%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE159+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 07:44:26 AM UTC 2026
% Result : Theorem 19.25s 2.95s
% Output : CNFRefutation 19.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 14
% Syntax : Number of formulae : 107 ( 87 unt; 0 def)
% Number of atoms : 127 ( 62 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 54 ( 34 ~; 13 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 170 ( 8 sgn 33 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('theBenchmark.p',additive_associativity) ).
fof(idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',idempotence) ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('theBenchmark.p',multiplicative_associativity) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(distributivity1,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',distributivity1) ).
fof(distributivity2,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',distributivity2) ).
fof(star_unfold1,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
file('theBenchmark.p',star_unfold1) ).
fof(star_unfold2,axiom,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
file('theBenchmark.p',star_unfold2) ).
fof(star_induction1,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,C),B),C)
=> leq(multiplication(star(A),B),C) ),
file('theBenchmark.p',star_induction1) ).
fof(star_induction2,axiom,
! [A,B,C] :
( leq(addition(multiplication(C,A),B),C)
=> leq(multiplication(B,star(A)),C) ),
file('theBenchmark.p',star_induction2) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( leq(multiplication(X0,X1),multiplication(X2,X0))
=> leq(multiplication(X0,star(X1)),multiplication(star(X2),X0)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(multiplication(X0,X1),multiplication(X2,X0))
=> leq(multiplication(X0,star(X1)),multiplication(star(X2),X0)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_21,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_23,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[idempotence]) ).
cnf(c_24,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_25,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_26,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_27,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[distributivity1]) ).
cnf(c_28,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_29,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[distributivity2]) ).
cnf(c_30,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_32,plain,
star(A) = addition(one,multiplication(A,star(A))),
inference(clausify,[status(thm)],[star_unfold1]) ).
cnf(c_33,plain,
addition(one,multiplication(A,star(A))) = star(A),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_34,plain,
star(A) = addition(one,multiplication(star(A),A)),
inference(clausify,[status(thm)],[star_unfold2]) ).
cnf(c_35,plain,
addition(one,multiplication(star(A),A)) = star(A),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_36,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(clausify,[status(thm)],[star_induction1]) ).
cnf(c_37,plain,
( leq(multiplication(C,star(B)),A)
| ~ leq(addition(multiplication(A,B),C),A) ),
inference(clausify,[status(thm)],[star_induction2]) ).
cnf(c_43,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_19,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X0,star(X1)),multiplication(star(X2),X0))
& leq(multiplication(X0,X1),multiplication(X2,X0)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(multiplication(sK0,star(sK1)),multiplication(star(sK2),sK0))
& leq(multiplication(sK0,sK1),multiplication(sK2,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_19]) ).
cnf(c_45,negated_conjecture,
leq(multiplication(sK0,sK1),multiplication(sK2,sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_46,negated_conjecture,
~ leq(multiplication(sK0,star(sK1)),multiplication(star(sK2),sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_17889,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_20,c_21]) ).
cnf(c_48,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_21,c_17889]) ).
cnf(c_17890,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_50,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_17890]) ).
cnf(c_53,plain,
addition(multiplication(A,addition(B,C)),D) = addition(multiplication(A,B),addition(multiplication(A,C),D)),
inference(paramod,[status(thm)],[c_28,c_21]) ).
cnf(c_17891,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_25,c_28]) ).
cnf(c_54,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_17891]) ).
cnf(c_56,plain,
addition(multiplication(addition(A,B),C),D) = addition(multiplication(A,C),addition(multiplication(B,C),D)),
inference(paramod,[status(thm)],[c_30,c_21]) ).
cnf(c_17892,plain,
addition(multiplication(A,one),multiplication(A,multiplication(B,star(B)))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_33,c_28]) ).
cnf(c_64,plain,
addition(A,multiplication(A,multiplication(B,star(B)))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_25,c_17892]) ).
cnf(c_17893,plain,
addition(multiplication(one,A),multiplication(multiplication(B,star(B)),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_33,c_30]) ).
cnf(c_17894,plain,
addition(A,multiplication(multiplication(B,star(B)),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_26,c_17893]) ).
cnf(c_65,plain,
addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_24,c_17894]) ).
cnf(c_70,plain,
( leq(multiplication(star(B),A),C)
| ~ leq(addition(A,multiplication(B,C)),C) ),
inference(paramod,[status(thm)],[c_20,c_36]) ).
cnf(c_74,plain,
( leq(multiplication(star(A),B),one)
| ~ leq(addition(A,B),one) ),
inference(paramod,[status(thm)],[c_25,c_36]) ).
cnf(c_78,plain,
( leq(multiplication(A,star(C)),B)
| ~ leq(addition(A,multiplication(B,C)),B) ),
inference(paramod,[status(thm)],[c_20,c_37]) ).
cnf(c_103,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_44,c_23]) ).
cnf(c_105,plain,
( addition(A,addition(B,C)) != C
| leq(addition(A,B),C) ),
inference(paramod,[status(thm)],[c_21,c_44]) ).
cnf(c_113,negated_conjecture,
addition(multiplication(sK0,sK1),multiplication(sK2,sK0)) = multiplication(sK2,sK0),
inference(resolve,[status(thm)],[c_43,c_45]) ).
cnf(c_17895,negated_conjecture,
~ leq(addition(multiplication(multiplication(star(sK2),sK0),sK1),sK0),multiplication(star(sK2),sK0)),
inference(resolve,[status(thm)],[c_37,c_46]) ).
cnf(c_17896,negated_conjecture,
~ leq(addition(multiplication(star(sK2),multiplication(sK0,sK1)),sK0),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_24,c_17895]) ).
cnf(c_115,negated_conjecture,
~ leq(addition(sK0,multiplication(star(sK2),multiplication(sK0,sK1))),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_20,c_17896]) ).
cnf(c_128,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_44,c_50]) ).
cnf(c_17897,plain,
addition(one,star(A)) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_33,c_50]) ).
cnf(c_131,plain,
addition(one,star(A)) = star(A),
inference(paramod,[status(thm)],[c_33,c_17897]) ).
cnf(c_144,plain,
leq(A,addition(B,addition(A,C))),
inference(paramod,[status(thm)],[c_48,c_128]) ).
cnf(c_17898,plain,
addition(multiplication(star(A),B),C) = addition(multiplication(one,B),addition(multiplication(star(A),B),C)),
inference(paramod,[status(thm)],[c_131,c_56]) ).
cnf(c_17899,plain,
addition(multiplication(star(A),B),C) = addition(B,addition(multiplication(star(A),B),C)),
inference(paramod,[status(thm)],[c_26,c_17898]) ).
cnf(c_277,plain,
addition(A,addition(multiplication(star(B),A),C)) = addition(multiplication(star(B),A),C),
inference(copy,[status(thm)],[c_17899]) ).
cnf(c_574,plain,
leq(A,addition(B,multiplication(A,star(C)))),
inference(paramod,[status(thm)],[c_64,c_144]) ).
cnf(c_17900,plain,
addition(A,multiplication(star(B),C)) = addition(C,addition(A,multiplication(B,multiplication(star(B),C)))),
inference(paramod,[status(thm)],[c_65,c_48]) ).
cnf(c_607,plain,
addition(A,addition(B,multiplication(C,multiplication(star(C),A)))) = addition(B,multiplication(star(C),A)),
inference(copy,[status(thm)],[c_17900]) ).
cnf(c_17901,plain,
multiplication(A,addition(one,multiplication(star(A),A))) = multiplication(star(A),A),
inference(paramod,[status(thm)],[c_65,c_54]) ).
cnf(c_17902,plain,
multiplication(A,star(A)) = multiplication(star(A),A),
inference(paramod,[status(thm)],[c_35,c_17901]) ).
cnf(c_613,plain,
multiplication(star(A),A) = multiplication(A,star(A)),
inference(copy,[status(thm)],[c_17902]) ).
cnf(c_680,plain,
leq(A,star(A)),
inference(paramod,[status(thm)],[c_33,c_574]) ).
cnf(c_683,plain,
addition(A,star(A)) = star(A),
inference(resolve,[status(thm)],[c_43,c_680]) ).
cnf(c_17903,plain,
( leq(multiplication(star(A),A),one)
| ~ leq(A,one) ),
inference(paramod,[status(thm)],[c_23,c_74]) ).
cnf(c_752,plain,
( leq(multiplication(A,star(A)),one)
| ~ leq(A,one) ),
inference(paramod,[status(thm)],[c_613,c_17903]) ).
cnf(c_864,plain,
( leq(multiplication(A,star(one)),B)
| ~ leq(addition(A,B),B) ),
inference(paramod,[status(thm)],[c_25,c_78]) ).
cnf(c_1839,plain,
leq(multiplication(sK0,sK1),addition(A,multiplication(sK2,sK0))),
inference(paramod,[status(thm)],[c_113,c_144]) ).
cnf(c_17904,plain,
leq(multiplication(one,star(one)),one),
inference(resolve,[status(thm)],[c_752,c_103]) ).
cnf(c_5787,plain,
leq(star(one),one),
inference(paramod,[status(thm)],[c_26,c_17904]) ).
cnf(c_17905,plain,
addition(star(one),one) = one,
inference(resolve,[status(thm)],[c_43,c_5787]) ).
cnf(c_17906,plain,
addition(one,star(one)) = one,
inference(paramod,[status(thm)],[c_20,c_17905]) ).
cnf(c_5790,plain,
star(one) = one,
inference(paramod,[status(thm)],[c_683,c_17906]) ).
cnf(c_17907,plain,
( leq(multiplication(A,one),B)
| ~ leq(addition(A,B),B) ),
inference(paramod,[status(thm)],[c_5790,c_864]) ).
cnf(c_5840,plain,
( leq(A,B)
| ~ leq(addition(A,B),B) ),
inference(paramod,[status(thm)],[c_25,c_17907]) ).
cnf(c_17908,plain,
~ leq(addition(addition(sK0,multiplication(star(sK2),multiplication(sK0,sK1))),multiplication(star(sK2),sK0)),multiplication(star(sK2),sK0)),
inference(resolve,[status(thm)],[c_5840,c_115]) ).
cnf(c_17909,plain,
~ leq(addition(multiplication(star(sK2),sK0),addition(sK0,multiplication(star(sK2),multiplication(sK0,sK1)))),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_20,c_17908]) ).
cnf(c_17910,plain,
~ leq(addition(sK0,addition(multiplication(star(sK2),sK0),multiplication(star(sK2),multiplication(sK0,sK1)))),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_48,c_17909]) ).
cnf(c_17911,plain,
~ leq(addition(sK0,multiplication(star(sK2),addition(sK0,multiplication(sK0,sK1)))),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_28,c_17910]) ).
cnf(c_5912,plain,
~ leq(addition(sK0,multiplication(star(sK2),multiplication(sK0,addition(one,sK1)))),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_54,c_17911]) ).
cnf(c_9888,plain,
leq(multiplication(sK0,sK1),addition(multiplication(sK2,sK0),A)),
inference(paramod,[status(thm)],[c_20,c_1839]) ).
cnf(c_17912,plain,
addition(A,multiplication(multiplication(star(B),A),addition(one,C))) = addition(multiplication(star(B),A),multiplication(multiplication(star(B),A),C)),
inference(paramod,[status(thm)],[c_54,c_277]) ).
cnf(c_17913,plain,
addition(A,multiplication(star(B),multiplication(A,addition(one,C)))) = addition(multiplication(star(B),A),multiplication(multiplication(star(B),A),C)),
inference(paramod,[status(thm)],[c_24,c_17912]) ).
cnf(c_17914,plain,
addition(A,multiplication(star(B),multiplication(A,addition(one,C)))) = addition(multiplication(star(B),A),multiplication(star(B),multiplication(A,C))),
inference(paramod,[status(thm)],[c_24,c_17913]) ).
cnf(c_15289,plain,
addition(A,multiplication(star(B),multiplication(A,addition(one,C)))) = multiplication(star(B),addition(A,multiplication(A,C))),
inference(paramod,[status(thm)],[c_28,c_17914]) ).
cnf(c_17915,plain,
~ leq(multiplication(star(sK2),addition(sK0,multiplication(sK0,sK1))),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_15289,c_5912]) ).
cnf(c_15326,plain,
~ leq(multiplication(star(sK2),multiplication(sK0,addition(one,sK1))),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_54,c_17915]) ).
cnf(c_17916,plain,
~ leq(addition(multiplication(sK0,addition(one,sK1)),multiplication(sK2,multiplication(star(sK2),sK0))),multiplication(star(sK2),sK0)),
inference(resolve,[status(thm)],[c_70,c_15326]) ).
cnf(c_17917,plain,
~ leq(addition(multiplication(sK0,one),addition(multiplication(sK0,sK1),multiplication(sK2,multiplication(star(sK2),sK0)))),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_53,c_17916]) ).
cnf(c_17918,plain,
~ leq(addition(sK0,addition(multiplication(sK0,sK1),multiplication(sK2,multiplication(star(sK2),sK0)))),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_25,c_17917]) ).
cnf(c_15330,plain,
~ leq(addition(multiplication(sK0,sK1),multiplication(star(sK2),sK0)),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_607,c_17918]) ).
cnf(c_17919,plain,
addition(multiplication(sK0,sK1),addition(multiplication(star(sK2),sK0),multiplication(star(sK2),sK0))) != multiplication(star(sK2),sK0),
inference(resolve,[status(thm)],[c_105,c_15330]) ).
cnf(c_15331,plain,
addition(multiplication(sK0,sK1),multiplication(star(sK2),sK0)) != multiplication(star(sK2),sK0),
inference(paramod,[status(thm)],[c_23,c_17919]) ).
cnf(c_15332,plain,
~ leq(multiplication(sK0,sK1),multiplication(star(sK2),sK0)),
inference(resolve,[status(thm)],[c_43,c_15331]) ).
cnf(c_16001,plain,
leq(multiplication(sK0,sK1),multiplication(addition(sK2,A),sK0)),
inference(paramod,[status(thm)],[c_30,c_9888]) ).
cnf(c_17887,plain,
leq(multiplication(sK0,sK1),multiplication(star(sK2),sK0)),
inference(paramod,[status(thm)],[c_683,c_16001]) ).
cnf(c_17888,plain,
$false,
inference(resolve,[status(thm)],[c_17887,c_15332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE159+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40 % Computer : n007.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Fri Sep 25 19:27:08 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.41 % Process 1680640 was started by sandbox on n007,
% 0.12/0.41 % Fri Sep 25 19:27:08 2026
% 0.12/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.42
% 0.12/0.42 % From the command line: assign(max_seconds, 300).
% 19.25/2.95
% 19.25/2.95 % given #500 (T,wt=8): 6018 leq(A,star(strong_iteration(strong_iteration(star(strong_iteration(A)))))). [para(858(a,1),5679(a,2))].
% 19.25/2.95
% 19.25/2.95 % SZS status Theorem for theBenchmark
% 19.25/2.95
% 19.25/2.95 % Proof 1 at 2.01 (+ 0.49) seconds.
% 19.25/2.95 % Length of proof is 73.
% 19.25/2.95 % Level of proof is 15.
% 19.25/2.95 % Maximum clause weight is 19.000.
% 19.25/2.95 % Given clauses 885.
% 19.25/2.95
% 19.25/2.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
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