%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE008+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 : n013.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 07:44:02 AM UTC 2026
% Result : Theorem 9.62s 11.89s
% Output : CNFRefutation 9.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 123 ( 61 unt; 0 def)
% Number of atoms : 224 ( 105 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 150 ( 49 ~; 76 |; 16 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 131 ( 4 sgn 38 !; 5 ?)
% 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(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_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(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('theBenchmark.p',test_1) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('theBenchmark.p',test_2) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('theBenchmark.p',test_3) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( test(X2)
=> ( leq(X0,multiplication(X2,X1))
<=> ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) ) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( test(X2)
=> ( leq(X0,multiplication(X2,X1))
<=> ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) ) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_13,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X3] : complement(X3,X0)
| ~ test(X0) ) ),
inference(fof_nnf,[status(thm)],[test_1]) ).
fof(sk_test_1_sk,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( complement(sK0(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0))],[nnf_13]) ).
fof(sk_test_1,plain,
( ! [VAR_0,VAR_1] :
( ~ complement(VAR_1,VAR_0)
| test(VAR_0) )
& ! [VAR_0] :
( complement(sK0(VAR_0),VAR_0)
| ~ test(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_test_1_sk]) ).
cnf(c_19,plain,
( complement(sK0(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_20,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_21,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
fof(nnf_17,plain,
? [X0,X1,X2] :
( ( ~ leq(multiplication(c(X2),X0),zero)
| ~ leq(X0,X1)
| ~ leq(X0,multiplication(X2,X1)) )
& ( ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) )
| leq(X0,multiplication(X2,X1)) )
& test(X2) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ( ~ leq(multiplication(c(sK1),sK2),zero)
| ~ leq(sK2,sK3)
| ~ leq(sK2,multiplication(sK1,sK3)) )
& ( ( leq(multiplication(c(sK1),sK2),zero)
& leq(sK2,sK3) )
| leq(sK2,multiplication(sK1,sK3)) )
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK1)],[nnf_17]) ).
fof(sk_goals_neg,plain,
( ( ~ leq(multiplication(c(sK1),sK2),zero)
| ~ leq(sK2,sK3)
| ~ leq(sK2,multiplication(sK1,sK3)) )
& ( leq(multiplication(c(sK1),sK2),zero)
| leq(sK2,multiplication(sK1,sK3)) )
& ( leq(sK2,sK3)
| leq(sK2,multiplication(sK1,sK3)) )
& test(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_23,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_24,negated_conjecture,
complement(sK0(sK1),sK1),
inference(resolve,[status(thm)],[c_23,c_19]) ).
cnf(c_25,negated_conjecture,
( complement(sK1,A)
| c(sK1) != A ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_26,negated_conjecture,
( ~ complement(sK1,A)
| c(sK1) = A ),
inference(resolve,[status(thm)],[c_23,c_21]) ).
cnf(c_33,negated_conjecture,
( ~ leq(multiplication(c(sK1),sK2),zero)
| ~ leq(sK2,sK3)
| ~ leq(sK2,multiplication(sK1,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_34,negated_conjecture,
( leq(multiplication(c(sK1),sK2),zero)
| leq(sK2,multiplication(sK1,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_35,negated_conjecture,
( leq(sK2,sK3)
| leq(sK2,multiplication(sK1,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_36,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_37,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_38,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_39,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_40,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_41,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_42,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_44,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_45,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_44]) ).
cnf(c_46,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_47,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_48,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_50,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_51,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_52,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_53,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_54,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_58,plain,
complement(sK1,c(sK1)),
inference(xxres,[status(thm)],[c_25]) ).
cnf(c_67,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_37,c_24]) ).
cnf(c_69,plain,
multiplication(sK0(sK1),sK1) = zero,
inference(resolve,[status(thm)],[c_38,c_24]) ).
cnf(c_71,plain,
multiplication(sK1,sK0(sK1)) = zero,
inference(resolve,[status(thm)],[c_39,c_24]) ).
cnf(c_73,plain,
( leq(sK2,sK3)
| addition(sK2,multiplication(sK1,sK3)) = multiplication(sK1,sK3) ),
inference(resolve,[status(thm)],[c_41,c_35]) ).
cnf(c_6264,negated_conjecture,
( leq(sK2,multiplication(sK1,sK3))
| addition(multiplication(c(sK1),sK2),zero) = zero ),
inference(resolve,[status(thm)],[c_41,c_34]) ).
cnf(c_74,negated_conjecture,
( leq(sK2,multiplication(sK1,sK3))
| addition(zero,multiplication(c(sK1),sK2)) = zero ),
inference(paramod,[status(thm)],[c_54,c_6264]) ).
cnf(c_75,plain,
( leq(multiplication(c(sK1),sK2),zero)
| addition(sK2,multiplication(sK1,sK3)) = multiplication(sK1,sK3) ),
inference(resolve,[status(thm)],[c_41,c_34]) ).
cnf(c_79,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_42,c_45]) ).
cnf(c_6265,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_42,c_45]) ).
cnf(c_6266,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_54,c_6265]) ).
cnf(c_6267,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_79,c_6266]) ).
cnf(c_80,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_52,c_6267]) ).
cnf(c_6268,negated_conjecture,
( leq(sK2,multiplication(sK1,sK3))
| multiplication(addition(zero,c(sK1)),sK2) = zero ),
inference(paramod,[status(thm)],[c_79,c_74]) ).
cnf(c_81,negated_conjecture,
( leq(sK2,multiplication(sK1,sK3))
| multiplication(c(sK1),sK2) = zero ),
inference(paramod,[status(thm)],[c_80,c_6268]) ).
cnf(c_83,plain,
( multiplication(A,addition(B,C)) != multiplication(A,C)
| leq(multiplication(A,B),multiplication(A,C)) ),
inference(paramod,[status(thm)],[c_47,c_40]) ).
cnf(c_6269,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_48,c_45]) ).
cnf(c_88,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_6269]) ).
cnf(c_6270,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_51,c_53]) ).
cnf(c_105,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_6270]) ).
cnf(c_111,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_54,c_52]) ).
cnf(c_6271,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_54,c_53]) ).
cnf(c_112,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_53,c_6271]) ).
cnf(c_6272,plain,
addition(c(sK1),sK1) = one,
inference(resolve,[status(thm)],[c_58,c_37]) ).
cnf(c_116,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_54,c_6272]) ).
cnf(c_6273,plain,
( addition(sK0(sK1),sK1) != one
| multiplication(sK1,sK0(sK1)) != zero
| complement(sK1,sK0(sK1)) ),
inference(resolve,[status(thm)],[c_69,c_36]) ).
cnf(c_6274,plain,
( addition(sK0(sK1),sK1) != one
| zero != zero
| complement(sK1,sK0(sK1)) ),
inference(paramod,[status(thm)],[c_71,c_6273]) ).
cnf(c_6275,plain,
( addition(sK1,sK0(sK1)) != one
| zero != zero
| complement(sK1,sK0(sK1)) ),
inference(paramod,[status(thm)],[c_54,c_6274]) ).
cnf(c_6276,plain,
( one != one
| zero != zero
| complement(sK1,sK0(sK1)) ),
inference(paramod,[status(thm)],[c_67,c_6275]) ).
cnf(c_6277,plain,
( one != one
| complement(sK1,sK0(sK1)) ),
inference(copy,[status(thm)],[c_6276]) ).
cnf(c_196,plain,
complement(sK1,sK0(sK1)),
inference(copy,[status(thm)],[c_6277]) ).
cnf(c_6278,plain,
multiplication(zero,A) = multiplication(sK0(sK1),multiplication(sK1,A)),
inference(paramod,[status(thm)],[c_69,c_50]) ).
cnf(c_6279,plain,
zero = multiplication(sK0(sK1),multiplication(sK1,A)),
inference(paramod,[status(thm)],[c_42,c_6278]) ).
cnf(c_201,plain,
multiplication(sK0(sK1),multiplication(sK1,A)) = zero,
inference(copy,[status(thm)],[c_6279]) ).
cnf(c_6280,negated_conjecture,
c(sK1) = sK0(sK1),
inference(resolve,[status(thm)],[c_196,c_26]) ).
cnf(c_209,negated_conjecture,
sK0(sK1) = c(sK1),
inference(copy,[status(thm)],[c_6280]) ).
cnf(c_214,plain,
multiplication(c(sK1),multiplication(sK1,A)) = zero,
inference(paramod,[status(thm)],[c_209,c_201]) ).
cnf(c_6281,plain,
( addition(addition(A,sK2),multiplication(sK1,sK3)) = addition(A,multiplication(sK1,sK3))
| leq(sK2,sK3) ),
inference(paramod,[status(thm)],[c_73,c_53]) ).
cnf(c_257,plain,
( addition(multiplication(sK1,sK3),addition(A,sK2)) = addition(A,multiplication(sK1,sK3))
| leq(sK2,sK3) ),
inference(paramod,[status(thm)],[c_54,c_6281]) ).
cnf(c_6282,plain,
( addition(multiplication(A,sK2),zero) = multiplication(addition(A,c(sK1)),sK2)
| leq(sK2,multiplication(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_81,c_45]) ).
cnf(c_6283,plain,
( addition(zero,multiplication(A,sK2)) = multiplication(addition(A,c(sK1)),sK2)
| leq(sK2,multiplication(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_54,c_6282]) ).
cnf(c_6284,plain,
( multiplication(A,sK2) = multiplication(addition(A,c(sK1)),sK2)
| leq(sK2,multiplication(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_111,c_6283]) ).
cnf(c_315,plain,
( multiplication(addition(A,c(sK1)),sK2) = multiplication(A,sK2)
| leq(sK2,multiplication(sK1,sK3)) ),
inference(copy,[status(thm)],[c_6284]) ).
cnf(c_6285,plain,
( multiplication(A,multiplication(sK1,sK3)) != multiplication(A,multiplication(sK1,sK3))
| leq(multiplication(A,sK2),multiplication(A,multiplication(sK1,sK3)))
| leq(multiplication(c(sK1),sK2),zero) ),
inference(paramod,[status(thm)],[c_75,c_83]) ).
cnf(c_341,plain,
( leq(multiplication(A,sK2),multiplication(A,multiplication(sK1,sK3)))
| leq(multiplication(c(sK1),sK2),zero) ),
inference(copy,[status(thm)],[c_6285]) ).
cnf(c_6286,plain,
addition(sK1,one) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_116,c_105]) ).
cnf(c_6287,plain,
addition(one,sK1) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_54,c_6286]) ).
cnf(c_665,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_116,c_6287]) ).
cnf(c_6288,plain,
addition(multiplication(one,A),multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_665,c_45]) ).
cnf(c_6289,plain,
addition(A,multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_48,c_6288]) ).
cnf(c_703,plain,
addition(A,multiplication(sK1,A)) = A,
inference(paramod,[status(thm)],[c_48,c_6289]) ).
cnf(c_6290,plain,
( multiplication(addition(one,sK1),sK3) = addition(multiplication(sK1,sK3),addition(sK3,sK2))
| leq(sK2,sK3) ),
inference(paramod,[status(thm)],[c_257,c_88]) ).
cnf(c_6291,plain,
( multiplication(one,sK3) = addition(multiplication(sK1,sK3),addition(sK3,sK2))
| leq(sK2,sK3) ),
inference(paramod,[status(thm)],[c_665,c_6290]) ).
cnf(c_6292,plain,
( sK3 = addition(multiplication(sK1,sK3),addition(sK3,sK2))
| leq(sK2,sK3) ),
inference(paramod,[status(thm)],[c_48,c_6291]) ).
cnf(c_6293,plain,
( sK3 = addition(multiplication(sK1,sK3),addition(sK2,sK3))
| leq(sK2,sK3) ),
inference(paramod,[status(thm)],[c_54,c_6292]) ).
cnf(c_6294,plain,
( sK3 = addition(sK2,addition(multiplication(sK1,sK3),sK3))
| leq(sK2,sK3) ),
inference(paramod,[status(thm)],[c_112,c_6293]) ).
cnf(c_6295,plain,
( sK3 = addition(sK2,addition(sK3,multiplication(sK1,sK3)))
| leq(sK2,sK3) ),
inference(paramod,[status(thm)],[c_54,c_6294]) ).
cnf(c_6296,plain,
( sK3 = addition(sK2,sK3)
| leq(sK2,sK3) ),
inference(paramod,[status(thm)],[c_703,c_6295]) ).
cnf(c_4140,plain,
( addition(sK2,sK3) = sK3
| leq(sK2,sK3) ),
inference(copy,[status(thm)],[c_6296]) ).
cnf(c_6297,plain,
( addition(sK2,sK3) = sK3
| addition(sK2,sK3) = sK3 ),
inference(resolve,[status(thm)],[c_4140,c_41]) ).
cnf(c_4169,plain,
addition(sK2,sK3) = sK3,
inference(copy,[status(thm)],[c_6297]) ).
cnf(c_6298,plain,
( leq(sK2,sK3)
| leq(sK2,sK3) ),
inference(resolve,[status(thm)],[c_4140,c_40]) ).
cnf(c_4170,plain,
leq(sK2,sK3),
inference(copy,[status(thm)],[c_6298]) ).
cnf(c_4185,negated_conjecture,
( ~ leq(multiplication(c(sK1),sK2),zero)
| ~ leq(sK2,multiplication(sK1,sK3)) ),
inference(resolve,[status(thm)],[c_4170,c_33]) ).
cnf(c_6299,plain,
( multiplication(A,sK3) != multiplication(A,sK3)
| leq(multiplication(A,sK2),multiplication(A,sK3)) ),
inference(paramod,[status(thm)],[c_4169,c_83]) ).
cnf(c_4191,plain,
leq(multiplication(A,sK2),multiplication(A,sK3)),
inference(copy,[status(thm)],[c_6299]) ).
cnf(c_6300,plain,
( multiplication(one,sK2) = multiplication(sK1,sK2)
| leq(sK2,multiplication(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_116,c_315]) ).
cnf(c_6301,plain,
( sK2 = multiplication(sK1,sK2)
| leq(sK2,multiplication(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_48,c_6300]) ).
cnf(c_5580,plain,
( multiplication(sK1,sK2) = sK2
| leq(sK2,multiplication(sK1,sK3)) ),
inference(copy,[status(thm)],[c_6301]) ).
cnf(c_6302,plain,
( leq(multiplication(c(sK1),sK2),zero)
| leq(multiplication(c(sK1),sK2),zero) ),
inference(paramod,[status(thm)],[c_214,c_341]) ).
cnf(c_6107,plain,
leq(multiplication(c(sK1),sK2),zero),
inference(copy,[status(thm)],[c_6302]) ).
cnf(c_6115,negated_conjecture,
~ leq(sK2,multiplication(sK1,sK3)),
inference(resolve,[status(thm)],[c_6107,c_4185]) ).
cnf(c_6163,negated_conjecture,
multiplication(sK1,sK2) = sK2,
inference(resolve,[status(thm)],[c_6115,c_5580]) ).
cnf(c_6303,plain,
leq(sK2,multiplication(sK1,sK3)),
inference(paramod,[status(thm)],[c_6163,c_4191]) ).
cnf(c_6263,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_6115,c_6303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE008+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.59 % Computer : n013.cluster.edu
% 0.10/10.59 % Model : x86_64 x86_64
% 0.10/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.59 % Memory : 8046.5625MB
% 0.10/10.59 % OS : Linux 6.8.0-71-generic
% 0.10/10.59 % CPULimit : 300
% 0.10/10.59 % WCLimit : 300
% 0.10/10.59 % DateTime : Fri Sep 25 19:11:02 UTC 2026
% 0.10/10.59 % CPUTime :
% 0.10/10.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.59 % Process 975000 was started by sandbox2 on n013,
% 0.10/10.59 % Fri Sep 25 19:11:02 2026
% 0.10/10.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/10.60
% 0.10/10.60 % From the command line: assign(max_seconds, 300).
% 9.62/11.89
% 9.62/11.89 % given #500 (T,wt=13): 5528 leq(c1,multiplication(addition(one,A),c2)). [para(88(a,2),5523(a,2))].
% 9.62/11.89
% 9.62/11.89 % SZS status Theorem for theBenchmark
% 9.62/11.89
% 9.62/11.89 % Proof 1 at 0.92 (+ 0.34) seconds.
% 9.62/11.89 % Length of proof is 76.
% 9.62/11.89 % Level of proof is 12.
% 9.62/11.89 % Maximum clause weight is 24.000.
% 9.62/11.89 % Given clauses 557.
% 9.62/11.89
% 9.62/11.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------