%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE040+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 : 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 07:44:10 AM UTC 2026
% Result : Theorem 4.31s 1.01s
% Output : CNFRefutation 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 42 unt; 0 def)
% Number of atoms : 56 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 5 |; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 7 sgn 18 !; 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_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_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(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(goals,conjecture,
! [X0] : multiplication(star(X0),star(X0)) = star(X0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : multiplication(star(X0),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_23,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_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_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]) ).
fof(nnf_17,plain,
? [X0] : star(X0) != multiplication(star(X0),star(X0)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
star(sK0) != multiplication(star(sK0),star(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_37,negated_conjecture,
star(sK0) != multiplication(star(sK0),star(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_38,negated_conjecture,
multiplication(star(sK0),star(sK0)) != star(sK0),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_2679,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_40,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_19,c_2679]) ).
cnf(c_2680,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_42,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_2680]) ).
cnf(c_53,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_2681,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_33,c_31]) ).
cnf(c_59,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_18,c_2681]) ).
cnf(c_64,plain,
( leq(multiplication(star(B),A),C)
| ~ leq(addition(A,multiplication(B,C)),C) ),
inference(paramod,[status(thm)],[c_18,c_35]) ).
cnf(c_95,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_42,c_32]) ).
cnf(c_101,plain,
leq(A,addition(B,A)),
inference(paramod,[status(thm)],[c_18,c_95]) ).
cnf(c_105,plain,
leq(A,addition(B,addition(A,C))),
inference(paramod,[status(thm)],[c_40,c_95]) ).
cnf(c_106,plain,
leq(A,addition(B,addition(C,A))),
inference(paramod,[status(thm)],[c_19,c_101]) ).
cnf(c_735,plain,
leq(one,star(A)),
inference(paramod,[status(thm)],[c_59,c_105]) ).
cnf(c_737,plain,
leq(multiplication(A,star(A)),star(A)),
inference(paramod,[status(thm)],[c_59,c_106]) ).
cnf(c_740,plain,
addition(one,star(A)) = star(A),
inference(resolve,[status(thm)],[c_735,c_31]) ).
cnf(c_2682,plain,
addition(multiplication(A,star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_737,c_31]) ).
cnf(c_744,plain,
addition(star(A),multiplication(A,star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_2682]) ).
cnf(c_2683,plain,
addition(multiplication(A,one),multiplication(A,star(B))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_740,c_26]) ).
cnf(c_751,plain,
addition(A,multiplication(A,star(B))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_23,c_2683]) ).
cnf(c_2684,plain,
( leq(multiplication(star(A),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_744,c_64]) ).
cnf(c_2523,plain,
leq(multiplication(star(A),star(A)),star(A)),
inference(resolve,[status(thm)],[c_53,c_2684]) ).
cnf(c_2685,plain,
addition(multiplication(star(A),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2523,c_31]) ).
cnf(c_2686,plain,
addition(star(A),multiplication(star(A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_2685]) ).
cnf(c_2677,plain,
multiplication(star(A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_751,c_2686]) ).
cnf(c_2678,plain,
$false,
inference(resolve,[status(thm)],[c_2677,c_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE040+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n016.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 19:21:59 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 3084540 was started by sandbox2 on n016,
% 0.19/0.46 % Fri Sep 25 19:21:59 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 4.31/1.01
% 4.31/1.01 % Assigning unary symbol star kb_weight 0 and highest precedence (8).
% 4.31/1.01
% 4.31/1.01 % SZS status Theorem for theBenchmark
% 4.31/1.01
% 4.31/1.01 % Proof 1 at 0.40 (+ 0.14) seconds.
% 4.31/1.01 % Length of proof is 38.
% 4.31/1.01 % Level of proof is 10.
% 4.31/1.01 % Maximum clause weight is 42.000.
% 4.31/1.01 % Given clauses 326.
% 4.31/1.01
% 4.31/1.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------