%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE039+2 : 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 : 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 : Sun Sep 27 07:44:10 AM UTC 2026
% Result : Theorem 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 93 ( 77 unt; 0 def)
% Number of atoms : 109 ( 58 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 33 ( 17 ~; 12 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 152 ( 15 sgn 26 !; 1 ?)
% 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(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_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(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',right_distributivity) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_distributivity) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(star_unfold_right,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('theBenchmark.p',star_unfold_right) ).
fof(star_unfold_left,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('theBenchmark.p',star_unfold_left) ).
fof(star_induction_right,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('theBenchmark.p',star_induction_right) ).
fof(goals,conjecture,
! [X0] :
( leq(star(X0),star(star(X0)))
& leq(star(star(X0)),star(X0)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( leq(star(X0),star(star(X0)))
& leq(star(star(X0)),star(X0)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_18,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_19,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_21,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_22,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_23,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_24,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_25,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_26,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_28,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_31,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_32,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_33,plain,
leq(addition(one,multiplication(A,star(A))),star(A)),
inference(clausify,[status(thm)],[star_unfold_right]) ).
cnf(c_34,plain,
leq(addition(one,multiplication(star(A),A)),star(A)),
inference(clausify,[status(thm)],[star_unfold_left]) ).
cnf(c_36,plain,
( leq(multiplication(C,star(B)),A)
| ~ leq(addition(multiplication(A,B),C),A) ),
inference(clausify,[status(thm)],[star_induction_right]) ).
fof(nnf_17,plain,
? [X0] :
( ~ leq(star(X0),star(star(X0)))
| ~ leq(star(star(X0)),star(X0)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(star(sK0),star(star(sK0)))
| ~ leq(star(star(sK0)),star(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_37,negated_conjecture,
( ~ leq(star(sK0),star(star(sK0)))
| ~ leq(star(star(sK0)),star(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_766,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_39,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_19,c_766]) ).
cnf(c_767,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_41,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_767]) ).
cnf(c_768,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_43,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_18,c_768]) ).
cnf(c_769,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_23,c_26]) ).
cnf(c_45,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_769]) ).
cnf(c_770,plain,
addition(multiplication(A,B),A) = multiplication(A,addition(B,one)),
inference(paramod,[status(thm)],[c_23,c_26]) ).
cnf(c_771,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)),
inference(paramod,[status(thm)],[c_18,c_770]) ).
cnf(c_46,plain,
multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_771]) ).
cnf(c_772,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_50,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_772]) ).
cnf(c_52,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_773,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_33]) ).
cnf(c_774,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_18,c_773]) ).
cnf(c_775,plain,
addition(one,addition(star(A),multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_39,c_774]) ).
cnf(c_58,plain,
addition(one,multiplication(addition(one,A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_50,c_775]) ).
cnf(c_776,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_34]) ).
cnf(c_777,plain,
addition(star(A),addition(one,multiplication(star(A),A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_776]) ).
cnf(c_778,plain,
addition(one,addition(star(A),multiplication(star(A),A))) = star(A),
inference(paramod,[status(thm)],[c_39,c_777]) ).
cnf(c_62,plain,
addition(one,multiplication(star(A),addition(one,A))) = star(A),
inference(paramod,[status(thm)],[c_45,c_778]) ).
cnf(c_779,plain,
( leq(multiplication(multiplication(A,B),star(B)),A)
| ~ leq(multiplication(A,B),A) ),
inference(paramod,[status(thm)],[c_21,c_36]) ).
cnf(c_75,plain,
( leq(multiplication(A,multiplication(B,star(B))),A)
| ~ leq(multiplication(A,B),A) ),
inference(paramod,[status(thm)],[c_22,c_779]) ).
cnf(c_780,plain,
( leq(multiplication(multiplication(A,C),star(B)),A)
| ~ leq(multiplication(A,addition(B,C)),A) ),
inference(paramod,[status(thm)],[c_26,c_36]) ).
cnf(c_79,plain,
( leq(multiplication(A,multiplication(C,star(B))),A)
| ~ leq(multiplication(A,addition(B,C)),A) ),
inference(paramod,[status(thm)],[c_22,c_780]) ).
cnf(c_94,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_32,c_41]) ).
cnf(c_107,plain,
leq(A,addition(B,addition(A,C))),
inference(paramod,[status(thm)],[c_39,c_94]) ).
cnf(c_137,plain,
leq(A,multiplication(A,addition(one,B))),
inference(paramod,[status(thm)],[c_45,c_94]) ).
cnf(c_230,plain,
addition(A,multiplication(addition(one,B),A)) = addition(A,multiplication(B,A)),
inference(paramod,[status(thm)],[c_50,c_41]) ).
cnf(c_781,plain,
addition(one,star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_58,c_41]) ).
cnf(c_310,plain,
addition(one,star(A)) = star(A),
inference(paramod,[status(thm)],[c_58,c_781]) ).
cnf(c_782,plain,
addition(multiplication(addition(one,A),star(A)),star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_58,c_43]) ).
cnf(c_783,plain,
addition(star(A),multiplication(addition(one,A),star(A))) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_18,c_782]) ).
cnf(c_784,plain,
addition(star(A),multiplication(A,star(A))) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_230,c_783]) ).
cnf(c_785,plain,
multiplication(addition(one,A),star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_50,c_784]) ).
cnf(c_312,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_58,c_785]) ).
cnf(c_318,plain,
leq(A,multiplication(A,star(B))),
inference(paramod,[status(thm)],[c_58,c_137]) ).
cnf(c_786,plain,
addition(one,multiplication(star(A),star(multiplication(addition(one,A),star(A))))) = star(multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_58,c_58]) ).
cnf(c_787,plain,
addition(one,multiplication(star(A),star(star(A)))) = star(multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_312,c_786]) ).
cnf(c_325,plain,
addition(one,multiplication(star(A),star(star(A)))) = star(star(A)),
inference(paramod,[status(thm)],[c_312,c_787]) ).
cnf(c_331,plain,
addition(one,multiplication(star(A),addition(A,one))) = star(A),
inference(paramod,[status(thm)],[c_18,c_62]) ).
cnf(c_432,plain,
leq(one,addition(A,star(B))),
inference(paramod,[status(thm)],[c_310,c_107]) ).
cnf(c_433,plain,
leq(one,addition(star(A),B)),
inference(paramod,[status(thm)],[c_18,c_432]) ).
cnf(c_436,plain,
leq(one,multiplication(star(A),addition(one,B))),
inference(paramod,[status(thm)],[c_45,c_433]) ).
cnf(c_437,plain,
leq(one,multiplication(star(A),addition(B,one))),
inference(paramod,[status(thm)],[c_46,c_433]) ).
cnf(c_442,plain,
leq(one,multiplication(star(A),star(B))),
inference(paramod,[status(thm)],[c_310,c_436]) ).
cnf(c_450,plain,
addition(one,multiplication(star(A),star(B))) = multiplication(star(A),star(B)),
inference(resolve,[status(thm)],[c_31,c_442]) ).
cnf(c_452,plain,
multiplication(star(A),star(star(A))) = star(star(A)),
inference(paramod,[status(thm)],[c_450,c_325]) ).
cnf(c_453,plain,
addition(one,multiplication(star(A),addition(B,one))) = multiplication(star(A),addition(B,one)),
inference(resolve,[status(thm)],[c_31,c_437]) ).
cnf(c_456,plain,
multiplication(star(A),addition(A,one)) = star(A),
inference(paramod,[status(thm)],[c_453,c_331]) ).
cnf(c_518,plain,
leq(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_312,c_318]) ).
cnf(c_532,plain,
leq(star(A),star(star(A))),
inference(paramod,[status(thm)],[c_310,c_518]) ).
cnf(c_533,negated_conjecture,
~ leq(star(star(sK0)),star(sK0)),
inference(resolve,[status(thm)],[c_532,c_37]) ).
cnf(c_788,plain,
( leq(multiplication(star(A),multiplication(one,star(A))),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_456,c_79]) ).
cnf(c_789,plain,
( leq(multiplication(star(A),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_24,c_788]) ).
cnf(c_761,plain,
leq(multiplication(star(A),star(A)),star(A)),
inference(resolve,[status(thm)],[c_52,c_789]) ).
cnf(c_790,plain,
leq(multiplication(star(A),multiplication(star(A),star(star(A)))),star(A)),
inference(resolve,[status(thm)],[c_75,c_761]) ).
cnf(c_791,plain,
leq(multiplication(star(A),star(star(A))),star(A)),
inference(paramod,[status(thm)],[c_452,c_790]) ).
cnf(c_764,plain,
leq(star(star(A)),star(A)),
inference(paramod,[status(thm)],[c_452,c_791]) ).
cnf(c_765,plain,
$false,
inference(resolve,[status(thm)],[c_764,c_533]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE039+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % 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 19:17:02 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 861663 was started by sandbox on n014,
% 0.08/0.35 % Fri Sep 25 19:17:02 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.47
% 0.12/0.47 % SZS status Theorem for theBenchmark
% 0.12/0.47
% 0.12/0.47 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.12/0.47 % Length of proof is 64.
% 0.12/0.47 % Level of proof is 13.
% 0.12/0.47 % Maximum clause weight is 26.000.
% 0.12/0.47 % Given clauses 143.
% 0.12/0.47
% 0.12/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------