%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE148+2 : 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 : n020.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 07:44:24 AM UTC 2026
% Result : Theorem 0.23s 0.64s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 48 unt; 0 def)
% Number of atoms : 72 ( 51 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 7 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 72 ( 6 sgn 22 !; 2 ?)
% 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_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
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(distributivity1,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',distributivity1) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('theBenchmark.p',infty_unfold1) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,conjecture,
! [X0,X1] :
( leq(X0,multiplication(X0,strong_iteration(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,multiplication(X0,strong_iteration(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) ) ),
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_22,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
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_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_31,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_38,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(clausify,[status(thm)],[infty_unfold1]) ).
cnf(c_1242,plain,
strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))),
inference(paramod,[status(thm)],[c_20,c_38]) ).
cnf(c_39,plain,
addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A),
inference(copy,[status(thm)],[c_1242]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_19,plain,
? [X0,X1] :
( ~ leq(X0,multiplication(X0,strong_iteration(X1)))
| ( ~ leq(multiplication(X0,strong_iteration(X1)),X0)
& multiplication(X0,X1) = zero ) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| ( ~ leq(multiplication(sK0,strong_iteration(sK1)),sK0)
& multiplication(sK0,sK1) = zero ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_19]) ).
fof(sk_goals_neg,plain,
( ( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| ~ leq(multiplication(sK0,strong_iteration(sK1)),sK0) )
& ( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| multiplication(sK0,sK1) = zero ) ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_45,negated_conjecture,
( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| multiplication(sK0,sK1) = zero ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_46,negated_conjecture,
( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| ~ leq(multiplication(sK0,strong_iteration(sK1)),sK0) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_1243,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_22,c_20]) ).
cnf(c_49,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_1243]) ).
cnf(c_1244,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_50,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_1244]) ).
cnf(c_1245,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_25,c_28]) ).
cnf(c_54,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_1245]) ).
cnf(c_1246,plain,
addition(multiplication(A,one),multiplication(A,multiplication(B,strong_iteration(B)))) = multiplication(A,strong_iteration(B)),
inference(paramod,[status(thm)],[c_39,c_28]) ).
cnf(c_90,plain,
addition(A,multiplication(A,multiplication(B,strong_iteration(B)))) = multiplication(A,strong_iteration(B)),
inference(paramod,[status(thm)],[c_25,c_1246]) ).
cnf(c_124,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_44,c_50]) ).
cnf(c_1247,plain,
addition(one,strong_iteration(A)) = addition(one,multiplication(A,strong_iteration(A))),
inference(paramod,[status(thm)],[c_39,c_50]) ).
cnf(c_130,plain,
addition(one,strong_iteration(A)) = strong_iteration(A),
inference(paramod,[status(thm)],[c_39,c_1247]) ).
cnf(c_207,plain,
leq(A,multiplication(A,addition(one,B))),
inference(paramod,[status(thm)],[c_54,c_124]) ).
cnf(c_322,plain,
leq(A,multiplication(A,strong_iteration(B))),
inference(paramod,[status(thm)],[c_39,c_207]) ).
cnf(c_324,negated_conjecture,
~ leq(multiplication(sK0,strong_iteration(sK1)),sK0),
inference(resolve,[status(thm)],[c_322,c_46]) ).
cnf(c_325,negated_conjecture,
multiplication(sK0,sK1) = zero,
inference(resolve,[status(thm)],[c_322,c_45]) ).
cnf(c_1248,plain,
multiplication(zero,A) = multiplication(sK0,multiplication(sK1,A)),
inference(paramod,[status(thm)],[c_325,c_24]) ).
cnf(c_1249,plain,
zero = multiplication(sK0,multiplication(sK1,A)),
inference(paramod,[status(thm)],[c_31,c_1248]) ).
cnf(c_326,plain,
multiplication(sK0,multiplication(sK1,A)) = zero,
inference(copy,[status(thm)],[c_1249]) ).
cnf(c_1250,negated_conjecture,
addition(multiplication(sK0,strong_iteration(sK1)),sK0) != sK0,
inference(resolve,[status(thm)],[c_44,c_324]) ).
cnf(c_1251,negated_conjecture,
addition(sK0,multiplication(sK0,strong_iteration(sK1))) != sK0,
inference(paramod,[status(thm)],[c_20,c_1250]) ).
cnf(c_1252,negated_conjecture,
multiplication(sK0,addition(one,strong_iteration(sK1))) != sK0,
inference(paramod,[status(thm)],[c_54,c_1251]) ).
cnf(c_353,negated_conjecture,
multiplication(sK0,strong_iteration(sK1)) != sK0,
inference(paramod,[status(thm)],[c_130,c_1252]) ).
cnf(c_1253,plain,
addition(sK0,zero) = multiplication(sK0,strong_iteration(sK1)),
inference(paramod,[status(thm)],[c_326,c_90]) ).
cnf(c_1254,plain,
addition(zero,sK0) = multiplication(sK0,strong_iteration(sK1)),
inference(paramod,[status(thm)],[c_20,c_1253]) ).
cnf(c_1255,plain,
sK0 = multiplication(sK0,strong_iteration(sK1)),
inference(paramod,[status(thm)],[c_49,c_1254]) ).
cnf(c_1256,plain,
multiplication(sK0,strong_iteration(sK1)) = sK0,
inference(copy,[status(thm)],[c_1255]) ).
cnf(c_1241,plain,
$false,
inference(resolve,[status(thm)],[c_353,c_1256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE148+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n020.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 19:28:18 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3576019 was started by sandbox2 on n020,
% 0.19/0.45 % Fri Sep 25 19:28:18 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.64
% 0.23/0.64 % SZS status Theorem for theBenchmark
% 0.23/0.64
% 0.23/0.64 % Proof 1 at 0.12 (+ 0.06) seconds.
% 0.23/0.64 % Length of proof is 38.
% 0.23/0.64 % Level of proof is 8.
% 0.23/0.64 % Maximum clause weight is 13.000.
% 0.23/0.64 % Given clauses 174.
% 0.23/0.64
% 0.23/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------