%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE147-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:58:57 PM UTC 2026
% Result : Unsatisfiable 108.15s 16.15s
% Output : CNFRefutation 108.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 23
% Syntax : Number of clauses : 136 ( 136 unt; 0 nHn; 8 RR)
% Number of literals : 136 ( 135 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% 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)
% Comments :
%------------------------------------------------------------------------------
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,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),
inference(fof_simplification,[status(thm)],[goals]) ).
cnf(c_0_125,plain,
leq(X1,multiplication(addition(one,X2),X1)) = true,
inference(spm,[status(thm)],[c_0_113,c_0_30]) ).
cnf(c_0_126,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_127,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_128,plain,
leq(star(X1),strong_iteration(multiplication(star(X2),X1))) = true,
inference(spm,[status(thm)],[c_0_123,c_0_43]) ).
cnf(c_0_129,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),
c_0_124 ).
cnf(c_0_130,plain,
leq(X1,multiplication(star(X2),X1)) = true,
inference(spm,[status(thm)],[c_0_125,c_0_43]) ).
cnf(c_0_131,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_126,c_0_127]),c_0_127]) ).
cnf(c_0_132,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_128]),c_0_39]) ).
cnf(c_0_133,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_129,c_0_130]) ).
cnf(c_0_134,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_131,c_0_132]),c_0_119]),c_0_30]),c_0_43]) ).
cnf(c_0_135,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE147-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 22:49:02 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 108.15/16.15 % Version: 3.5.1
% 108.15/16.15 % Preprocessing class: FSMSSMSSSSSNFFN.
% 108.15/16.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 108.15/16.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 108.15/16.15 % Starting new_bool_3 with 300s (1) cores
% 108.15/16.15 % Starting new_bool_1 with 300s (1) cores
% 108.15/16.15 % Starting sh5l with 300s (1) cores
% 108.15/16.15 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1871714 completed with status 0
% 108.15/16.15 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 108.15/16.15 % Preprocessing class: FSMSSMSSSSSNFFN.
% 108.15/16.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 108.15/16.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 108.15/16.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 108.15/16.15 % No SInE strategy applied
% 108.15/16.15 % Search class: FUUPM-FFMF32-DFFFFFNN
% 108.15/16.15 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 108.15/16.15 % Starting SubtermCWHack with 136s (1) cores
% 108.15/16.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 108.15/16.15 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 226s (1) cores
% 108.15/16.15 % Starting new_bool_3 with 226s (1) cores
% 108.15/16.15 % Starting new_bool_1 with 226s (1) cores
% 108.15/16.15 % new_bool_1 with pid 1871722 completed with status 0
% 108.15/16.15 % Result found by new_bool_1
% 108.15/16.15 % Preprocessing class: FSMSSMSSSSSNFFN.
% 108.15/16.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 108.15/16.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 108.15/16.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 108.15/16.15 % No SInE strategy applied
% 108.15/16.15 % Search class: FUUPM-FFMF32-DFFFFFNN
% 108.15/16.15 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 108.15/16.15 % Starting SubtermCWHack with 136s (1) cores
% 108.15/16.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 108.15/16.15 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 226s (1) cores
% 108.15/16.15 % Starting new_bool_3 with 226s (1) cores
% 108.15/16.15 % Starting new_bool_1 with 226s (1) cores
% 108.15/16.15 % Preprocessing time : 0.001 s
% 108.15/16.15 % Presaturation interreduction done
% 108.15/16.15
% 108.15/16.15 % Proof found!
% 108.15/16.15 % SZS status Unsatisfiable
% 108.15/16.15 % SZS output start CNFRefutation
% See solution above
% 108.15/16.15 % Parsed axioms : 23
% 108.15/16.15 % Removed by relevancy pruning/SinE : 0
% 108.15/16.15 % Initial clauses : 23
% 108.15/16.15 % Removed in clause preprocessing : 0
% 108.15/16.15 % Initial clauses in saturation : 23
% 108.15/16.15 % Processed clauses : 15863
% 108.15/16.15 % ...of these trivial : 10177
% 108.15/16.15 % ...subsumed : 879
% 108.15/16.15 % ...remaining for further processing : 4807
% 108.15/16.15 % Other redundant clauses eliminated : 0
% 108.15/16.15 % Clauses deleted for lack of memory : 0
% 108.15/16.15 % Backward-subsumed : 0
% 108.15/16.15 % Backward-rewritten : 1237
% 108.15/16.15 % Generated clauses : 1474402
% 108.15/16.15 % ...of the previous two non-redundant : 630982
% 108.15/16.15 % ...aggressively subsumed : 0
% 108.15/16.15 % Contextual simplify-reflections : 0
% 108.15/16.15 % Paramodulations : 1474402
% 108.15/16.15 % Factorizations : 0
% 108.15/16.15 % NegExts : 0
% 108.15/16.15 % Equation resolutions : 0
% 108.15/16.15 % Disequality decompositions : 0
% 108.15/16.15 % Total rewrite steps : 3728927
% 108.15/16.15 % ...of those cached : 3539001
% 108.15/16.15 % Propositional unsat checks : 0
% 108.15/16.15 % Propositional check models : 0
% 108.15/16.15 % Propositional check unsatisfiable : 0
% 108.15/16.15 % Propositional clauses : 0
% 108.15/16.15 % Propositional clauses after purity: 0
% 108.15/16.15 % Propositional unsat core size : 0
% 108.15/16.15 % Propositional preprocessing time : 0.000
% 108.15/16.15 % Propositional encoding time : 0.000
% 108.15/16.15 % Propositional solver time : 0.000
% 108.15/16.15 % Success case prop preproc time : 0.000
% 108.15/16.15 % Success case prop encoding time : 0.000
% 108.15/16.15 % Success case prop solver time : 0.000
% 108.15/16.15 % Current number of processed clauses : 3547
% 108.15/16.15 % Positive orientable unit clauses : 3525
% 108.15/16.15 % Positive unorientable unit clauses: 21
% 108.15/16.15 % Negative unit clauses : 1
% 108.15/16.15 % Non-unit-clauses : 0
% 108.15/16.15 % Current number of unprocessed clauses: 613414
% 108.15/16.15 % ...number of literals in the above : 613414
% 108.15/16.15 % Current number of archived formulas : 0
% 108.15/16.15 % Current number of archived clauses : 1260
% 108.15/16.15 % Clause-clause subsumption calls (NU) : 0
% 108.15/16.15 % Rec. Clause-clause subsumption calls : 0
% 108.15/16.15 % Non-unit clause-clause subsumptions : 0
% 108.15/16.15 % Unit Clause-clause subsumption calls : 298
% 108.15/16.15 % Rewrite failures with RHS unbound : 0
% 108.15/16.15 % BW rewrite match attempts : 190337
% 108.15/16.15 % BW rewrite match successes : 850
% 108.15/16.15 % Condensation attempts : 0
% 108.15/16.15 % Condensation successes : 0
% 108.15/16.15 % Termbank termtop insertions : 23042704
% 108.15/16.15 % Search garbage collected termcells : 2
% 108.15/16.15
% 108.15/16.15 % -------------------------------------------------
% 108.15/16.15 % User time : 14.722 s
% 108.15/16.15 % System time : 0.569 s
% 108.15/16.15 % Total time : 15.291 s
% 108.15/16.15 % Maximum resident set size: 3648 pages
% 108.15/16.15
% 108.15/16.15 % -------------------------------------------------
% 108.15/16.15 % User time : 74.104 s
% 108.15/16.15 % System time : 2.711 s
% 108.15/16.15 % Total time : 76.815 s
% 108.15/16.15 % Maximum resident set size: 4864 pages
% 108.15/16.15 % E exiting
%------------------------------------------------------------------------------