%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE170+1.004 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 07:44:27 AM UTC 2026
% Result : Theorem 75.42s 11.04s
% Output : CNFRefutation 75.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 12
% Syntax : Number of formulae : 100 ( 92 unt; 0 def)
% Number of atoms : 108 ( 67 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 6 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 5 ( 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 : 173 ( 16 sgn 23 !; 0 ?)
% 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_induction_left,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('theBenchmark.p',star_induction_left) ).
fof(a,conjecture,
leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)),
file('theBenchmark.p',a) ).
fof(a_neg,negated_conjecture,
~ leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)),
inference(assume_negation,[status(cth)],[a]) ).
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_35,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(clausify,[status(thm)],[star_induction_left]) ).
cnf(c_37,negated_conjecture,
~ leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)),
inference(clausify,[status(thm)],[a_neg]) ).
cnf(c_5498,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_5498]) ).
cnf(c_5499,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_5499]) ).
cnf(c_5500,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_5500]) ).
cnf(c_44,plain,
addition(multiplication(A,addition(B,C)),D) = addition(multiplication(A,B),addition(multiplication(A,C),D)),
inference(paramod,[status(thm)],[c_26,c_19]) ).
cnf(c_5501,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_5501]) ).
cnf(c_5502,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_5502]) ).
cnf(c_52,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_5503,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_33,c_31]) ).
cnf(c_5504,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_18,c_5503]) ).
cnf(c_5505,plain,
addition(one,addition(star(A),multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_39,c_5504]) ).
cnf(c_58,plain,
addition(one,multiplication(addition(one,A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_50,c_5505]) ).
cnf(c_63,plain,
( leq(multiplication(star(B),A),C)
| ~ leq(addition(A,multiplication(B,C)),C) ),
inference(paramod,[status(thm)],[c_18,c_35]) ).
cnf(c_109,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_41,c_32]) ).
cnf(c_115,plain,
leq(A,addition(B,A)),
inference(paramod,[status(thm)],[c_18,c_109]) ).
cnf(c_117,plain,
leq(multiplication(A,B),multiplication(A,addition(B,C))),
inference(paramod,[status(thm)],[c_26,c_109]) ).
cnf(c_118,plain,
leq(multiplication(A,B),multiplication(addition(A,C),B)),
inference(paramod,[status(thm)],[c_28,c_109]) ).
cnf(c_119,plain,
leq(A,addition(B,addition(C,A))),
inference(paramod,[status(thm)],[c_19,c_115]) ).
cnf(c_143,plain,
leq(A,multiplication(addition(one,B),A)),
inference(paramod,[status(thm)],[c_24,c_118]) ).
cnf(c_145,plain,
addition(A,multiplication(addition(one,B),A)) = multiplication(addition(one,B),A),
inference(resolve,[status(thm)],[c_143,c_31]) ).
cnf(c_152,plain,
leq(multiplication(A,B),addition(C,multiplication(A,addition(D,B)))),
inference(paramod,[status(thm)],[c_26,c_119]) ).
cnf(c_5506,plain,
multiplication(A,addition(one,A)) = multiplication(addition(one,A),A),
inference(paramod,[status(thm)],[c_50,c_45]) ).
cnf(c_260,plain,
multiplication(addition(one,A),A) = multiplication(A,addition(one,A)),
inference(copy,[status(thm)],[c_5506]) ).
cnf(c_377,plain,
leq(multiplication(A,addition(one,A)),multiplication(addition(one,A),addition(A,B))),
inference(paramod,[status(thm)],[c_260,c_117]) ).
cnf(c_533,plain,
( leq(multiplication(star(A),B),B)
| ~ leq(multiplication(addition(one,A),B),B) ),
inference(paramod,[status(thm)],[c_50,c_63]) ).
cnf(c_5507,plain,
addition(one,star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_58,c_41]) ).
cnf(c_1567,plain,
addition(one,star(A)) = star(A),
inference(paramod,[status(thm)],[c_58,c_5507]) ).
cnf(c_5508,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_5509,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_5508]) ).
cnf(c_5510,plain,
multiplication(addition(one,A),star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_145,c_5509]) ).
cnf(c_1578,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_58,c_5510]) ).
cnf(c_5511,plain,
addition(A,star(B)) = addition(one,addition(A,multiplication(addition(one,B),star(B)))),
inference(paramod,[status(thm)],[c_58,c_39]) ).
cnf(c_5512,plain,
addition(A,star(B)) = addition(one,addition(A,star(B))),
inference(paramod,[status(thm)],[c_1578,c_5511]) ).
cnf(c_1613,plain,
addition(one,addition(A,star(B))) = addition(A,star(B)),
inference(copy,[status(thm)],[c_5512]) ).
cnf(c_5513,plain,
multiplication(addition(one,A),addition(one,star(A))) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_1578,c_45]) ).
cnf(c_5514,plain,
multiplication(addition(one,A),star(A)) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_1567,c_5513]) ).
cnf(c_5515,plain,
star(A) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_1578,c_5514]) ).
cnf(c_5516,plain,
star(A) = addition(one,addition(A,star(A))),
inference(paramod,[status(thm)],[c_19,c_5515]) ).
cnf(c_5517,plain,
star(A) = addition(A,star(A)),
inference(paramod,[status(thm)],[c_1613,c_5516]) ).
cnf(c_1696,plain,
addition(A,star(A)) = star(A),
inference(copy,[status(thm)],[c_5517]) ).
cnf(c_5518,plain,
( leq(multiplication(star(A),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_1578,c_533]) ).
cnf(c_1699,plain,
leq(multiplication(star(A),star(A)),star(A)),
inference(resolve,[status(thm)],[c_52,c_5518]) ).
cnf(c_5519,plain,
leq(multiplication(A,addition(one,A)),multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_1696,c_377]) ).
cnf(c_1737,plain,
leq(multiplication(A,addition(one,A)),star(A)),
inference(paramod,[status(thm)],[c_1578,c_5519]) ).
cnf(c_5520,plain,
addition(A,star(B)) = addition(B,addition(A,star(B))),
inference(paramod,[status(thm)],[c_1696,c_39]) ).
cnf(c_1752,plain,
addition(A,addition(B,star(A))) = addition(B,star(A)),
inference(copy,[status(thm)],[c_5520]) ).
cnf(c_5521,plain,
addition(multiplication(star(A),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_1699,c_31]) ).
cnf(c_5522,plain,
addition(star(A),multiplication(star(A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_5521]) ).
cnf(c_5523,plain,
multiplication(star(A),addition(one,star(A))) = star(A),
inference(paramod,[status(thm)],[c_45,c_5522]) ).
cnf(c_1767,plain,
multiplication(star(A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_1567,c_5523]) ).
cnf(c_5524,plain,
addition(multiplication(A,addition(one,A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_1737,c_31]) ).
cnf(c_5525,plain,
addition(multiplication(A,one),addition(multiplication(A,A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_44,c_5524]) ).
cnf(c_5526,plain,
addition(A,addition(multiplication(A,A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_23,c_5525]) ).
cnf(c_1801,plain,
addition(multiplication(A,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_1752,c_5526]) ).
cnf(c_1899,plain,
leq(multiplication(A,multiplication(B,B)),multiplication(A,star(B))),
inference(paramod,[status(thm)],[c_1801,c_117]) ).
cnf(c_5527,plain,
leq(multiplication(addition(one,star(A)),multiplication(A,A)),multiplication(star(A),addition(one,star(A)))),
inference(paramod,[status(thm)],[c_260,c_1899]) ).
cnf(c_5528,plain,
leq(multiplication(star(A),multiplication(A,A)),multiplication(star(A),addition(one,star(A)))),
inference(paramod,[status(thm)],[c_1567,c_5527]) ).
cnf(c_5529,plain,
leq(multiplication(star(A),multiplication(A,A)),multiplication(star(A),star(A))),
inference(paramod,[status(thm)],[c_1567,c_5528]) ).
cnf(c_2129,plain,
leq(multiplication(star(A),multiplication(A,A)),star(A)),
inference(paramod,[status(thm)],[c_1767,c_5529]) ).
cnf(c_5530,plain,
addition(multiplication(star(A),multiplication(A,A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2129,c_31]) ).
cnf(c_5531,plain,
addition(star(A),multiplication(star(A),multiplication(A,A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_5530]) ).
cnf(c_2132,plain,
multiplication(star(A),addition(one,multiplication(A,A))) = star(A),
inference(paramod,[status(thm)],[c_45,c_5531]) ).
cnf(c_3948,plain,
leq(multiplication(A,B),multiplication(addition(C,A),addition(D,B))),
inference(paramod,[status(thm)],[c_28,c_152]) ).
cnf(c_3977,plain,
leq(multiplication(A,B),multiplication(addition(A,C),addition(D,B))),
inference(paramod,[status(thm)],[c_18,c_3948]) ).
cnf(c_5532,plain,
leq(multiplication(multiplication(A,A),B),multiplication(star(A),addition(C,B))),
inference(paramod,[status(thm)],[c_1801,c_3977]) ).
cnf(c_4047,plain,
leq(multiplication(A,multiplication(A,B)),multiplication(star(A),addition(C,B))),
inference(paramod,[status(thm)],[c_22,c_5532]) ).
cnf(c_5496,plain,
leq(multiplication(A,multiplication(A,multiplication(A,A))),star(A)),
inference(paramod,[status(thm)],[c_2132,c_4047]) ).
cnf(c_5497,plain,
$false,
inference(resolve,[status(thm)],[c_5496,c_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE170+1.004 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n004.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Fri Sep 25 19:30:21 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 3887813 was started by sandbox on n004,
% 0.20/0.45 % Fri Sep 25 19:30:21 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.46
% 0.20/0.46 % From the command line: assign(max_seconds, 300).
% 75.42/11.04
% 75.42/11.04 % given #500 (W,wt=29): 2741 leq(addition(multiplication(A,A),addition(B,A)),addition(star(A),B)). [para(2567(a,1),1969(a,2)),rewrite([18(3)])].
% 75.42/11.04
% 75.42/11.04 % SZS status Theorem for theBenchmark
% 75.42/11.04
% 75.42/11.04 % Proof 1 at 1.70 (+ 0.79) seconds.
% 75.42/11.04 % Length of proof is 64.
% 75.42/11.04 % Level of proof is 16.
% 75.42/11.04 % Maximum clause weight is 39.000.
% 75.42/11.04 % Given clauses 887.
% 75.42/11.04
% 75.42/11.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------