%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG037-2 : 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 : n009.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 05:05:05 PM UTC 2026
% Result : Unsatisfiable 2.86s 5.74s
% Output : CNFRefutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 29
% Syntax : Number of clauses : 154 ( 81 unt; 0 nHn; 88 RR)
% Number of literals : 331 ( 0 equ; 191 neg)
% Maximal clause size : 5 ( 2 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 : 433 ( 14 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/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',product_substitution1) ).
cnf(product_substitution2,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution2) ).
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
cnf(sum_substitution1,axiom,
( sum(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ sum(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution1) ).
cnf(sum_substitution2,axiom,
( sum(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ sum(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution2) ).
cnf(sum_substitution3,axiom,
( sum(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ sum(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution3) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(multiply_substitution1,axiom,
( equalish(multiply(X1,X3),multiply(X2,X3))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_substitution1) ).
cnf(add_substitution1,axiom,
( equalish(add(X1,X3),add(X2,X3))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(prove_sum_is_additive_identity,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
cnf(additive_inverse2,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
cnf(a_inverse_times_b,hypothesis,
product(a,additive_inverse(b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
cnf(multiplicative_identity1,axiom,
product(additive_identity,X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
cnf(multiplicative_identity2,axiom,
product(X1,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
cnf(a_times_b,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
cnf(additive_inverse_substitution,axiom,
( equalish(additive_inverse(X1),additive_inverse(X2))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_substitution) ).
cnf(i_0_29,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_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(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
distributivity3,
[final] ).
cnf(i_0_32,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_33,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity_of_multiplication1,
[final] ).
cnf(i_0_34,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2,
[final] ).
cnf(i_0_35,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1,
[final] ).
cnf(i_0_36,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2,
[final] ).
cnf(i_0_37,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined,
[final] ).
cnf(i_0_38,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined,
[final] ).
cnf(i_0_39,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
product_substitution1,
[final] ).
cnf(i_0_40,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
product_substitution2,
[final] ).
cnf(i_0_41,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3,
[final] ).
cnf(i_0_42,axiom,
( sum(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ sum(X1,X3,X4) ),
sum_substitution1,
[final] ).
cnf(i_0_43,axiom,
( sum(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ sum(X3,X1,X4) ),
sum_substitution2,
[final] ).
cnf(i_0_44,axiom,
( sum(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ sum(X3,X4,X1) ),
sum_substitution3,
[final] ).
cnf(i_0_45,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition,
[final] ).
cnf(i_0_46,axiom,
( equalish(multiply(X1,X3),multiply(X2,X3))
| ~ equalish(X1,X2) ),
multiply_substitution1,
[final] ).
cnf(i_0_47,axiom,
( equalish(add(X1,X3),add(X2,X3))
| ~ equalish(X1,X2) ),
add_substitution1,
[final] ).
cnf(i_0_48,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication,
[final] ).
cnf(i_0_49,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition,
[final] ).
cnf(i_0_50,negated_conjecture,
~ sum(c,d,additive_identity),
prove_sum_is_additive_identity,
[final] ).
cnf(i_0_51,axiom,
sum(X1,additive_inverse(X1),additive_identity),
additive_inverse2,
[final] ).
cnf(i_0_52,hypothesis,
product(a,additive_inverse(b),c),
a_inverse_times_b,
[final] ).
cnf(i_0_53,axiom,
sum(X1,additive_identity,X1),
additive_identity2,
[final] ).
cnf(i_0_54,axiom,
product(additive_identity,X1,additive_identity),
multiplicative_identity1,
[final] ).
cnf(i_0_55,axiom,
product(X1,additive_identity,additive_identity),
multiplicative_identity2,
[final] ).
cnf(i_0_56,hypothesis,
product(a,b,d),
a_times_b,
[final] ).
cnf(i_0_57,axiom,
( equalish(additive_inverse(X1),additive_inverse(X2))
| ~ equalish(X1,X2) ),
additive_inverse_substitution,
[final] ).
cnf(i_0_58,plain,
sum(additive_identity,X1,X1),
inference(scs_inference,[],[i_0_53,i_0_45]) ).
cnf(i_0_59,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_60,plain,
equalish(multiply(X1,X2),multiply(X1,X2)),
inference(scs_inference,[],[i_0_53,i_0_48,i_0_45,i_0_37]) ).
cnf(i_0_61,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_62,plain,
equalish(X1,X1),
inference(scs_inference,[],[i_0_53,i_0_48,i_0_45,i_0_37,i_0_38]) ).
cnf(i_0_63,plain,
( ~ sum(X1,X2,X3)
| equalish(X4,X3)
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_64,plain,
~ equalish(additive_inverse(c),d),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_48,i_0_51,i_0_45,i_0_37,i_0_38,i_0_43]) ).
cnf(i_0_65,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_66,plain,
( ~ sum(X1,X2,X3)
| sum(X1,X4,X3)
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_67,plain,
~ equalish(add(c,d),additive_identity),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_48,i_0_49,i_0_51,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44]) ).
cnf(i_0_68,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_69,plain,
( ~ sum(X1,X2,X3)
| sum(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_70,plain,
~ sum(additive_inverse(c),additive_identity,d),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_48,i_0_49,i_0_51,i_0_65,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35]) ).
cnf(i_0_71,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_72,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_73,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_74,plain,
~ sum(additive_identity,d,additive_inverse(c)),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_71,i_0_48,i_0_49,i_0_51,i_0_65,i_0_72,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35,i_0_36]) ).
cnf(i_0_75,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_76,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_77,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_78,plain,
product(additive_identity,multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_71,i_0_48,i_0_49,i_0_54,i_0_51,i_0_65,i_0_72,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35,i_0_36,i_0_33]) ).
cnf(i_0_79,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_80,plain,
product(additive_identity,X1,additive_identity),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_81,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_82,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_83,plain,
product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity)),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_71,i_0_48,i_0_81,i_0_49,i_0_54,i_0_80,i_0_51,i_0_65,i_0_72,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35,i_0_36,i_0_33,i_0_34]) ).
cnf(i_0_84,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_85,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_86,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_87,plain,
sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_71,i_0_76,i_0_48,i_0_81,i_0_85,i_0_49,i_0_54,i_0_80,i_0_51,i_0_65,i_0_72,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31]) ).
cnf(i_0_88,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_89,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_90,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_91,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_92,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_31]) ).
cnf(i_0_93,plain,
sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_71,i_0_76,i_0_91,i_0_48,i_0_81,i_0_85,i_0_90,i_0_49,i_0_54,i_0_80,i_0_51,i_0_65,i_0_72,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32]) ).
cnf(i_0_94,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_95,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_96,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_97,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_98,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_32]) ).
cnf(i_0_99,plain,
product(additive_identity,add(X1,X2),multiply(additive_identity,X1)),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_71,i_0_76,i_0_91,i_0_97,i_0_48,i_0_81,i_0_85,i_0_90,i_0_96,i_0_49,i_0_68,i_0_54,i_0_80,i_0_51,i_0_65,i_0_72,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_29]) ).
cnf(i_0_100,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_101,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_102,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_103,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_29]) ).
cnf(i_0_104,plain,
product(add(X1,additive_identity),X2,multiply(X1,X2)),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_71,i_0_76,i_0_91,i_0_97,i_0_101,i_0_48,i_0_81,i_0_85,i_0_90,i_0_96,i_0_102,i_0_49,i_0_68,i_0_100,i_0_54,i_0_80,i_0_51,i_0_65,i_0_72,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_29,i_0_30]) ).
cnf(i_0_105,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_106,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_107,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_108,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_30]) ).
cnf(i_0_109,plain,
~ equalish(d,additive_inverse(c)),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_71,i_0_76,i_0_91,i_0_97,i_0_101,i_0_106,i_0_48,i_0_81,i_0_85,i_0_90,i_0_96,i_0_102,i_0_49,i_0_68,i_0_100,i_0_54,i_0_80,i_0_51,i_0_65,i_0_72,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_29,i_0_30,i_0_42]) ).
cnf(i_0_110,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_111,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X2,X3)
| ~ equalish(X1,X4) ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_112,plain,
( product(X1,b,d)
| ~ equalish(a,X1) ),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_71,i_0_76,i_0_91,i_0_97,i_0_101,i_0_106,i_0_48,i_0_81,i_0_85,i_0_90,i_0_96,i_0_102,i_0_49,i_0_68,i_0_100,i_0_54,i_0_80,i_0_51,i_0_65,i_0_72,i_0_56,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_29,i_0_30,i_0_42,i_0_39]) ).
cnf(i_0_113,plain,
( ~ product(X1,X2,X3)
| product(X4,X2,X3)
| ~ equalish(X1,X4) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_114,plain,
( product(a,X1,d)
| ~ equalish(b,X1) ),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_71,i_0_76,i_0_91,i_0_97,i_0_101,i_0_106,i_0_48,i_0_81,i_0_85,i_0_90,i_0_96,i_0_102,i_0_49,i_0_68,i_0_100,i_0_54,i_0_80,i_0_51,i_0_65,i_0_72,i_0_56,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_29,i_0_30,i_0_42,i_0_39,i_0_40]) ).
cnf(i_0_115,plain,
( ~ product(X1,X2,X3)
| product(X1,X4,X3)
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_116,plain,
( product(a,b,X1)
| ~ equalish(d,X1) ),
inference(scs_inference,[],[i_0_50,i_0_53,i_0_71,i_0_76,i_0_91,i_0_97,i_0_101,i_0_106,i_0_48,i_0_81,i_0_85,i_0_90,i_0_96,i_0_102,i_0_49,i_0_68,i_0_100,i_0_54,i_0_80,i_0_51,i_0_65,i_0_72,i_0_56,i_0_45,i_0_37,i_0_38,i_0_43,i_0_44,i_0_35,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_29,i_0_30,i_0_42,i_0_39,i_0_40,i_0_41]) ).
cnf(i_0_117,plain,
( ~ product(X1,X2,X3)
| product(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_118,plain,
sum(X1,X2,add(X2,X1)),
inference(scs_inference,[],[i_0_49,i_0_45]) ).
cnf(i_0_119,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_120,plain,
~ product(X1,additive_identity,add(c,d)),
inference(scs_inference,[],[i_0_55,i_0_67,i_0_49,i_0_45,i_0_37]) ).
cnf(i_0_121,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_122,plain,
~ sum(additive_identity,additive_inverse(c),d),
inference(scs_inference,[],[i_0_109,i_0_55,i_0_58,i_0_67,i_0_49,i_0_45,i_0_37,i_0_38]) ).
cnf(i_0_123,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_124,plain,
( ~ sum(X1,X2,X3)
| equalish(X4,X3)
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_125,plain,
~ equalish(add(d,c),additive_identity),
inference(scs_inference,[],[i_0_50,i_0_109,i_0_55,i_0_58,i_0_67,i_0_49,i_0_45,i_0_37,i_0_38,i_0_44]) ).
cnf(i_0_126,plain,
( ~ sum(X1,X2,X3)
| sum(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_127,plain,
~ equalish(additive_identity,add(c,d)),
inference(scs_inference,[],[i_0_50,i_0_109,i_0_55,i_0_58,i_0_67,i_0_49,i_0_45,i_0_37,i_0_38,i_0_44,i_0_41]) ).
cnf(i_0_128,plain,
( ~ product(X1,X2,X3)
| product(X1,X2,X4)
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_129,plain,
~ sum(c,d,additive_inverse(additive_identity)),
inference(scs_inference,[],[i_0_50,i_0_109,i_0_55,i_0_58,i_0_123,i_0_67,i_0_49,i_0_51,i_0_45,i_0_37,i_0_38,i_0_44,i_0_41,i_0_36]) ).
cnf(i_0_130,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_131,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_132,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_133,plain,
product(X1,multiply(additive_identity,X2),multiply(additive_identity,X2)),
inference(scs_inference,[],[i_0_50,i_0_109,i_0_55,i_0_58,i_0_123,i_0_99,i_0_67,i_0_49,i_0_51,i_0_45,i_0_37,i_0_38,i_0_44,i_0_41,i_0_36,i_0_33]) ).
cnf(i_0_134,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_135,plain,
product(additive_identity,add(X1,X2),multiply(X3,multiply(additive_identity,X1))),
inference(scs_inference,[],[i_0_50,i_0_109,i_0_55,i_0_104,i_0_58,i_0_123,i_0_99,i_0_67,i_0_49,i_0_51,i_0_45,i_0_37,i_0_38,i_0_44,i_0_41,i_0_36,i_0_33,i_0_34]) ).
cnf(i_0_136,plain,
product(add(X1,additive_identity),X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_104]) ).
cnf(i_0_137,plain,
product(X1,additive_identity,additive_identity),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_138,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_139,plain,
~ product(additive_inverse(a),additive_inverse(b),d),
inference(scs_inference,[],[i_0_50,i_0_109,i_0_55,i_0_52,i_0_104,i_0_58,i_0_123,i_0_99,i_0_67,i_0_49,i_0_54,i_0_51,i_0_130,i_0_45,i_0_37,i_0_38,i_0_44,i_0_41,i_0_36,i_0_33,i_0_34,i_0_31]) ).
cnf(i_0_140,plain,
product(additive_identity,X1,additive_identity),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_141,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_142,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_31]) ).
cnf(i_0_143,plain,
~ sum(additive_inverse(b),b,additive_identity),
inference(scs_inference,[],[i_0_50,i_0_109,i_0_55,i_0_137,i_0_52,i_0_104,i_0_58,i_0_123,i_0_99,i_0_67,i_0_49,i_0_54,i_0_51,i_0_130,i_0_56,i_0_45,i_0_37,i_0_38,i_0_44,i_0_41,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32]) ).
cnf(i_0_144,plain,
product(X1,additive_identity,additive_identity),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_145,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_32]) ).
cnf(i_0_146,plain,
( product(add(additive_identity,additive_identity),additive_identity,multiply(additive_identity,X1))
| ~ product(add(additive_identity,additive_identity),additive_inverse(X1),multiply(additive_identity,X1)) ),
inference(scs_inference,[],[i_0_50,i_0_87,i_0_109,i_0_55,i_0_137,i_0_52,i_0_104,i_0_136,i_0_58,i_0_123,i_0_99,i_0_67,i_0_49,i_0_54,i_0_51,i_0_130,i_0_141,i_0_56,i_0_45,i_0_37,i_0_38,i_0_44,i_0_41,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_29]) ).
cnf(i_0_147,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_148,plain,
sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_149,plain,
product(add(X1,additive_identity),X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_104]) ).
cnf(i_0_150,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_29]) ).
cnf(i_0_151,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_152,plain,
( product(add(d,c),X1,add(d,c))
| ~ product(d,X1,d)
| ~ product(c,X1,c) ),
inference(scs_inference,[],[i_0_50,i_0_87,i_0_109,i_0_55,i_0_137,i_0_52,i_0_104,i_0_136,i_0_58,i_0_123,i_0_99,i_0_67,i_0_49,i_0_54,i_0_51,i_0_130,i_0_141,i_0_56,i_0_45,i_0_37,i_0_38,i_0_44,i_0_41,i_0_36,i_0_33,i_0_34,i_0_31,i_0_32,i_0_30]) ).
cnf(i_0_153,plain,
$false,
inference(scs_inference,[],[i_0_143,i_0_51,i_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.17 % Problem : RNG037-2 : TPTP v9.2.1. Released v1.0.0.
% 0.03/0.17 % 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
% 0.12/0.42 % Computer : n009.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8042.1875MB
% 0.12/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Tue May 5 01:46:56 EDT 2026
% 0.12/0.43 % CPUTime :
% 0.14/0.46 % start to proof: theBenchmark
% 2.86/5.74 % Version : CSE_E---1.7
% 2.86/5.74 % Problem : theBenchmark.p
% 2.86/5.74 % SZS status Unsatisfiable for theBenchmark.p
% 2.86/5.74 % SZS output start CNFRefutation
% See solution above
% 3.25/5.99 % Total time : 5.278s
%------------------------------------------------------------------------------