%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE147+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 : Fri Sep 25 01:52:31 PM UTC 2026
% Result : Theorem 110.31s 18.45s
% Output : CNFRefutation 110.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of formulae : 145 ( 119 unt; 5 def)
% Number of atoms : 329 ( 89 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 58 ( 30 ~; 23 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn 146 !; 2 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(f11,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
fof(f12,axiom,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(f13,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X2),X1),X2)
=> leq(multiplication(star(X0),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction1) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(f19,conjecture,
! [X0,X1] :
( leq(multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),strong_iteration(multiplication(star(X0),X1)))
& leq(strong_iteration(multiplication(star(X0),X1)),multiplication(star(X1),strong_iteration(multiplication(star(X0),X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( leq(multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),strong_iteration(multiplication(star(X0),X1)))
& leq(strong_iteration(multiplication(star(X0),X1)),multiplication(star(X1),strong_iteration(multiplication(star(X0),X1)))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X2),X1),X2)
| leq(multiplication(star(X0),X1),X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f24,plain,
? [X0,X1] :
( ~ leq(multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),strong_iteration(multiplication(star(X0),X1)))
| ~ leq(strong_iteration(multiplication(star(X0),X1)),multiplication(star(X1),strong_iteration(multiplication(star(X0),X1)))) ),
inference(ennf_transformation,[],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f26,plain,
( ~ leq(multiplication(star(sK1),strong_iteration(multiplication(star(sK0),sK1))),strong_iteration(multiplication(star(sK0),sK1)))
| ~ leq(strong_iteration(multiplication(star(sK0),sK1)),multiplication(star(sK1),strong_iteration(multiplication(star(sK0),sK1)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f24]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f37,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f38,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X2),X1),X2)
| leq(multiplication(star(X0),X1),X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f44,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( ~ leq(multiplication(star(sK1),strong_iteration(multiplication(star(sK0),sK1))),strong_iteration(multiplication(star(sK0),sK1)))
| ~ leq(strong_iteration(multiplication(star(sK0),sK1)),multiplication(star(sK1),strong_iteration(multiplication(star(sK0),sK1)))) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f27]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f32]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f35]) ).
tcf(c_59,plain,
! [X0: $i] : addition(one,multiplication(X0,star(X0))) = star(X0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_60,plain,
! [X0: $i] : addition(one,multiplication(star(X0),X0)) = star(X0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_63,plain,
! [X0: $i] : addition(multiplication(X0,strong_iteration(X0)),one) = strong_iteration(X0),
inference(cnf_transformation,[],[f41]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_68,negated_conjecture,
( ~ leq(strong_iteration(multiplication(star(sK0),sK1)),multiplication(star(sK1),strong_iteration(multiplication(star(sK0),sK1))))
| ~ leq(multiplication(star(sK1),strong_iteration(multiplication(star(sK0),sK1))),strong_iteration(multiplication(star(sK0),sK1))) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_87,plain,
! [X0: $i] : addition(one,multiplication(X0,strong_iteration(X0))) = strong_iteration(X0),
inference(theory_normalisation,[status(thm)],[c_63,c_50,c_49]) ).
tcf(c_219,definition,
iPr_def_10 = star(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_220,definition,
iPr_def_11 = star(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_221,definition,
iPr_def_12 = multiplication(iPr_def_11,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_222,definition,
iPr_def_13 = strong_iteration(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_223,definition,
iPr_def_14 = multiplication(iPr_def_10,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_224,negated_conjecture,
( ~ leq(iPr_def_14,iPr_def_13)
| ~ leq(iPr_def_13,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_68,c_220,c_221,c_222,c_219,c_223]) ).
tcf(c_683,plain,
( leq(iPr_def_13,iPr_def_14)
| ( addition(iPr_def_13,iPr_def_14) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_1300,plain,
! [X0: $i] : leq(X0,X0),
inference(superposition,[status(thm)],[c_52,c_66]) ).
tcf(c_9954,plain,
addition(one,star(one)) = star(one),
inference(superposition,[status(thm)],[c_55,c_59]) ).
tcf(c_9962,plain,
! [X0: $i] : addition(one,addition(star(one),X0)) = addition(star(one),X0),
inference(superposition,[status(thm)],[c_9954,c_50]) ).
tcf(c_9967,plain,
addition(one,multiplication(iPr_def_10,sK1)) = iPr_def_10,
inference(superposition,[status(thm)],[c_219,c_60]) ).
tcf(c_10058,plain,
! [X0: $i] : leq(one,addition(star(one),X0)),
inference(superposition,[status(thm)],[c_9962,c_66]) ).
tcf(c_10219,plain,
! [X0: $i,X1: $i] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_52,c_61]) ).
tcf(c_10356,plain,
! [X0: $i] :
( leq(multiplication(star(one),X0),X0)
| ~ leq(multiplication(one,X0),X0) ),
inference(superposition,[status(thm)],[c_55,c_10219]) ).
tcf(c_10371,plain,
! [X0: $i] :
( leq(multiplication(star(one),X0),X0)
| ~ leq(X0,X0) ),
inference(light_normalisation,[status(thm)],[c_10356,c_55]) ).
tcf(c_10372,plain,
! [X0: $i] : leq(multiplication(star(one),X0),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_10371,c_1300]) ).
tcf(c_10502,plain,
leq(star(one),one),
inference(superposition,[status(thm)],[c_54,c_10372]) ).
tcf(c_10506,plain,
addition(star(one),one) = one,
inference(superposition,[status(thm)],[c_10502,c_67]) ).
tcf(c_10507,plain,
addition(one,star(one)) = one,
inference(theory_normalisation,[status(thm)],[c_10506,c_50,c_49]) ).
tcf(c_10508,plain,
star(one) = one,
inference(demodulation,[status(thm)],[c_9954,c_10507]) ).
tcf(c_10514,plain,
! [X0: $i] : leq(one,addition(one,X0)),
inference(demodulation,[status(thm)],[c_10058,c_10508]) ).
tcf(c_10552,plain,
leq(one,iPr_def_10),
inference(superposition,[status(thm)],[c_9967,c_10514]) ).
tcf(c_10559,plain,
addition(one,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_10552,c_67]) ).
tcf(c_10560,plain,
addition(iPr_def_10,one) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_10559,c_50,c_49]) ).
tcf(c_10711,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(one,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_10560,c_57]) ).
tcf(c_10716,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),X0) = multiplication(iPr_def_10,X0),
inference(light_normalisation,[status(thm)],[c_10711,c_55]) ).
tcf(c_10717,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_10,X0),
inference(theory_normalisation,[status(thm)],[c_10716,c_50,c_49]) ).
tcf(c_18378,plain,
addition(iPr_def_13,iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_223,c_10717]) ).
tcf(c_164305,negated_conjecture,
~ leq(iPr_def_14,iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_224,c_224,c_683,c_18378]) ).
tcf(c_164330,plain,
addition(one,multiplication(iPr_def_11,sK0)) = iPr_def_11,
inference(superposition,[status(thm)],[c_220,c_60]) ).
tcf(c_164331,plain,
addition(one,multiplication(iPr_def_10,sK1)) = iPr_def_10,
inference(superposition,[status(thm)],[c_219,c_60]) ).
tcf(c_164341,plain,
! [X0: $i] : addition(iPr_def_14,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_10,addition(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_223,c_56]) ).
tcf(c_164411,plain,
addition(one,multiplication(iPr_def_12,iPr_def_13)) = iPr_def_13,
inference(superposition,[status(thm)],[c_222,c_87]) ).
tcf(c_164471,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_164523,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_164574,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(multiplication(star(X0),multiplication(X1,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(superposition,[status(thm)],[c_57,c_61]) ).
tcf(c_164914,plain,
! [X0: $i] : addition(one,star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_59,c_164523]) ).
tcf(c_164922,plain,
addition(one,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_164411,c_164523]) ).
tcf(c_164928,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_164523,c_66]) ).
tcf(c_164933,plain,
addition(iPr_def_13,one) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_164922,c_50,c_49]) ).
tcf(c_164971,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_164928]) ).
tcf(c_164976,plain,
! [X0: $i,X1: $i,X2: $i] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[c_56,c_164928]) ).
tcf(c_164977,plain,
! [X0: $i,X1: $i,X2: $i] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(superposition,[status(thm)],[c_57,c_164928]) ).
tcf(c_165173,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_164971]) ).
tcf(c_165187,plain,
leq(multiplication(iPr_def_12,iPr_def_13),iPr_def_13),
inference(superposition,[status(thm)],[c_164411,c_164971]) ).
tcf(c_165257,plain,
addition(multiplication(iPr_def_12,iPr_def_13),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_165187,c_67]) ).
tcf(c_165258,plain,
addition(iPr_def_13,multiplication(iPr_def_12,iPr_def_13)) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_165257,c_50,c_49]) ).
tcf(c_165409,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X0,X2))),
inference(superposition,[status(thm)],[c_49,c_165173]) ).
tcf(c_165424,plain,
! [X0: $i] : leq(multiplication(iPr_def_10,sK1),addition(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_164331,c_165173]) ).
tcf(c_166049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(superposition,[status(thm)],[c_56,c_165409]) ).
tcf(c_166208,plain,
! [X0: $i,X1: $i] :
( leq(multiplication(star(X0),X1),X1)
| ~ leq(multiplication(addition(X0,one),X1),X1) ),
inference(superposition,[status(thm)],[c_55,c_164574]) ).
tcf(c_166366,plain,
! [X0: $i] : leq(multiplication(iPr_def_10,sK1),addition(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_49,c_165424]) ).
tcf(c_167462,plain,
multiplication(addition(iPr_def_12,one),iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_165258,c_49,c_164471]) ).
tcf(c_170076,plain,
! [X0: $i] : leq(multiplication(X0,one),multiplication(X0,iPr_def_13)),
inference(superposition,[status(thm)],[c_164411,c_164976]) ).
tcf(c_170092,plain,
! [X0: $i] : leq(X0,multiplication(X0,iPr_def_13)),
inference(light_normalisation,[status(thm)],[c_170076,c_54]) ).
tcf(c_170118,plain,
leq(iPr_def_10,iPr_def_14),
inference(superposition,[status(thm)],[c_223,c_170092]) ).
tcf(c_170119,plain,
leq(addition(iPr_def_12,one),iPr_def_13),
inference(superposition,[status(thm)],[c_167462,c_170092]) ).
tcf(c_170136,plain,
addition(iPr_def_10,iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_170118,c_67]) ).
tcf(c_170167,plain,
addition(addition(iPr_def_12,one),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_170119,c_67]) ).
tcf(c_170168,plain,
addition(iPr_def_12,addition(iPr_def_13,one)) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_170167,c_50,c_49]) ).
tcf(c_170169,plain,
addition(iPr_def_12,iPr_def_13) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_170168,c_164933]) ).
tcf(c_170224,plain,
leq(multiplication(iPr_def_10,sK1),iPr_def_14),
inference(superposition,[status(thm)],[c_170136,c_166366]) ).
tcf(c_170601,plain,
addition(multiplication(iPr_def_10,sK1),iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_170224,c_67]) ).
tcf(c_170602,plain,
addition(iPr_def_14,multiplication(iPr_def_10,sK1)) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_170601,c_50,c_49]) ).
tcf(c_171622,plain,
multiplication(iPr_def_10,addition(iPr_def_13,sK1)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_170602,c_164341]) ).
tcf(c_179853,plain,
! [X0: $i] : leq(multiplication(one,X0),multiplication(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_164330,c_164977]) ).
tcf(c_179864,plain,
! [X0: $i,X1: $i] : leq(multiplication(one,X0),multiplication(star(X1),X0)),
inference(superposition,[status(thm)],[c_164914,c_164977]) ).
tcf(c_179888,plain,
! [X0: $i] : leq(X0,multiplication(iPr_def_11,X0)),
inference(light_normalisation,[status(thm)],[c_179853,c_55]) ).
tcf(c_179893,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(star(X1),X0)),
inference(light_normalisation,[status(thm)],[c_179864,c_55]) ).
tcf(c_180226,plain,
leq(sK1,iPr_def_12),
inference(superposition,[status(thm)],[c_221,c_179888]) ).
tcf(c_180250,plain,
addition(sK1,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_180226,c_67]) ).
tcf(c_180251,plain,
addition(iPr_def_12,sK1) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_180250,c_50,c_49]) ).
tcf(c_180261,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(superposition,[status(thm)],[c_179893,c_67]) ).
tcf(c_180652,plain,
! [X0: $i] : leq(sK1,addition(X0,iPr_def_12)),
inference(superposition,[status(thm)],[c_180251,c_165173]) ).
tcf(c_180942,plain,
! [X0: $i] : leq(sK1,addition(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_49,c_180652]) ).
tcf(c_181403,plain,
leq(sK1,iPr_def_13),
inference(superposition,[status(thm)],[c_170169,c_180942]) ).
tcf(c_181578,plain,
addition(sK1,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_181403,c_67]) ).
tcf(c_181579,plain,
addition(iPr_def_13,sK1) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_181578,c_50,c_49]) ).
tcf(c_181582,plain,
multiplication(iPr_def_10,iPr_def_13) = iPr_def_14,
inference(demodulation,[status(thm)],[c_171622,c_181579]) ).
tcf(c_208545,plain,
! [X0: $i,X1: $i,X2: $i] : leq(multiplication(X0,one),addition(X1,multiplication(X0,star(X2)))),
inference(superposition,[status(thm)],[c_164914,c_166049]) ).
tcf(c_208573,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,multiplication(X0,star(X2)))),
inference(light_normalisation,[status(thm)],[c_208545,c_54]) ).
tcf(c_209097,plain,
! [X0: $i] : leq(X0,star(X0)),
inference(superposition,[status(thm)],[c_59,c_208573]) ).
tcf(c_209144,plain,
! [X0: $i] : addition(X0,star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_209097,c_67]) ).
tcf(c_210873,plain,
leq(sK1,star(iPr_def_12)),
inference(superposition,[status(thm)],[c_209144,c_180942]) ).
tcf(c_211828,plain,
addition(sK1,star(iPr_def_12)) = star(iPr_def_12),
inference(superposition,[status(thm)],[c_210873,c_67]) ).
tcf(c_213671,plain,
! [X0: $i] : leq(multiplication(sK1,X0),multiplication(star(iPr_def_12),X0)),
inference(superposition,[status(thm)],[c_211828,c_164977]) ).
tcf(c_214681,plain,
( leq(multiplication(star(iPr_def_12),iPr_def_13),iPr_def_13)
| ~ leq(iPr_def_13,iPr_def_13) ),
inference(superposition,[status(thm)],[c_167462,c_166208]) ).
tcf(c_214692,plain,
leq(multiplication(star(iPr_def_12),iPr_def_13),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_214681,c_1300]) ).
tcf(c_220644,plain,
addition(multiplication(star(iPr_def_12),iPr_def_13),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_214692,c_67]) ).
tcf(c_220647,plain,
addition(iPr_def_13,multiplication(star(iPr_def_12),iPr_def_13)) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_220644,c_50,c_49]) ).
tcf(c_263084,plain,
multiplication(star(iPr_def_12),iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_220647,c_180261]) ).
tcf(c_263186,plain,
leq(multiplication(sK1,iPr_def_13),iPr_def_13),
inference(superposition,[status(thm)],[c_263084,c_213671]) ).
tcf(c_263655,plain,
addition(multiplication(sK1,iPr_def_13),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_263186,c_67]) ).
tcf(c_263660,plain,
addition(iPr_def_13,multiplication(sK1,iPr_def_13)) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_263655,c_50,c_49]) ).
tcf(c_264172,plain,
multiplication(addition(sK1,one),iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_263660,c_49,c_164471]) ).
tcf(c_264275,plain,
( leq(multiplication(star(sK1),iPr_def_13),iPr_def_13)
| ~ leq(iPr_def_13,iPr_def_13) ),
inference(superposition,[status(thm)],[c_264172,c_166208]) ).
tcf(c_264285,plain,
( leq(iPr_def_14,iPr_def_13)
| ~ leq(iPr_def_13,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_264275,c_219,c_181582]) ).
tcf(c_264286,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_264285,c_164305,c_1300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE147+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 19:05:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 110.31/18.45 % SZS status Started for theBenchmark.p
% 110.31/18.45 % SZS status Theorem for theBenchmark.p
% 110.31/18.45
% 110.31/18.45 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 110.31/18.45
% 110.31/18.45 % ------ iProver source info
% 110.31/18.45
% 110.31/18.45 % git: date: 2026-07-19 20:42:38 +0200
% 110.31/18.45 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 110.31/18.45 % git: non_committed_changes: false
% 110.31/18.45
% 110.31/18.45 % ------ Parsing...
% 110.31/18.45 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 110.31/18.45
% 110.31/18.45 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 110.31/18.45
% 110.31/18.45 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 110.31/18.45
% 110.31/18.45 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 110.31/18.45 % ------ Proving...
% 110.31/18.45 % ------ Problem Properties
% 110.31/18.45
% 110.31/18.45 %
% 110.31/18.45 % clauses 25
% 110.31/18.45 % conjectures 1
% 110.31/18.45 % EPR 1
% 110.31/18.45 % Horn 25
% 110.31/18.45 % unary 19
% 110.31/18.45 % binary 6
% 110.31/18.45 % lits 31
% 110.31/18.45 % lits eq 21
% 110.31/18.45 % fd_pure 0
% 110.31/18.45 % fd_pseudo 0
% 110.31/18.45 % fd_cond 0
% 110.31/18.45 % fd_pseudo_cond 0
% 110.31/18.45 % AC symbols 1
% 110.31/18.45
% 110.31/18.45 % ------ Schedule dynamic 5 is on
% 110.31/18.45
% 110.31/18.45 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 110.31/18.45
% 110.31/18.45
% 110.31/18.45 % ------
% 110.31/18.45 % Current options:
% 110.31/18.45 % ------
% 110.31/18.45
% 110.31/18.45
% 110.31/18.45 %
% 110.31/18.45
% 110.31/18.45 % ------ Proving...
% 110.31/18.45 % Proof_search_loop: time out after: 5350 full_loop iterations
% 110.31/18.45
% 110.31/18.45 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 110.31/18.45
% 110.31/18.45
% 110.31/18.45 % ------
% 110.31/18.45 % Current options:
% 110.31/18.45 % ------
% 110.31/18.45
% 110.31/18.45
% 110.31/18.45 %
% 110.31/18.45
% 110.31/18.45 % ------ Proving...
% 110.31/18.45 %
% 110.31/18.45
% 110.31/18.45 % SZS status Theorem for theBenchmark.p
% 110.31/18.45
% 110.31/18.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 110.31/18.45
% 110.31/18.45
%------------------------------------------------------------------------------