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