%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE144+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 07:44:23 AM UTC 2026
% Result : Theorem 20.46s 8.41s
% Output : CNFRefutation 20.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 55 ( 49 unt; 0 def)
% Number of atoms : 61 ( 45 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 4 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 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 : 92 ( 17 sgn 24 !; 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_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
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(distributivity2,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',distributivity2) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(star_unfold1,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
file('theBenchmark.p',star_unfold1) ).
fof(infty_coinduction,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('theBenchmark.p',infty_coinduction) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,conjecture,
! [X0] : strong_iteration(star(X0)) = strong_iteration(one),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : strong_iteration(star(X0)) = strong_iteration(one),
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_22,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
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_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_31,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
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_40,plain,
( leq(A,multiplication(strong_iteration(B),C))
| ~ leq(A,addition(multiplication(B,A),C)) ),
inference(clausify,[status(thm)],[infty_coinduction]) ).
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] : strong_iteration(star(X0)) != strong_iteration(one),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
strong_iteration(star(sK0)) != strong_iteration(one),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_19]) ).
cnf(c_45,negated_conjecture,
strong_iteration(star(sK0)) != strong_iteration(one),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_9035,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_9035]) ).
cnf(c_9036,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_9036]) ).
cnf(c_9037,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_9038,plain,
addition(A,multiplication(multiplication(B,star(B)),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_26,c_9037]) ).
cnf(c_64,plain,
addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_24,c_9038]) ).
cnf(c_9039,plain,
addition(one,zero) = star(zero),
inference(paramod,[status(thm)],[c_31,c_33]) ).
cnf(c_9040,plain,
one = star(zero),
inference(paramod,[status(thm)],[c_22,c_9039]) ).
cnf(c_65,plain,
star(zero) = one,
inference(copy,[status(thm)],[c_9040]) ).
cnf(c_92,plain,
( leq(A,multiplication(strong_iteration(C),B))
| ~ leq(A,addition(B,multiplication(C,A))) ),
inference(paramod,[status(thm)],[c_20,c_40]) ).
cnf(c_123,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_44,c_49]) ).
cnf(c_139,plain,
leq(A,addition(B,addition(A,C))),
inference(paramod,[status(thm)],[c_47,c_123]) ).
cnf(c_607,plain,
leq(A,addition(B,multiplication(star(C),A))),
inference(paramod,[status(thm)],[c_64,c_139]) ).
cnf(c_1339,plain,
leq(A,multiplication(strong_iteration(star(B)),C)),
inference(resolve,[status(thm)],[c_92,c_607]) ).
cnf(c_1362,plain,
leq(A,strong_iteration(star(B))),
inference(paramod,[status(thm)],[c_25,c_1339]) ).
cnf(c_1364,plain,
addition(A,strong_iteration(star(B))) = strong_iteration(star(B)),
inference(resolve,[status(thm)],[c_43,c_1362]) ).
cnf(c_1365,plain,
leq(A,strong_iteration(one)),
inference(paramod,[status(thm)],[c_65,c_1362]) ).
cnf(c_1366,plain,
addition(A,strong_iteration(one)) = strong_iteration(one),
inference(resolve,[status(thm)],[c_43,c_1365]) ).
cnf(c_9041,plain,
strong_iteration(one) = addition(strong_iteration(one),A),
inference(paramod,[status(thm)],[c_1366,c_20]) ).
cnf(c_1385,plain,
addition(strong_iteration(one),A) = strong_iteration(one),
inference(copy,[status(thm)],[c_9041]) ).
cnf(c_9033,plain,
strong_iteration(star(A)) = strong_iteration(one),
inference(paramod,[status(thm)],[c_1364,c_1385]) ).
cnf(c_9034,plain,
$false,
inference(resolve,[status(thm)],[c_9033,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE144+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n007.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Fri Sep 25 19:24:29 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 1678730 was started by sandbox on n007,
% 0.11/5.39 % Fri Sep 25 19:24:29 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.40
% 0.11/5.40 % From the command line: assign(max_seconds, 300).
% 20.46/8.41
% 20.46/8.41 % given #500 (T,wt=8): 6740 leq(A,addition(strong_iteration(strong_iteration(strong_iteration(A))),B)). [para(100(a,1),6016(a,2))].
% 20.46/8.41
% 20.46/8.41 % SZS status Theorem for theBenchmark
% 20.46/8.41
% 20.46/8.41 % Proof 1 at 2.23 (+ 0.68) seconds.
% 20.46/8.41 % Length of proof is 45.
% 20.46/8.41 % Level of proof is 12.
% 20.46/8.41 % Maximum clause weight is 13.000.
% 20.46/8.41 % Given clauses 573.
% 20.46/8.41
% 20.46/8.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------