%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE160+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 : n012.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 07:44:26 AM UTC 2026
% Result : Theorem 144.25s 22.07s
% Output : CNFRefutation 144.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 100 ( 80 unt; 0 def)
% Number of atoms : 120 ( 59 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 53 ( 33 ~; 13 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 146 ( 9 sgn 33 !; 3 ?)
% 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(idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',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(distributivity1,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',distributivity1) ).
fof(distributivity2,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',distributivity2) ).
fof(star_unfold1,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
file('theBenchmark.p',star_unfold1) ).
fof(star_unfold2,axiom,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
file('theBenchmark.p',star_unfold2) ).
fof(star_induction1,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,C),B),C)
=> leq(multiplication(star(A),B),C) ),
file('theBenchmark.p',star_induction1) ).
fof(star_induction2,axiom,
! [A,B,C] :
( leq(addition(multiplication(C,A),B),C)
=> leq(multiplication(B,star(A)),C) ),
file('theBenchmark.p',star_induction2) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( leq(multiplication(X0,X1),multiplication(X1,X2))
=> leq(multiplication(star(X0),X1),multiplication(X1,star(X2))) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(multiplication(X0,X1),multiplication(X1,X2))
=> leq(multiplication(star(X0),X1),multiplication(X1,star(X2))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_21,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_23,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[idempotence]) ).
cnf(c_24,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_25,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_26,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_27,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[distributivity1]) ).
cnf(c_28,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_29,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[distributivity2]) ).
cnf(c_30,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_32,plain,
star(A) = addition(one,multiplication(A,star(A))),
inference(clausify,[status(thm)],[star_unfold1]) ).
cnf(c_33,plain,
addition(one,multiplication(A,star(A))) = star(A),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_34,plain,
star(A) = addition(one,multiplication(star(A),A)),
inference(clausify,[status(thm)],[star_unfold2]) ).
cnf(c_35,plain,
addition(one,multiplication(star(A),A)) = star(A),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_36,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(clausify,[status(thm)],[star_induction1]) ).
cnf(c_37,plain,
( leq(multiplication(C,star(B)),A)
| ~ leq(addition(multiplication(A,B),C),A) ),
inference(clausify,[status(thm)],[star_induction2]) ).
cnf(c_43,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_19,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(star(X0),X1),multiplication(X1,star(X2)))
& leq(multiplication(X0,X1),multiplication(X1,X2)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(multiplication(star(sK0),sK1),multiplication(sK1,star(sK2)))
& leq(multiplication(sK0,sK1),multiplication(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_19]) ).
cnf(c_45,negated_conjecture,
leq(multiplication(sK0,sK1),multiplication(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_46,negated_conjecture,
~ leq(multiplication(star(sK0),sK1),multiplication(sK1,star(sK2))),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_16237,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_57,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_16237]) ).
cnf(c_58,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_69,plain,
addition(multiplication(multiplication(A,B),C),multiplication(A,D)) = multiplication(A,addition(multiplication(B,C),D)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_71,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_25,c_28]) ).
cnf(c_74,plain,
addition(addition(A,multiplication(B,C)),multiplication(D,C)) = addition(A,multiplication(addition(B,D),C)),
inference(paramod,[status(thm)],[c_30,c_21]) ).
cnf(c_78,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_26,c_30]) ).
cnf(c_79,plain,
addition(multiplication(A,B),B) = multiplication(addition(A,one),B),
inference(paramod,[status(thm)],[c_26,c_30]) ).
cnf(c_16238,plain,
star(A) = addition(multiplication(star(A),A),one),
inference(paramod,[status(thm)],[c_35,c_20]) ).
cnf(c_86,plain,
addition(multiplication(star(A),A),one) = star(A),
inference(copy,[status(thm)],[c_16238]) ).
cnf(c_89,plain,
( leq(multiplication(star(B),A),C)
| ~ leq(addition(A,multiplication(B,C)),C) ),
inference(paramod,[status(thm)],[c_20,c_36]) ).
cnf(c_92,plain,
( leq(multiplication(star(A),multiplication(A,B)),B)
| ~ leq(multiplication(A,B),B) ),
inference(paramod,[status(thm)],[c_23,c_36]) ).
cnf(c_131,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_44,c_23]) ).
cnf(c_132,plain,
( addition(B,A) != B
| leq(A,B) ),
inference(paramod,[status(thm)],[c_20,c_44]) ).
cnf(c_143,plain,
addition(multiplication(sK0,sK1),multiplication(sK1,sK2)) = multiplication(sK1,sK2),
inference(resolve,[status(thm)],[c_45,c_43]) ).
cnf(c_16239,negated_conjecture,
~ leq(addition(multiplication(sK0,multiplication(sK1,star(sK2))),sK1),multiplication(sK1,star(sK2))),
inference(resolve,[status(thm)],[c_36,c_46]) ).
cnf(c_145,negated_conjecture,
~ leq(addition(multiplication(multiplication(sK0,sK1),star(sK2)),sK1),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_24,c_16239]) ).
cnf(c_173,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_57,c_44]) ).
cnf(c_16240,plain,
addition(one,star(A)) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_33,c_57]) ).
cnf(c_177,plain,
addition(one,star(A)) = star(A),
inference(paramod,[status(thm)],[c_33,c_16240]) ).
cnf(c_16241,plain,
addition(star(A),multiplication(A,star(A))) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_33,c_58]) ).
cnf(c_16242,plain,
multiplication(addition(one,A),star(A)) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_78,c_16241]) ).
cnf(c_187,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_33,c_16242]) ).
cnf(c_198,plain,
leq(A,addition(addition(A,B),C)),
inference(paramod,[status(thm)],[c_21,c_173]) ).
cnf(c_301,plain,
( addition(A,B) != A
| leq(addition(A,B),A) ),
inference(paramod,[status(thm)],[c_57,c_132]) ).
cnf(c_311,plain,
( addition(B,A) != A
| leq(addition(A,B),A) ),
inference(paramod,[status(thm)],[c_20,c_301]) ).
cnf(c_16243,plain,
star(A) = addition(star(A),one),
inference(paramod,[status(thm)],[c_177,c_20]) ).
cnf(c_614,plain,
addition(star(A),one) = star(A),
inference(copy,[status(thm)],[c_16243]) ).
cnf(c_626,plain,
leq(one,addition(star(A),B)),
inference(paramod,[status(thm)],[c_33,c_198]) ).
cnf(c_631,plain,
leq(one,addition(A,star(B))),
inference(paramod,[status(thm)],[c_20,c_626]) ).
cnf(c_726,plain,
addition(multiplication(multiplication(A,B),C),A) = multiplication(A,addition(multiplication(B,C),one)),
inference(paramod,[status(thm)],[c_25,c_69]) ).
cnf(c_16244,plain,
addition(one,addition(A,star(B))) = addition(A,star(B)),
inference(resolve,[status(thm)],[c_631,c_43]) ).
cnf(c_758,plain,
addition(addition(one,A),star(B)) = addition(A,star(B)),
inference(paramod,[status(thm)],[c_21,c_16244]) ).
cnf(c_1550,plain,
( leq(multiplication(star(one),A),B)
| ~ leq(addition(A,B),B) ),
inference(paramod,[status(thm)],[c_26,c_89]) ).
cnf(c_16245,plain,
( leq(multiplication(star(one),multiplication(one,A)),A)
| ~ leq(A,A) ),
inference(paramod,[status(thm)],[c_26,c_92]) ).
cnf(c_16246,plain,
( leq(multiplication(star(one),A),A)
| ~ leq(A,A) ),
inference(paramod,[status(thm)],[c_26,c_16245]) ).
cnf(c_1668,plain,
leq(multiplication(star(one),A),A),
inference(resolve,[status(thm)],[c_131,c_16246]) ).
cnf(c_16247,plain,
addition(multiplication(star(one),A),A) = A,
inference(resolve,[status(thm)],[c_1668,c_43]) ).
cnf(c_16248,plain,
multiplication(addition(star(one),one),A) = A,
inference(paramod,[status(thm)],[c_79,c_16247]) ).
cnf(c_1685,plain,
multiplication(star(one),A) = A,
inference(paramod,[status(thm)],[c_614,c_16248]) ).
cnf(c_1691,plain,
( leq(A,B)
| ~ leq(addition(A,B),B) ),
inference(paramod,[status(thm)],[c_1685,c_1550]) ).
cnf(c_16249,plain,
~ leq(addition(addition(multiplication(multiplication(sK0,sK1),star(sK2)),sK1),multiplication(sK1,star(sK2))),multiplication(sK1,star(sK2))),
inference(resolve,[status(thm)],[c_1691,c_145]) ).
cnf(c_16250,plain,
~ leq(addition(multiplication(multiplication(sK0,sK1),star(sK2)),addition(sK1,multiplication(sK1,star(sK2)))),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_21,c_16249]) ).
cnf(c_16251,plain,
~ leq(addition(multiplication(multiplication(sK0,sK1),star(sK2)),multiplication(sK1,addition(one,star(sK2)))),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_71,c_16250]) ).
cnf(c_16252,plain,
~ leq(addition(multiplication(multiplication(sK0,sK1),star(sK2)),multiplication(sK1,star(sK2))),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_177,c_16251]) ).
cnf(c_16253,plain,
~ leq(multiplication(addition(multiplication(sK0,sK1),sK1),star(sK2)),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_30,c_16252]) ).
cnf(c_1695,plain,
~ leq(multiplication(multiplication(addition(sK0,one),sK1),star(sK2)),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_79,c_16253]) ).
cnf(c_1805,plain,
~ leq(multiplication(multiplication(addition(one,sK0),sK1),star(sK2)),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_20,c_1695]) ).
cnf(c_1806,plain,
~ leq(addition(multiplication(multiplication(sK1,star(sK2)),sK2),multiplication(addition(one,sK0),sK1)),multiplication(sK1,star(sK2))),
inference(resolve,[status(thm)],[c_37,c_1805]) ).
cnf(c_16254,plain,
~ leq(addition(addition(multiplication(multiplication(sK1,star(sK2)),sK2),multiplication(one,sK1)),multiplication(sK0,sK1)),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_74,c_1806]) ).
cnf(c_16255,plain,
~ leq(addition(addition(multiplication(multiplication(sK1,star(sK2)),sK2),sK1),multiplication(sK0,sK1)),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_26,c_16254]) ).
cnf(c_16256,plain,
~ leq(addition(multiplication(sK1,addition(multiplication(star(sK2),sK2),one)),multiplication(sK0,sK1)),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_726,c_16255]) ).
cnf(c_2105,plain,
~ leq(addition(multiplication(sK1,star(sK2)),multiplication(sK0,sK1)),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_86,c_16256]) ).
cnf(c_2106,plain,
addition(multiplication(sK0,sK1),multiplication(sK1,star(sK2))) != multiplication(sK1,star(sK2)),
inference(resolve,[status(thm)],[c_311,c_2105]) ).
cnf(c_2109,plain,
~ leq(multiplication(sK0,sK1),multiplication(sK1,star(sK2))),
inference(resolve,[status(thm)],[c_43,c_2106]) ).
cnf(c_16257,plain,
addition(addition(one,A),star(A)) = multiplication(addition(one,A),addition(one,star(A))),
inference(paramod,[status(thm)],[c_187,c_71]) ).
cnf(c_16258,plain,
addition(A,star(A)) = multiplication(addition(one,A),addition(one,star(A))),
inference(paramod,[status(thm)],[c_758,c_16257]) ).
cnf(c_16259,plain,
addition(A,star(A)) = multiplication(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_177,c_16258]) ).
cnf(c_2818,plain,
addition(A,star(A)) = star(A),
inference(paramod,[status(thm)],[c_187,c_16259]) ).
cnf(c_3881,plain,
leq(multiplication(sK0,sK1),addition(multiplication(sK1,sK2),A)),
inference(paramod,[status(thm)],[c_143,c_198]) ).
cnf(c_14429,plain,
leq(multiplication(sK0,sK1),multiplication(sK1,addition(sK2,A))),
inference(paramod,[status(thm)],[c_28,c_3881]) ).
cnf(c_16260,plain,
leq(multiplication(sK0,sK1),multiplication(sK1,star(sK2))),
inference(paramod,[status(thm)],[c_2818,c_14429]) ).
cnf(c_16236,plain,
$false,
inference(resolve,[status(thm)],[c_2109,c_16260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE160+1 : 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 : n012.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
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Fri Sep 25 19:28:50 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 2776295 was started by sandbox on n012,
% 0.02/0.36 % Fri Sep 25 19:28:50 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.36
% 0.02/0.36 % From the command line: assign(max_seconds, 300).
% 144.25/22.07
% 144.25/22.07 % given #500 (T,wt=22): 11952 leq(star(A),multiplication(A,zero)) | star(A) != multiplication(A,zero). [para(187(a,1),3585(b,2)),rewrite([187(4),1215(5),1215(8)]),flip(b)].
% 144.25/22.07
% 144.25/22.07 % SZS status Theorem for theBenchmark
% 144.25/22.07
% 144.25/22.07 % Proof 1 at 2.11 (+ 0.45) seconds.
% 144.25/22.07 % Length of proof is 73.
% 144.25/22.07 % Level of proof is 13.
% 144.25/22.07 % Maximum clause weight is 42.000.
% 144.25/22.07 % Given clauses 571.
% 144.25/22.07
% 144.25/22.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------