%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE044+2 : 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 : n006.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 22.37s 3.61s
% Output : CNFRefutation 22.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 99 ( 73 unt; 0 def)
% Number of atoms : 125 ( 52 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 52 ( 26 ~; 21 |; 2 &)
% ( 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 : 168 ( 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] :
( leq(star(X0),star(addition(one,X0)))
& leq(star(addition(one,X0)),star(X0)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( leq(star(X0),star(addition(one,X0)))
& leq(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] :
( ~ leq(star(X0),star(addition(one,X0)))
| ~ leq(star(addition(one,X0)),star(X0)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(star(sK0),star(addition(one,sK0)))
| ~ leq(star(addition(one,sK0)),star(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_37,negated_conjecture,
( ~ leq(star(sK0),star(addition(one,sK0)))
| ~ leq(star(addition(one,sK0)),star(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_8487,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_8487]) ).
cnf(c_8488,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_8488]) ).
cnf(c_8489,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_8489]) ).
cnf(c_8490,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_8490]) ).
cnf(c_52,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_8491,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_8491]) ).
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_8492,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_8492]) ).
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_8493,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_8493]) ).
cnf(c_8494,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_8494]) ).
cnf(c_8495,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_8495]) ).
cnf(c_8496,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_8496]) ).
cnf(c_8497,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_8497]) ).
cnf(c_8498,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_8498]) ).
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_8499,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_8499]) ).
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_8500,plain,
addition(multiplication(star(A),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2522,c_31]) ).
cnf(c_8501,plain,
addition(star(A),multiplication(star(A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_8500]) ).
cnf(c_2676,plain,
multiplication(star(A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_750,c_8501]) ).
cnf(c_2892,plain,
multiplication(star(A),star(star(A))) = star(star(A)),
inference(paramod,[status(thm)],[c_739,c_2512]) ).
cnf(c_8502,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_8503,plain,
( leq(multiplication(star(addition(one,A)),star(A)),star(A))
| ~ leq(star(A),star(A)) ),
inference(paramod,[status(thm)],[c_2512,c_8502]) ).
cnf(c_2894,plain,
leq(multiplication(star(addition(one,A)),star(A)),star(A)),
inference(resolve,[status(thm)],[c_52,c_8503]) ).
cnf(c_2926,plain,
leq(star(star(A)),star(A)),
inference(paramod,[status(thm)],[c_2892,c_2672]) ).
cnf(c_8504,plain,
addition(star(star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2926,c_31]) ).
cnf(c_8505,plain,
addition(star(A),star(star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_8504]) ).
cnf(c_3649,plain,
star(star(A)) = star(A),
inference(paramod,[status(thm)],[c_2553,c_8505]) ).
cnf(c_8506,plain,
leq(multiplication(star(star(addition(one,A))),star(addition(one,A))),star(A)),
inference(resolve,[status(thm)],[c_2894,c_892]) ).
cnf(c_8507,plain,
leq(multiplication(star(addition(one,A)),star(addition(one,A))),star(A)),
inference(paramod,[status(thm)],[c_3649,c_8506]) ).
cnf(c_8477,plain,
leq(star(addition(one,A)),star(A)),
inference(paramod,[status(thm)],[c_2676,c_8507]) ).
cnf(c_8508,plain,
addition(multiplication(star(addition(one,A)),star(A)),star(A)) = star(A),
inference(resolve,[status(thm)],[c_2894,c_31]) ).
cnf(c_8509,plain,
addition(star(A),multiplication(star(addition(one,A)),star(A))) = star(A),
inference(paramod,[status(thm)],[c_18,c_8508]) ).
cnf(c_8478,plain,
multiplication(star(addition(one,A)),star(A)) = star(A),
inference(paramod,[status(thm)],[c_751,c_8509]) ).
cnf(c_8484,negated_conjecture,
~ leq(star(sK0),star(addition(one,sK0))),
inference(resolve,[status(thm)],[c_8477,c_37]) ).
cnf(c_8485,plain,
leq(star(A),star(addition(one,A))),
inference(paramod,[status(thm)],[c_8478,c_2293]) ).
cnf(c_8486,plain,
$false,
inference(resolve,[status(thm)],[c_8485,c_8484]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE044+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 19:17:10 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 3538938 was started by sandbox on n006,
% 0.12/0.36 % Fri Sep 25 19:17:10 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 22.37/3.61
% 22.37/3.61 % Assigning unary symbol star kb_weight 0 and highest precedence (8).
% 22.37/3.61
% 22.37/3.61 % given #500 (W,wt=29): 6023 leq(one,multiplication(addition(star(A),B),star(C))). [para(28(a,1),6003(a,2))].
% 22.37/3.61
% 22.37/3.61 % SZS status Theorem for theBenchmark
% 22.37/3.61
% 22.37/3.61 % Proof 1 at 2.55 (+ 0.65) seconds.
% 22.37/3.61 % Length of proof is 73.
% 22.37/3.61 % Level of proof is 14.
% 22.37/3.61 % Maximum clause weight is 42.000.
% 22.37/3.61 % Given clauses 535.
% 22.37/3.61
% 22.37/3.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------