%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE169+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 266.42s 40.74s
% Output : CNFRefutation 266.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 43 unt; 0 def)
% Number of atoms : 49 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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; 4 con; 0-2 aty)
% Number of variables : 86 ( 16 sgn 16 !; 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_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(a,conjecture,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
file('theBenchmark.p',a) ).
fof(a_neg,negated_conjecture,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,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_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]) ).
fof(an,axiom,
sigma = addition(a,b),
file('theBenchmark.p',an) ).
cnf(c_37,plain,
sigma = addition(a,b),
inference(clausify,[status(thm)],[an]) ).
cnf(c_38,negated_conjecture,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
inference(clausify,[status(thm)],[a_neg]) ).
cnf(c_10436,negated_conjecture,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(sigma,a)))),
inference(paramod,[status(thm)],[c_37,c_38]) ).
cnf(c_39,negated_conjecture,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))),
inference(paramod,[status(thm)],[c_37,c_10436]) ).
cnf(c_10437,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_41,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_19,c_10437]) ).
cnf(c_10438,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_43,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_10438]) ).
cnf(c_10439,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_52,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_10439]) ).
cnf(c_10440,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_33]) ).
cnf(c_10441,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_18,c_10440]) ).
cnf(c_10442,plain,
addition(one,addition(star(A),multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_41,c_10441]) ).
cnf(c_55,plain,
addition(one,multiplication(addition(one,A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_52,c_10442]) ).
cnf(c_71,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_32,c_43]) ).
cnf(c_74,plain,
leq(A,addition(B,A)),
inference(paramod,[status(thm)],[c_18,c_71]) ).
cnf(c_78,plain,
leq(A,addition(B,addition(C,A))),
inference(paramod,[status(thm)],[c_19,c_74]) ).
cnf(c_82,plain,
leq(A,addition(B,addition(A,C))),
inference(paramod,[status(thm)],[c_18,c_78]) ).
cnf(c_298,plain,
leq(A,addition(B,multiplication(addition(one,C),A))),
inference(paramod,[status(thm)],[c_52,c_82]) ).
cnf(c_1137,plain,
leq(A,multiplication(addition(one,B),addition(C,A))),
inference(paramod,[status(thm)],[c_26,c_298]) ).
cnf(c_1897,plain,
leq(A,multiplication(star(B),addition(C,A))),
inference(paramod,[status(thm)],[c_55,c_1137]) ).
cnf(c_1973,plain,
leq(multiplication(A,B),multiplication(star(C),multiplication(A,addition(D,B)))),
inference(paramod,[status(thm)],[c_26,c_1897]) ).
cnf(c_10434,plain,
leq(multiplication(A,multiplication(B,C)),multiplication(star(D),multiplication(A,multiplication(addition(E,B),C)))),
inference(paramod,[status(thm)],[c_28,c_1973]) ).
cnf(c_10435,plain,
$false,
inference(resolve,[status(thm)],[c_10434,c_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE169+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n018.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 19:32:56 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 2666057 was started by sandbox2 on n018,
% 0.10/5.38 % Fri Sep 25 19:32:56 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 266.42/40.74
% 266.42/40.74 % given #500 (W,wt=25): 2935 leq(addition(A,one),multiplication(star(A),addition(one,B))). [para(47(a,2),2920(a,2))].
% 266.42/40.74
% 266.42/40.74 % given #1000 (T,wt=30): 6506 leq(multiplication(A,A),star(multiplication(star(B),star(A)))). [para(1879(a,1),3353(a,2,1))].
% 266.42/40.74
% 266.42/40.74 % SZS status Theorem for theBenchmark
% 266.42/40.74
% 266.42/40.74 % Proof 1 at 2.14 (+ 0.94) seconds.
% 266.42/40.74 % Length of proof is 37.
% 266.42/40.74 % Level of proof is 12.
% 266.42/40.74 % Maximum clause weight is 43.000.
% 266.42/40.74 % Given clauses 1440.
% 266.42/40.74
% 266.42/40.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------