%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE044-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 07:44:11 AM UTC 2026
% Result : Unsatisfiable 16.46s 2.54s
% Output : CNFRefutation 16.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 18
% Syntax : Number of formulae : 139 ( 139 unt; 0 def)
% Number of atoms : 139 ( 138 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 226 ( 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_idempotence,axiom,
! [VAR_0] : addition(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',additive_idempotence) ).
cnf(c_8,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_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(right_distributivity,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',right_distributivity) ).
cnf(c_13,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_14,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_13]) ).
fof(left_distributivity,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',left_distributivity) ).
cnf(c_15,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_16,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_15]) ).
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_19,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_20,plain,
ifeq3(addition(A,B),B,leq(A,B),true) = true,
inference(clausify,[status(thm)],[order]) ).
fof(star_unfold_right,axiom,
! [VAR_0] : leq(addition(one,multiplication(VAR_0,star(VAR_0))),star(VAR_0)) = true,
file('theBenchmark.p',star_unfold_right) ).
cnf(c_21,plain,
leq(addition(one,multiplication(A,star(A))),star(A)) = true,
inference(clausify,[status(thm)],[star_unfold_right]) ).
fof(star_unfold_left,axiom,
! [VAR_0] : leq(addition(one,multiplication(star(VAR_0),VAR_0)),star(VAR_0)) = true,
file('theBenchmark.p',star_unfold_left) ).
cnf(c_22,plain,
leq(addition(one,multiplication(star(A),A)),star(A)) = true,
inference(clausify,[status(thm)],[star_unfold_left]) ).
fof(star_induction_left,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_induction_left) ).
cnf(c_23,plain,
ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true,
inference(clausify,[status(thm)],[star_induction_left]) ).
fof(star_induction_right,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(leq(addition(multiplication(VAR_0,VAR_1),VAR_2),VAR_0),true,leq(multiplication(VAR_2,star(VAR_1)),VAR_0),true) = true,
file('theBenchmark.p',star_induction_right) ).
cnf(c_24,plain,
ifeq(leq(addition(multiplication(A,B),C),A),true,leq(multiplication(C,star(B)),A),true) = true,
inference(clausify,[status(thm)],[star_induction_right]) ).
fof(goals,axiom,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
file('theBenchmark.p',goals) ).
cnf(c_25,plain,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_4985,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_27,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_6,c_4985]) ).
cnf(c_4986,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_29,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_4986]) ).
cnf(c_4987,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_11,c_14]) ).
cnf(c_33,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_4987]) ).
cnf(c_4988,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_12,c_16]) ).
cnf(c_38,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_4988]) ).
cnf(c_40,plain,
ifeq2(leq(A,B),true,addition(B,A),B) = B,
inference(paramod,[status(thm)],[c_4,c_19]) ).
cnf(c_41,plain,
ifeq2(leq(addition(A,B),C),true,addition(A,addition(B,C)),C) = C,
inference(paramod,[status(thm)],[c_6,c_19]) ).
cnf(c_4989,plain,
ifeq3(A,A,leq(A,A),true) = true,
inference(paramod,[status(thm)],[c_8,c_20]) ).
cnf(c_49,plain,
leq(A,A) = true,
inference(paramod,[status(thm)],[c_1,c_4989]) ).
cnf(c_4990,plain,
ifeq2(true,true,addition(addition(one,multiplication(A,star(A))),star(A)),star(A)) = star(A),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_4991,plain,
ifeq2(true,true,addition(star(A),addition(one,multiplication(A,star(A)))),star(A)) = star(A),
inference(paramod,[status(thm)],[c_4,c_4990]) ).
cnf(c_55,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_2,c_4991]) ).
cnf(c_57,plain,
ifeq(leq(addition(A,multiplication(B,C)),C),true,leq(multiplication(star(B),A),C),true) = true,
inference(paramod,[status(thm)],[c_4,c_23]) ).
cnf(c_4992,plain,
ifeq(leq(addition(multiplication(A,B),one),B),true,leq(star(A),B),true) = true,
inference(paramod,[status(thm)],[c_11,c_23]) ).
cnf(c_62,plain,
ifeq(leq(addition(one,multiplication(A,B)),B),true,leq(star(A),B),true) = true,
inference(paramod,[status(thm)],[c_4,c_4992]) ).
cnf(c_4993,plain,
ifeq(leq(multiplication(A,addition(B,C)),A),true,leq(multiplication(multiplication(A,C),star(B)),A),true) = true,
inference(paramod,[status(thm)],[c_14,c_24]) ).
cnf(c_76,plain,
ifeq(leq(multiplication(A,addition(B,C)),A),true,leq(multiplication(A,multiplication(C,star(B))),A),true) = true,
inference(paramod,[status(thm)],[c_10,c_4993]) ).
cnf(c_4994,plain,
ifeq3(addition(A,B),addition(A,B),leq(A,addition(A,B)),true) = true,
inference(paramod,[status(thm)],[c_29,c_20]) ).
cnf(c_101,plain,
leq(A,addition(A,B)) = true,
inference(paramod,[status(thm)],[c_1,c_4994]) ).
cnf(c_110,plain,
leq(A,addition(B,addition(A,C))) = true,
inference(paramod,[status(thm)],[c_27,c_101]) ).
cnf(c_4995,plain,
ifeq2(true,true,addition(one,addition(multiplication(A,star(A)),star(A))),star(A)) = star(A),
inference(paramod,[status(thm)],[c_21,c_41]) ).
cnf(c_4996,plain,
ifeq2(true,true,addition(one,addition(star(A),multiplication(A,star(A)))),star(A)) = star(A),
inference(paramod,[status(thm)],[c_4,c_4995]) ).
cnf(c_516,plain,
addition(one,addition(star(A),multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_2,c_4996]) ).
cnf(c_4997,plain,
ifeq2(true,true,addition(one,addition(multiplication(star(A),A),star(A))),star(A)) = star(A),
inference(paramod,[status(thm)],[c_22,c_41]) ).
cnf(c_4998,plain,
ifeq2(true,true,addition(one,addition(star(A),multiplication(star(A),A))),star(A)) = star(A),
inference(paramod,[status(thm)],[c_4,c_4997]) ).
cnf(c_517,plain,
addition(one,addition(star(A),multiplication(star(A),A))) = star(A),
inference(paramod,[status(thm)],[c_2,c_4998]) ).
cnf(c_1105,plain,
leq(one,star(A)) = true,
inference(paramod,[status(thm)],[c_55,c_110]) ).
cnf(c_4999,plain,
ifeq2(true,true,addition(one,star(A)),star(A)) = star(A),
inference(paramod,[status(thm)],[c_1105,c_19]) ).
cnf(c_1106,plain,
addition(one,star(A)) = star(A),
inference(paramod,[status(thm)],[c_2,c_4999]) ).
cnf(c_5000,plain,
ifeq2(true,true,addition(star(A),one),star(A)) = star(A),
inference(paramod,[status(thm)],[c_1105,c_40]) ).
cnf(c_1107,plain,
addition(star(A),one) = star(A),
inference(paramod,[status(thm)],[c_2,c_5000]) ).
cnf(c_5001,plain,
addition(star(A),B) = addition(one,addition(star(A),B)),
inference(paramod,[status(thm)],[c_1106,c_6]) ).
cnf(c_1114,plain,
addition(one,addition(star(A),B)) = addition(star(A),B),
inference(copy,[status(thm)],[c_5001]) ).
cnf(c_5002,plain,
addition(multiplication(A,one),multiplication(A,star(B))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_1106,c_14]) ).
cnf(c_1115,plain,
addition(A,multiplication(A,star(B))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_11,c_5002]) ).
cnf(c_1130,plain,
addition(star(A),multiplication(star(A),A)) = star(A),
inference(paramod,[status(thm)],[c_1114,c_517]) ).
cnf(c_1131,plain,
addition(star(A),multiplication(A,star(A))) = star(A),
inference(paramod,[status(thm)],[c_1114,c_516]) ).
cnf(c_5003,plain,
addition(star(A),B) = addition(star(A),addition(one,B)),
inference(paramod,[status(thm)],[c_1107,c_6]) ).
cnf(c_1156,plain,
addition(star(A),addition(one,B)) = addition(star(A),B),
inference(copy,[status(thm)],[c_5003]) ).
cnf(c_1185,plain,
multiplication(star(A),addition(one,A)) = star(A),
inference(paramod,[status(thm)],[c_1130,c_33]) ).
cnf(c_5004,plain,
addition(star(addition(one,A)),addition(star(addition(one,A)),multiplication(star(addition(one,A)),A))) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_33,c_1130]) ).
cnf(c_5005,plain,
addition(star(addition(one,A)),multiplication(star(addition(one,A)),addition(one,A))) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_33,c_5004]) ).
cnf(c_5006,plain,
multiplication(star(addition(one,A)),addition(one,addition(one,A))) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_33,c_5005]) ).
cnf(c_1186,plain,
multiplication(star(addition(one,A)),addition(one,A)) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_29,c_5006]) ).
cnf(c_5007,plain,
multiplication(addition(one,star(A)),addition(one,A)) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_1185,c_38]) ).
cnf(c_5008,plain,
multiplication(star(A),addition(one,A)) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_1106,c_5007]) ).
cnf(c_5009,plain,
star(A) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_1185,c_5008]) ).
cnf(c_5010,plain,
star(A) = addition(star(A),addition(one,A)),
inference(paramod,[status(thm)],[c_4,c_5009]) ).
cnf(c_5011,plain,
star(A) = addition(star(A),A),
inference(paramod,[status(thm)],[c_1156,c_5010]) ).
cnf(c_5012,plain,
star(A) = addition(A,star(A)),
inference(paramod,[status(thm)],[c_4,c_5011]) ).
cnf(c_1219,plain,
addition(A,star(A)) = star(A),
inference(copy,[status(thm)],[c_5012]) ).
cnf(c_5013,plain,
addition(addition(A,B),star(B)) = addition(A,star(B)),
inference(paramod,[status(thm)],[c_1219,c_6]) ).
cnf(c_1240,plain,
addition(star(A),addition(B,A)) = addition(B,star(A)),
inference(paramod,[status(thm)],[c_4,c_5013]) ).
cnf(c_1387,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_1131,c_38]) ).
cnf(c_5014,plain,
ifeq(leq(star(A),star(A)),true,leq(multiplication(star(A),star(A)),star(A)),true) = true,
inference(paramod,[status(thm)],[c_1131,c_57]) ).
cnf(c_5015,plain,
ifeq(true,true,leq(multiplication(star(A),star(A)),star(A)),true) = true,
inference(paramod,[status(thm)],[c_49,c_5014]) ).
cnf(c_1400,plain,
leq(multiplication(star(A),star(A)),star(A)) = true,
inference(paramod,[status(thm)],[c_3,c_5015]) ).
cnf(c_5016,plain,
ifeq(leq(addition(one,star(A)),star(A)),true,leq(star(addition(one,A)),star(A)),true) = true,
inference(paramod,[status(thm)],[c_1387,c_62]) ).
cnf(c_5017,plain,
ifeq(leq(star(A),star(A)),true,leq(star(addition(one,A)),star(A)),true) = true,
inference(paramod,[status(thm)],[c_1106,c_5016]) ).
cnf(c_5018,plain,
ifeq(true,true,leq(star(addition(one,A)),star(A)),true) = true,
inference(paramod,[status(thm)],[c_49,c_5017]) ).
cnf(c_1473,plain,
leq(star(addition(one,A)),star(A)) = true,
inference(paramod,[status(thm)],[c_3,c_5018]) ).
cnf(c_1475,plain,
tuple(true,leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
inference(paramod,[status(thm)],[c_1473,c_25]) ).
cnf(c_5019,plain,
ifeq2(true,true,addition(star(addition(one,A)),star(A)),star(A)) = star(A),
inference(paramod,[status(thm)],[c_1473,c_19]) ).
cnf(c_5020,plain,
ifeq2(true,true,addition(star(A),star(addition(one,A))),star(A)) = star(A),
inference(paramod,[status(thm)],[c_4,c_5019]) ).
cnf(c_1476,plain,
addition(star(A),star(addition(one,A))) = star(A),
inference(paramod,[status(thm)],[c_2,c_5020]) ).
cnf(c_5021,plain,
ifeq2(true,true,addition(multiplication(star(A),star(A)),star(A)),star(A)) = star(A),
inference(paramod,[status(thm)],[c_1400,c_19]) ).
cnf(c_5022,plain,
ifeq2(true,true,addition(star(A),multiplication(star(A),star(A))),star(A)) = star(A),
inference(paramod,[status(thm)],[c_4,c_5021]) ).
cnf(c_5023,plain,
ifeq2(true,true,multiplication(star(A),star(A)),star(A)) = star(A),
inference(paramod,[status(thm)],[c_1115,c_5022]) ).
cnf(c_1647,plain,
multiplication(star(A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_2,c_5023]) ).
cnf(c_1651,plain,
addition(star(A),multiplication(B,star(A))) = multiplication(addition(star(A),B),star(A)),
inference(paramod,[status(thm)],[c_1647,c_16]) ).
cnf(c_1711,plain,
ifeq2(leq(star(A),star(addition(one,A))),true,star(A),star(addition(one,A))) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_1476,c_19]) ).
cnf(c_5024,plain,
addition(addition(one,A),multiplication(addition(one,A),star(B))) = addition(star(B),multiplication(A,star(B))),
inference(paramod,[status(thm)],[c_38,c_1115]) ).
cnf(c_5025,plain,
multiplication(addition(one,A),addition(one,star(B))) = addition(star(B),multiplication(A,star(B))),
inference(paramod,[status(thm)],[c_33,c_5024]) ).
cnf(c_5026,plain,
multiplication(addition(one,A),star(B)) = addition(star(B),multiplication(A,star(B))),
inference(paramod,[status(thm)],[c_1106,c_5025]) ).
cnf(c_5027,plain,
multiplication(addition(one,A),star(B)) = multiplication(addition(star(B),A),star(B)),
inference(paramod,[status(thm)],[c_1651,c_5026]) ).
cnf(c_1891,plain,
multiplication(addition(star(A),B),star(A)) = multiplication(addition(one,B),star(A)),
inference(copy,[status(thm)],[c_5027]) ).
cnf(c_5028,plain,
addition(star(addition(A,B)),addition(A,B)) = addition(A,star(addition(A,B))),
inference(paramod,[status(thm)],[c_29,c_1240]) ).
cnf(c_5029,plain,
addition(addition(A,B),star(addition(A,B))) = addition(A,star(addition(A,B))),
inference(paramod,[status(thm)],[c_4,c_5028]) ).
cnf(c_5030,plain,
star(addition(A,B)) = addition(A,star(addition(A,B))),
inference(paramod,[status(thm)],[c_1219,c_5029]) ).
cnf(c_2025,plain,
addition(A,star(addition(A,B))) = star(addition(A,B)),
inference(copy,[status(thm)],[c_5030]) ).
cnf(c_2590,plain,
multiplication(star(addition(one,A)),addition(A,one)) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_4,c_1186]) ).
cnf(c_5031,plain,
ifeq(leq(star(addition(one,A)),star(addition(one,A))),true,leq(multiplication(star(addition(one,A)),multiplication(one,star(A))),star(addition(one,A))),true) = true,
inference(paramod,[status(thm)],[c_2590,c_76]) ).
cnf(c_5032,plain,
ifeq(true,true,leq(multiplication(star(addition(one,A)),multiplication(one,star(A))),star(addition(one,A))),true) = true,
inference(paramod,[status(thm)],[c_49,c_5031]) ).
cnf(c_5033,plain,
ifeq(true,true,leq(multiplication(star(addition(one,A)),star(A)),star(addition(one,A))),true) = true,
inference(paramod,[status(thm)],[c_12,c_5032]) ).
cnf(c_3970,plain,
leq(multiplication(star(addition(one,A)),star(A)),star(addition(one,A))) = true,
inference(paramod,[status(thm)],[c_3,c_5033]) ).
cnf(c_5034,plain,
multiplication(star(A),star(A)) = multiplication(addition(one,star(addition(one,A))),star(A)),
inference(paramod,[status(thm)],[c_1476,c_1891]) ).
cnf(c_5035,plain,
star(A) = multiplication(addition(one,star(addition(one,A))),star(A)),
inference(paramod,[status(thm)],[c_1647,c_5034]) ).
cnf(c_5036,plain,
star(A) = multiplication(star(addition(one,A)),star(A)),
inference(paramod,[status(thm)],[c_2025,c_5035]) ).
cnf(c_4918,plain,
multiplication(star(addition(one,A)),star(A)) = star(A),
inference(copy,[status(thm)],[c_5036]) ).
cnf(c_4979,plain,
leq(star(A),star(addition(one,A))) = true,
inference(paramod,[status(thm)],[c_4918,c_3970]) ).
cnf(c_5037,plain,
ifeq2(true,true,star(A),star(addition(one,A))) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_4979,c_1711]) ).
cnf(c_5038,plain,
star(A) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_2,c_5037]) ).
cnf(c_4983,plain,
star(addition(one,A)) = star(A),
inference(copy,[status(thm)],[c_5038]) ).
cnf(c_5039,plain,
tuple(true,leq(star(sK1_goals_X0),star(sK1_goals_X0))) != tuple(true,true),
inference(paramod,[status(thm)],[c_4983,c_1475]) ).
cnf(c_5040,plain,
tuple(true,true) != tuple(true,true),
inference(paramod,[status(thm)],[c_49,c_5039]) ).
cnf(c_4984,plain,
$false,
inference(copy,[status(thm)],[c_5040]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE044-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n018.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 19:19:35 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2626152 was started by sandbox on n018,
% 0.16/0.43 % Fri Sep 25 19:19:35 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 16.46/2.54
% 16.46/2.54 % Assigning unary symbol star kb_weight 0 and highest precedence (14).
% 16.46/2.54
% 16.46/2.54 % SZS status Unsatisfiable for theBenchmark
% 16.46/2.54
% 16.46/2.54 % Proof 1 at 1.57 (+ 0.51) seconds.
% 16.46/2.54 % Length of proof is 65.
% 16.46/2.54 % Level of proof is 16.
% 16.46/2.54 % Maximum clause weight is 55.000.
% 16.46/2.54 % Given clauses 328.
% 16.46/2.54
% 16.46/2.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------