom,
( equalish(multiply(X1,X3),multiply(X2,X3))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution1) ).
cnf(add_substitution1,axiom,
( equalish(add(X1,X3),add(X2,X3))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_substitution1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(prove_sum_is_additive_identity,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(a_inverse_times_b,hypothesis,
product(additive_inverse(a),b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
cnf(multiplicative_identity1,axiom,
product(additive_identity,X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
cnf(multiplicative_identity2,axiom,
product(X1,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
cnf(a_times_b,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(additive_inverse_substitution,axiom,
( equalish(additive_inverse(X1),additive_inverse(X2))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_substitution) ).
cnf(i_0_31,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_32,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_33,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_34,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_35,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity_of_multiplication1,
[final] ).
cnf(i_0_36,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2,
[final] ).
cnf(i_0_37,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1,
[final] ).
cnf(i_0_38,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2,
[final] ).
cnf(i_0_39,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined,
[final] ).
cnf(i_0_40,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined,
[final] ).
cnf(i_0_41,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
product_substitution1,
[final] ).
cnf(i_0_42,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
product_substitution2,
[final] ).
cnf(i_0_43,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3,
[final] ).
cnf(i_0_44,axiom,
( sum(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ sum(X1,X3,X4) ),
sum_substitution1,
[final] ).
cnf(i_0_45,axiom,
( sum(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ sum(X3,X1,X4) ),
sum_substitution2,
[final] ).
cnf(i_0_46,axiom,
( sum(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ sum(X3,X4,X1) ),
sum_substitution3,
[final] ).
cnf(i_0_47,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition,
[final] ).
cnf(i_0_48,axiom,
( equalish(multiply(X1,X3),multiply(X2,X3))
| ~ equalish(X1,X2) ),
multiply_substitution1,
[final] ).
cnf(i_0_49,axiom,
( equalish(add(X1,X3),add(X2,X3))
| ~ equalish(X1,X2) ),
add_substitution1,
[final] ).
cnf(i_0_50,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication,
[final] ).
cnf(i_0_51,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition,
[final] ).
cnf(i_0_52,negated_conjecture,
~ sum(c,d,additive_identity),
prove_sum_is_additive_identity,
[final] ).
cnf(i_0_53,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse,
[final] ).
cnf(i_0_54,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse,
[final] ).
cnf(i_0_55,hypothesis,
product(additive_inverse(a),b,c),
a_inverse_times_b,
[final] ).
cnf(i_0_56,axiom,
sum(additive_identity,X1,X1),
additive_identity1,
[final] ).
cnf(i_0_57,axiom,
sum(X1,additive_identity,X1),
additive_identity2,
[final] ).
cnf(i_0_58,axiom,
product(additive_identity,X1,additive_identity),
multiplicative_identity1,
[final] ).
cnf(i_0_59,axiom,
product(X1,additive_identity,additive_identity),
multiplicative_identity2,
[final] ).
cnf(i_0_60,hypothesis,
product(a,b,d),
a_times_b,
[final] ).
cnf(i_0_61,axiom,
( equalish(additive_inverse(X1),additive_inverse(X2))
| ~ equalish(X1,X2) ),
additive_inverse_substitution,
[final] ).
cnf(i_0_62,plain,
sum(X1,X2,add(X2,X1)),
inference(scs_inference,[],[i_0_51,i_0_47]) ).
cnf(i_0_63,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_64,plain,
~ equalish(additive_inverse(d),c),
inference(scs_inference,[],[i_0_52,i_0_51,i_0_53,i_0_47,i_0_44]) ).
cnf(i_0_65,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_66,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X2,X3)
| ~ equalish(X1,X4) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_67,plain,
equalish(multiply(X1,X2),multiply(X1,X2)),
inference(scs_inference,[],[i_0_52,i_0_50,i_0_51,i_0_53,i_0_47,i_0_44,i_0_39]) ).
cnf(i_0_68,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_69,plain,
~ sum(additive_identity,c,additive_inverse(d)),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_50,i_0_51,i_0_53,i_0_47,i_0_44,i_0_39,i_0_40]) ).
cnf(i_0_70,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_71,plain,
( ~ sum(X1,X2,X3)
| equalish(X4,X3)
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_72,plain,
~ equalish(additive_inverse(c),d),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_50,i_0_51,i_0_53,i_0_54,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45]) ).
cnf(i_0_73,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_74,plain,
( ~ sum(X1,X2,X3)
| sum(X1,X4,X3)
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_75,plain,
~ equalish(c,additive_inverse(d)),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_50,i_0_51,i_0_53,i_0_54,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46]) ).
cnf(i_0_76,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_77,plain,
( ~ sum(X1,X2,X3)
| sum(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_78,plain,
~ sum(additive_inverse(c),additive_identity,d),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_76,i_0_50,i_0_51,i_0_53,i_0_54,i_0_73,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46,i_0_37]) ).
cnf(i_0_79,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_80,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_81,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_82,plain,
~ sum(additive_identity,additive_inverse(d),c),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_76,i_0_79,i_0_50,i_0_51,i_0_53,i_0_65,i_0_54,i_0_73,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46,i_0_37,i_0_38]) ).
cnf(i_0_83,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_84,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_85,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_86,plain,
product(additive_identity,multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_76,i_0_79,i_0_50,i_0_51,i_0_58,i_0_53,i_0_65,i_0_54,i_0_73,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46,i_0_37,i_0_38,i_0_35]) ).
cnf(i_0_87,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_88,plain,
product(additive_identity,X1,additive_identity),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_89,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_90,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_91,plain,
product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity)),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_76,i_0_79,i_0_50,i_0_89,i_0_51,i_0_58,i_0_88,i_0_53,i_0_65,i_0_54,i_0_73,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36]) ).
cnf(i_0_92,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_93,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_94,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_95,plain,
sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_76,i_0_79,i_0_83,i_0_50,i_0_89,i_0_93,i_0_51,i_0_58,i_0_88,i_0_53,i_0_65,i_0_54,i_0_73,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33]) ).
cnf(i_0_96,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_97,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_98,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_99,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_100,plain,
( ~ product(X1,X2,X3)
| sum(X4,X5,X3)
| ~ product(X6,X2,X4)
| ~ product(X7,X2,X5)
| ~ sum(X6,X7,X1) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_101,plain,
sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_76,i_0_79,i_0_83,i_0_99,i_0_50,i_0_89,i_0_93,i_0_98,i_0_51,i_0_58,i_0_88,i_0_53,i_0_65,i_0_54,i_0_73,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34]) ).
cnf(i_0_102,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_103,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_104,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_105,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_106,plain,
( ~ product(X1,X2,X3)
| sum(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X1,X7,X5)
| ~ sum(X6,X7,X2) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_107,plain,
product(additive_identity,X1,multiply(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_76,i_0_79,i_0_83,i_0_99,i_0_105,i_0_57,i_0_50,i_0_89,i_0_93,i_0_98,i_0_104,i_0_51,i_0_58,i_0_88,i_0_53,i_0_65,i_0_54,i_0_73,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31]) ).
cnf(i_0_108,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_109,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_110,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_111,plain,
( ~ sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| product(X7,X3,X6)
| ~ product(X7,X1,X4)
| ~ product(X7,X2,X5) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_112,plain,
product(add(additive_identity,X1),X2,multiply(X1,X2)),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_76,i_0_79,i_0_83,i_0_99,i_0_105,i_0_109,i_0_57,i_0_50,i_0_89,i_0_93,i_0_98,i_0_104,i_0_110,i_0_51,i_0_58,i_0_88,i_0_53,i_0_65,i_0_54,i_0_73,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32]) ).
cnf(i_0_113,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_114,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_115,plain,
product(additive_identity,X1,additive_identity),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_116,plain,
( ~ sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| product(X3,X7,X6)
| ~ product(X1,X7,X4)
| ~ product(X2,X7,X5) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_117,plain,
( product(X1,X2,additive_identity)
| ~ equalish(additive_identity,X1) ),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_76,i_0_79,i_0_83,i_0_99,i_0_105,i_0_109,i_0_57,i_0_50,i_0_89,i_0_93,i_0_98,i_0_104,i_0_110,i_0_51,i_0_58,i_0_88,i_0_115,i_0_53,i_0_65,i_0_54,i_0_73,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_41]) ).
cnf(i_0_118,plain,
( ~ product(X1,X2,X3)
| product(X4,X2,X3)
| ~ equalish(X1,X4) ),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_119,plain,
( product(X1,X2,additive_identity)
| ~ equalish(additive_identity,X2) ),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_76,i_0_79,i_0_83,i_0_99,i_0_105,i_0_109,i_0_57,i_0_50,i_0_89,i_0_93,i_0_98,i_0_104,i_0_110,i_0_51,i_0_58,i_0_88,i_0_115,i_0_59,i_0_53,i_0_65,i_0_54,i_0_73,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_41,i_0_42]) ).
cnf(i_0_120,plain,
( ~ product(X1,X2,X3)
| product(X1,X4,X3)
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_121,plain,
( product(additive_identity,X1,X2)
| ~ equalish(additive_identity,X2) ),
inference(scs_inference,[],[i_0_52,i_0_56,i_0_70,i_0_76,i_0_79,i_0_83,i_0_99,i_0_105,i_0_109,i_0_57,i_0_50,i_0_89,i_0_93,i_0_98,i_0_104,i_0_110,i_0_51,i_0_58,i_0_88,i_0_115,i_0_59,i_0_53,i_0_65,i_0_54,i_0_73,i_0_47,i_0_44,i_0_39,i_0_40,i_0_45,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_41,i_0_42,i_0_43]) ).
cnf(i_0_122,plain,
( ~ product(X1,X2,X3)
| product(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_123,plain,
~ equalish(d,additive_inverse(c)),
inference(scs_inference,[],[i_0_78,i_0_57,i_0_44]) ).
cnf(i_0_124,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_125,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X2,X3)
| ~ equalish(X1,X4) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_126,plain,
equalish(multiply(additive_identity,X1),multiply(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_78,i_0_86,i_0_107,i_0_57,i_0_44,i_0_39]) ).
cnf(i_0_127,plain,
product(additive_identity,X1,multiply(additive_identity,additive_identity)),
inference(rename_variables,[],[i_0_107]) ).
cnf(i_0_128,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_129,plain,
equalish(multiply(additive_identity,X1),add(multiply(additive_identity,X1),multiply(additive_identity,X1))),
inference(scs_inference,[],[i_0_95,i_0_78,i_0_62,i_0_86,i_0_107,i_0_57,i_0_44,i_0_39,i_0_40]) ).
cnf(i_0_130,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_131,plain,
( ~ sum(X1,X2,X3)
| equalish(X4,X3)
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_132,plain,
~ equalish(add(d,c),additive_identity),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_78,i_0_62,i_0_130,i_0_86,i_0_107,i_0_57,i_0_44,i_0_39,i_0_40,i_0_46]) ).
cnf(i_0_133,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_134,plain,
( ~ sum(X1,X2,X3)
| sum(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_135,plain,
~ sum(c,additive_identity,additive_inverse(d)),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_78,i_0_62,i_0_130,i_0_86,i_0_107,i_0_56,i_0_57,i_0_53,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37]) ).
cnf(i_0_136,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_137,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_138,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_139,plain,
~ sum(additive_inverse(add(d,X1)),X1,c),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_78,i_0_62,i_0_130,i_0_133,i_0_86,i_0_107,i_0_56,i_0_57,i_0_53,i_0_136,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37,i_0_38]) ).
cnf(i_0_140,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_141,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_142,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_143,plain,
product(add(additive_identity,X1),multiply(additive_identity,X2),multiply(X1,additive_identity)),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_78,i_0_62,i_0_130,i_0_133,i_0_112,i_0_91,i_0_86,i_0_107,i_0_56,i_0_57,i_0_53,i_0_136,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37,i_0_38,i_0_35]) ).
cnf(i_0_144,plain,
product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity)),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_145,plain,
product(add(additive_identity,X1),X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_146,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_147,plain,
product(multiply(additive_identity,additive_identity),X1,additive_identity),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_78,i_0_62,i_0_130,i_0_133,i_0_112,i_0_91,i_0_144,i_0_86,i_0_107,i_0_56,i_0_57,i_0_58,i_0_53,i_0_136,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36]) ).
cnf(i_0_148,plain,
product(additive_identity,X1,additive_identity),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_149,plain,
product(additive_identity,multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_150,plain,
product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity)),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_151,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_152,plain,
~ product(a,b,additive_inverse(c)),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_78,i_0_62,i_0_130,i_0_133,i_0_112,i_0_91,i_0_144,i_0_86,i_0_107,i_0_60,i_0_56,i_0_57,i_0_124,i_0_58,i_0_148,i_0_53,i_0_136,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33]) ).
cnf(i_0_153,plain,
product(additive_identity,X1,additive_identity),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_154,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_155,plain,
( ~ product(X1,X2,X3)
| sum(X4,X5,X3)
| ~ product(X6,X2,X4)
| ~ product(X7,X2,X5)
| ~ sum(X6,X7,X1) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_156,plain,
sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_78,i_0_62,i_0_130,i_0_133,i_0_112,i_0_91,i_0_144,i_0_86,i_0_149,i_0_107,i_0_127,i_0_60,i_0_56,i_0_57,i_0_124,i_0_58,i_0_148,i_0_53,i_0_136,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34]) ).
cnf(i_0_157,plain,
product(additive_identity,X1,multiply(additive_identity,additive_identity)),
inference(rename_variables,[],[i_0_107]) ).
cnf(i_0_158,plain,
product(additive_identity,multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_159,plain,
product(additive_identity,multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_160,plain,
( ~ product(X1,X2,X3)
| sum(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X1,X7,X5)
| ~ sum(X6,X7,X2) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_161,plain,
product(add(additive_identity,additive_identity),add(X1,X1),multiply(additive_identity,X1)),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_78,i_0_62,i_0_130,i_0_133,i_0_141,i_0_112,i_0_145,i_0_91,i_0_144,i_0_86,i_0_149,i_0_107,i_0_127,i_0_60,i_0_56,i_0_57,i_0_124,i_0_58,i_0_148,i_0_53,i_0_136,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31]) ).
cnf(i_0_162,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_163,plain,
sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(rename_variables,[],[i_0_95]) ).
cnf(i_0_164,plain,
product(add(additive_identity,X1),X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_165,plain,
product(add(additive_identity,X1),X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_166,plain,
( ~ sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| product(X7,X3,X6)
| ~ product(X7,X1,X4)
| ~ product(X7,X2,X5) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_167,plain,
product(add(add(additive_identity,additive_identity),add(additive_identity,additive_identity)),X1,multiply(additive_identity,X1)),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_163,i_0_78,i_0_62,i_0_130,i_0_133,i_0_141,i_0_162,i_0_112,i_0_145,i_0_165,i_0_91,i_0_144,i_0_86,i_0_149,i_0_107,i_0_127,i_0_60,i_0_56,i_0_57,i_0_124,i_0_58,i_0_148,i_0_53,i_0_136,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32]) ).
cnf(i_0_168,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_169,plain,
sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(rename_variables,[],[i_0_95]) ).
cnf(i_0_170,plain,
product(add(additive_identity,X1),X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_171,plain,
product(add(additive_identity,X1),X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_172,plain,
( ~ sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| product(X3,X7,X6)
| ~ product(X1,X7,X4)
| ~ product(X2,X7,X5) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_173,plain,
( product(a,X1,d)
| ~ equalish(b,X1) ),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_163,i_0_78,i_0_62,i_0_130,i_0_133,i_0_141,i_0_162,i_0_112,i_0_145,i_0_165,i_0_91,i_0_144,i_0_86,i_0_149,i_0_107,i_0_127,i_0_60,i_0_56,i_0_57,i_0_124,i_0_58,i_0_148,i_0_53,i_0_136,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_42]) ).
cnf(i_0_174,plain,
( ~ product(X1,X2,X3)
| product(X1,X4,X3)
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_175,plain,
~ equalish(multiply(a,b),additive_inverse(c)),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_163,i_0_78,i_0_62,i_0_130,i_0_133,i_0_141,i_0_162,i_0_112,i_0_145,i_0_165,i_0_91,i_0_144,i_0_86,i_0_149,i_0_107,i_0_127,i_0_60,i_0_56,i_0_57,i_0_124,i_0_58,i_0_148,i_0_53,i_0_136,i_0_50,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_42,i_0_43]) ).
cnf(i_0_176,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_177,plain,
( ~ product(X1,X2,X3)
| product(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_178,plain,
( sum(X1,X2,X1)
| ~ equalish(additive_identity,X2) ),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_163,i_0_78,i_0_62,i_0_130,i_0_133,i_0_141,i_0_162,i_0_112,i_0_145,i_0_165,i_0_91,i_0_144,i_0_86,i_0_149,i_0_107,i_0_127,i_0_60,i_0_56,i_0_57,i_0_124,i_0_154,i_0_58,i_0_148,i_0_53,i_0_136,i_0_50,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_42,i_0_43,i_0_45]) ).
cnf(i_0_179,plain,
( ~ sum(X1,X2,X3)
| sum(X1,X4,X3)
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_180,plain,
( product(X1,X2,multiply(X3,X2))
| ~ equalish(add(additive_identity,X3),X1) ),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_163,i_0_78,i_0_62,i_0_130,i_0_133,i_0_141,i_0_162,i_0_112,i_0_145,i_0_165,i_0_171,i_0_91,i_0_144,i_0_86,i_0_149,i_0_107,i_0_127,i_0_60,i_0_56,i_0_57,i_0_124,i_0_154,i_0_58,i_0_148,i_0_53,i_0_136,i_0_50,i_0_44,i_0_39,i_0_40,i_0_46,i_0_37,i_0_38,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_42,i_0_43,i_0_45,i_0_41]) ).
cnf(i_0_181,plain,
( ~ product(X1,X2,X3)
| product(X4,X2,X3)
| ~ equalish(X1,X4) ),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_182,plain,
~ sum(X1,additive_inverse(X1),add(d,c)),
inference(scs_inference,[],[i_0_54,i_0_132,i_0_40]) ).
cnf(i_0_183,plain,
( ~ sum(X1,X2,X3)
| equalish(X4,X3)
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_184,plain,
~ equalish(additive_identity,add(d,c)),
inference(scs_inference,[],[i_0_54,i_0_132,i_0_40,i_0_46]) ).
cnf(i_0_185,plain,
( ~ sum(X1,X2,X3)
| sum(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_186,plain,
~ equalish(additive_identity,additive_inverse(add(d,c))),
inference(scs_inference,[],[i_0_139,i_0_54,i_0_132,i_0_56,i_0_40,i_0_46,i_0_44]) ).
cnf(i_0_187,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_188,plain,
~ sum(additive_inverse(add(d,X1)),X1,c),
inference(rename_variables,[],[i_0_139]) ).
cnf(i_0_189,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X2,X3)
| ~ equalish(X1,X4) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_190,plain,
~ product(X1,additive_identity,add(d,c)),
inference(scs_inference,[],[i_0_139,i_0_54,i_0_59,i_0_132,i_0_56,i_0_40,i_0_46,i_0_44,i_0_39]) ).
cnf(i_0_191,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_192,plain,
~ equalish(multiply(additive_identity,additive_identity),add(d,c)),
inference(scs_inference,[],[i_0_139,i_0_54,i_0_59,i_0_167,i_0_132,i_0_56,i_0_40,i_0_46,i_0_44,i_0_39,i_0_43]) ).
cnf(i_0_193,plain,
product(add(add(additive_identity,additive_identity),add(additive_identity,additive_identity)),X1,multiply(additive_identity,X1)),
inference(rename_variables,[],[i_0_167]) ).
cnf(i_0_194,plain,
( ~ product(X1,X2,X3)
| product(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_195,plain,
product(add(add(additive_identity,additive_identity),add(additive_identity,additive_identity)),multiply(additive_identity,additive_identity),additive_identity),
inference(scs_inference,[],[i_0_139,i_0_54,i_0_59,i_0_167,i_0_193,i_0_147,i_0_132,i_0_107,i_0_56,i_0_40,i_0_46,i_0_44,i_0_39,i_0_43,i_0_35]) ).
cnf(i_0_196,plain,
product(multiply(additive_identity,additive_identity),X1,additive_identity),
inference(rename_variables,[],[i_0_147]) ).
cnf(i_0_197,plain,
product(add(add(additive_identity,additive_identity),add(additive_identity,additive_identity)),X1,multiply(additive_identity,X1)),
inference(rename_variables,[],[i_0_167]) ).
cnf(i_0_198,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_199,plain,
~ sum(X1,additive_inverse(add(c,X1)),d),
inference(scs_inference,[],[i_0_52,i_0_139,i_0_54,i_0_51,i_0_59,i_0_167,i_0_193,i_0_147,i_0_132,i_0_107,i_0_56,i_0_40,i_0_46,i_0_44,i_0_39,i_0_43,i_0_35,i_0_37]) ).
cnf(i_0_200,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_201,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_202,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_203,plain,
~ sum(c,d,additive_inverse(additive_identity)),
inference(scs_inference,[],[i_0_52,i_0_139,i_0_54,i_0_200,i_0_51,i_0_59,i_0_167,i_0_193,i_0_147,i_0_132,i_0_107,i_0_56,i_0_187,i_0_40,i_0_46,i_0_44,i_0_39,i_0_43,i_0_35,i_0_37,i_0_38]) ).
cnf(i_0_204,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_205,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_206,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_207,plain,
product(additive_identity,X1,multiply(additive_identity,multiply(additive_identity,additive_identity))),
inference(scs_inference,[],[i_0_52,i_0_139,i_0_54,i_0_200,i_0_51,i_0_59,i_0_167,i_0_193,i_0_197,i_0_147,i_0_132,i_0_107,i_0_56,i_0_187,i_0_40,i_0_46,i_0_44,i_0_39,i_0_43,i_0_35,i_0_37,i_0_38,i_0_36]) ).
cnf(i_0_208,plain,
product(add(add(additive_identity,additive_identity),add(additive_identity,additive_identity)),X1,multiply(additive_identity,X1)),
inference(rename_variables,[],[i_0_167]) ).
cnf(i_0_209,plain,
product(X1,additive_identity,additive_identity),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_210,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_211,plain,
~ sum(additive_inverse(a),a,multiply(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_52,i_0_139,i_0_54,i_0_200,i_0_51,i_0_59,i_0_60,i_0_167,i_0_193,i_0_197,i_0_147,i_0_196,i_0_132,i_0_55,i_0_107,i_0_56,i_0_187,i_0_40,i_0_46,i_0_44,i_0_39,i_0_43,i_0_35,i_0_37,i_0_38,i_0_36,i_0_33]) ).
cnf(i_0_212,plain,
product(multiply(additive_identity,additive_identity),X1,additive_identity),
inference(rename_variables,[],[i_0_147]) ).
cnf(i_0_213,plain,
( ~ product(X1,X2,X3)
| sum(X4,X5,X3)
| ~ product(X6,X2,X4)
| ~ product(X7,X2,X5)
| ~ sum(X6,X7,X1) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_214,plain,
~ product(additive_inverse(a),additive_inverse(b),d),
inference(scs_inference,[],[i_0_52,i_0_139,i_0_54,i_0_200,i_0_204,i_0_51,i_0_59,i_0_209,i_0_60,i_0_167,i_0_193,i_0_197,i_0_147,i_0_196,i_0_132,i_0_55,i_0_107,i_0_56,i_0_187,i_0_40,i_0_46,i_0_44,i_0_39,i_0_43,i_0_35,i_0_37,i_0_38,i_0_36,i_0_33,i_0_34]) ).
cnf(i_0_215,plain,
product(X1,additive_identity,additive_identity),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_216,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_217,plain,
( ~ product(X1,X2,X3)
| sum(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X1,X7,X5)
| ~ sum(X6,X7,X2) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_218,plain,
product(add(add(additive_identity,additive_identity),add(additive_identity,additive_identity)),add(X1,X1),multiply(additive_identity,X1)),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_139,i_0_54,i_0_200,i_0_204,i_0_51,i_0_201,i_0_59,i_0_209,i_0_60,i_0_167,i_0_193,i_0_197,i_0_208,i_0_147,i_0_196,i_0_132,i_0_55,i_0_107,i_0_56,i_0_187,i_0_40,i_0_46,i_0_44,i_0_39,i_0_43,i_0_35,i_0_37,i_0_38,i_0_36,i_0_33,i_0_34,i_0_31]) ).
cnf(i_0_219,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_220,plain,
sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(rename_variables,[],[i_0_95]) ).
cnf(i_0_221,plain,
( ~ sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| product(X7,X3,X6)
| ~ product(X7,X1,X4)
| ~ product(X7,X2,X5) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_222,plain,
~ equalish(additive_identity,additive_inverse(add(c,d))),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_139,i_0_54,i_0_200,i_0_204,i_0_51,i_0_201,i_0_59,i_0_209,i_0_60,i_0_167,i_0_193,i_0_197,i_0_208,i_0_147,i_0_196,i_0_132,i_0_55,i_0_107,i_0_56,i_0_187,i_0_57,i_0_40,i_0_46,i_0_44,i_0_39,i_0_43,i_0_35,i_0_37,i_0_38,i_0_36,i_0_33,i_0_34,i_0_31,i_0_45]) ).
cnf(i_0_223,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_224,plain,
( ~ sum(X1,X2,X3)
| sum(X1,X4,X3)
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_225,plain,
( product(X1,b,d)
| ~ equalish(a,X1) ),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_139,i_0_54,i_0_200,i_0_204,i_0_51,i_0_201,i_0_59,i_0_209,i_0_60,i_0_167,i_0_193,i_0_197,i_0_208,i_0_147,i_0_196,i_0_132,i_0_55,i_0_107,i_0_56,i_0_187,i_0_57,i_0_40,i_0_46,i_0_44,i_0_39,i_0_43,i_0_35,i_0_37,i_0_38,i_0_36,i_0_33,i_0_34,i_0_31,i_0_45,i_0_41]) ).
cnf(i_0_226,plain,
( ~ product(X1,X2,X3)
| product(X4,X2,X3)
| ~ equalish(X1,X4) ),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_227,plain,
( ~ equalish(b,additive_inverse(b))
| ~ equalish(a,additive_inverse(a)) ),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_139,i_0_54,i_0_200,i_0_204,i_0_51,i_0_201,i_0_59,i_0_209,i_0_60,i_0_167,i_0_193,i_0_197,i_0_208,i_0_147,i_0_196,i_0_132,i_0_55,i_0_107,i_0_56,i_0_187,i_0_57,i_0_40,i_0_46,i_0_44,i_0_39,i_0_43,i_0_35,i_0_37,i_0_38,i_0_36,i_0_33,i_0_34,i_0_31,i_0_45,i_0_41,i_0_42]) ).
cnf(i_0_228,plain,
( ~ product(X1,X2,X3)
| product(X1,X4,X3)
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_230,plain,
equalish(multiply(X1,additive_identity),multiply(X1,multiply(additive_identity,X2))),
inference(scs_inference,[],[i_0_143,i_0_112,i_0_39]) ).
cnf(i_0_231,plain,
product(add(additive_identity,X1),X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_232,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_233,plain,
~ sum(d,c,multiply(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_51,i_0_143,i_0_112,i_0_192,i_0_39,i_0_40]) ).
cnf(i_0_234,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_235,plain,
( ~ sum(X1,X2,X3)
| equalish(X4,X3)
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_236,plain,
~ equalish(add(c,d),additive_identity),
inference(scs_inference,[],[i_0_52,i_0_51,i_0_234,i_0_143,i_0_112,i_0_192,i_0_39,i_0_40,i_0_46]) ).
cnf(i_0_237,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_238,plain,
( ~ sum(X1,X2,X3)
| sum(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_239,plain,
~ equalish(multiply(X1,additive_identity),add(d,c)),
inference(scs_inference,[],[i_0_52,i_0_51,i_0_234,i_0_143,i_0_112,i_0_231,i_0_192,i_0_190,i_0_39,i_0_40,i_0_46,i_0_43]) ).
cnf(i_0_240,plain,
product(add(additive_identity,X1),X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_241,plain,
~ product(X1,additive_identity,add(d,c)),
inference(rename_variables,[],[i_0_190]) ).
cnf(i_0_242,plain,
( ~ product(X1,X2,X3)
| product(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_243,plain,
product(add(additive_identity,X1),multiply(additive_identity,additive_identity),multiply(multiply(X1,additive_identity),X2)),
inference(scs_inference,[],[i_0_52,i_0_51,i_0_234,i_0_143,i_0_112,i_0_231,i_0_91,i_0_50,i_0_192,i_0_190,i_0_39,i_0_40,i_0_46,i_0_43,i_0_35]) ).
cnf(i_0_244,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_245,plain,
product(add(additive_identity,X1),multiply(additive_identity,X2),multiply(X1,additive_identity)),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_246,plain,
product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity)),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_247,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_248,plain,
~ sum(d,c,additive_inverse(additive_identity)),
inference(scs_inference,[],[i_0_52,i_0_51,i_0_234,i_0_237,i_0_143,i_0_112,i_0_231,i_0_91,i_0_50,i_0_192,i_0_182,i_0_190,i_0_56,i_0_39,i_0_40,i_0_46,i_0_43,i_0_35,i_0_37]) ).
cnf(i_0_249,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_250,plain,
~ sum(X1,additive_inverse(X1),add(d,c)),
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_251,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_252,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_253,plain,
~ sum(c,additive_inverse(add(d,c)),c),
inference(scs_inference,[],[i_0_52,i_0_51,i_0_234,i_0_237,i_0_249,i_0_143,i_0_112,i_0_231,i_0_91,i_0_50,i_0_192,i_0_182,i_0_250,i_0_190,i_0_56,i_0_39,i_0_40,i_0_46,i_0_43,i_0_35,i_0_37,i_0_38]) ).
cnf(i_0_254,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_255,plain,
~ sum(X1,additive_inverse(X1),add(d,c)),
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_256,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_257,plain,
product(multiply(X1,additive_identity),X2,multiply(X1,multiply(additive_identity,additive_identity))),
inference(scs_inference,[],[i_0_52,i_0_51,i_0_234,i_0_237,i_0_249,i_0_143,i_0_245,i_0_112,i_0_231,i_0_240,i_0_91,i_0_246,i_0_50,i_0_192,i_0_182,i_0_250,i_0_190,i_0_56,i_0_39,i_0_40,i_0_46,i_0_43,i_0_35,i_0_37,i_0_38,i_0_36]) ).
cnf(i_0_258,plain,
product(add(additive_identity,X1),X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_259,plain,
product(add(additive_identity,X1),multiply(additive_identity,X2),multiply(X1,additive_identity)),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_260,plain,
product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity)),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_261,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_262,plain,
product(add(add(additive_identity,additive_identity),add(additive_identity,additive_identity)),multiply(additive_identity,X1),multiply(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_52,i_0_95,i_0_51,i_0_234,i_0_237,i_0_249,i_0_254,i_0_143,i_0_245,i_0_259,i_0_112,i_0_231,i_0_240,i_0_91,i_0_246,i_0_50,i_0_192,i_0_182,i_0_250,i_0_190,i_0_56,i_0_39,i_0_40,i_0_46,i_0_43,i_0_35,i_0_37,i_0_38,i_0_36,i_0_32]) ).
cnf(i_0_263,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_264,plain,
sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(rename_variables,[],[i_0_95]) ).
cnf(i_0_265,plain,
product(add(additive_identity,X1),multiply(additive_identity,X2),multiply(X1,additive_identity)),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_266,plain,
product(add(additive_identity,X1),multiply(additive_identity,X2),multiply(X1,additive_identity)),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_267,plain,
( ~ sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| product(X3,X7,X6)
| ~ product(X1,X7,X4)
| ~ product(X2,X7,X5) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_268,plain,
$false,
inference(scs_inference,[],[i_0_52,i_0_95,i_0_51,i_0_234,i_0_237,i_0_249,i_0_254,i_0_143,i_0_245,i_0_259,i_0_112,i_0_231,i_0_240,i_0_91,i_0_246,i_0_58,i_0_53,i_0_60,i_0_50,i_0_192,i_0_182,i_0_250,i_0_190,i_0_55,i_0_56,i_0_39,i_0_40,i_0_46,i_0_43,i_0_35,i_0_37,i_0_38,i_0_36,i_0_32,i_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG005-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n031.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 01:48:08 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 5.49/5.63 % Version : CSE_E---1.7
% 5.49/5.63 % Problem : theBenchmark.p
% 5.49/5.63 % SZS status Unsatisfiable for theBenchmark.p
% 5.49/5.63 % SZS output start CNFRefutation
% See solution above
% 6.31/6.12 % Total time : 5.281s
%------------------------------------------------------------------------------