%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE145-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 : Sun Sep 27 07:44:24 AM UTC 2026
% Result : Unsatisfiable 47.76s 7.20s
% Output : CNFRefutation 47.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 20
% Syntax : Number of formulae : 135 ( 135 unt; 0 def)
% Number of atoms : 135 ( 134 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 224 ( 7 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq3(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq3(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
fof(ifeq_axiom_001,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq2(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom_001) ).
cnf(c_2,plain,
ifeq2(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom_001]) ).
fof(ifeq_axiom_002,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom_002) ).
cnf(c_3,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom_002]) ).
fof(additive_commutativity,axiom,
! [VAR_0,VAR_1] : addition(VAR_0,VAR_1) = addition(VAR_1,VAR_0),
file('theBenchmark.p',additive_commutativity) ).
cnf(c_4,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
fof(additive_associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : addition(VAR_0,addition(VAR_1,VAR_2)) = addition(addition(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',additive_associativity) ).
cnf(c_5,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_6,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(copy,[status(thm)],[c_5]) ).
fof(additive_identity,axiom,
! [VAR_0] : addition(VAR_0,zero) = VAR_0,
file('theBenchmark.p',additive_identity) ).
cnf(c_7,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
fof(idempotence,axiom,
! [VAR_0] : addition(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence) ).
cnf(c_8,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[idempotence]) ).
fof(multiplicative_associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiplication(VAR_0,multiplication(VAR_1,VAR_2)) = multiplication(multiplication(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',multiplicative_associativity) ).
cnf(c_9,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_10,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(copy,[status(thm)],[c_9]) ).
fof(multiplicative_right_identity,axiom,
! [VAR_0] : multiplication(VAR_0,one) = VAR_0,
file('theBenchmark.p',multiplicative_right_identity) ).
cnf(c_11,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
fof(multiplicative_left_identity,axiom,
! [VAR_0] : multiplication(one,VAR_0) = VAR_0,
file('theBenchmark.p',multiplicative_left_identity) ).
cnf(c_12,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
fof(distributivity1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiplication(VAR_0,addition(VAR_1,VAR_2)) = addition(multiplication(VAR_0,VAR_1),multiplication(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity1) ).
cnf(c_13,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[distributivity1]) ).
cnf(c_14,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_13]) ).
fof(distributivity2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiplication(addition(VAR_0,VAR_1),VAR_2) = addition(multiplication(VAR_0,VAR_2),multiplication(VAR_1,VAR_2)),
file('theBenchmark.p',distributivity2) ).
cnf(c_15,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[distributivity2]) ).
cnf(c_16,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_15]) ).
fof(left_annihilation,axiom,
! [VAR_0] : multiplication(zero,VAR_0) = zero,
file('theBenchmark.p',left_annihilation) ).
cnf(c_17,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
fof(star_unfold1,axiom,
! [VAR_0] : addition(one,multiplication(VAR_0,star(VAR_0))) = star(VAR_0),
file('theBenchmark.p',star_unfold1) ).
cnf(c_18,plain,
addition(one,multiplication(A,star(A))) = star(A),
inference(clausify,[status(thm)],[star_unfold1]) ).
fof(star_induction1,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(leq(addition(multiplication(VAR_0,VAR_1),VAR_2),VAR_1),true,leq(multiplication(star(VAR_0),VAR_2),VAR_1),true) = true,
file('theBenchmark.p',star_induction1) ).
cnf(c_20,plain,
ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true,
inference(clausify,[status(thm)],[star_induction1]) ).
fof(infty_unfold1,axiom,
! [VAR_0] : strong_iteration(VAR_0) = addition(multiplication(VAR_0,strong_iteration(VAR_0)),one),
file('theBenchmark.p',infty_unfold1) ).
cnf(c_22,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(clausify,[status(thm)],[infty_unfold1]) ).
cnf(c_21258,plain,
strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))),
inference(paramod,[status(thm)],[c_4,c_22]) ).
cnf(c_23,plain,
addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A),
inference(copy,[status(thm)],[c_21258]) ).
fof(isolation,axiom,
! [VAR_0] : strong_iteration(VAR_0) = addition(star(VAR_0),multiplication(strong_iteration(VAR_0),zero)),
file('theBenchmark.p',isolation) ).
cnf(c_25,plain,
strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
inference(clausify,[status(thm)],[isolation]) ).
cnf(c_26,plain,
addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A),
inference(copy,[status(thm)],[c_25]) ).
fof(order_1,axiom,
! [VAR_0,VAR_1] : ifeq2(leq(VAR_0,VAR_1),true,addition(VAR_0,VAR_1),VAR_1) = VAR_1,
file('theBenchmark.p',order_1) ).
cnf(c_27,plain,
ifeq2(leq(A,B),true,addition(A,B),B) = B,
inference(clausify,[status(thm)],[order_1]) ).
fof(order,axiom,
! [VAR_0,VAR_1] : ifeq3(addition(VAR_0,VAR_1),VAR_1,leq(VAR_0,VAR_1),true) = true,
file('theBenchmark.p',order) ).
cnf(c_28,plain,
ifeq3(addition(A,B),B,leq(A,B),true) = true,
inference(clausify,[status(thm)],[order]) ).
fof(goals,axiom,
star(strong_iteration(sK1_goals_X0)) != strong_iteration(sK1_goals_X0),
file('theBenchmark.p',goals) ).
cnf(c_29,plain,
star(strong_iteration(sK1_goals_X0)) != strong_iteration(sK1_goals_X0),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_21259,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_31,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_6,c_21259]) ).
cnf(c_21260,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_32,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_21260]) ).
cnf(c_21261,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_33,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_21261]) ).
cnf(c_21262,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_35,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_4,c_21262]) ).
cnf(c_21263,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_11,c_14]) ).
cnf(c_37,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_21263]) ).
cnf(c_40,plain,
addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(multiplication(A,B),D),C),
inference(paramod,[status(thm)],[c_10,c_16]) ).
cnf(c_21264,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_12,c_16]) ).
cnf(c_42,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_21264]) ).
cnf(c_21265,plain,
addition(multiplication(one,A),multiplication(multiplication(B,star(B)),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_18,c_16]) ).
cnf(c_21266,plain,
addition(A,multiplication(multiplication(B,star(B)),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_12,c_21265]) ).
cnf(c_48,plain,
addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_10,c_21266]) ).
cnf(c_21267,plain,
ifeq(leq(addition(multiplication(A,B),one),B),true,leq(star(A),B),true) = true,
inference(paramod,[status(thm)],[c_11,c_20]) ).
cnf(c_58,plain,
ifeq(leq(addition(one,multiplication(A,B)),B),true,leq(star(A),B),true) = true,
inference(paramod,[status(thm)],[c_4,c_21267]) ).
cnf(c_61,plain,
ifeq(leq(multiplication(addition(A,B),C),C),true,leq(multiplication(star(A),multiplication(B,C)),C),true) = true,
inference(paramod,[status(thm)],[c_16,c_20]) ).
cnf(c_21268,plain,
addition(strong_iteration(A),B) = addition(star(A),addition(multiplication(strong_iteration(A),zero),B)),
inference(paramod,[status(thm)],[c_26,c_6]) ).
cnf(c_89,plain,
addition(star(A),addition(multiplication(strong_iteration(A),zero),B)) = addition(strong_iteration(A),B),
inference(copy,[status(thm)],[c_21268]) ).
cnf(c_21269,plain,
ifeq3(A,A,leq(A,A),true) = true,
inference(paramod,[status(thm)],[c_8,c_28]) ).
cnf(c_104,plain,
leq(A,A) = true,
inference(paramod,[status(thm)],[c_1,c_21269]) ).
cnf(c_21270,plain,
addition(one,star(A)) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_18,c_33]) ).
cnf(c_135,plain,
addition(one,star(A)) = star(A),
inference(paramod,[status(thm)],[c_18,c_21270]) ).
cnf(c_21271,plain,
addition(one,strong_iteration(A)) = addition(one,multiplication(A,strong_iteration(A))),
inference(paramod,[status(thm)],[c_23,c_33]) ).
cnf(c_138,plain,
addition(one,strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_23,c_21271]) ).
cnf(c_21272,plain,
addition(multiplication(one,A),multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_135,c_16]) ).
cnf(c_146,plain,
addition(A,multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_12,c_21272]) ).
cnf(c_21273,plain,
addition(A,star(B)) = addition(one,addition(A,star(B))),
inference(paramod,[status(thm)],[c_135,c_31]) ).
cnf(c_149,plain,
addition(one,addition(A,star(B))) = addition(A,star(B)),
inference(copy,[status(thm)],[c_21273]) ).
cnf(c_21274,plain,
addition(A,addition(B,addition(C,A))) = addition(addition(B,C),A),
inference(paramod,[status(thm)],[c_6,c_35]) ).
cnf(c_165,plain,
addition(A,addition(B,addition(C,A))) = addition(B,addition(C,A)),
inference(paramod,[status(thm)],[c_6,c_21274]) ).
cnf(c_21275,plain,
addition(multiplication(A,star(A)),star(A)) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_18,c_35]) ).
cnf(c_21276,plain,
addition(star(A),multiplication(A,star(A))) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_4,c_21275]) ).
cnf(c_21277,plain,
multiplication(addition(one,A),star(A)) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_42,c_21276]) ).
cnf(c_166,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_18,c_21277]) ).
cnf(c_21278,plain,
addition(multiplication(A,strong_iteration(A)),strong_iteration(A)) = addition(one,multiplication(A,strong_iteration(A))),
inference(paramod,[status(thm)],[c_23,c_35]) ).
cnf(c_21279,plain,
addition(strong_iteration(A),multiplication(A,strong_iteration(A))) = addition(one,multiplication(A,strong_iteration(A))),
inference(paramod,[status(thm)],[c_4,c_21278]) ).
cnf(c_21280,plain,
multiplication(addition(one,A),strong_iteration(A)) = addition(one,multiplication(A,strong_iteration(A))),
inference(paramod,[status(thm)],[c_42,c_21279]) ).
cnf(c_170,plain,
multiplication(addition(one,A),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_23,c_21280]) ).
cnf(c_239,plain,
multiplication(addition(A,one),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_4,c_170]) ).
cnf(c_21281,plain,
multiplication(A,one) = addition(A,multiplication(A,zero)),
inference(paramod,[status(thm)],[c_7,c_37]) ).
cnf(c_21282,plain,
A = addition(A,multiplication(A,zero)),
inference(paramod,[status(thm)],[c_11,c_21281]) ).
cnf(c_289,plain,
addition(A,multiplication(A,zero)) = A,
inference(copy,[status(thm)],[c_21282]) ).
cnf(c_21283,plain,
multiplication(addition(one,A),addition(one,star(A))) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_166,c_37]) ).
cnf(c_21284,plain,
multiplication(addition(one,A),star(A)) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_135,c_21283]) ).
cnf(c_21285,plain,
star(A) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_166,c_21284]) ).
cnf(c_21286,plain,
star(A) = addition(star(A),addition(one,A)),
inference(paramod,[status(thm)],[c_4,c_21285]) ).
cnf(c_21287,plain,
star(A) = addition(one,addition(star(A),A)),
inference(paramod,[status(thm)],[c_31,c_21286]) ).
cnf(c_21288,plain,
star(A) = addition(one,addition(A,star(A))),
inference(paramod,[status(thm)],[c_4,c_21287]) ).
cnf(c_21289,plain,
star(A) = addition(A,star(A)),
inference(paramod,[status(thm)],[c_149,c_21288]) ).
cnf(c_309,plain,
addition(A,star(A)) = star(A),
inference(copy,[status(thm)],[c_21289]) ).
cnf(c_491,plain,
addition(multiplication(A,zero),multiplication(B,C)) = multiplication(addition(multiplication(A,zero),B),C),
inference(paramod,[status(thm)],[c_17,c_40]) ).
cnf(c_21290,plain,
ifeq(leq(strong_iteration(A),strong_iteration(A)),true,leq(multiplication(star(A),multiplication(one,strong_iteration(A))),strong_iteration(A)),true) = true,
inference(paramod,[status(thm)],[c_239,c_61]) ).
cnf(c_21291,plain,
ifeq(true,true,leq(multiplication(star(A),multiplication(one,strong_iteration(A))),strong_iteration(A)),true) = true,
inference(paramod,[status(thm)],[c_104,c_21290]) ).
cnf(c_21292,plain,
ifeq(true,true,leq(multiplication(star(A),strong_iteration(A)),strong_iteration(A)),true) = true,
inference(paramod,[status(thm)],[c_12,c_21291]) ).
cnf(c_1252,plain,
leq(multiplication(star(A),strong_iteration(A)),strong_iteration(A)) = true,
inference(paramod,[status(thm)],[c_3,c_21292]) ).
cnf(c_21293,plain,
ifeq2(true,true,addition(multiplication(star(A),strong_iteration(A)),strong_iteration(A)),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_1252,c_27]) ).
cnf(c_21294,plain,
ifeq2(true,true,addition(strong_iteration(A),multiplication(star(A),strong_iteration(A))),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_4,c_21293]) ).
cnf(c_21295,plain,
ifeq2(true,true,multiplication(star(A),strong_iteration(A)),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_146,c_21294]) ).
cnf(c_1369,plain,
multiplication(star(A),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_2,c_21295]) ).
cnf(c_21296,plain,
addition(star(A),multiplication(strong_iteration(A),addition(zero,B))) = addition(strong_iteration(A),multiplication(strong_iteration(A),B)),
inference(paramod,[status(thm)],[c_14,c_89]) ).
cnf(c_21297,plain,
addition(star(A),multiplication(strong_iteration(A),B)) = addition(strong_iteration(A),multiplication(strong_iteration(A),B)),
inference(paramod,[status(thm)],[c_32,c_21296]) ).
cnf(c_3286,plain,
addition(star(A),multiplication(strong_iteration(A),B)) = multiplication(strong_iteration(A),addition(one,B)),
inference(paramod,[status(thm)],[c_37,c_21297]) ).
cnf(c_21298,plain,
addition(multiplication(A,zero),addition(B,A)) = addition(B,addition(A,multiplication(A,zero))),
inference(paramod,[status(thm)],[c_289,c_165]) ).
cnf(c_10054,plain,
addition(multiplication(A,zero),addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_289,c_21298]) ).
cnf(c_21299,plain,
ifeq3(addition(A,B),addition(A,B),leq(multiplication(B,zero),addition(A,B)),true) = true,
inference(paramod,[status(thm)],[c_10054,c_28]) ).
cnf(c_10322,plain,
leq(multiplication(A,zero),addition(B,A)) = true,
inference(paramod,[status(thm)],[c_1,c_21299]) ).
cnf(c_10368,plain,
leq(multiplication(A,zero),addition(A,B)) = true,
inference(paramod,[status(thm)],[c_4,c_10322]) ).
cnf(c_10402,plain,
leq(multiplication(A,zero),multiplication(star(B),A)) = true,
inference(paramod,[status(thm)],[c_48,c_10368]) ).
cnf(c_21300,plain,
ifeq2(true,true,addition(multiplication(A,zero),multiplication(star(B),A)),multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_10402,c_27]) ).
cnf(c_21301,plain,
ifeq2(true,true,multiplication(addition(multiplication(A,zero),star(B)),A),multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_491,c_21300]) ).
cnf(c_10502,plain,
multiplication(addition(multiplication(A,zero),star(B)),A) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_2,c_21301]) ).
cnf(c_21302,plain,
multiplication(addition(multiplication(strong_iteration(A),zero),star(A)),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_1369,c_10502]) ).
cnf(c_21303,plain,
multiplication(addition(star(A),multiplication(strong_iteration(A),zero)),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_4,c_21302]) ).
cnf(c_21304,plain,
multiplication(multiplication(strong_iteration(A),addition(one,zero)),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_3286,c_21303]) ).
cnf(c_21305,plain,
multiplication(multiplication(strong_iteration(A),one),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_7,c_21304]) ).
cnf(c_21146,plain,
multiplication(strong_iteration(A),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_11,c_21305]) ).
cnf(c_21306,plain,
ifeq(leq(addition(one,strong_iteration(A)),strong_iteration(A)),true,leq(star(strong_iteration(A)),strong_iteration(A)),true) = true,
inference(paramod,[status(thm)],[c_21146,c_58]) ).
cnf(c_21307,plain,
ifeq(leq(strong_iteration(A),strong_iteration(A)),true,leq(star(strong_iteration(A)),strong_iteration(A)),true) = true,
inference(paramod,[status(thm)],[c_138,c_21306]) ).
cnf(c_21308,plain,
ifeq(true,true,leq(star(strong_iteration(A)),strong_iteration(A)),true) = true,
inference(paramod,[status(thm)],[c_104,c_21307]) ).
cnf(c_21240,plain,
leq(star(strong_iteration(A)),strong_iteration(A)) = true,
inference(paramod,[status(thm)],[c_3,c_21308]) ).
cnf(c_21309,plain,
ifeq2(true,true,addition(star(strong_iteration(A)),strong_iteration(A)),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_21240,c_27]) ).
cnf(c_21310,plain,
ifeq2(true,true,addition(strong_iteration(A),star(strong_iteration(A))),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_4,c_21309]) ).
cnf(c_21311,plain,
ifeq2(true,true,star(strong_iteration(A)),strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_309,c_21310]) ).
cnf(c_21256,plain,
star(strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_2,c_21311]) ).
cnf(c_21257,plain,
$false,
inference(resolve,[status(thm)],[c_21256,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE145-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 19:28:37 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 887339 was started by sandbox2 on n003,
% 0.08/0.36 % Fri Sep 25 19:28:37 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 47.76/7.20
% 47.76/7.20 % given #500 (A,wt=36): 149 addition(one,addition(A,star(B))) = addition(A,star(B)). [para(135(a,1),31(a,1,2)),flip(a)].
% 47.76/7.20
% 47.76/7.20 % SZS status Unsatisfiable for theBenchmark
% 47.76/7.20
% 47.76/7.20 % Proof 1 at 5.41 (+ 1.35) seconds.
% 47.76/7.20 % Length of proof is 61.
% 47.76/7.20 % Level of proof is 12.
% 47.76/7.20 % Maximum clause weight is 50.000.
% 47.76/7.20 % Given clauses 894.
% 47.76/7.20
% 47.76/7.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------