%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE044+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 : n001.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 07:44:11 AM UTC 2026
% Result : Theorem 25.11s 3.69s
% Output : CNFRefutation 25.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 103 ( 82 unt; 0 def)
% Number of atoms : 124 ( 62 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 43 ( 22 ~; 18 |; 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 : 173 ( 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(addition(one,X0)) = star(X0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : star(addition(one,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(addition(one,X0)) != star(X0),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
star(addition(one,sK0)) != star(sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_37,negated_conjecture,
star(addition(one,sK0)) != star(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_8790,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_8790]) ).
cnf(c_8791,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_8791]) ).
cnf(c_8792,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_8792]) ).
cnf(c_8793,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_8793]) ).
cnf(c_52,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_8794,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_8794]) ).
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_65,plain,
( leq(multiplication(star(A),multiplication(A,B)),B)
| ~ leq(multiplication(A,B),B) ),
inference(paramod,[status(thm)],[c_21,c_35]) ).
cnf(c_69,plain,
( leq(multiplication(star(A),multiplication(A,C)),B)
| ~ leq(multiplication(A,addition(B,C)),B) ),
inference(paramod,[status(thm)],[c_26,c_35]) ).
cnf(c_73,plain,
( leq(multiplication(A,star(C)),B)
| ~ leq(addition(A,multiplication(B,C)),B) ),
inference(paramod,[status(thm)],[c_18,c_36]) ).
cnf(c_8795,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_8795]) ).
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_689,plain,
( leq(multiplication(A,star(B)),A)
| ~ leq(multiplication(A,addition(one,B)),A) ),
inference(paramod,[status(thm)],[c_45,c_73]) ).
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_8796,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_8796]) ).
cnf(c_8797,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_8797]) ).
cnf(c_8798,plain,
addition(multiplication(A,one),multiplication(A,star(B))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_739,c_26]) ).
cnf(c_750,plain,
addition(A,multiplication(A,star(B))) = multiplication(A,star(B)),
inference(paramod,[status(thm)],[c_23,c_8798]) ).
cnf(c_8799,plain,
addition(multiplication(one,A),multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_739,c_28]) ).
cnf(c_751,plain,
addition(A,multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_24,c_8799]) ).
cnf(c_8800,plain,
( leq(multiplication(star(A),multiplication(A,one)),star(B))
| ~ leq(multiplication(A,star(B)),star(B)) ),
inference(paramod,[status(thm)],[c_748,c_69]) ).
cnf(c_892,plain,
( leq(multiplication(star(A),A),star(B))
| ~ leq(multiplication(A,star(B)),star(B)) ),
inference(paramod,[status(thm)],[c_23,c_8800]) ).
cnf(c_8801,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_8801]) ).
cnf(c_1906,plain,
leq(A,addition(B,multiplication(A,star(C)))),
inference(paramod,[status(thm)],[c_739,c_592]) ).
cnf(c_2288,plain,
leq(multiplication(star(A),A),star(A)),
inference(resolve,[status(thm)],[c_892,c_736]) ).
cnf(c_2293,plain,
leq(multiplication(star(addition(one,A)),star(A)),star(addition(one,A))),
inference(resolve,[status(thm)],[c_2288,c_689]) ).
cnf(c_2512,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_743,c_50]) ).
cnf(c_8802,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_8802]) ).
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_8803,plain,
addition(multiplication(star(A),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2522,c_31]) ).
cnf(c_8804,plain,
addition(star(A),multiplication(star(A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_8803]) ).
cnf(c_2676,plain,
multiplication(star(A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_750,c_8804]) ).
cnf(c_2892,plain,
multiplication(star(A),star(star(A))) = star(star(A)),
inference(paramod,[status(thm)],[c_739,c_2512]) ).
cnf(c_8805,plain,
( leq(multiplication(star(addition(one,A)),multiplication(addition(one,A),star(A))),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_2512,c_65]) ).
cnf(c_8806,plain,
( leq(multiplication(star(addition(one,A)),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_2512,c_8805]) ).
cnf(c_2894,plain,
leq(multiplication(star(addition(one,A)),star(A)),star(A)),
inference(resolve,[status(thm)],[c_52,c_8806]) ).
cnf(c_2926,plain,
leq(star(star(A)),star(A)),
inference(paramod,[status(thm)],[c_2892,c_2672]) ).
cnf(c_8807,plain,
addition(star(star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2926,c_31]) ).
cnf(c_8808,plain,
addition(star(A),star(star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_8807]) ).
cnf(c_3649,plain,
star(star(A)) = star(A),
inference(paramod,[status(thm)],[c_2553,c_8808]) ).
cnf(c_8809,plain,
leq(multiplication(star(star(addition(one,A))),star(addition(one,A))),star(A)),
inference(resolve,[status(thm)],[c_2894,c_892]) ).
cnf(c_8810,plain,
leq(multiplication(star(addition(one,A)),star(addition(one,A))),star(A)),
inference(paramod,[status(thm)],[c_3649,c_8809]) ).
cnf(c_8477,plain,
leq(star(addition(one,A)),star(A)),
inference(paramod,[status(thm)],[c_2676,c_8810]) ).
cnf(c_8811,plain,
addition(multiplication(star(addition(one,A)),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2894,c_31]) ).
cnf(c_8812,plain,
addition(star(A),multiplication(star(addition(one,A)),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_8811]) ).
cnf(c_8478,plain,
multiplication(star(addition(one,A)),star(A)) = star(A),
inference(paramod,[status(thm)],[c_751,c_8812]) ).
cnf(c_8484,plain,
leq(star(A),star(addition(one,A))),
inference(paramod,[status(thm)],[c_8478,c_2293]) ).
cnf(c_8813,plain,
addition(star(addition(one,A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_8477,c_31]) ).
cnf(c_8485,plain,
addition(star(A),star(addition(one,A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_8813]) ).
cnf(c_8814,plain,
addition(star(A),star(addition(one,A))) = star(addition(one,A)),
inference(resolve,[status(thm)],[c_8484,c_31]) ).
cnf(c_8815,plain,
star(A) = star(addition(one,A)),
inference(paramod,[status(thm)],[c_8485,c_8814]) ).
cnf(c_8788,plain,
star(addition(one,A)) = star(A),
inference(copy,[status(thm)],[c_8815]) ).
cnf(c_8789,plain,
$false,
inference(resolve,[status(thm)],[c_8788,c_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE044+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n001.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 19:22:55 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 4020478 was started by sandbox on n001,
% 0.16/0.42 % Fri Sep 25 19:22:55 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 25.11/3.69
% 25.11/3.69 % Assigning unary symbol star kb_weight 0 and highest precedence (8).
% 25.11/3.69
% 25.11/3.69 % given #500 (W,wt=29): 6023 leq(one,multiplication(addition(star(A),B),star(C))). [para(28(a,1),6003(a,2))].
% 25.11/3.69
% 25.11/3.69 % SZS status Theorem for theBenchmark
% 25.11/3.69
% 25.11/3.69 % Proof 1 at 2.51 (+ 0.71) seconds.
% 25.11/3.69 % Length of proof is 74.
% 25.11/3.69 % Level of proof is 15.
% 25.11/3.69 % Maximum clause weight is 42.000.
% 25.11/3.69 % Given clauses 538.
% 25.11/3.69
% 25.11/3.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------