%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE170+1.002 : 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 : n016.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 0.16s 10.53s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 66 unt; 0 def)
% Number of atoms : 76 ( 62 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 4 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 112 ( 0 sgn 17 !; 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_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(a,conjecture,
leq(multiplication(a,a),star(a)),
file('theBenchmark.p',a) ).
fof(a_neg,negated_conjecture,
~ leq(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_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_37,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(clausify,[status(thm)],[a_neg]) ).
cnf(c_607,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_607]) ).
cnf(c_608,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_608]) ).
cnf(c_609,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_609]) ).
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_610,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_610]) ).
cnf(c_611,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_611]) ).
cnf(c_56,plain,
( multiplication(A,addition(B,C)) != multiplication(A,C)
| leq(multiplication(A,B),multiplication(A,C)) ),
inference(paramod,[status(thm)],[c_26,c_32]) ).
cnf(c_612,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_33]) ).
cnf(c_613,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_18,c_612]) ).
cnf(c_614,plain,
addition(one,addition(star(A),multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_39,c_613]) ).
cnf(c_58,plain,
addition(one,multiplication(addition(one,A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_50,c_614]) ).
cnf(c_83,negated_conjecture,
addition(multiplication(a,a),star(a)) != star(a),
inference(resolve,[status(thm)],[c_32,c_37]) ).
cnf(c_231,plain,
addition(A,multiplication(addition(one,B),A)) = addition(A,multiplication(B,A)),
inference(paramod,[status(thm)],[c_50,c_41]) ).
cnf(c_615,plain,
multiplication(A,addition(one,A)) = multiplication(addition(one,A),A),
inference(paramod,[status(thm)],[c_50,c_45]) ).
cnf(c_234,plain,
multiplication(addition(one,A),A) = multiplication(A,addition(one,A)),
inference(copy,[status(thm)],[c_615]) ).
cnf(c_616,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_308,plain,
addition(one,addition(A,multiplication(addition(one,B),star(B)))) = addition(A,star(B)),
inference(copy,[status(thm)],[c_616]) ).
cnf(c_617,plain,
addition(one,star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_58,c_41]) ).
cnf(c_311,plain,
addition(one,star(A)) = star(A),
inference(paramod,[status(thm)],[c_58,c_617]) ).
cnf(c_618,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_619,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_618]) ).
cnf(c_620,plain,
addition(star(A),multiplication(A,star(A))) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_231,c_619]) ).
cnf(c_621,plain,
multiplication(addition(one,A),star(A)) = addition(one,multiplication(addition(one,A),star(A))),
inference(paramod,[status(thm)],[c_50,c_620]) ).
cnf(c_313,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_58,c_621]) ).
cnf(c_327,plain,
addition(one,addition(A,star(B))) = addition(A,star(B)),
inference(paramod,[status(thm)],[c_313,c_308]) ).
cnf(c_622,plain,
multiplication(addition(one,A),addition(one,star(A))) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_313,c_45]) ).
cnf(c_623,plain,
multiplication(addition(one,A),star(A)) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_311,c_622]) ).
cnf(c_624,plain,
star(A) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_313,c_623]) ).
cnf(c_625,plain,
star(A) = addition(one,addition(A,star(A))),
inference(paramod,[status(thm)],[c_19,c_624]) ).
cnf(c_626,plain,
star(A) = addition(A,star(A)),
inference(paramod,[status(thm)],[c_327,c_625]) ).
cnf(c_473,plain,
addition(A,star(A)) = star(A),
inference(copy,[status(thm)],[c_626]) ).
cnf(c_627,plain,
addition(A,star(B)) = addition(B,addition(A,star(B))),
inference(paramod,[status(thm)],[c_473,c_39]) ).
cnf(c_519,plain,
addition(A,addition(B,star(A))) = addition(B,star(A)),
inference(copy,[status(thm)],[c_627]) ).
cnf(c_628,plain,
( multiplication(A,star(B)) != multiplication(A,star(B))
| leq(multiplication(A,B),multiplication(A,star(B))) ),
inference(paramod,[status(thm)],[c_473,c_56]) ).
cnf(c_524,plain,
leq(multiplication(A,B),multiplication(A,star(B))),
inference(copy,[status(thm)],[c_628]) ).
cnf(c_629,plain,
leq(multiplication(addition(one,A),A),star(A)),
inference(paramod,[status(thm)],[c_313,c_524]) ).
cnf(c_554,plain,
leq(multiplication(A,addition(one,A)),star(A)),
inference(paramod,[status(thm)],[c_234,c_629]) ).
cnf(c_630,plain,
addition(multiplication(A,addition(one,A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_31,c_554]) ).
cnf(c_631,plain,
addition(multiplication(A,one),addition(multiplication(A,A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_44,c_630]) ).
cnf(c_632,plain,
addition(A,addition(multiplication(A,A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_23,c_631]) ).
cnf(c_605,plain,
addition(multiplication(A,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_519,c_632]) ).
cnf(c_606,plain,
$false,
inference(resolve,[status(thm)],[c_605,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE170+1.002 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.39 % Computer : n016.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Fri Sep 25 19:35:41 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/10.39 % Process 3114447 was started by sandbox2 on n016,
% 0.12/10.39 % Fri Sep 25 19:35:41 2026
% 0.12/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/10.40
% 0.16/10.40 % From the command line: assign(max_seconds, 300).
% 0.16/10.53
% 0.16/10.53 % SZS status Theorem for theBenchmark
% 0.16/10.53
% 0.16/10.53 % Proof 1 at 0.07 (+ 0.04) seconds.
% 0.16/10.53 % Length of proof is 44.
% 0.16/10.53 % Level of proof is 11.
% 0.16/10.53 % Maximum clause weight is 27.000.
% 0.16/10.53 % Given clauses 127.
% 0.16/10.53
% 0.16/10.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------