%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE017+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 : 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 07:44:05 AM UTC 2026
% Result : Theorem 19.66s 3.23s
% Output : CNFRefutation 19.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 13
% Syntax : Number of formulae : 156 ( 94 unt; 0 def)
% Number of atoms : 266 ( 136 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 162 ( 52 ~; 75 |; 26 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 134 ( 0 sgn 35 !; 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_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(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)
& test(X1)
& test(X0) )
=> ( leq(X2,multiplication(X0,X1))
<=> ( leq(X2,X1)
& leq(X2,X0) ) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> ( leq(X2,multiplication(X0,X1))
<=> ( leq(X2,X1)
& leq(X2,X0) ) ) ),
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(X2,X1)
| ~ leq(X2,X0)
| ~ leq(X2,multiplication(X0,X1)) )
& ( ( leq(X2,X1)
& leq(X2,X0) )
| leq(X2,multiplication(X0,X1)) )
& test(X2)
& test(X1)
& test(X0) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ( ~ leq(sK3,sK2)
| ~ leq(sK3,sK1)
| ~ leq(sK3,multiplication(sK1,sK2)) )
& ( ( leq(sK3,sK2)
& leq(sK3,sK1) )
| leq(sK3,multiplication(sK1,sK2)) )
& test(sK3)
& test(sK2)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[nnf_17]) ).
fof(sk_goals_neg,plain,
( ( ~ leq(sK3,sK2)
| ~ leq(sK3,sK1)
| ~ leq(sK3,multiplication(sK1,sK2)) )
& ( leq(sK3,sK2)
| leq(sK3,multiplication(sK1,sK2)) )
& ( leq(sK3,sK1)
| leq(sK3,multiplication(sK1,sK2)) )
& test(sK3)
& test(sK2)
& 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,
test(sK2),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_25,negated_conjecture,
test(sK3),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_26,negated_conjecture,
complement(sK0(sK3),sK3),
inference(resolve,[status(thm)],[c_25,c_19]) ).
cnf(c_27,negated_conjecture,
( complement(sK3,A)
| c(sK3) != A ),
inference(resolve,[status(thm)],[c_25,c_20]) ).
cnf(c_28,negated_conjecture,
( ~ complement(sK3,A)
| c(sK3) = A ),
inference(resolve,[status(thm)],[c_25,c_21]) ).
cnf(c_30,negated_conjecture,
( complement(sK2,A)
| c(sK2) != A ),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_33,negated_conjecture,
( complement(sK1,A)
| c(sK1) != A ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_41,negated_conjecture,
( ~ leq(sK3,sK2)
| ~ leq(sK3,sK1)
| ~ leq(sK3,multiplication(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_42,negated_conjecture,
( leq(sK3,sK2)
| leq(sK3,multiplication(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_43,negated_conjecture,
( leq(sK3,sK1)
| leq(sK3,multiplication(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_44,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_45,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_46,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_47,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_48,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_49,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_52,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_53,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_54,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_55,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_54]) ).
cnf(c_56,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_57,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_59,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_60,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_61,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_62,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_66,plain,
complement(sK3,c(sK3)),
inference(xxres,[status(thm)],[c_27]) ).
cnf(c_67,plain,
complement(sK2,c(sK2)),
inference(xxres,[status(thm)],[c_30]) ).
cnf(c_68,plain,
complement(sK1,c(sK1)),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_83,plain,
addition(sK3,sK0(sK3)) = one,
inference(resolve,[status(thm)],[c_45,c_26]) ).
cnf(c_87,plain,
multiplication(sK0(sK3),sK3) = zero,
inference(resolve,[status(thm)],[c_46,c_26]) ).
cnf(c_91,plain,
multiplication(sK3,sK0(sK3)) = zero,
inference(resolve,[status(thm)],[c_47,c_26]) ).
cnf(c_93,plain,
( leq(sK3,sK1)
| addition(sK3,multiplication(sK1,sK2)) = multiplication(sK1,sK2) ),
inference(resolve,[status(thm)],[c_49,c_43]) ).
cnf(c_11700,negated_conjecture,
( leq(sK3,multiplication(sK1,sK2))
| addition(sK3,sK2) = sK2 ),
inference(resolve,[status(thm)],[c_49,c_42]) ).
cnf(c_94,negated_conjecture,
( leq(sK3,multiplication(sK1,sK2))
| addition(sK2,sK3) = sK2 ),
inference(paramod,[status(thm)],[c_62,c_11700]) ).
cnf(c_11701,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_56,c_53]) ).
cnf(c_107,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_11701]) ).
cnf(c_11702,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_57,c_55]) ).
cnf(c_109,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_11702]) ).
cnf(c_11703,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_59,c_61]) ).
cnf(c_126,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_11703]) ).
cnf(c_131,plain,
( addition(B,A) != B
| leq(A,B) ),
inference(paramod,[status(thm)],[c_62,c_48]) ).
cnf(c_132,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_62,c_60]) ).
cnf(c_11704,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_62,c_61]) ).
cnf(c_133,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_61,c_11704]) ).
cnf(c_11705,plain,
addition(c(sK3),sK3) = one,
inference(resolve,[status(thm)],[c_66,c_45]) ).
cnf(c_137,plain,
addition(sK3,c(sK3)) = one,
inference(paramod,[status(thm)],[c_62,c_11705]) ).
cnf(c_11706,plain,
addition(c(sK2),sK2) = one,
inference(resolve,[status(thm)],[c_67,c_45]) ).
cnf(c_143,plain,
addition(sK2,c(sK2)) = one,
inference(paramod,[status(thm)],[c_62,c_11706]) ).
cnf(c_11707,plain,
addition(c(sK1),sK1) = one,
inference(resolve,[status(thm)],[c_68,c_45]) ).
cnf(c_154,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_62,c_11707]) ).
cnf(c_11708,plain,
( addition(sK0(sK3),sK3) != one
| multiplication(sK3,sK0(sK3)) != zero
| complement(sK3,sK0(sK3)) ),
inference(resolve,[status(thm)],[c_87,c_44]) ).
cnf(c_11709,plain,
( addition(sK0(sK3),sK3) != one
| zero != zero
| complement(sK3,sK0(sK3)) ),
inference(paramod,[status(thm)],[c_91,c_11708]) ).
cnf(c_11710,plain,
( addition(sK3,sK0(sK3)) != one
| zero != zero
| complement(sK3,sK0(sK3)) ),
inference(paramod,[status(thm)],[c_62,c_11709]) ).
cnf(c_11711,plain,
( one != one
| zero != zero
| complement(sK3,sK0(sK3)) ),
inference(paramod,[status(thm)],[c_83,c_11710]) ).
cnf(c_11712,plain,
( one != one
| complement(sK3,sK0(sK3)) ),
inference(copy,[status(thm)],[c_11711]) ).
cnf(c_297,plain,
complement(sK3,sK0(sK3)),
inference(copy,[status(thm)],[c_11712]) ).
cnf(c_11713,plain,
addition(multiplication(A,sK3),zero) = multiplication(addition(A,sK0(sK3)),sK3),
inference(paramod,[status(thm)],[c_87,c_53]) ).
cnf(c_11714,plain,
addition(zero,multiplication(A,sK3)) = multiplication(addition(A,sK0(sK3)),sK3),
inference(paramod,[status(thm)],[c_62,c_11713]) ).
cnf(c_11715,plain,
multiplication(A,sK3) = multiplication(addition(A,sK0(sK3)),sK3),
inference(paramod,[status(thm)],[c_132,c_11714]) ).
cnf(c_299,plain,
multiplication(addition(A,sK0(sK3)),sK3) = multiplication(A,sK3),
inference(copy,[status(thm)],[c_11715]) ).
cnf(c_11716,negated_conjecture,
c(sK3) = sK0(sK3),
inference(resolve,[status(thm)],[c_297,c_28]) ).
cnf(c_324,negated_conjecture,
sK0(sK3) = c(sK3),
inference(copy,[status(thm)],[c_11716]) ).
cnf(c_332,plain,
multiplication(addition(A,c(sK3)),sK3) = multiplication(A,sK3),
inference(paramod,[status(thm)],[c_324,c_299]) ).
cnf(c_11717,plain,
( addition(addition(A,sK3),multiplication(sK1,sK2)) = addition(A,multiplication(sK1,sK2))
| leq(sK3,sK1) ),
inference(paramod,[status(thm)],[c_93,c_61]) ).
cnf(c_350,plain,
( addition(multiplication(sK1,sK2),addition(A,sK3)) = addition(A,multiplication(sK1,sK2))
| leq(sK3,sK1) ),
inference(paramod,[status(thm)],[c_62,c_11717]) ).
cnf(c_351,plain,
( multiplication(addition(C,A),B) != multiplication(C,B)
| leq(multiplication(A,B),multiplication(C,B)) ),
inference(paramod,[status(thm)],[c_53,c_131]) ).
cnf(c_11718,plain,
( addition(multiplication(A,sK2),multiplication(A,sK3)) = multiplication(A,sK2)
| leq(sK3,multiplication(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_94,c_55]) ).
cnf(c_368,plain,
( multiplication(A,addition(sK2,sK3)) = multiplication(A,sK2)
| leq(sK3,multiplication(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_55,c_11718]) ).
cnf(c_11719,plain,
addition(sK2,one) = addition(sK2,c(sK2)),
inference(paramod,[status(thm)],[c_143,c_126]) ).
cnf(c_11720,plain,
addition(one,sK2) = addition(sK2,c(sK2)),
inference(paramod,[status(thm)],[c_62,c_11719]) ).
cnf(c_644,plain,
addition(one,sK2) = one,
inference(paramod,[status(thm)],[c_143,c_11720]) ).
cnf(c_11721,plain,
addition(sK1,one) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_154,c_126]) ).
cnf(c_11722,plain,
addition(one,sK1) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_62,c_11721]) ).
cnf(c_647,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_154,c_11722]) ).
cnf(c_11723,plain,
addition(multiplication(A,one),multiplication(A,sK2)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_644,c_55]) ).
cnf(c_11724,plain,
addition(A,multiplication(A,sK2)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_57,c_11723]) ).
cnf(c_720,plain,
addition(A,multiplication(A,sK2)) = A,
inference(paramod,[status(thm)],[c_57,c_11724]) ).
cnf(c_11725,plain,
addition(multiplication(one,A),multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_647,c_53]) ).
cnf(c_11726,plain,
addition(A,multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_56,c_11725]) ).
cnf(c_784,plain,
addition(A,multiplication(sK1,A)) = A,
inference(paramod,[status(thm)],[c_56,c_11726]) ).
cnf(c_11727,plain,
addition(A,B) = addition(B,addition(A,multiplication(B,sK2))),
inference(paramod,[status(thm)],[c_720,c_133]) ).
cnf(c_1470,plain,
addition(A,addition(B,multiplication(A,sK2))) = addition(B,A),
inference(copy,[status(thm)],[c_11727]) ).
cnf(c_11728,plain,
multiplication(one,sK3) = multiplication(sK3,sK3),
inference(paramod,[status(thm)],[c_137,c_332]) ).
cnf(c_11729,plain,
sK3 = multiplication(sK3,sK3),
inference(paramod,[status(thm)],[c_56,c_11728]) ).
cnf(c_4074,plain,
multiplication(sK3,sK3) = sK3,
inference(copy,[status(thm)],[c_11729]) ).
cnf(c_11730,plain,
addition(multiplication(sK3,A),sK3) = multiplication(sK3,addition(A,sK3)),
inference(paramod,[status(thm)],[c_4074,c_55]) ).
cnf(c_11731,plain,
addition(sK3,multiplication(sK3,A)) = multiplication(sK3,addition(A,sK3)),
inference(paramod,[status(thm)],[c_62,c_11730]) ).
cnf(c_4132,plain,
multiplication(sK3,addition(one,A)) = multiplication(sK3,addition(A,sK3)),
inference(paramod,[status(thm)],[c_109,c_11731]) ).
cnf(c_11732,plain,
( multiplication(sK1,addition(one,sK2)) = addition(multiplication(sK1,sK2),addition(sK1,sK3))
| leq(sK3,sK1) ),
inference(paramod,[status(thm)],[c_350,c_109]) ).
cnf(c_11733,plain,
( multiplication(sK1,one) = addition(multiplication(sK1,sK2),addition(sK1,sK3))
| leq(sK3,sK1) ),
inference(paramod,[status(thm)],[c_644,c_11732]) ).
cnf(c_11734,plain,
( sK1 = addition(multiplication(sK1,sK2),addition(sK1,sK3))
| leq(sK3,sK1) ),
inference(paramod,[status(thm)],[c_57,c_11733]) ).
cnf(c_11735,plain,
( sK1 = addition(sK1,addition(multiplication(sK1,sK2),sK3))
| leq(sK3,sK1) ),
inference(paramod,[status(thm)],[c_133,c_11734]) ).
cnf(c_11736,plain,
( sK1 = addition(sK1,addition(sK3,multiplication(sK1,sK2)))
| leq(sK3,sK1) ),
inference(paramod,[status(thm)],[c_62,c_11735]) ).
cnf(c_11737,plain,
( sK1 = addition(sK3,sK1)
| leq(sK3,sK1) ),
inference(paramod,[status(thm)],[c_1470,c_11736]) ).
cnf(c_11738,plain,
( sK1 = addition(sK1,sK3)
| leq(sK3,sK1) ),
inference(paramod,[status(thm)],[c_62,c_11737]) ).
cnf(c_4891,plain,
( addition(sK1,sK3) = sK1
| leq(sK3,sK1) ),
inference(copy,[status(thm)],[c_11738]) ).
cnf(c_11739,plain,
( addition(sK3,sK1) = sK1
| addition(sK1,sK3) = sK1 ),
inference(resolve,[status(thm)],[c_4891,c_49]) ).
cnf(c_11740,plain,
( addition(sK1,sK3) = sK1
| addition(sK1,sK3) = sK1 ),
inference(paramod,[status(thm)],[c_62,c_11739]) ).
cnf(c_4957,plain,
addition(sK1,sK3) = sK1,
inference(copy,[status(thm)],[c_11740]) ).
cnf(c_11741,plain,
( leq(sK3,sK1)
| leq(sK3,sK1) ),
inference(resolve,[status(thm)],[c_4891,c_131]) ).
cnf(c_4958,plain,
leq(sK3,sK1),
inference(copy,[status(thm)],[c_11741]) ).
cnf(c_4986,negated_conjecture,
( ~ leq(sK3,sK2)
| ~ leq(sK3,multiplication(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_4958,c_41]) ).
cnf(c_11742,plain,
( multiplication(sK1,A) != multiplication(sK1,A)
| leq(multiplication(sK3,A),multiplication(sK1,A)) ),
inference(paramod,[status(thm)],[c_4957,c_351]) ).
cnf(c_5078,plain,
leq(multiplication(sK3,A),multiplication(sK1,A)),
inference(copy,[status(thm)],[c_11742]) ).
cnf(c_5114,plain,
leq(sK3,multiplication(sK1,sK3)),
inference(paramod,[status(thm)],[c_4074,c_5078]) ).
cnf(c_11743,plain,
addition(sK3,multiplication(sK1,sK3)) = multiplication(sK1,sK3),
inference(resolve,[status(thm)],[c_5114,c_49]) ).
cnf(c_11744,plain,
sK3 = multiplication(sK1,sK3),
inference(paramod,[status(thm)],[c_784,c_11743]) ).
cnf(c_5116,plain,
multiplication(sK1,sK3) = sK3,
inference(copy,[status(thm)],[c_11744]) ).
cnf(c_5127,plain,
addition(sK3,multiplication(sK1,A)) = multiplication(sK1,addition(sK3,A)),
inference(paramod,[status(thm)],[c_5116,c_55]) ).
cnf(c_11745,plain,
( addition(sK3,multiplication(sK1,sK2)) = multiplication(sK1,sK2)
| multiplication(A,addition(sK2,sK3)) = multiplication(A,sK2) ),
inference(resolve,[status(thm)],[c_368,c_49]) ).
cnf(c_11746,plain,
( multiplication(sK1,addition(sK3,sK2)) = multiplication(sK1,sK2)
| multiplication(A,addition(sK2,sK3)) = multiplication(A,sK2) ),
inference(paramod,[status(thm)],[c_5127,c_11745]) ).
cnf(c_5663,plain,
( multiplication(sK1,addition(sK2,sK3)) = multiplication(sK1,sK2)
| multiplication(A,addition(sK2,sK3)) = multiplication(A,sK2) ),
inference(paramod,[status(thm)],[c_62,c_11746]) ).
cnf(c_11747,plain,
( leq(multiplication(sK3,addition(sK2,sK3)),multiplication(sK1,sK2))
| leq(sK3,multiplication(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_368,c_5078]) ).
cnf(c_11748,plain,
( leq(multiplication(sK3,addition(one,sK2)),multiplication(sK1,sK2))
| leq(sK3,multiplication(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_4132,c_11747]) ).
cnf(c_11749,plain,
( leq(multiplication(sK3,one),multiplication(sK1,sK2))
| leq(sK3,multiplication(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_644,c_11748]) ).
cnf(c_11750,plain,
( leq(sK3,multiplication(sK1,sK2))
| leq(sK3,multiplication(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_57,c_11749]) ).
cnf(c_5698,plain,
leq(sK3,multiplication(sK1,sK2)),
inference(copy,[status(thm)],[c_11750]) ).
cnf(c_5699,plain,
multiplication(sK1,addition(sK2,sK3)) = multiplication(sK1,sK2),
inference(factor,[status(thm)],[c_5663]) ).
cnf(c_5701,negated_conjecture,
~ leq(sK3,sK2),
inference(resolve,[status(thm)],[c_5698,c_4986]) ).
cnf(c_5717,negated_conjecture,
addition(sK2,sK3) != sK2,
inference(resolve,[status(thm)],[c_131,c_5701]) ).
cnf(c_11751,plain,
multiplication(addition(one,sK1),addition(sK2,sK3)) = addition(addition(sK2,sK3),multiplication(sK1,sK2)),
inference(paramod,[status(thm)],[c_5699,c_107]) ).
cnf(c_11752,plain,
multiplication(one,addition(sK2,sK3)) = addition(addition(sK2,sK3),multiplication(sK1,sK2)),
inference(paramod,[status(thm)],[c_647,c_11751]) ).
cnf(c_11753,plain,
addition(sK2,sK3) = addition(addition(sK2,sK3),multiplication(sK1,sK2)),
inference(paramod,[status(thm)],[c_56,c_11752]) ).
cnf(c_11754,plain,
addition(sK2,sK3) = addition(multiplication(sK1,sK2),addition(sK2,sK3)),
inference(paramod,[status(thm)],[c_62,c_11753]) ).
cnf(c_11755,plain,
addition(sK2,sK3) = addition(sK2,addition(multiplication(sK1,sK2),sK3)),
inference(paramod,[status(thm)],[c_133,c_11754]) ).
cnf(c_11756,plain,
addition(sK2,sK3) = addition(sK2,addition(sK3,multiplication(sK1,sK2))),
inference(paramod,[status(thm)],[c_62,c_11755]) ).
cnf(c_11757,plain,
addition(sK2,sK3) = addition(sK2,multiplication(sK1,addition(sK3,sK2))),
inference(paramod,[status(thm)],[c_5127,c_11756]) ).
cnf(c_11758,plain,
addition(sK2,sK3) = addition(sK2,multiplication(sK1,addition(sK2,sK3))),
inference(paramod,[status(thm)],[c_62,c_11757]) ).
cnf(c_11759,plain,
addition(sK2,sK3) = addition(sK2,multiplication(sK1,sK2)),
inference(paramod,[status(thm)],[c_5699,c_11758]) ).
cnf(c_11760,plain,
addition(sK2,sK3) = sK2,
inference(paramod,[status(thm)],[c_784,c_11759]) ).
cnf(c_11699,plain,
$false,
inference(resolve,[status(thm)],[c_5717,c_11760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE017+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 19:12:36 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 977551 was started by sandbox on n013,
% 0.02/0.36 % Fri Sep 25 19:12:36 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).
% 19.66/3.23
% 19.66/3.23 % given #500 (T,wt=11): 5399 leq(multiplication(c2,A),addition(A,B)). [para(62(a,1),5185(a,2))].
% 19.66/3.23
% 19.66/3.23 % SZS status Theorem for theBenchmark
% 19.66/3.23
% 19.66/3.23 % Proof 1 at 2.10 (+ 0.72) seconds.
% 19.66/3.23 % Length of proof is 88.
% 19.66/3.23 % Level of proof is 16.
% 19.66/3.23 % Maximum clause weight is 24.000.
% 19.66/3.23 % Given clauses 888.
% 19.66/3.23
% 19.66/3.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------