TSTP Solution File: KLE147-10 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE147-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n026.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 : Thu Aug 31 05:26:36 EDT 2023

% Result   : Unsatisfiable 10.00s 10.09s
% Output   : CNFRefutation 10.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   39
% Syntax   : Number of formulae    :  151 ( 135 unt;  16 typ;   0 def)
%            Number of atoms       :  135 ( 134 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   22 (   9   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   7 con; 0-4 aty)
%            Number of variables   :  241 (  36 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    ifeq3: ( $i * $i * $i * $i ) > $i ).

tff(decl_23,type,
    ifeq2: ( $i * $i * $i * $i ) > $i ).

tff(decl_24,type,
    ifeq: ( $i * $i * $i * $i ) > $i ).

tff(decl_25,type,
    addition: ( $i * $i ) > $i ).

tff(decl_26,type,
    zero: $i ).

tff(decl_27,type,
    multiplication: ( $i * $i ) > $i ).

tff(decl_28,type,
    one: $i ).

tff(decl_29,type,
    star: $i > $i ).

tff(decl_30,type,
    leq: ( $i * $i ) > $i ).

tff(decl_31,type,
    true: $i ).

tff(decl_32,type,
    strong_iteration: $i > $i ).

tff(decl_33,type,
    sK1_goals_X1: $i ).

tff(decl_34,type,
    sK2_goals_X0: $i ).

tff(decl_35,type,
    sK4_goals_X0: $i ).

tff(decl_36,type,
    sK3_goals_X1: $i ).

tff(decl_37,type,
    tuple: ( $i * $i ) > $i ).

cnf(additive_associativity,axiom,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).

cnf(idempotence,axiom,
    addition(X1,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).

cnf(order,axiom,
    ifeq3(addition(X1,X2),X2,leq(X1,X2),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).

cnf(ifeq_axiom,axiom,
    ifeq3(X1,X1,X2,X3) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).

cnf(distributivity1,axiom,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).

cnf(multiplicative_right_identity,axiom,
    multiplication(X1,one) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).

cnf(additive_commutativity,axiom,
    addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).

cnf(star_unfold1,axiom,
    addition(one,multiplication(X1,star(X1))) = star(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold1) ).

cnf(star_unfold2,axiom,
    addition(one,multiplication(star(X1),X1)) = star(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold2) ).

cnf(order_1,axiom,
    ifeq2(leq(X1,X2),true,addition(X1,X2),X2) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order_1) ).

cnf(ifeq_axiom_001,axiom,
    ifeq2(X1,X1,X2,X3) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).

cnf(distributivity2,axiom,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).

cnf(multiplicative_left_identity,axiom,
    multiplication(one,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).

cnf(star_induction2,axiom,
    ifeq(leq(addition(multiplication(X1,X2),X3),X1),true,leq(multiplication(X3,star(X2)),X1),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction2) ).

cnf(additive_identity,axiom,
    addition(X1,zero) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).

cnf(ifeq_axiom_002,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).

cnf(left_annihilation,axiom,
    multiplication(zero,X1) = zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).

cnf(multiplicative_associativity,axiom,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).

cnf(infty_unfold1,axiom,
    strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).

cnf(star_induction1,axiom,
    ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction1) ).

cnf(isolation,axiom,
    strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isolation) ).

cnf(infty_coinduction,axiom,
    ifeq(leq(X1,addition(multiplication(X2,X1),X3)),true,leq(X1,multiplication(strong_iteration(X2),X3)),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_coinduction) ).

cnf(goals,negated_conjecture,
    tuple(leq(multiplication(star(sK1_goals_X1),strong_iteration(multiplication(star(sK2_goals_X0),sK1_goals_X1))),strong_iteration(multiplication(star(sK2_goals_X0),sK1_goals_X1))),leq(strong_iteration(multiplication(star(sK4_goals_X0),sK3_goals_X1)),multiplication(star(sK3_goals_X1),strong_iteration(multiplication(star(sK4_goals_X0),sK3_goals_X1))))) != tuple(true,true),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

cnf(c_0_23,axiom,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    additive_associativity ).

cnf(c_0_24,axiom,
    addition(X1,X1) = X1,
    idempotence ).

cnf(c_0_25,axiom,
    ifeq3(addition(X1,X2),X2,leq(X1,X2),true) = true,
    order ).

cnf(c_0_26,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_27,axiom,
    ifeq3(X1,X1,X2,X3) = X2,
    ifeq_axiom ).

cnf(c_0_28,axiom,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    distributivity1 ).

cnf(c_0_29,axiom,
    multiplication(X1,one) = X1,
    multiplicative_right_identity ).

cnf(c_0_30,axiom,
    addition(X1,X2) = addition(X2,X1),
    additive_commutativity ).

cnf(c_0_31,plain,
    leq(X1,addition(X1,X2)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

cnf(c_0_32,plain,
    addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

cnf(c_0_33,plain,
    leq(X1,addition(X2,X1)) = true,
    inference(spm,[status(thm)],[c_0_31,c_0_30]) ).

cnf(c_0_34,axiom,
    addition(one,multiplication(X1,star(X1))) = star(X1),
    star_unfold1 ).

cnf(c_0_35,plain,
    leq(X1,multiplication(X1,addition(X2,one))) = true,
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_36,axiom,
    addition(one,multiplication(star(X1),X1)) = star(X1),
    star_unfold2 ).

cnf(c_0_37,axiom,
    ifeq2(leq(X1,X2),true,addition(X1,X2),X2) = X2,
    order_1 ).

cnf(c_0_38,plain,
    leq(multiplication(X1,star(X1)),star(X1)) = true,
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_39,axiom,
    ifeq2(X1,X1,X2,X3) = X2,
    ifeq_axiom_001 ).

cnf(c_0_40,axiom,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    distributivity2 ).

cnf(c_0_41,axiom,
    multiplication(one,X1) = X1,
    multiplicative_left_identity ).

cnf(c_0_42,plain,
    leq(X1,multiplication(X1,addition(one,X2))) = true,
    inference(spm,[status(thm)],[c_0_35,c_0_30]) ).

cnf(c_0_43,plain,
    addition(one,star(X1)) = star(X1),
    inference(spm,[status(thm)],[c_0_26,c_0_36]) ).

cnf(c_0_44,plain,
    addition(star(X1),multiplication(X1,star(X1))) = star(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_30]) ).

cnf(c_0_45,plain,
    addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_30]) ).

cnf(c_0_46,plain,
    leq(X1,multiplication(X1,star(X2))) = true,
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_47,plain,
    multiplication(addition(X1,one),star(X1)) = star(X1),
    inference(rw,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_48,plain,
    addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
    inference(spm,[status(thm)],[c_0_30,c_0_23]) ).

cnf(c_0_49,plain,
    leq(addition(X1,one),star(X1)) = true,
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_50,plain,
    leq(X1,addition(X2,addition(X1,X3))) = true,
    inference(spm,[status(thm)],[c_0_31,c_0_48]) ).

cnf(c_0_51,plain,
    addition(X1,star(X1)) = star(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_49]),c_0_23]),c_0_43]),c_0_39]) ).

cnf(c_0_52,plain,
    leq(multiplication(star(X1),X1),star(X1)) = true,
    inference(spm,[status(thm)],[c_0_33,c_0_36]) ).

cnf(c_0_53,plain,
    leq(X1,addition(X2,star(X1))) = true,
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_54,plain,
    addition(star(X1),multiplication(star(X1),X1)) = star(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_52]),c_0_39]),c_0_30]) ).

cnf(c_0_55,plain,
    leq(X1,addition(star(X1),X2)) = true,
    inference(spm,[status(thm)],[c_0_53,c_0_30]) ).

cnf(c_0_56,axiom,
    ifeq(leq(addition(multiplication(X1,X2),X3),X1),true,leq(multiplication(X3,star(X2)),X1),true) = true,
    star_induction2 ).

cnf(c_0_57,plain,
    multiplication(star(X1),addition(X1,one)) = star(X1),
    inference(rw,[status(thm)],[c_0_54,c_0_32]) ).

cnf(c_0_58,axiom,
    addition(X1,zero) = X1,
    additive_identity ).

cnf(c_0_59,plain,
    addition(multiplication(X1,addition(X2,one)),X3) = addition(X1,addition(multiplication(X1,X2),X3)),
    inference(spm,[status(thm)],[c_0_23,c_0_32]) ).

cnf(c_0_60,plain,
    leq(X1,multiplication(star(X1),addition(X2,one))) = true,
    inference(spm,[status(thm)],[c_0_55,c_0_32]) ).

cnf(c_0_61,plain,
    ifeq(leq(addition(one,multiplication(X1,X2)),X1),true,leq(star(X2),X1),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_41]),c_0_30]) ).

cnf(c_0_62,plain,
    multiplication(star(X1),addition(one,X1)) = star(X1),
    inference(spm,[status(thm)],[c_0_57,c_0_30]) ).

cnf(c_0_63,plain,
    leq(X1,X1) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_27]) ).

cnf(c_0_64,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    ifeq_axiom_002 ).

cnf(c_0_65,axiom,
    multiplication(zero,X1) = zero,
    left_annihilation ).

cnf(c_0_66,plain,
    addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_30]),c_0_23]) ).

cnf(c_0_67,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_58,c_0_30]) ).

cnf(c_0_68,plain,
    leq(X1,addition(multiplication(X1,addition(X2,one)),X3)) = true,
    inference(spm,[status(thm)],[c_0_31,c_0_59]) ).

cnf(c_0_69,plain,
    leq(X1,multiplication(star(X1),addition(one,X2))) = true,
    inference(spm,[status(thm)],[c_0_60,c_0_30]) ).

cnf(c_0_70,plain,
    leq(star(addition(one,X1)),star(X1)) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_43]),c_0_63]),c_0_64]) ).

cnf(c_0_71,plain,
    star(zero) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_65]),c_0_58]) ).

cnf(c_0_72,axiom,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    multiplicative_associativity ).

cnf(c_0_73,plain,
    ifeq3(addition(X1,addition(X2,X3)),addition(X1,X3),leq(X2,addition(X1,X3)),true) = true,
    inference(spm,[status(thm)],[c_0_25,c_0_66]) ).

cnf(c_0_74,plain,
    addition(X1,addition(multiplication(X1,zero),X2)) = addition(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_67]),c_0_29]) ).

cnf(c_0_75,plain,
    leq(X1,star(multiplication(X1,addition(X2,one)))) = true,
    inference(spm,[status(thm)],[c_0_68,c_0_51]) ).

cnf(c_0_76,plain,
    leq(X1,multiplication(star(X1),star(X2))) = true,
    inference(spm,[status(thm)],[c_0_69,c_0_43]) ).

cnf(c_0_77,plain,
    leq(star(one),one) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_58]) ).

cnf(c_0_78,plain,
    ifeq(leq(multiplication(X1,addition(X2,X3)),X1),true,leq(multiplication(X1,multiplication(X3,star(X2))),X1),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_28]),c_0_72]) ).

cnf(c_0_79,plain,
    multiplication(addition(one,X1),star(X1)) = star(X1),
    inference(spm,[status(thm)],[c_0_47,c_0_30]) ).

cnf(c_0_80,plain,
    leq(multiplication(X1,zero),addition(X1,X2)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_27]) ).

cnf(c_0_81,plain,
    leq(X1,star(multiplication(X1,addition(one,X2)))) = true,
    inference(spm,[status(thm)],[c_0_75,c_0_30]) ).

cnf(c_0_82,plain,
    addition(X1,multiplication(star(X1),star(X2))) = multiplication(star(X1),star(X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_76]),c_0_39]) ).

cnf(c_0_83,plain,
    star(one) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_77]),c_0_30]),c_0_43]),c_0_39]) ).

cnf(c_0_84,plain,
    ifeq(leq(multiplication(X1,X2),X1),true,leq(multiplication(X1,multiplication(X2,star(X2))),X1),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_24]),c_0_72]) ).

cnf(c_0_85,plain,
    leq(multiplication(star(X1),star(X1)),star(X1)) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_57]),c_0_63]),c_0_41]),c_0_64]) ).

cnf(c_0_86,plain,
    multiplication(star(X1),star(star(X1))) = star(star(X1)),
    inference(spm,[status(thm)],[c_0_79,c_0_43]) ).

cnf(c_0_87,axiom,
    strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    infty_unfold1 ).

cnf(c_0_88,plain,
    leq(multiplication(X1,zero),multiplication(addition(X2,one),X1)) = true,
    inference(spm,[status(thm)],[c_0_80,c_0_45]) ).

cnf(c_0_89,plain,
    leq(X1,star(multiplication(X1,star(X2)))) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_41]) ).

cnf(c_0_90,plain,
    ifeq2(leq(X1,X2),true,addition(X2,X1),X2) = X2,
    inference(spm,[status(thm)],[c_0_37,c_0_30]) ).

cnf(c_0_91,plain,
    leq(star(star(X1)),star(X1)) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]),c_0_86]),c_0_64]) ).

cnf(c_0_92,plain,
    addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
    inference(rw,[status(thm)],[c_0_87,c_0_30]) ).

cnf(c_0_93,plain,
    leq(multiplication(X1,zero),multiplication(addition(one,X2),X1)) = true,
    inference(spm,[status(thm)],[c_0_88,c_0_30]) ).

cnf(c_0_94,plain,
    addition(X1,star(multiplication(X1,star(X2)))) = star(multiplication(X1,star(X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_89]),c_0_39]) ).

cnf(c_0_95,plain,
    star(star(X1)) = star(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_51]),c_0_39]) ).

cnf(c_0_96,plain,
    leq(multiplication(X1,strong_iteration(X1)),strong_iteration(X1)) = true,
    inference(spm,[status(thm)],[c_0_33,c_0_92]) ).

cnf(c_0_97,plain,
    leq(multiplication(X1,zero),multiplication(star(X2),X1)) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_41]),c_0_95]) ).

cnf(c_0_98,plain,
    addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
    inference(spm,[status(thm)],[c_0_40,c_0_72]) ).

cnf(c_0_99,axiom,
    ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
    star_induction1 ).

cnf(c_0_100,plain,
    addition(strong_iteration(X1),multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_96]),c_0_39]),c_0_30]) ).

cnf(c_0_101,plain,
    addition(multiplication(X1,zero),multiplication(star(X2),X1)) = multiplication(star(X2),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_97]),c_0_39]) ).

cnf(c_0_102,plain,
    addition(multiplication(X1,zero),multiplication(X2,X3)) = multiplication(addition(multiplication(X1,zero),X2),X3),
    inference(spm,[status(thm)],[c_0_98,c_0_65]) ).

cnf(c_0_103,axiom,
    strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
    isolation ).

cnf(c_0_104,plain,
    ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true) = true,
    inference(spm,[status(thm)],[c_0_99,c_0_40]) ).

cnf(c_0_105,plain,
    multiplication(addition(X1,one),strong_iteration(X1)) = strong_iteration(X1),
    inference(rw,[status(thm)],[c_0_100,c_0_45]) ).

cnf(c_0_106,axiom,
    ifeq(leq(X1,addition(multiplication(X2,X1),X3)),true,leq(X1,multiplication(strong_iteration(X2),X3)),true) = true,
    infty_coinduction ).

cnf(c_0_107,plain,
    addition(one,addition(multiplication(X1,star(X1)),X2)) = addition(star(X1),X2),
    inference(spm,[status(thm)],[c_0_23,c_0_34]) ).

cnf(c_0_108,plain,
    multiplication(addition(multiplication(X1,zero),star(X2)),X1) = multiplication(star(X2),X1),
    inference(rw,[status(thm)],[c_0_101,c_0_102]) ).

cnf(c_0_109,plain,
    addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
    inference(spm,[status(thm)],[c_0_23,c_0_103]) ).

cnf(c_0_110,plain,
    leq(multiplication(star(X1),strong_iteration(X1)),strong_iteration(X1)) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_63]),c_0_41]),c_0_64]) ).

cnf(c_0_111,plain,
    ifeq(leq(X1,addition(X2,multiplication(X3,X1))),true,leq(X1,multiplication(strong_iteration(X3),X2)),true) = true,
    inference(spm,[status(thm)],[c_0_106,c_0_30]) ).

cnf(c_0_112,plain,
    addition(one,multiplication(addition(X1,X2),star(X1))) = multiplication(addition(X2,one),star(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_40]),c_0_45]) ).

cnf(c_0_113,plain,
    leq(X1,multiplication(addition(X2,one),X1)) = true,
    inference(spm,[status(thm)],[c_0_31,c_0_45]) ).

cnf(c_0_114,plain,
    multiplication(addition(star(X1),multiplication(X2,zero)),X2) = multiplication(star(X1),X2),
    inference(spm,[status(thm)],[c_0_108,c_0_30]) ).

cnf(c_0_115,plain,
    addition(star(X1),multiplication(strong_iteration(X1),X2)) = multiplication(strong_iteration(X1),addition(X2,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_28]),c_0_67]),c_0_32]) ).

cnf(c_0_116,plain,
    multiplication(star(X1),strong_iteration(X1)) = strong_iteration(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_110]),c_0_45]),c_0_30]),c_0_43]),c_0_39]) ).

cnf(c_0_117,plain,
    leq(star(X1),strong_iteration(addition(X1,X2))) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]),c_0_29]),c_0_64]) ).

cnf(c_0_118,plain,
    addition(one,strong_iteration(X1)) = strong_iteration(X1),
    inference(spm,[status(thm)],[c_0_26,c_0_92]) ).

cnf(c_0_119,plain,
    multiplication(strong_iteration(X1),strong_iteration(X1)) = strong_iteration(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_67]),c_0_29]),c_0_116]) ).

cnf(c_0_120,plain,
    leq(star(X1),strong_iteration(multiplication(addition(X2,one),X1))) = true,
    inference(spm,[status(thm)],[c_0_117,c_0_45]) ).

cnf(c_0_121,plain,
    multiplication(strong_iteration(X1),star(strong_iteration(X1))) = star(strong_iteration(X1)),
    inference(spm,[status(thm)],[c_0_79,c_0_118]) ).

cnf(c_0_122,plain,
    leq(star(strong_iteration(X1)),strong_iteration(X1)) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_119]),c_0_118]),c_0_63]),c_0_64]) ).

cnf(c_0_123,plain,
    leq(star(X1),strong_iteration(multiplication(addition(one,X2),X1))) = true,
    inference(spm,[status(thm)],[c_0_120,c_0_30]) ).

cnf(c_0_124,plain,
    leq(X1,multiplication(addition(one,X2),X1)) = true,
    inference(spm,[status(thm)],[c_0_113,c_0_30]) ).

cnf(c_0_125,plain,
    multiplication(addition(X1,strong_iteration(X2)),star(strong_iteration(X2))) = multiplication(addition(X1,one),star(strong_iteration(X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_121]),c_0_30]),c_0_45]) ).

cnf(c_0_126,plain,
    star(strong_iteration(X1)) = strong_iteration(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_122]),c_0_30]),c_0_51]),c_0_39]) ).

cnf(c_0_127,plain,
    leq(star(X1),strong_iteration(multiplication(star(X2),X1))) = true,
    inference(spm,[status(thm)],[c_0_123,c_0_43]) ).

cnf(c_0_128,negated_conjecture,
    tuple(leq(multiplication(star(sK1_goals_X1),strong_iteration(multiplication(star(sK2_goals_X0),sK1_goals_X1))),strong_iteration(multiplication(star(sK2_goals_X0),sK1_goals_X1))),leq(strong_iteration(multiplication(star(sK4_goals_X0),sK3_goals_X1)),multiplication(star(sK3_goals_X1),strong_iteration(multiplication(star(sK4_goals_X0),sK3_goals_X1))))) != tuple(true,true),
    goals ).

cnf(c_0_129,plain,
    leq(X1,multiplication(star(X2),X1)) = true,
    inference(spm,[status(thm)],[c_0_124,c_0_43]) ).

cnf(c_0_130,plain,
    multiplication(addition(X1,strong_iteration(X2)),strong_iteration(X2)) = multiplication(addition(X1,one),strong_iteration(X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_126]),c_0_126]) ).

cnf(c_0_131,plain,
    addition(star(X1),strong_iteration(multiplication(star(X2),X1))) = strong_iteration(multiplication(star(X2),X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_127]),c_0_39]) ).

cnf(c_0_132,negated_conjecture,
    tuple(leq(multiplication(star(sK1_goals_X1),strong_iteration(multiplication(star(sK2_goals_X0),sK1_goals_X1))),strong_iteration(multiplication(star(sK2_goals_X0),sK1_goals_X1))),true) != tuple(true,true),
    inference(rw,[status(thm)],[c_0_128,c_0_129]) ).

cnf(c_0_133,plain,
    multiplication(star(X1),strong_iteration(multiplication(star(X2),X1))) = strong_iteration(multiplication(star(X2),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_119]),c_0_30]),c_0_43]) ).

cnf(c_0_134,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_63])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : KLE147-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.18/0.34  % Computer : n026.cluster.edu
% 0.18/0.34  % Model    : x86_64 x86_64
% 0.18/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34  % Memory   : 8042.1875MB
% 0.18/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34  % CPULimit   : 300
% 0.18/0.34  % WCLimit    : 300
% 0.18/0.34  % DateTime   : Tue Aug 29 12:46:05 EDT 2023
% 0.18/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 10.00/10.09  % Version  : CSE_E---1.5
% 10.00/10.09  % Problem  : theBenchmark.p
% 10.00/10.09  % Proof found
% 10.00/10.09  % SZS status Theorem for theBenchmark.p
% 10.00/10.09  % SZS output start Proof
% See solution above
% 10.00/10.10  % Total time : 9.511000 s
% 10.00/10.10  % SZS output end Proof
% 10.00/10.10  % Total time : 9.514000 s
%------------------------------------------------------------------------------