%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG001-4 : 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 : n019.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 05:04:56 PM UTC 2026
% Result : Unsatisfiable 1.27s 2.60s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 83)
% 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/Axioms/RNG001-0.ax',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/Axioms/RNG001-0.ax',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/Axioms/RNG001-0.ax',distributivity3) ).
cnf(distributivity1,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',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/Axioms/RNG001-0.ax',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/Axioms/RNG001-0.ax',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/Axioms/RNG001-0.ax',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/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(cancellation2,axiom,
( X1 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation2) ).
cnf(cancellation1,axiom,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation1) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(prove_a_times_additive_id_is_additive_id,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
cnf(i_0_20,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_21,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_22,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_23,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_24,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity_of_multiplication1,
[final] ).
cnf(i_0_25,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2,
[final] ).
cnf(i_0_26,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1,
[final] ).
cnf(i_0_27,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2,
[final] ).
cnf(i_0_28,axiom,
( X1 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X3) ),
cancellation2,
[final] ).
cnf(i_0_29,axiom,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
cancellation1,
[final] ).
cnf(i_0_30,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined,
[final] ).
cnf(i_0_31,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined,
[final] ).
cnf(i_0_32,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition,
[final] ).
cnf(i_0_33,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication,
[final] ).
cnf(i_0_34,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition,
[final] ).
cnf(i_0_35,negated_conjecture,
~ product(a,additive_identity,additive_identity),
prove_a_times_additive_id_is_additive_id,
[final] ).
cnf(i_0_36,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse,
[final] ).
cnf(i_0_37,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse,
[final] ).
cnf(i_0_38,axiom,
sum(additive_identity,X1,X1),
additive_identity1,
[final] ).
cnf(i_0_39,axiom,
sum(X1,additive_identity,X1),
additive_identity2,
[final] ).
cnf(i_0_40,axiom,
X1 = X1 ).
cnf(i_0_41,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_42,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_43,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| ~ sum(X1,X3,X4)
| sum(X2,X3,X4) ) ).
cnf(i_0_47,axiom,
( X1 != X2
| ~ sum(X3,X1,X4)
| sum(X3,X2,X4) ) ).
cnf(i_0_48,axiom,
( X1 != X2
| ~ sum(X3,X4,X1)
| sum(X3,X4,X2) ) ).
cnf(i_0_40_001,axiom,
X1 = X1 ).
cnf(i_0_41_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_42_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_43_004,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_44_005,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_45_006,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_46_007,axiom,
( X1 != X2
| ~ sum(X1,X3,X4)
| sum(X2,X3,X4) ) ).
cnf(i_0_47_008,axiom,
( X1 != X2
| ~ sum(X3,X1,X4)
| sum(X3,X2,X4) ) ).
cnf(i_0_48_009,axiom,
( X1 != X2
| ~ sum(X3,X4,X1)
| sum(X3,X4,X2) ) ).
cnf(i_0_49,plain,
sum(X1,X2,add(X2,X1)),
inference(scs_inference,[],[i_0_34,i_0_32]) ).
cnf(i_0_50,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_51,plain,
add(X1,additive_identity) = X1,
inference(scs_inference,[],[i_0_39,i_0_34,i_0_32,i_0_28]) ).
cnf(i_0_52,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_53,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_54,plain,
( ~ sum(X1,X2,X3)
| X4 = X1
| ~ sum(X4,X2,X3) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_55,plain,
add(additive_identity,X1) = X1,
inference(scs_inference,[],[i_0_38,i_0_39,i_0_34,i_0_52,i_0_32,i_0_28,i_0_29]) ).
cnf(i_0_56,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_57,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_58,plain,
( ~ sum(X1,X2,X3)
| X4 = X2
| ~ sum(X1,X4,X3) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_59,plain,
X1 = add(additive_identity,X1),
inference(scs_inference,[],[i_0_38,i_0_57,i_0_39,i_0_34,i_0_52,i_0_56,i_0_32,i_0_28,i_0_29,i_0_31]) ).
cnf(i_0_60,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_61,plain,
( ~ sum(X1,X2,X3)
| X4 = X3
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_62,plain,
add(additive_identity,add(X1,additive_identity)) = X1,
inference(scs_inference,[],[i_0_38,i_0_57,i_0_39,i_0_34,i_0_52,i_0_56,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42]) ).
cnf(i_0_63,plain,
~ product(a,add(additive_identity,additive_identity),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_57,i_0_39,i_0_34,i_0_52,i_0_56,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42,i_0_44]) ).
cnf(i_0_64,plain,
~ product(a,additive_identity,add(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_57,i_0_39,i_0_34,i_0_52,i_0_56,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42,i_0_44,i_0_45]) ).
cnf(i_0_65,plain,
sum(additive_identity,add(X1,additive_inverse(X1)),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_57,i_0_39,i_0_34,i_0_52,i_0_56,i_0_60,i_0_37,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42,i_0_44,i_0_45,i_0_26]) ).
cnf(i_0_66,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_67,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_68,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_69,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_70,plain,
sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,X1)),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_57,i_0_67,i_0_39,i_0_33,i_0_34,i_0_52,i_0_56,i_0_60,i_0_37,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42,i_0_44,i_0_45,i_0_26,i_0_22]) ).
cnf(i_0_71,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_72,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_73,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_74,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_75,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_22]) ).
cnf(i_0_76,plain,
sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_57,i_0_67,i_0_74,i_0_39,i_0_33,i_0_73,i_0_34,i_0_52,i_0_56,i_0_60,i_0_37,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42,i_0_44,i_0_45,i_0_26,i_0_22,i_0_23]) ).
cnf(i_0_77,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_78,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_79,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_80,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_81,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_23]) ).
cnf(i_0_82,plain,
additive_identity = add(additive_identity,add(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_57,i_0_67,i_0_74,i_0_39,i_0_33,i_0_73,i_0_34,i_0_52,i_0_56,i_0_60,i_0_37,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42,i_0_44,i_0_45,i_0_26,i_0_22,i_0_23,i_0_41]) ).
cnf(i_0_83,plain,
( X1 != a
| ~ product(X1,additive_identity,additive_identity) ),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_57,i_0_67,i_0_74,i_0_39,i_0_33,i_0_73,i_0_34,i_0_52,i_0_56,i_0_60,i_0_37,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42,i_0_44,i_0_45,i_0_26,i_0_22,i_0_23,i_0_41,i_0_43]) ).
cnf(i_0_84,plain,
product(X1,multiply(X1,X1),multiply(multiply(X1,X1),X1)),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_57,i_0_67,i_0_74,i_0_39,i_0_33,i_0_73,i_0_79,i_0_78,i_0_34,i_0_52,i_0_56,i_0_60,i_0_37,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42,i_0_44,i_0_45,i_0_26,i_0_22,i_0_23,i_0_41,i_0_43,i_0_24]) ).
cnf(i_0_85,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_86,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_87,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_88,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_89,plain,
product(multiply(X1,X1),X1,multiply(X1,multiply(X1,X1))),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_57,i_0_67,i_0_74,i_0_39,i_0_33,i_0_73,i_0_79,i_0_85,i_0_78,i_0_87,i_0_34,i_0_52,i_0_56,i_0_60,i_0_37,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42,i_0_44,i_0_45,i_0_26,i_0_22,i_0_23,i_0_41,i_0_43,i_0_24,i_0_25]) ).
cnf(i_0_90,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_91,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_92,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_93,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_94,plain,
( ~ product(a,additive_inverse(X1),additive_identity)
| ~ product(a,X1,additive_identity) ),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_57,i_0_67,i_0_74,i_0_80,i_0_39,i_0_33,i_0_73,i_0_79,i_0_85,i_0_78,i_0_87,i_0_34,i_0_52,i_0_56,i_0_60,i_0_36,i_0_37,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42,i_0_44,i_0_45,i_0_26,i_0_22,i_0_23,i_0_41,i_0_43,i_0_24,i_0_25,i_0_20]) ).
cnf(i_0_95,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_96,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_20]) ).
cnf(i_0_97,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_98,plain,
( add(X1,X2) != a
| ~ product(X1,additive_identity,additive_identity)
| ~ product(X2,additive_identity,additive_identity) ),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_57,i_0_67,i_0_74,i_0_80,i_0_95,i_0_39,i_0_33,i_0_73,i_0_79,i_0_85,i_0_78,i_0_87,i_0_34,i_0_52,i_0_56,i_0_60,i_0_68,i_0_36,i_0_37,i_0_32,i_0_28,i_0_29,i_0_31,i_0_42,i_0_44,i_0_45,i_0_26,i_0_22,i_0_23,i_0_41,i_0_43,i_0_24,i_0_25,i_0_21]) ).
cnf(i_0_99,plain,
~ product(a,additive_identity,additive_identity),
inference(equality_inference,[],[83]) ).
cnf(i_0_100,plain,
sum(add(X1,additive_inverse(X1)),additive_identity,additive_identity),
inference(scs_inference,[],[i_0_65,i_0_32]) ).
cnf(i_0_101,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_102,plain,
X1 = add(X1,additive_identity),
inference(scs_inference,[],[i_0_51,i_0_65,i_0_32,i_0_41]) ).
cnf(i_0_103,plain,
additive_inverse(additive_identity) = additive_identity,
inference(scs_inference,[],[i_0_36,i_0_51,i_0_65,i_0_38,i_0_32,i_0_41,i_0_28]) ).
cnf(i_0_104,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_105,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_106,plain,
( ~ sum(X1,X2,X3)
| X4 = X1
| ~ sum(X4,X2,X3) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_107,plain,
multiply(additive_identity,X1) = additive_identity,
inference(scs_inference,[],[i_0_36,i_0_51,i_0_70,i_0_65,i_0_38,i_0_39,i_0_32,i_0_41,i_0_28,i_0_29]) ).
cnf(i_0_108,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_109,plain,
( ~ sum(X1,X2,X3)
| X4 = X2
| ~ sum(X1,X4,X3) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_110,plain,
additive_identity = add(X1,additive_inverse(X1)),
inference(scs_inference,[],[i_0_36,i_0_105,i_0_49,i_0_51,i_0_70,i_0_65,i_0_38,i_0_39,i_0_32,i_0_41,i_0_28,i_0_29,i_0_31]) ).
cnf(i_0_111,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_112,plain,
( ~ sum(X1,X2,X3)
| X4 = X3
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_113,plain,
~ product(add(a,additive_identity),additive_identity,additive_identity),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_105,i_0_49,i_0_51,i_0_70,i_0_65,i_0_38,i_0_39,i_0_32,i_0_41,i_0_28,i_0_29,i_0_31,i_0_43]) ).
cnf(i_0_114,plain,
add(X1,additive_identity) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_115,plain,
add(add(additive_identity,X1),additive_identity) = X1,
inference(scs_inference,[],[i_0_35,i_0_36,i_0_105,i_0_49,i_0_51,i_0_114,i_0_55,i_0_70,i_0_65,i_0_38,i_0_39,i_0_32,i_0_41,i_0_28,i_0_29,i_0_31,i_0_43,i_0_42]) ).
cnf(i_0_116,plain,
add(X1,additive_identity) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_117,plain,
~ product(a,add(additive_identity,additive_identity),add(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_105,i_0_49,i_0_51,i_0_114,i_0_116,i_0_55,i_0_70,i_0_65,i_0_64,i_0_38,i_0_39,i_0_32,i_0_41,i_0_28,i_0_29,i_0_31,i_0_43,i_0_42,i_0_44]) ).
cnf(i_0_118,plain,
add(X1,additive_identity) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_119,plain,
~ product(a,additive_identity,add(add(additive_identity,additive_identity),additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_105,i_0_49,i_0_51,i_0_114,i_0_116,i_0_118,i_0_55,i_0_70,i_0_65,i_0_64,i_0_38,i_0_39,i_0_32,i_0_41,i_0_28,i_0_29,i_0_31,i_0_43,i_0_42,i_0_44,i_0_45]) ).
cnf(i_0_120,plain,
add(X1,additive_identity) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_121,plain,
sum(additive_identity,multiply(additive_identity,X1),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_105,i_0_49,i_0_51,i_0_114,i_0_116,i_0_118,i_0_55,i_0_70,i_0_65,i_0_64,i_0_38,i_0_39,i_0_32,i_0_41,i_0_28,i_0_29,i_0_31,i_0_43,i_0_42,i_0_44,i_0_45,i_0_27]) ).
cnf(i_0_122,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_123,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_124,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_125,plain,
sum(additive_inverse(additive_inverse(X1)),additive_identity,add(X1,additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_105,i_0_123,i_0_122,i_0_49,i_0_111,i_0_51,i_0_114,i_0_116,i_0_118,i_0_55,i_0_70,i_0_65,i_0_64,i_0_38,i_0_39,i_0_32,i_0_41,i_0_28,i_0_29,i_0_31,i_0_43,i_0_42,i_0_44,i_0_45,i_0_27,i_0_26]) ).
cnf(i_0_126,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_127,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_128,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_129,plain,
~ product(additive_identity,additive_identity,additive_inverse(multiply(a,additive_identity))),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_105,i_0_123,i_0_127,i_0_122,i_0_49,i_0_111,i_0_126,i_0_51,i_0_114,i_0_116,i_0_118,i_0_55,i_0_70,i_0_65,i_0_64,i_0_38,i_0_39,i_0_33,i_0_32,i_0_41,i_0_28,i_0_29,i_0_31,i_0_43,i_0_42,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21]) ).
cnf(i_0_130,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_131,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_132,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_133,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_21]) ).
cnf(i_0_134,plain,
~ product(a,additive_identity,additive_inverse(multiply(a,additive_identity))),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_105,i_0_123,i_0_127,i_0_131,i_0_122,i_0_49,i_0_111,i_0_126,i_0_130,i_0_51,i_0_114,i_0_116,i_0_118,i_0_55,i_0_70,i_0_65,i_0_64,i_0_63,i_0_38,i_0_39,i_0_33,i_0_132,i_0_32,i_0_41,i_0_28,i_0_29,i_0_31,i_0_43,i_0_42,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21,i_0_20]) ).
cnf(i_0_135,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_136,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_137,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_138,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_20]) ).
cnf(i_0_139,plain,
sum(additive_identity,additive_inverse(additive_inverse(X1)),add(X1,additive_identity)),
inference(scs_inference,[],[i_0_125,i_0_32]) ).
cnf(i_0_140,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_141,plain,
X1 = add(additive_identity,add(X1,additive_identity)),
inference(scs_inference,[],[i_0_62,i_0_125,i_0_32,i_0_41]) ).
cnf(i_0_142,plain,
additive_inverse(additive_inverse(additive_identity)) = additive_identity,
inference(scs_inference,[],[i_0_62,i_0_125,i_0_49,i_0_32,i_0_41,i_0_28]) ).
cnf(i_0_143,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_144,plain,
sum(additive_inverse(additive_inverse(X1)),additive_identity,add(X1,additive_identity)),
inference(rename_variables,[],[i_0_125]) ).
cnf(i_0_145,plain,
( ~ sum(X1,X2,X3)
| X4 = X1
| ~ sum(X4,X2,X3) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_146,plain,
add(additive_inverse(X1),X1) = additive_identity,
inference(scs_inference,[],[i_0_62,i_0_125,i_0_49,i_0_143,i_0_37,i_0_32,i_0_41,i_0_28,i_0_31]) ).
cnf(i_0_147,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_148,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_149,plain,
( ~ sum(X1,X2,X3)
| X4 = X3
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_150,plain,
X1 = additive_inverse(additive_inverse(X1)),
inference(scs_inference,[],[i_0_36,i_0_62,i_0_125,i_0_49,i_0_143,i_0_37,i_0_147,i_0_32,i_0_41,i_0_28,i_0_31,i_0_29]) ).
cnf(i_0_151,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_152,plain,
( ~ sum(X1,X2,X3)
| X4 = X2
| ~ sum(X1,X4,X3) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_153,plain,
~ product(add(additive_identity,add(a,additive_identity)),additive_identity,additive_identity),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_62,i_0_125,i_0_49,i_0_143,i_0_37,i_0_147,i_0_32,i_0_41,i_0_28,i_0_31,i_0_29,i_0_43]) ).
cnf(i_0_154,plain,
add(additive_identity,add(X1,additive_identity)) = X1,
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_155,plain,
X1 = add(add(additive_identity,X1),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_59,i_0_102,i_0_62,i_0_125,i_0_49,i_0_143,i_0_37,i_0_147,i_0_32,i_0_41,i_0_28,i_0_31,i_0_29,i_0_43,i_0_42]) ).
cnf(i_0_156,plain,
X1 = add(X1,additive_identity),
inference(rename_variables,[],[i_0_102]) ).
cnf(i_0_157,plain,
~ product(a,add(additive_identity,add(additive_identity,additive_identity)),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_59,i_0_102,i_0_62,i_0_154,i_0_125,i_0_49,i_0_143,i_0_37,i_0_147,i_0_32,i_0_41,i_0_28,i_0_31,i_0_29,i_0_43,i_0_42,i_0_44]) ).
cnf(i_0_158,plain,
add(additive_identity,add(X1,additive_identity)) = X1,
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_159,plain,
~ product(a,additive_identity,add(additive_identity,add(additive_identity,additive_identity))),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_59,i_0_102,i_0_62,i_0_154,i_0_158,i_0_125,i_0_49,i_0_143,i_0_37,i_0_147,i_0_32,i_0_41,i_0_28,i_0_31,i_0_29,i_0_43,i_0_42,i_0_44,i_0_45]) ).
cnf(i_0_160,plain,
add(additive_identity,add(X1,additive_identity)) = X1,
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_161,plain,
sum(additive_identity,multiply(X1,additive_identity),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_59,i_0_102,i_0_76,i_0_62,i_0_154,i_0_158,i_0_125,i_0_49,i_0_143,i_0_37,i_0_147,i_0_32,i_0_41,i_0_28,i_0_31,i_0_29,i_0_43,i_0_42,i_0_44,i_0_45,i_0_27]) ).
cnf(i_0_162,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_163,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_164,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_165,plain,
sum(additive_inverse(additive_inverse(additive_identity)),additive_identity,additive_identity),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_163,i_0_59,i_0_102,i_0_76,i_0_62,i_0_154,i_0_158,i_0_125,i_0_100,i_0_49,i_0_143,i_0_148,i_0_37,i_0_147,i_0_32,i_0_41,i_0_28,i_0_31,i_0_29,i_0_43,i_0_42,i_0_44,i_0_45,i_0_27,i_0_26]) ).
cnf(i_0_166,plain,
sum(add(X1,additive_inverse(X1)),additive_identity,additive_identity),
inference(rename_variables,[],[i_0_100]) ).
cnf(i_0_167,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_168,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_169,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_170,plain,
~ product(a,additive_identity,additive_inverse(multiply(additive_identity,additive_identity))),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_163,i_0_168,i_0_59,i_0_102,i_0_76,i_0_62,i_0_154,i_0_158,i_0_125,i_0_100,i_0_49,i_0_143,i_0_148,i_0_37,i_0_147,i_0_39,i_0_33,i_0_32,i_0_41,i_0_28,i_0_31,i_0_29,i_0_43,i_0_42,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21]) ).
cnf(i_0_171,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_172,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_173,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_174,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_21]) ).
cnf(i_0_175,plain,
( ~ product(a,additive_inverse(X1),additive_inverse(X1))
| ~ product(a,X1,X1) ),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_163,i_0_168,i_0_172,i_0_59,i_0_102,i_0_76,i_0_62,i_0_154,i_0_158,i_0_125,i_0_100,i_0_49,i_0_143,i_0_148,i_0_37,i_0_147,i_0_39,i_0_33,i_0_32,i_0_41,i_0_28,i_0_31,i_0_29,i_0_43,i_0_42,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21,i_0_20]) ).
cnf(i_0_176,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_20]) ).
cnf(i_0_177,plain,
( ~ product(a,additive_inverse(multiply(X1,X2)),additive_inverse(multiply(X1,X2)))
| ~ product(X1,X3,a)
| ~ product(X3,multiply(X1,X2),X2) ),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_163,i_0_168,i_0_172,i_0_59,i_0_102,i_0_76,i_0_62,i_0_154,i_0_158,i_0_125,i_0_100,i_0_49,i_0_143,i_0_148,i_0_37,i_0_147,i_0_39,i_0_33,i_0_173,i_0_32,i_0_41,i_0_28,i_0_31,i_0_29,i_0_43,i_0_42,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21,i_0_20,i_0_25]) ).
cnf(i_0_178,plain,
sum(multiply(additive_identity,X1),additive_identity,additive_identity),
inference(scs_inference,[],[i_0_121,i_0_32]) ).
cnf(i_0_179,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_180,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(scs_inference,[],[i_0_150,i_0_121,i_0_32,i_0_41]) ).
cnf(i_0_181,plain,
additive_inverse(additive_inverse(X1)) = add(X1,additive_identity),
inference(scs_inference,[],[i_0_150,i_0_139,i_0_121,i_0_38,i_0_32,i_0_41,i_0_29]) ).
cnf(i_0_182,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_183,plain,
( ~ sum(X1,X2,X3)
| X4 = X2
| ~ sum(X1,X4,X3) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_184,plain,
additive_identity = add(additive_inverse(X1),X1),
inference(scs_inference,[],[i_0_36,i_0_150,i_0_139,i_0_121,i_0_38,i_0_34,i_0_32,i_0_41,i_0_29,i_0_31]) ).
cnf(i_0_185,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_186,plain,
( ~ sum(X1,X2,X3)
| X4 = X3
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_187,plain,
~ product(add(add(additive_identity,a),additive_identity),additive_identity,additive_identity),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_150,i_0_115,i_0_139,i_0_121,i_0_38,i_0_34,i_0_32,i_0_41,i_0_29,i_0_31,i_0_43]) ).
cnf(i_0_188,plain,
add(add(additive_identity,X1),additive_identity) = X1,
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_189,plain,
~ product(a,add(add(additive_identity,additive_identity),additive_identity),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_150,i_0_115,i_0_188,i_0_139,i_0_121,i_0_38,i_0_34,i_0_32,i_0_41,i_0_29,i_0_31,i_0_43,i_0_44]) ).
cnf(i_0_190,plain,
add(add(additive_identity,X1),additive_identity) = X1,
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_191,plain,
~ product(add(a,additive_identity),additive_identity,add(add(additive_identity,additive_identity),additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_113,i_0_36,i_0_150,i_0_115,i_0_188,i_0_190,i_0_139,i_0_121,i_0_38,i_0_34,i_0_32,i_0_41,i_0_29,i_0_31,i_0_43,i_0_44,i_0_45]) ).
cnf(i_0_192,plain,
add(add(additive_identity,X1),additive_identity) = X1,
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_193,plain,
sum(add(X1,additive_identity),additive_inverse(X1),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_113,i_0_36,i_0_150,i_0_115,i_0_188,i_0_190,i_0_139,i_0_121,i_0_38,i_0_182,i_0_34,i_0_32,i_0_41,i_0_29,i_0_31,i_0_43,i_0_44,i_0_45,i_0_27]) ).
cnf(i_0_194,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_195,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_196,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_197,plain,
sum(additive_inverse(additive_identity),add(X1,additive_identity),add(X1,additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_113,i_0_36,i_0_195,i_0_150,i_0_115,i_0_188,i_0_190,i_0_139,i_0_121,i_0_38,i_0_182,i_0_34,i_0_32,i_0_41,i_0_29,i_0_31,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26]) ).
cnf(i_0_198,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_199,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_200,plain,
~ product(add(a,additive_identity),additive_identity,additive_inverse(multiply(additive_identity,additive_identity))),
inference(scs_inference,[],[i_0_35,i_0_153,i_0_113,i_0_36,i_0_195,i_0_198,i_0_150,i_0_115,i_0_188,i_0_190,i_0_139,i_0_121,i_0_49,i_0_38,i_0_182,i_0_34,i_0_33,i_0_32,i_0_41,i_0_29,i_0_31,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21]) ).
cnf(i_0_201,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_202,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_203,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_204,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_21]) ).
cnf(i_0_205,plain,
~ product(a,add(additive_identity,additive_identity),additive_inverse(multiply(a,additive_identity))),
inference(scs_inference,[],[i_0_35,i_0_153,i_0_113,i_0_36,i_0_195,i_0_198,i_0_202,i_0_150,i_0_115,i_0_188,i_0_190,i_0_139,i_0_157,i_0_121,i_0_49,i_0_201,i_0_38,i_0_182,i_0_34,i_0_33,i_0_203,i_0_32,i_0_41,i_0_29,i_0_31,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21,i_0_20]) ).
cnf(i_0_206,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_207,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_208,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_209,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_20]) ).
cnf(i_0_210,plain,
sum(add(X1,additive_identity),additive_inverse(additive_identity),add(X1,additive_identity)),
inference(scs_inference,[],[i_0_197,i_0_32]) ).
cnf(i_0_211,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_212,plain,
additive_identity = additive_inverse(additive_identity),
inference(scs_inference,[],[i_0_103,i_0_197,i_0_32,i_0_41]) ).
cnf(i_0_213,plain,
multiply(X1,additive_identity) = additive_identity,
inference(scs_inference,[],[i_0_103,i_0_197,i_0_161,i_0_38,i_0_32,i_0_41,i_0_29]) ).
cnf(i_0_214,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_215,plain,
( ~ sum(X1,X2,X3)
| X4 = X2
| ~ sum(X1,X4,X3) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_216,plain,
additive_identity = multiply(X1,additive_identity),
inference(scs_inference,[],[i_0_103,i_0_197,i_0_161,i_0_38,i_0_214,i_0_32,i_0_41,i_0_29,i_0_31]) ).
cnf(i_0_217,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_218,plain,
( ~ sum(X1,X2,X3)
| X4 = X3
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_219,plain,
additive_inverse(additive_inverse(X1)) = add(additive_identity,X1),
inference(scs_inference,[],[i_0_180,i_0_103,i_0_197,i_0_161,i_0_59,i_0_38,i_0_214,i_0_32,i_0_41,i_0_29,i_0_31,i_0_42]) ).
cnf(i_0_220,plain,
X1 = add(additive_identity,X1),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_221,plain,
~ product(additive_inverse(additive_inverse(a)),additive_identity,additive_identity),
inference(scs_inference,[],[i_0_35,i_0_180,i_0_103,i_0_197,i_0_161,i_0_59,i_0_38,i_0_214,i_0_32,i_0_41,i_0_29,i_0_31,i_0_42,i_0_43]) ).
cnf(i_0_222,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rename_variables,[],[i_0_180]) ).
cnf(i_0_223,plain,
~ product(a,additive_inverse(additive_inverse(additive_identity)),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_180,i_0_222,i_0_103,i_0_197,i_0_161,i_0_59,i_0_38,i_0_214,i_0_32,i_0_41,i_0_29,i_0_31,i_0_42,i_0_43,i_0_44]) ).
cnf(i_0_224,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rename_variables,[],[i_0_180]) ).
cnf(i_0_225,plain,
~ product(a,additive_identity,additive_inverse(additive_inverse(additive_identity))),
inference(scs_inference,[],[i_0_35,i_0_180,i_0_222,i_0_224,i_0_103,i_0_197,i_0_161,i_0_59,i_0_38,i_0_214,i_0_32,i_0_41,i_0_29,i_0_31,i_0_42,i_0_43,i_0_44,i_0_45]) ).
cnf(i_0_226,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rename_variables,[],[i_0_180]) ).
cnf(i_0_227,plain,
sum(add(X1,additive_identity),multiply(X2,additive_identity),add(X1,additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_180,i_0_222,i_0_224,i_0_103,i_0_197,i_0_161,i_0_59,i_0_125,i_0_38,i_0_214,i_0_32,i_0_41,i_0_29,i_0_31,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27]) ).
cnf(i_0_228,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_229,plain,
sum(additive_inverse(additive_inverse(additive_identity)),add(X1,additive_identity),add(X1,additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_180,i_0_222,i_0_224,i_0_103,i_0_197,i_0_161,i_0_59,i_0_125,i_0_38,i_0_214,i_0_217,i_0_32,i_0_41,i_0_29,i_0_31,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26]) ).
cnf(i_0_230,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_231,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_232,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_233,plain,
~ product(add(additive_identity,a),additive_identity,additive_inverse(multiply(additive_identity,additive_identity))),
inference(scs_inference,[],[i_0_35,i_0_187,i_0_36,i_0_231,i_0_180,i_0_222,i_0_224,i_0_103,i_0_197,i_0_161,i_0_59,i_0_125,i_0_38,i_0_214,i_0_217,i_0_34,i_0_33,i_0_32,i_0_41,i_0_29,i_0_31,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21]) ).
cnf(i_0_234,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_235,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_236,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_237,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_21]) ).
cnf(i_0_238,plain,
( ~ product(a,add(X1,additive_identity),add(X1,additive_identity))
| ~ product(a,additive_inverse(X1),additive_inverse(X1)) ),
inference(scs_inference,[],[i_0_35,i_0_187,i_0_36,i_0_231,i_0_180,i_0_222,i_0_224,i_0_103,i_0_197,i_0_193,i_0_161,i_0_59,i_0_125,i_0_38,i_0_214,i_0_217,i_0_34,i_0_33,i_0_32,i_0_41,i_0_29,i_0_31,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21,i_0_20]) ).
cnf(i_0_239,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_20]) ).
cnf(i_0_240,plain,
sum(add(X1,additive_identity),additive_inverse(additive_inverse(additive_identity)),add(X1,additive_identity)),
inference(scs_inference,[],[i_0_229,i_0_32]) ).
cnf(i_0_241,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_242,plain,
add(X1,additive_identity) = additive_inverse(additive_inverse(X1)),
inference(scs_inference,[],[i_0_181,i_0_229,i_0_32,i_0_41]) ).
cnf(i_0_243,plain,
add(additive_inverse(X1),X1) = multiply(X2,additive_identity),
inference(scs_inference,[],[i_0_181,i_0_229,i_0_146,i_0_216,i_0_32,i_0_41,i_0_42]) ).
cnf(i_0_244,plain,
~ product(add(additive_identity,a),additive_identity,additive_identity),
inference(scs_inference,[],[i_0_35,i_0_181,i_0_229,i_0_146,i_0_216,i_0_55,i_0_32,i_0_41,i_0_42,i_0_43]) ).
cnf(i_0_245,plain,
add(additive_identity,X1) = X1,
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_246,plain,
~ product(a,add(additive_inverse(X1),X1),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_181,i_0_229,i_0_146,i_0_216,i_0_55,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44]) ).
cnf(i_0_247,plain,
~ product(a,additive_identity,add(additive_inverse(X1),X1)),
inference(scs_inference,[],[i_0_35,i_0_181,i_0_229,i_0_146,i_0_216,i_0_55,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44,i_0_45]) ).
cnf(i_0_248,plain,
sum(additive_identity,additive_inverse(additive_inverse(additive_identity)),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_37,i_0_181,i_0_229,i_0_146,i_0_216,i_0_55,i_0_38,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27]) ).
cnf(i_0_249,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_250,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_251,plain,
sum(additive_identity,X1,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_252,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_253,plain,
sum(additive_inverse(additive_identity),add(add(X1,additive_identity),additive_identity),add(X1,additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_197,i_0_37,i_0_49,i_0_39,i_0_181,i_0_229,i_0_146,i_0_216,i_0_55,i_0_38,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26]) ).
cnf(i_0_254,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_255,plain,
sum(X1,X2,add(X2,X1)),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_256,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_257,plain,
( product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity))
| ~ product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity)) ),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_197,i_0_37,i_0_49,i_0_39,i_0_181,i_0_229,i_0_146,i_0_216,i_0_55,i_0_76,i_0_38,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21]) ).
cnf(i_0_258,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_21]) ).
cnf(i_0_259,plain,
( multiply(additive_identity,multiply(additive_identity,additive_identity)) = multiply(additive_identity,additive_identity)
| ~ product(multiply(additive_identity,additive_identity),additive_identity,multiply(additive_identity,additive_identity)) ),
inference(scs_inference,[],[i_0_35,i_0_89,i_0_36,i_0_197,i_0_37,i_0_49,i_0_39,i_0_181,i_0_229,i_0_146,i_0_216,i_0_55,i_0_76,i_0_38,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21,i_0_30]) ).
cnf(i_0_260,plain,
product(multiply(X1,X1),X1,multiply(X1,multiply(X1,X1))),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_261,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_262,plain,
( product(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))
| ~ product(multiply(additive_identity,additive_identity),additive_identity,multiply(additive_identity,additive_identity)) ),
inference(scs_inference,[],[i_0_35,i_0_89,i_0_36,i_0_197,i_0_37,i_0_49,i_0_39,i_0_181,i_0_229,i_0_146,i_0_216,i_0_55,i_0_76,i_0_38,i_0_33,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_21,i_0_30,i_0_24]) ).
cnf(i_0_263,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_264,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_266,plain,
sum(multiply(X1,additive_identity),add(X2,additive_identity),add(X2,additive_identity)),
inference(scs_inference,[],[i_0_227,i_0_32]) ).
cnf(i_0_267,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_268,plain,
add(additive_identity,X1) = additive_inverse(additive_inverse(X1)),
inference(scs_inference,[],[i_0_219,i_0_227,i_0_32,i_0_41]) ).
cnf(i_0_269,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(scs_inference,[],[i_0_34,i_0_37,i_0_219,i_0_227,i_0_32,i_0_41,i_0_31]) ).
cnf(i_0_270,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_271,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_272,plain,
( ~ sum(X1,X2,X3)
| X4 = X3
| ~ sum(X1,X2,X4) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_273,plain,
multiply(additive_identity,X1) = additive_inverse(additive_identity),
inference(scs_inference,[],[i_0_34,i_0_37,i_0_212,i_0_219,i_0_227,i_0_107,i_0_32,i_0_41,i_0_31,i_0_42]) ).
cnf(i_0_274,plain,
~ product(multiply(additive_identity,X1),additive_identity,additive_inverse(multiply(a,additive_identity))),
inference(scs_inference,[],[i_0_129,i_0_34,i_0_37,i_0_212,i_0_219,i_0_227,i_0_107,i_0_32,i_0_41,i_0_31,i_0_42,i_0_43]) ).
cnf(i_0_275,plain,
~ product(a,multiply(additive_identity,X1),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_129,i_0_34,i_0_37,i_0_212,i_0_219,i_0_227,i_0_107,i_0_32,i_0_41,i_0_31,i_0_42,i_0_43,i_0_44]) ).
cnf(i_0_276,plain,
~ product(a,additive_identity,multiply(additive_identity,X1)),
inference(scs_inference,[],[i_0_35,i_0_129,i_0_34,i_0_37,i_0_212,i_0_219,i_0_227,i_0_107,i_0_32,i_0_41,i_0_31,i_0_42,i_0_43,i_0_44,i_0_45]) ).
cnf(i_0_277,plain,
sum(add(additive_inverse(additive_identity),additive_inverse(additive_identity)),additive_identity,additive_identity),
inference(scs_inference,[],[i_0_35,i_0_129,i_0_34,i_0_271,i_0_36,i_0_37,i_0_212,i_0_219,i_0_227,i_0_107,i_0_32,i_0_41,i_0_31,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27]) ).
cnf(i_0_278,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_279,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_280,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_281,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_282,plain,
sum(additive_inverse(additive_identity),add(additive_identity,X1),add(additive_identity,X1)),
inference(scs_inference,[],[i_0_35,i_0_129,i_0_34,i_0_271,i_0_279,i_0_36,i_0_280,i_0_37,i_0_212,i_0_219,i_0_227,i_0_107,i_0_32,i_0_41,i_0_31,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26]) ).
cnf(i_0_283,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_284,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_285,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_286,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_287,plain,
( ~ product(a,X1,multiply(additive_identity,additive_identity))
| ~ product(X1,additive_identity,additive_identity) ),
inference(scs_inference,[],[i_0_35,i_0_89,i_0_129,i_0_34,i_0_271,i_0_279,i_0_36,i_0_280,i_0_37,i_0_212,i_0_219,i_0_227,i_0_107,i_0_32,i_0_41,i_0_31,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_24]) ).
cnf(i_0_288,plain,
product(multiply(X1,X1),X1,multiply(X1,multiply(X1,X1))),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_289,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_290,plain,
( ~ product(multiply(additive_identity,additive_identity),X1,a)
| ~ product(X1,additive_identity,additive_identity) ),
inference(scs_inference,[],[i_0_35,i_0_89,i_0_288,i_0_129,i_0_34,i_0_271,i_0_279,i_0_36,i_0_280,i_0_37,i_0_212,i_0_219,i_0_227,i_0_107,i_0_32,i_0_41,i_0_31,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_24,i_0_25]) ).
cnf(i_0_291,plain,
product(multiply(X1,X1),X1,multiply(X1,multiply(X1,X1))),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_292,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_293,plain,
( ~ product(a,additive_inverse(X1),add(additive_identity,additive_identity))
| ~ product(a,X1,additive_identity) ),
inference(scs_inference,[],[i_0_35,i_0_89,i_0_288,i_0_129,i_0_34,i_0_271,i_0_279,i_0_285,i_0_36,i_0_280,i_0_284,i_0_37,i_0_212,i_0_219,i_0_227,i_0_119,i_0_107,i_0_32,i_0_41,i_0_31,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_24,i_0_25,i_0_21,i_0_20]) ).
cnf(i_0_294,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_295,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_20]) ).
cnf(i_0_296,plain,
sum(add(additive_identity,X1),additive_inverse(additive_identity),add(additive_identity,X1)),
inference(scs_inference,[],[i_0_282,i_0_32]) ).
cnf(i_0_297,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_298,plain,
multiply(X1,additive_identity) = add(additive_inverse(X2),X2),
inference(scs_inference,[],[i_0_243,i_0_282,i_0_32,i_0_41]) ).
cnf(i_0_299,plain,
add(additive_inverse(X1),X1) = additive_inverse(additive_identity),
inference(scs_inference,[],[i_0_243,i_0_282,i_0_273,i_0_32,i_0_41,i_0_42]) ).
cnf(i_0_300,plain,
multiply(additive_identity,X1) = additive_inverse(additive_identity),
inference(rename_variables,[],[i_0_273]) ).
cnf(i_0_301,plain,
add(additive_inverse(X1),X1) = multiply(X2,additive_identity),
inference(rename_variables,[],[i_0_243]) ).
cnf(i_0_302,plain,
~ product(add(add(additive_identity,a),additive_identity),add(additive_identity,additive_identity),add(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_117,i_0_243,i_0_282,i_0_273,i_0_115,i_0_32,i_0_41,i_0_42,i_0_43]) ).
cnf(i_0_303,plain,
add(add(additive_identity,X1),additive_identity) = X1,
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_304,plain,
~ product(a,add(X1,additive_inverse(X1)),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_117,i_0_243,i_0_282,i_0_273,i_0_269,i_0_115,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44]) ).
cnf(i_0_305,plain,
~ product(a,additive_identity,add(X1,additive_inverse(X1))),
inference(scs_inference,[],[i_0_35,i_0_117,i_0_243,i_0_282,i_0_273,i_0_269,i_0_115,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44,i_0_45]) ).
cnf(i_0_306,plain,
sum(additive_inverse(add(additive_identity,X1)),X1,additive_identity),
inference(scs_inference,[],[i_0_35,i_0_39,i_0_34,i_0_36,i_0_117,i_0_243,i_0_282,i_0_273,i_0_269,i_0_115,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27]) ).
cnf(i_0_307,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_308,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_309,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_310,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X1,X6,X4)
| ~ sum(X6,X5,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_311,plain,
sum(additive_inverse(X1),add(additive_identity,X1),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_39,i_0_308,i_0_34,i_0_309,i_0_36,i_0_307,i_0_117,i_0_243,i_0_282,i_0_273,i_0_269,i_0_115,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26]) ).
cnf(i_0_312,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_313,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_314,plain,
sum(X1,X2,add(X1,X2)),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_315,plain,
( ~ sum(X1,X2,X3)
| sum(X4,X5,X3)
| ~ sum(X4,X6,X1)
| ~ sum(X6,X2,X5) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_316,plain,
additive_identity = additive_inverse(add(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_35,i_0_39,i_0_308,i_0_313,i_0_34,i_0_309,i_0_36,i_0_307,i_0_117,i_0_243,i_0_282,i_0_273,i_0_269,i_0_115,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_28]) ).
cnf(i_0_317,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_318,plain,
( ~ sum(X1,X2,X3)
| X4 = X1
| ~ sum(X4,X2,X3) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_319,plain,
( ~ product(a,X1,additive_identity)
| ~ product(X1,X2,additive_identity) ),
inference(scs_inference,[],[i_0_35,i_0_39,i_0_308,i_0_313,i_0_34,i_0_309,i_0_36,i_0_307,i_0_117,i_0_243,i_0_282,i_0_273,i_0_269,i_0_276,i_0_115,i_0_33,i_0_32,i_0_41,i_0_42,i_0_43,i_0_44,i_0_45,i_0_27,i_0_26,i_0_28,i_0_24]) ).
cnf(i_0_320,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_321,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_322,plain,
sum(X1,additive_identity,X1),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_324,plain,
sum(add(add(X1,additive_identity),additive_identity),additive_inverse(additive_identity),add(X1,additive_identity)),
inference(scs_inference,[],[i_0_253,i_0_32]) ).
cnf(i_0_325,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_326,plain,
additive_inverse(additive_identity) = add(additive_inverse(X1),X1),
inference(scs_inference,[],[i_0_299,i_0_253,i_0_32,i_0_41]) ).
cnf(i_0_327,plain,
multiply(X1,additive_identity) = additive_inverse(additive_identity),
inference(scs_inference,[],[i_0_298,i_0_299,i_0_253,i_0_32,i_0_41,i_0_42]) ).
cnf(i_0_328,plain,
add(additive_inverse(X1),X1) = additive_inverse(additive_identity),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_329,plain,
~ product(a,multiply(X1,additive_identity),additive_identity),
inference(scs_inference,[],[i_0_35,i_0_298,i_0_299,i_0_253,i_0_213,i_0_32,i_0_41,i_0_42,i_0_44]) ).
cnf(i_0_330,plain,
$false,
inference(scs_inference,[],[i_0_35,i_0_298,i_0_299,i_0_253,i_0_213,i_0_33,i_0_32,i_0_41,i_0_42,i_0_44,i_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG001-4 : 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
% 0.12/0.32 % Computer : n019.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue May 5 01:44:59 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.34 % start to proof: theBenchmark
% 1.27/2.60 % Version : CSE_E---1.7
% 1.27/2.60 % Problem : theBenchmark.p
% 1.27/2.60 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/2.60 % SZS output start CNFRefutation
% See solution above
% 1.56/3.00 % Total time : 2.269s
%------------------------------------------------------------------------------