%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG040-2 : 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 : n003.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 05:05:06 PM UTC 2026
% Result : Unsatisfiable 5.37s 5.62s
% Output : CNFRefutation 5.76s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 95)
% 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(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,
( 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,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(product_symmetry,hypothesis,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_symmetry) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
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_equation,negated_conjecture,
~ sum(l,n,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(clause31,hypothesis,
( product(h(X1),X1,multiplicative_identity)
| X1 = additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
cnf(clause30,hypothesis,
( product(X1,h(X1),multiplicative_identity)
| X1 = additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
cnf(additive_inverse1,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
cnf(additive_inverse2,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
cnf(left_multiplicative_identity,hypothesis,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_identity) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
cnf(right_multiplicative_identity,hypothesis,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_multiplicative_identity) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
cnf(d_plus_a,negated_conjecture,
product(d,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_plus_a) ).
cnf(c_plus_a,negated_conjecture,
product(c,a,n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_plus_a) ).
cnf(b_plus_a,negated_conjecture,
product(b,a,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_a) ).
cnf(b_plus_c,negated_conjecture,
sum(b,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_c) ).
cnf(i_0_25,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_26,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_27,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity_of_multiplication1,
[final] ).
cnf(i_0_28,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2,
[final] ).
cnf(i_0_29,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1,
[final] ).
cnf(i_0_30,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2,
[final] ).
cnf(i_0_31,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined,
[final] ).
cnf(i_0_32,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined,
[final] ).
cnf(i_0_33,hypothesis,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
product_symmetry,
[final] ).
cnf(i_0_34,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition,
[final] ).
cnf(i_0_35,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication,
[final] ).
cnf(i_0_36,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition,
[final] ).
cnf(i_0_37,negated_conjecture,
~ sum(l,n,additive_identity),
prove_equation,
[final] ).
cnf(i_0_38,hypothesis,
( product(h(X1),X1,multiplicative_identity)
| X1 = additive_identity ),
clause31,
[final] ).
cnf(i_0_39,hypothesis,
( product(X1,h(X1),multiplicative_identity)
| X1 = additive_identity ),
clause30,
[final] ).
cnf(i_0_40,axiom,
sum(additive_inverse(X1),X1,additive_identity),
additive_inverse1,
[final] ).
cnf(i_0_41,axiom,
sum(X1,additive_inverse(X1),additive_identity),
additive_inverse2,
[final] ).
cnf(i_0_42,hypothesis,
product(multiplicative_identity,X1,X1),
left_multiplicative_identity,
[final] ).
cnf(i_0_43,axiom,
sum(additive_identity,X1,X1),
additive_identity1,
[final] ).
cnf(i_0_44,hypothesis,
product(X1,multiplicative_identity,X1),
right_multiplicative_identity,
[final] ).
cnf(i_0_45,axiom,
sum(X1,additive_identity,X1),
additive_identity2,
[final] ).
cnf(i_0_46,negated_conjecture,
product(d,a,additive_identity),
d_plus_a,
[final] ).
cnf(i_0_47,negated_conjecture,
product(c,a,n),
c_plus_a,
[final] ).
cnf(i_0_48,negated_conjecture,
product(b,a,l),
b_plus_a,
[final] ).
cnf(i_0_49,negated_conjecture,
sum(b,c,d),
b_plus_c,
[final] ).
cnf(i_0_50,axiom,
X1 = X1 ).
cnf(i_0_51,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_52,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_53,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_54,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_55,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_56,axiom,
( X1 != X2
| ~ sum(X1,X3,X4)
| sum(X2,X3,X4) ) ).
cnf(i_0_57,axiom,
( X1 != X2
| ~ sum(X3,X1,X4)
| sum(X3,X2,X4) ) ).
cnf(i_0_58,axiom,
( X1 != X2
| ~ sum(X3,X4,X1)
| sum(X3,X4,X2) ) ).
cnf(i_0_50_001,axiom,
X1 = X1 ).
cnf(i_0_51_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_52_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_53_004,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_54_005,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_55_006,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_56_007,axiom,
( X1 != X2
| ~ sum(X1,X3,X4)
| sum(X2,X3,X4) ) ).
cnf(i_0_57_008,axiom,
( X1 != X2
| ~ sum(X3,X1,X4)
| sum(X3,X2,X4) ) ).
cnf(i_0_58_009,axiom,
( X1 != X2
| ~ sum(X3,X4,X1)
| sum(X3,X4,X2) ) ).
cnf(i_0_59,plain,
sum(c,b,d),
inference(scs_inference,[],[i_0_49,i_0_34]) ).
cnf(i_0_60,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_61,plain,
product(a,d,additive_identity),
inference(scs_inference,[],[i_0_46,i_0_49,i_0_34,i_0_33]) ).
cnf(i_0_62,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_63,plain,
additive_inverse(n) != l,
inference(scs_inference,[],[i_0_37,i_0_46,i_0_49,i_0_40,i_0_34,i_0_33,i_0_56]) ).
cnf(i_0_64,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_65,plain,
~ product(b,a,additive_inverse(n)),
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_40,i_0_34,i_0_33,i_0_56,i_0_31]) ).
cnf(i_0_66,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_67,plain,
~ sum(additive_identity,l,additive_inverse(n)),
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_43,i_0_40,i_0_34,i_0_33,i_0_56,i_0_31,i_0_32]) ).
cnf(i_0_68,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_69,plain,
( ~ sum(X1,X2,X3)
| X4 = X3
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_70,plain,
l != additive_inverse(n),
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_43,i_0_40,i_0_34,i_0_33,i_0_56,i_0_31,i_0_32,i_0_55]) ).
cnf(i_0_71,plain,
additive_inverse(l) != n,
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_43,i_0_40,i_0_41,i_0_34,i_0_33,i_0_56,i_0_31,i_0_32,i_0_55,i_0_57]) ).
cnf(i_0_72,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_73,plain,
add(l,n) != additive_identity,
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_43,i_0_36,i_0_40,i_0_41,i_0_34,i_0_33,i_0_56,i_0_31,i_0_32,i_0_55,i_0_57,i_0_58]) ).
cnf(i_0_74,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_75,plain,
~ sum(additive_inverse(l),additive_identity,n),
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_43,i_0_68,i_0_36,i_0_40,i_0_41,i_0_72,i_0_34,i_0_33,i_0_56,i_0_31,i_0_32,i_0_55,i_0_57,i_0_58,i_0_29]) ).
cnf(i_0_76,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_77,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_78,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_79,plain,
~ sum(additive_identity,additive_inverse(n),l),
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_43,i_0_68,i_0_76,i_0_36,i_0_40,i_0_64,i_0_41,i_0_72,i_0_34,i_0_33,i_0_56,i_0_31,i_0_32,i_0_55,i_0_57,i_0_58,i_0_29,i_0_30]) ).
cnf(i_0_80,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_81,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_82,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_83,plain,
product(d,a,multiply(additive_identity,multiplicative_identity)),
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_43,i_0_68,i_0_76,i_0_44,i_0_35,i_0_36,i_0_40,i_0_64,i_0_41,i_0_72,i_0_34,i_0_33,i_0_56,i_0_31,i_0_32,i_0_55,i_0_57,i_0_58,i_0_29,i_0_30,i_0_27]) ).
cnf(i_0_84,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_85,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_86,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_87,plain,
product(additive_identity,multiplicative_identity,multiply(d,a)),
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_43,i_0_68,i_0_76,i_0_44,i_0_85,i_0_35,i_0_84,i_0_36,i_0_40,i_0_64,i_0_41,i_0_72,i_0_34,i_0_33,i_0_56,i_0_31,i_0_32,i_0_55,i_0_57,i_0_58,i_0_29,i_0_30,i_0_27,i_0_28]) ).
cnf(i_0_88,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_89,plain,
product(X1,multiplicative_identity,X1),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_90,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_91,plain,
sum(additive_identity,additive_identity,multiply(d,add(a,a))),
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_43,i_0_68,i_0_76,i_0_44,i_0_85,i_0_35,i_0_84,i_0_88,i_0_36,i_0_74,i_0_40,i_0_64,i_0_41,i_0_72,i_0_34,i_0_33,i_0_56,i_0_31,i_0_32,i_0_55,i_0_57,i_0_58,i_0_29,i_0_30,i_0_27,i_0_28,i_0_26]) ).
cnf(i_0_92,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_93,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_94,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_26]) ).
cnf(i_0_95,plain,
( X1 != b
| ~ product(X1,a,additive_inverse(n)) ),
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_43,i_0_68,i_0_76,i_0_44,i_0_85,i_0_35,i_0_84,i_0_88,i_0_36,i_0_74,i_0_40,i_0_64,i_0_41,i_0_72,i_0_34,i_0_33,i_0_56,i_0_31,i_0_32,i_0_55,i_0_57,i_0_58,i_0_29,i_0_30,i_0_27,i_0_28,i_0_26,i_0_53]) ).
cnf(i_0_96,plain,
( additive_inverse(n) != a
| multiplicative_identity != b ),
inference(scs_inference,[],[i_0_37,i_0_46,i_0_48,i_0_49,i_0_42,i_0_43,i_0_68,i_0_76,i_0_44,i_0_85,i_0_35,i_0_84,i_0_88,i_0_36,i_0_74,i_0_40,i_0_64,i_0_41,i_0_72,i_0_34,i_0_33,i_0_56,i_0_31,i_0_32,i_0_55,i_0_57,i_0_58,i_0_29,i_0_30,i_0_27,i_0_28,i_0_26,i_0_53,i_0_54]) ).
cnf(i_0_97,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_98,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_99,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_25]) ).
cnf(i_0_101,plain,
~ product(b,a,additive_inverse(n)),
inference(equality_inference,[],[95]) ).
cnf(i_0_102,plain,
sum(X1,X2,add(X2,X1)),
inference(scs_inference,[],[i_0_36,i_0_34]) ).
cnf(i_0_103,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_104,plain,
product(a,c,n),
inference(scs_inference,[],[i_0_47,i_0_36,i_0_34,i_0_33]) ).
cnf(i_0_105,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_106,plain,
~ product(c,a,additive_inverse(l)),
inference(scs_inference,[],[i_0_47,i_0_71,i_0_36,i_0_34,i_0_33,i_0_31]) ).
cnf(i_0_107,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_108,plain,
~ sum(l,additive_identity,additive_inverse(n)),
inference(scs_inference,[],[i_0_47,i_0_63,i_0_45,i_0_71,i_0_36,i_0_34,i_0_33,i_0_31,i_0_32]) ).
cnf(i_0_109,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_110,plain,
( ~ sum(X1,X2,X3)
| X4 = X3
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_111,plain,
n != additive_inverse(l),
inference(scs_inference,[],[i_0_47,i_0_63,i_0_75,i_0_45,i_0_109,i_0_71,i_0_36,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56]) ).
cnf(i_0_112,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_113,plain,
~ sum(l,n,additive_inverse(additive_identity)),
inference(scs_inference,[],[i_0_37,i_0_47,i_0_63,i_0_75,i_0_45,i_0_109,i_0_112,i_0_71,i_0_36,i_0_40,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56,i_0_29]) ).
cnf(i_0_114,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_115,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_116,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_117,plain,
~ sum(additive_inverse(n),additive_identity,l),
inference(scs_inference,[],[i_0_37,i_0_47,i_0_63,i_0_75,i_0_45,i_0_109,i_0_112,i_0_71,i_0_43,i_0_36,i_0_40,i_0_114,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56,i_0_29,i_0_30]) ).
cnf(i_0_118,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_119,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_120,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_121,plain,
product(c,additive_identity,multiply(n,d)),
inference(scs_inference,[],[i_0_37,i_0_47,i_0_63,i_0_75,i_0_45,i_0_109,i_0_112,i_0_71,i_0_61,i_0_43,i_0_35,i_0_36,i_0_40,i_0_114,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56,i_0_29,i_0_30,i_0_27]) ).
cnf(i_0_122,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_123,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_124,plain,
product(n,d,multiply(c,additive_identity)),
inference(scs_inference,[],[i_0_37,i_0_47,i_0_63,i_0_75,i_0_45,i_0_109,i_0_112,i_0_71,i_0_61,i_0_43,i_0_35,i_0_122,i_0_36,i_0_40,i_0_114,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56,i_0_29,i_0_30,i_0_27,i_0_28]) ).
cnf(i_0_125,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_126,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_127,plain,
~ product(a,b,l),
inference(scs_inference,[],[i_0_37,i_0_47,i_0_49,i_0_63,i_0_75,i_0_45,i_0_109,i_0_112,i_0_71,i_0_61,i_0_43,i_0_35,i_0_122,i_0_36,i_0_40,i_0_114,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56,i_0_29,i_0_30,i_0_27,i_0_28,i_0_26]) ).
cnf(i_0_128,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_26]) ).
cnf(i_0_129,plain,
product(multiplicative_identity,additive_identity,multiply(d,add(a,a))),
inference(scs_inference,[],[i_0_37,i_0_91,i_0_47,i_0_49,i_0_63,i_0_75,i_0_45,i_0_109,i_0_112,i_0_71,i_0_61,i_0_42,i_0_43,i_0_119,i_0_35,i_0_122,i_0_36,i_0_40,i_0_114,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56,i_0_29,i_0_30,i_0_27,i_0_28,i_0_26,i_0_25]) ).
cnf(i_0_130,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_131,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_132,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_133,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_25]) ).
cnf(i_0_134,plain,
( X1 != c
| ~ product(X1,a,additive_inverse(l)) ),
inference(scs_inference,[],[i_0_37,i_0_91,i_0_47,i_0_49,i_0_63,i_0_75,i_0_45,i_0_109,i_0_112,i_0_71,i_0_61,i_0_42,i_0_43,i_0_119,i_0_35,i_0_122,i_0_36,i_0_40,i_0_114,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56,i_0_29,i_0_30,i_0_27,i_0_28,i_0_26,i_0_25,i_0_53]) ).
cnf(i_0_135,plain,
( additive_inverse(l) != a
| multiplicative_identity != c ),
inference(scs_inference,[],[i_0_37,i_0_91,i_0_47,i_0_49,i_0_63,i_0_75,i_0_45,i_0_109,i_0_112,i_0_71,i_0_61,i_0_42,i_0_132,i_0_43,i_0_119,i_0_35,i_0_122,i_0_36,i_0_40,i_0_114,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56,i_0_29,i_0_30,i_0_27,i_0_28,i_0_26,i_0_25,i_0_53,i_0_54]) ).
cnf(i_0_136,plain,
product(multiplicative_identity,X1,X1),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_137,plain,
( multiply(a,b) != l
| multiplicative_identity != c ),
inference(scs_inference,[],[i_0_37,i_0_91,i_0_47,i_0_49,i_0_63,i_0_75,i_0_45,i_0_109,i_0_112,i_0_71,i_0_61,i_0_42,i_0_132,i_0_43,i_0_119,i_0_35,i_0_122,i_0_125,i_0_36,i_0_40,i_0_114,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56,i_0_29,i_0_30,i_0_27,i_0_28,i_0_26,i_0_25,i_0_53,i_0_54,i_0_55]) ).
cnf(i_0_138,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_139,plain,
( add(l,n) != additive_inverse(additive_identity)
| multiplicative_identity != c ),
inference(scs_inference,[],[i_0_37,i_0_91,i_0_47,i_0_49,i_0_63,i_0_75,i_0_45,i_0_109,i_0_112,i_0_71,i_0_61,i_0_42,i_0_132,i_0_43,i_0_119,i_0_35,i_0_122,i_0_125,i_0_36,i_0_40,i_0_114,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56,i_0_29,i_0_30,i_0_27,i_0_28,i_0_26,i_0_25,i_0_53,i_0_54,i_0_55,i_0_58]) ).
cnf(i_0_140,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_141,plain,
( multiplicative_identity != c
| X1 != additive_identity
| ~ sum(additive_inverse(l),X1,n) ),
inference(scs_inference,[],[i_0_37,i_0_91,i_0_47,i_0_49,i_0_63,i_0_75,i_0_45,i_0_109,i_0_112,i_0_71,i_0_61,i_0_42,i_0_132,i_0_43,i_0_119,i_0_35,i_0_122,i_0_125,i_0_36,i_0_40,i_0_114,i_0_34,i_0_33,i_0_31,i_0_32,i_0_56,i_0_29,i_0_30,i_0_27,i_0_28,i_0_26,i_0_25,i_0_53,i_0_54,i_0_55,i_0_58,i_0_57]) ).
cnf(i_0_142,plain,
~ product(c,a,additive_inverse(l)),
inference(equality_inference,[],[134]) ).
cnf(i_0_143,plain,
$false,
inference(scs_inference,[],[i_0_48,i_0_127,i_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG040-2 : 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 : n003.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 01:47:41 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 5.37/5.62 % Version : CSE_E---1.7
% 5.37/5.62 % Problem : theBenchmark.p
% 5.37/5.62 % SZS status Unsatisfiable for theBenchmark.p
% 5.37/5.62 % SZS output start CNFRefutation
% See solution above
% 5.76/5.88 % Total time : 5.280s
%------------------------------------------------------------------------------