%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE039+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 07:44:10 AM UTC 2026
% Result : Theorem 9.77s 1.79s
% Output : CNFRefutation 9.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 73 ( 60 unt; 0 def)
% Number of atoms : 86 ( 47 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 14 ~; 10 |; 0 &)
% ( 1 <=>; 2 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 131 ( 11 sgn 28 !; 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_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(star_induction_right,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('theBenchmark.p',star_induction_right) ).
fof(goals,conjecture,
! [X0] : star(star(X0)) = star(X0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : star(star(X0)) = star(X0),
inference(assume_negation,[status(cth)],[goals]) ).
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_36,plain,
( leq(multiplication(C,star(B)),A)
| ~ leq(addition(multiplication(A,B),C),A) ),
inference(clausify,[status(thm)],[star_induction_right]) ).
fof(nnf_17,plain,
? [X0] : star(star(X0)) != star(X0),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
star(star(sK0)) != star(sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_37,negated_conjecture,
star(star(sK0)) != star(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_3651,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_3651]) ).
cnf(c_3652,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_3652]) ).
cnf(c_3653,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_3653]) ).
cnf(c_3654,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_3654]) ).
cnf(c_52,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_3655,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_33,c_31]) ).
cnf(c_58,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_18,c_3655]) ).
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_3656,plain,
( leq(multiplication(multiplication(B,C),star(C)),A)
| ~ leq(multiplication(addition(A,B),C),A) ),
inference(paramod,[status(thm)],[c_28,c_36]) ).
cnf(c_80,plain,
( leq(multiplication(B,multiplication(C,star(C))),A)
| ~ leq(multiplication(addition(A,B),C),A) ),
inference(paramod,[status(thm)],[c_22,c_3656]) ).
cnf(c_94,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_41,c_32]) ).
cnf(c_100,plain,
leq(A,addition(B,A)),
inference(paramod,[status(thm)],[c_18,c_94]) ).
cnf(c_104,plain,
leq(A,addition(B,addition(A,C))),
inference(paramod,[status(thm)],[c_39,c_94]) ).
cnf(c_105,plain,
leq(A,addition(B,addition(C,A))),
inference(paramod,[status(thm)],[c_19,c_100]) ).
cnf(c_592,plain,
leq(A,addition(B,multiplication(A,addition(one,C)))),
inference(paramod,[status(thm)],[c_45,c_104]) ).
cnf(c_734,plain,
leq(one,star(A)),
inference(paramod,[status(thm)],[c_58,c_104]) ).
cnf(c_736,plain,
leq(multiplication(A,star(A)),star(A)),
inference(paramod,[status(thm)],[c_58,c_105]) ).
cnf(c_739,plain,
addition(one,star(A)) = star(A),
inference(resolve,[status(thm)],[c_734,c_31]) ).
cnf(c_3657,plain,
addition(multiplication(A,star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_736,c_31]) ).
cnf(c_743,plain,
addition(star(A),multiplication(A,star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_3657]) ).
cnf(c_3658,plain,
star(A) = addition(star(A),one),
inference(paramod,[status(thm)],[c_739,c_18]) ).
cnf(c_748,plain,
addition(star(A),one) = star(A),
inference(copy,[status(thm)],[c_3658]) ).
cnf(c_3659,plain,
( leq(multiplication(one,multiplication(B,star(B))),star(A))
| ~ leq(multiplication(star(A),B),star(A)) ),
inference(paramod,[status(thm)],[c_748,c_80]) ).
cnf(c_1177,plain,
( leq(multiplication(B,star(B)),star(A))
| ~ leq(multiplication(star(A),B),star(A)) ),
inference(paramod,[status(thm)],[c_24,c_3659]) ).
cnf(c_1906,plain,
leq(A,addition(B,multiplication(A,star(C)))),
inference(paramod,[status(thm)],[c_739,c_592]) ).
cnf(c_2512,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_743,c_50]) ).
cnf(c_3660,plain,
( leq(multiplication(star(A),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_743,c_63]) ).
cnf(c_2522,plain,
leq(multiplication(star(A),star(A)),star(A)),
inference(resolve,[status(thm)],[c_52,c_3660]) ).
cnf(c_2544,plain,
leq(A,star(A)),
inference(paramod,[status(thm)],[c_743,c_1906]) ).
cnf(c_2553,plain,
addition(A,star(A)) = star(A),
inference(resolve,[status(thm)],[c_2544,c_31]) ).
cnf(c_2672,plain,
leq(multiplication(star(A),star(star(A))),star(A)),
inference(resolve,[status(thm)],[c_2522,c_1177]) ).
cnf(c_2892,plain,
multiplication(star(A),star(star(A))) = star(star(A)),
inference(paramod,[status(thm)],[c_739,c_2512]) ).
cnf(c_2926,plain,
leq(star(star(A)),star(A)),
inference(paramod,[status(thm)],[c_2892,c_2672]) ).
cnf(c_3661,plain,
addition(star(star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2926,c_31]) ).
cnf(c_3662,plain,
addition(star(A),star(star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_3661]) ).
cnf(c_3649,plain,
star(star(A)) = star(A),
inference(paramod,[status(thm)],[c_2553,c_3662]) ).
cnf(c_3650,plain,
$false,
inference(resolve,[status(thm)],[c_3649,c_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE039+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n014.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 19:16:32 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 859507 was started by sandbox2 on n014,
% 0.18/0.44 % Fri Sep 25 19:16:32 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 9.77/1.79
% 9.77/1.79 % Assigning unary symbol star kb_weight 0 and highest precedence (8).
% 9.77/1.79
% 9.77/1.79 % SZS status Theorem for theBenchmark
% 9.77/1.79
% 9.77/1.79 % Proof 1 at 0.97 (+ 0.35) seconds.
% 9.77/1.79 % Length of proof is 58.
% 9.77/1.79 % Level of proof is 12.
% 9.77/1.79 % Maximum clause weight is 42.000.
% 9.77/1.79 % Given clauses 394.
% 9.77/1.79
% 9.77/1.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------