%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE147+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 : n019.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 07:44:24 AM UTC 2026
% Result : Theorem 92.85s 16.51s
% Output : CNFRefutation 92.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 53 unt; 0 def)
% Number of atoms : 71 ( 48 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 17 ~; 5 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 2 sgn 24 !; 2 ?)
% 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_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
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_induction1,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,C),B),C)
=> leq(multiplication(star(A),B),C) ),
file('theBenchmark.p',star_induction1) ).
fof(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('theBenchmark.p',infty_unfold1) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,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('theBenchmark.p',goals) ).
fof(goals_neg,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(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_26,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
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_36,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(clausify,[status(thm)],[star_induction1]) ).
cnf(c_38,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(clausify,[status(thm)],[infty_unfold1]) ).
cnf(c_21249,plain,
strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))),
inference(paramod,[status(thm)],[c_20,c_38]) ).
cnf(c_39,plain,
addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A),
inference(copy,[status(thm)],[c_21249]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_19,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(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,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)],[nnf_19]) ).
cnf(c_45,negated_conjecture,
( ~ 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(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_21250,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_20,c_21]) ).
cnf(c_47,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_21,c_21250]) ).
cnf(c_21251,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_49,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_21251]) ).
cnf(c_21252,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_26,c_30]) ).
cnf(c_58,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_21252]) ).
cnf(c_21253,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_21254,plain,
addition(A,multiplication(multiplication(B,star(B)),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_26,c_21253]) ).
cnf(c_64,plain,
addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_24,c_21254]) ).
cnf(c_70,plain,
addition(one,multiplication(A,multiplication(B,strong_iteration(multiplication(A,B))))) = strong_iteration(multiplication(A,B)),
inference(paramod,[status(thm)],[c_24,c_39]) ).
cnf(c_85,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_49,c_44]) ).
cnf(c_21255,plain,
addition(one,star(A)) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_33,c_49]) ).
cnf(c_88,plain,
addition(one,star(A)) = star(A),
inference(paramod,[status(thm)],[c_33,c_21255]) ).
cnf(c_21256,plain,
addition(multiplication(one,A),multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_88,c_30]) ).
cnf(c_182,plain,
addition(A,multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_26,c_21256]) ).
cnf(c_222,plain,
addition(A,multiplication(addition(one,B),A)) = addition(A,multiplication(B,A)),
inference(paramod,[status(thm)],[c_58,c_49]) ).
cnf(c_329,plain,
leq(A,multiplication(star(B),A)),
inference(paramod,[status(thm)],[c_64,c_85]) ).
cnf(c_337,negated_conjecture,
~ leq(multiplication(star(sK1),strong_iteration(multiplication(star(sK0),sK1))),strong_iteration(multiplication(star(sK0),sK1))),
inference(resolve,[status(thm)],[c_329,c_45]) ).
cnf(c_21257,plain,
addition(A,strong_iteration(multiplication(B,C))) = addition(one,addition(A,multiplication(B,multiplication(C,strong_iteration(multiplication(B,C)))))),
inference(paramod,[status(thm)],[c_70,c_47]) ).
cnf(c_362,plain,
addition(one,addition(A,multiplication(B,multiplication(C,strong_iteration(multiplication(B,C)))))) = addition(A,strong_iteration(multiplication(B,C))),
inference(copy,[status(thm)],[c_21257]) ).
cnf(c_21258,negated_conjecture,
~ leq(addition(multiplication(sK1,strong_iteration(multiplication(star(sK0),sK1))),strong_iteration(multiplication(star(sK0),sK1))),strong_iteration(multiplication(star(sK0),sK1))),
inference(resolve,[status(thm)],[c_36,c_337]) ).
cnf(c_21259,negated_conjecture,
~ leq(addition(strong_iteration(multiplication(star(sK0),sK1)),multiplication(sK1,strong_iteration(multiplication(star(sK0),sK1)))),strong_iteration(multiplication(star(sK0),sK1))),
inference(paramod,[status(thm)],[c_20,c_21258]) ).
cnf(c_377,negated_conjecture,
~ leq(multiplication(addition(one,sK1),strong_iteration(multiplication(star(sK0),sK1))),strong_iteration(multiplication(star(sK0),sK1))),
inference(paramod,[status(thm)],[c_58,c_21259]) ).
cnf(c_21260,plain,
addition(multiplication(addition(one,sK1),strong_iteration(multiplication(star(sK0),sK1))),strong_iteration(multiplication(star(sK0),sK1))) != strong_iteration(multiplication(star(sK0),sK1)),
inference(resolve,[status(thm)],[c_44,c_377]) ).
cnf(c_21261,plain,
addition(strong_iteration(multiplication(star(sK0),sK1)),multiplication(addition(one,sK1),strong_iteration(multiplication(star(sK0),sK1)))) != strong_iteration(multiplication(star(sK0),sK1)),
inference(paramod,[status(thm)],[c_20,c_21260]) ).
cnf(c_21262,plain,
addition(strong_iteration(multiplication(star(sK0),sK1)),multiplication(sK1,strong_iteration(multiplication(star(sK0),sK1)))) != strong_iteration(multiplication(star(sK0),sK1)),
inference(paramod,[status(thm)],[c_222,c_21261]) ).
cnf(c_378,plain,
multiplication(addition(one,sK1),strong_iteration(multiplication(star(sK0),sK1))) != strong_iteration(multiplication(star(sK0),sK1)),
inference(paramod,[status(thm)],[c_58,c_21262]) ).
cnf(c_21263,plain,
addition(one,multiplication(star(A),multiplication(B,strong_iteration(multiplication(star(A),B))))) = addition(multiplication(B,strong_iteration(multiplication(star(A),B))),strong_iteration(multiplication(star(A),B))),
inference(paramod,[status(thm)],[c_182,c_362]) ).
cnf(c_21264,plain,
strong_iteration(multiplication(star(A),B)) = addition(multiplication(B,strong_iteration(multiplication(star(A),B))),strong_iteration(multiplication(star(A),B))),
inference(paramod,[status(thm)],[c_70,c_21263]) ).
cnf(c_21265,plain,
strong_iteration(multiplication(star(A),B)) = addition(strong_iteration(multiplication(star(A),B)),multiplication(B,strong_iteration(multiplication(star(A),B)))),
inference(paramod,[status(thm)],[c_20,c_21264]) ).
cnf(c_21266,plain,
strong_iteration(multiplication(star(A),B)) = multiplication(addition(one,B),strong_iteration(multiplication(star(A),B))),
inference(paramod,[status(thm)],[c_58,c_21265]) ).
cnf(c_21247,plain,
multiplication(addition(one,A),strong_iteration(multiplication(star(B),A))) = strong_iteration(multiplication(star(B),A)),
inference(copy,[status(thm)],[c_21266]) ).
cnf(c_21248,plain,
$false,
inference(resolve,[status(thm)],[c_21247,c_378]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE147+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.43 % Computer : n019.cluster.edu
% 0.07/0.43 % Model : x86_64 x86_64
% 0.07/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.43 % Memory : 8046.5625MB
% 0.07/0.43 % OS : Linux 6.8.0-71-generic
% 0.07/0.43 % CPULimit : 300
% 0.07/0.43 % WCLimit : 300
% 0.07/0.43 % DateTime : Fri Sep 25 19:27:19 UTC 2026
% 0.07/0.43 % CPUTime :
% 0.07/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.43 % Process 3470177 was started by sandbox on n019,
% 0.07/0.43 % Fri Sep 25 19:27:19 2026
% 0.07/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.44
% 0.07/0.44 % From the command line: assign(max_seconds, 300).
% 92.85/16.51
% 92.85/16.51 % given #500 (T,wt=16): 18811 leq(multiplication(addition(A,one),addition(one,A)),star(A)). [para(870(a,1),16435(a,2))].
% 92.85/16.51
% 92.85/16.51 % SZS status Theorem for theBenchmark
% 92.85/16.51
% 92.85/16.51 % Proof 1 at 6.39 (+ 1.59) seconds.
% 92.85/16.51 % Length of proof is 41.
% 92.85/16.51 % Level of proof is 8.
% 92.85/16.51 % Maximum clause weight is 38.000.
% 92.85/16.51 % Given clauses 554.
% 92.85/16.51
% 92.85/16.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------