%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE010+4 : 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 : n004.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 07:44:04 AM UTC 2026
% Result : Theorem 0.22s 5.64s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 17
% Syntax : Number of formulae : 159 ( 72 unt; 0 def)
% Number of atoms : 282 ( 131 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 268 ( 145 ~; 102 |; 12 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 124 ( 3 sgn 32 !; 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(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(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('theBenchmark.p',right_annihilation) ).
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(test_deMorgan1,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(addition(X0,X1)) = multiplication(c(X0),c(X1)) ),
file('theBenchmark.p',test_deMorgan1) ).
fof(test_deMorgan2,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
file('theBenchmark.p',test_deMorgan2) ).
fof(goals,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
( ~ complement(B,A)
| test(A) ),
inference(clausify,[status(thm)],[test_1]) ).
cnf(c_22,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_23,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_24,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_25,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_26,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_27,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_29,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| c(A) = B
| ~ test(A) ),
inference(resolve,[status(thm)],[c_27,c_25]) ).
cnf(c_30,plain,
( test(B)
| c(A) != B
| ~ test(A) ),
inference(resolve,[status(thm)],[c_26,c_20]) ).
cnf(c_31,plain,
( multiplication(B,A) = zero
| c(A) != B
| ~ test(A) ),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_32,plain,
( multiplication(A,B) = zero
| c(A) != B
| ~ test(A) ),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_33,plain,
( addition(B,A) = one
| c(A) != B
| ~ test(A) ),
inference(resolve,[status(thm)],[c_26,c_24]) ).
cnf(c_34,plain,
( test(A)
| addition(A,B) != one
| multiplication(B,A) != zero
| multiplication(A,B) != zero ),
inference(resolve,[status(thm)],[c_25,c_20]) ).
fof(nnf_19,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( ~ leq(addition(addition(addition(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK1)),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK1)),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0)))) )
& test(sK1)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_19]) ).
cnf(c_38,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK1)),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK1)),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0)))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_39,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_40,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_41,plain,
( c(multiplication(A,B)) = addition(c(A),c(B))
| ~ test(B)
| ~ test(A) ),
inference(clausify,[status(thm)],[test_deMorgan2]) ).
cnf(c_42,plain,
( addition(c(A),c(B)) = c(multiplication(A,B))
| ~ test(B)
| ~ test(A) ),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_43,plain,
( c(addition(A,B)) = multiplication(c(A),c(B))
| ~ test(B)
| ~ test(A) ),
inference(clausify,[status(thm)],[test_deMorgan1]) ).
cnf(c_44,plain,
( multiplication(c(A),c(B)) = c(addition(A,B))
| ~ test(B)
| ~ test(A) ),
inference(copy,[status(thm)],[c_43]) ).
cnf(c_46,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_48,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_49,plain,
multiplication(A,zero) = zero,
inference(clausify,[status(thm)],[right_annihilation]) ).
cnf(c_50,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_51,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_52,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_53,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_54,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_55,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_57,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_58,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_59,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_60,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_582,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK1)),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(addition(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0)))) ),
inference(paramod,[status(thm)],[c_51,c_38]) ).
cnf(c_583,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK1)),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0)))) ),
inference(paramod,[status(thm)],[c_60,c_582]) ).
cnf(c_584,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK1)),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1))),multiplication(c(sK1),c(sK0)))) ),
inference(paramod,[status(thm)],[c_60,c_583]) ).
cnf(c_585,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK1)),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1))))) ),
inference(paramod,[status(thm)],[c_60,c_584]) ).
cnf(c_586,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1))))) ),
inference(paramod,[status(thm)],[c_51,c_585]) ).
cnf(c_587,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1))))) ),
inference(paramod,[status(thm)],[c_60,c_586]) ).
cnf(c_588,negated_conjecture,
( ~ leq(addition(addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1))),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1))))) ),
inference(paramod,[status(thm)],[c_60,c_587]) ).
cnf(c_65,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1)))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1))))) ),
inference(paramod,[status(thm)],[c_60,c_588]) ).
cnf(c_589,negated_conjecture,
( addition(A,sK1) = one
| c(sK1) != A ),
inference(resolve,[status(thm)],[c_33,c_39]) ).
cnf(c_590,plain,
addition(c(sK1),sK1) = one,
inference(xxres,[status(thm)],[c_589]) ).
cnf(c_74,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_60,c_590]) ).
cnf(c_591,negated_conjecture,
( addition(A,sK0) = one
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_33,c_40]) ).
cnf(c_592,plain,
addition(c(sK0),sK0) = one,
inference(xxres,[status(thm)],[c_591]) ).
cnf(c_87,plain,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_60,c_592]) ).
cnf(c_593,negated_conjecture,
( multiplication(sK0,A) = zero
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_32,c_40]) ).
cnf(c_88,plain,
multiplication(sK0,c(sK0)) = zero,
inference(xxres,[status(thm)],[c_593]) ).
cnf(c_594,negated_conjecture,
( multiplication(A,sK0) = zero
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_31,c_40]) ).
cnf(c_89,plain,
multiplication(c(sK0),sK0) = zero,
inference(xxres,[status(thm)],[c_594]) ).
cnf(c_595,negated_conjecture,
( test(A)
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_30,c_40]) ).
cnf(c_90,plain,
test(c(sK0)),
inference(xxres,[status(thm)],[c_595]) ).
cnf(c_596,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1)))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(one,sK1))))) ),
inference(paramod,[status(thm)],[c_87,c_65]) ).
cnf(c_597,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1)))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),sK1)))) ),
inference(paramod,[status(thm)],[c_54,c_596]) ).
cnf(c_598,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1)))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_60,c_597]) ).
cnf(c_599,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(one,sK1)))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_87,c_598]) ).
cnf(c_600,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),sK1))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_54,c_599]) ).
cnf(c_92,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(sK1,sK0)))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_60,c_600]) ).
cnf(c_601,negated_conjecture,
( multiplication(c(sK0),c(A)) = c(addition(sK0,A))
| ~ test(A) ),
inference(resolve,[status(thm)],[c_44,c_40]) ).
cnf(c_602,negated_conjecture,
multiplication(c(sK0),c(sK1)) = c(addition(sK0,sK1)),
inference(resolve,[status(thm)],[c_601,c_39]) ).
cnf(c_107,negated_conjecture,
multiplication(c(sK0),c(sK1)) = c(addition(sK1,sK0)),
inference(paramod,[status(thm)],[c_60,c_602]) ).
cnf(c_603,negated_conjecture,
( multiplication(c(sK1),c(A)) = c(addition(sK1,A))
| ~ test(A) ),
inference(resolve,[status(thm)],[c_44,c_39]) ).
cnf(c_108,negated_conjecture,
multiplication(c(sK1),c(sK0)) = c(addition(sK1,sK0)),
inference(resolve,[status(thm)],[c_603,c_40]) ).
cnf(c_604,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(sK1,sK0)))),one)
| ~ leq(one,addition(c(addition(sK1,sK0)),addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_108,c_92]) ).
cnf(c_110,negated_conjecture,
( ~ leq(addition(c(addition(sK1,sK0)),addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(sK1,sK0)))),one)
| ~ leq(one,addition(c(addition(sK1,sK0)),addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_108,c_604]) ).
cnf(c_605,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_55,c_53]) ).
cnf(c_159,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_605]) ).
cnf(c_606,negated_conjecture,
( ~ leq(addition(c(addition(sK1,sK0)),addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(sK1,sK0)))),one)
| ~ leq(one,addition(c(addition(sK1,sK0)),addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(one,sK0))))) ),
inference(paramod,[status(thm)],[c_159,c_110]) ).
cnf(c_161,negated_conjecture,
( ~ leq(addition(c(addition(sK1,sK0)),addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(one,sK0)))),one)
| ~ leq(one,addition(c(addition(sK1,sK0)),addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(one,sK0))))) ),
inference(paramod,[status(thm)],[c_159,c_606]) ).
cnf(c_164,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_57,c_46]) ).
cnf(c_607,plain,
( test(one)
| multiplication(zero,one) != zero
| multiplication(one,zero) != zero ),
inference(resolve,[status(thm)],[c_58,c_34]) ).
cnf(c_608,plain,
( test(one)
| multiplication(zero,one) != zero
| zero != zero ),
inference(paramod,[status(thm)],[c_49,c_607]) ).
cnf(c_609,plain,
( test(one)
| zero != zero
| zero != zero ),
inference(paramod,[status(thm)],[c_55,c_608]) ).
cnf(c_610,plain,
( test(one)
| zero != zero ),
inference(copy,[status(thm)],[c_609]) ).
cnf(c_166,plain,
test(one),
inference(copy,[status(thm)],[c_610]) ).
cnf(c_188,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_60,c_58]) ).
cnf(c_611,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_60,c_59]) ).
cnf(c_189,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_59,c_611]) ).
cnf(c_612,negated_conjecture,
( ~ leq(addition(c(addition(sK1,sK0)),addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(one,sK0)))),one)
| ~ leq(one,addition(multiplication(c(sK1),sK0),addition(c(addition(sK1,sK0)),multiplication(sK1,addition(one,sK0))))) ),
inference(paramod,[status(thm)],[c_189,c_161]) ).
cnf(c_191,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(c(addition(sK1,sK0)),multiplication(sK1,addition(one,sK0)))),one)
| ~ leq(one,addition(multiplication(c(sK1),sK0),addition(c(addition(sK1,sK0)),multiplication(sK1,addition(one,sK0))))) ),
inference(paramod,[status(thm)],[c_189,c_612]) ).
cnf(c_613,plain,
( multiplication(one,A) = zero
| c(one) != A ),
inference(resolve,[status(thm)],[c_32,c_166]) ).
cnf(c_614,plain,
A = addition(A,zero),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_615,plain,
multiplication(one,addition(c(one),zero)) = zero,
inference(resolve,[status(thm)],[c_613,c_614]) ).
cnf(c_616,plain,
multiplication(one,addition(zero,c(one))) = zero,
inference(paramod,[status(thm)],[c_60,c_615]) ).
cnf(c_617,plain,
multiplication(one,c(one)) = zero,
inference(paramod,[status(thm)],[c_188,c_616]) ).
cnf(c_219,plain,
c(one) = zero,
inference(paramod,[status(thm)],[c_54,c_617]) ).
cnf(c_618,plain,
( test(A)
| c(one) != A ),
inference(resolve,[status(thm)],[c_30,c_166]) ).
cnf(c_619,plain,
A = addition(A,zero),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_620,plain,
test(addition(c(one),zero)),
inference(resolve,[status(thm)],[c_618,c_619]) ).
cnf(c_621,plain,
test(addition(zero,zero)),
inference(paramod,[status(thm)],[c_219,c_620]) ).
cnf(c_220,plain,
test(zero),
inference(paramod,[status(thm)],[c_57,c_621]) ).
cnf(c_622,plain,
( addition(A,zero) = one
| c(zero) != A ),
inference(resolve,[status(thm)],[c_33,c_220]) ).
cnf(c_623,plain,
A = addition(A,zero),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_624,plain,
addition(addition(c(zero),zero),zero) = one,
inference(resolve,[status(thm)],[c_622,c_623]) ).
cnf(c_625,plain,
addition(addition(zero,c(zero)),zero) = one,
inference(paramod,[status(thm)],[c_60,c_624]) ).
cnf(c_626,plain,
addition(c(zero),zero) = one,
inference(paramod,[status(thm)],[c_188,c_625]) ).
cnf(c_627,plain,
addition(zero,c(zero)) = one,
inference(paramod,[status(thm)],[c_60,c_626]) ).
cnf(c_249,plain,
c(zero) = one,
inference(paramod,[status(thm)],[c_188,c_627]) ).
cnf(c_628,negated_conjecture,
( multiplication(c(sK1),c(A)) = c(addition(sK1,A))
| ~ test(A) ),
inference(resolve,[status(thm)],[c_44,c_39]) ).
cnf(c_304,negated_conjecture,
multiplication(c(sK1),c(c(sK0))) = c(addition(sK1,c(sK0))),
inference(resolve,[status(thm)],[c_628,c_90]) ).
cnf(c_629,plain,
( multiplication(c(c(sK0)),c(A)) = c(addition(c(sK0),A))
| ~ test(A) ),
inference(resolve,[status(thm)],[c_44,c_90]) ).
cnf(c_630,negated_conjecture,
multiplication(c(c(sK0)),c(sK1)) = c(addition(c(sK0),sK1)),
inference(resolve,[status(thm)],[c_629,c_39]) ).
cnf(c_308,negated_conjecture,
multiplication(c(c(sK0)),c(sK1)) = c(addition(sK1,c(sK0))),
inference(paramod,[status(thm)],[c_60,c_630]) ).
cnf(c_631,plain,
( addition(c(zero),c(A)) = c(multiplication(zero,A))
| ~ test(A) ),
inference(resolve,[status(thm)],[c_42,c_220]) ).
cnf(c_632,plain,
addition(c(zero),c(c(sK0))) = c(multiplication(zero,c(sK0))),
inference(resolve,[status(thm)],[c_631,c_90]) ).
cnf(c_633,plain,
addition(one,c(c(sK0))) = c(multiplication(zero,c(sK0))),
inference(paramod,[status(thm)],[c_249,c_632]) ).
cnf(c_634,plain,
addition(one,c(c(sK0))) = c(zero),
inference(paramod,[status(thm)],[c_48,c_633]) ).
cnf(c_309,plain,
addition(one,c(c(sK0))) = one,
inference(paramod,[status(thm)],[c_249,c_634]) ).
cnf(c_635,plain,
( addition(A,c(sK0)) != one
| multiplication(c(sK0),A) != zero
| multiplication(A,c(sK0)) != zero
| c(c(sK0)) = A ),
inference(resolve,[status(thm)],[c_29,c_90]) ).
cnf(c_636,plain,
( addition(sK0,c(sK0)) != one
| multiplication(c(sK0),sK0) != zero
| c(c(sK0)) = sK0 ),
inference(resolve,[status(thm)],[c_635,c_88]) ).
cnf(c_637,plain,
( addition(sK0,c(sK0)) != one
| c(c(sK0)) = sK0 ),
inference(resolve,[status(thm)],[c_636,c_89]) ).
cnf(c_461,plain,
c(c(sK0)) = sK0,
inference(resolve,[status(thm)],[c_637,c_87]) ).
cnf(c_477,plain,
addition(one,sK0) = one,
inference(paramod,[status(thm)],[c_461,c_309]) ).
cnf(c_638,negated_conjecture,
multiplication(sK0,c(sK1)) = c(addition(sK1,c(sK0))),
inference(paramod,[status(thm)],[c_461,c_308]) ).
cnf(c_478,negated_conjecture,
c(addition(sK1,c(sK0))) = multiplication(sK0,c(sK1)),
inference(copy,[status(thm)],[c_638]) ).
cnf(c_639,negated_conjecture,
multiplication(c(sK1),sK0) = c(addition(sK1,c(sK0))),
inference(paramod,[status(thm)],[c_461,c_304]) ).
cnf(c_480,negated_conjecture,
multiplication(c(sK1),sK0) = multiplication(sK0,c(sK1)),
inference(paramod,[status(thm)],[c_478,c_639]) ).
cnf(c_640,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(c(addition(sK1,sK0)),multiplication(sK1,addition(one,sK0)))),one)
| ~ leq(one,addition(multiplication(sK0,c(sK1)),addition(c(addition(sK1,sK0)),multiplication(sK1,addition(one,sK0))))) ),
inference(paramod,[status(thm)],[c_480,c_191]) ).
cnf(c_641,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(c(addition(sK1,sK0)),multiplication(sK1,addition(one,sK0)))),one)
| ~ leq(one,addition(multiplication(sK0,c(sK1)),addition(c(addition(sK1,sK0)),multiplication(sK1,one)))) ),
inference(paramod,[status(thm)],[c_477,c_640]) ).
cnf(c_642,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(c(addition(sK1,sK0)),multiplication(sK1,addition(one,sK0)))),one)
| ~ leq(one,addition(multiplication(sK0,c(sK1)),addition(c(addition(sK1,sK0)),sK1))) ),
inference(paramod,[status(thm)],[c_55,c_641]) ).
cnf(c_643,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(c(addition(sK1,sK0)),multiplication(sK1,addition(one,sK0)))),one)
| ~ leq(one,addition(multiplication(sK0,c(sK1)),addition(sK1,c(addition(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_60,c_642]) ).
cnf(c_644,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(c(addition(sK1,sK0)),multiplication(sK1,addition(one,sK0)))),one)
| ~ leq(one,addition(sK1,addition(multiplication(sK0,c(sK1)),c(addition(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_189,c_643]) ).
cnf(c_645,negated_conjecture,
( ~ leq(addition(multiplication(sK0,c(sK1)),addition(c(addition(sK1,sK0)),multiplication(sK1,addition(one,sK0)))),one)
| ~ leq(one,addition(sK1,addition(multiplication(sK0,c(sK1)),c(addition(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_480,c_644]) ).
cnf(c_646,negated_conjecture,
( ~ leq(addition(multiplication(sK0,c(sK1)),addition(c(addition(sK1,sK0)),multiplication(sK1,one))),one)
| ~ leq(one,addition(sK1,addition(multiplication(sK0,c(sK1)),c(addition(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_477,c_645]) ).
cnf(c_647,negated_conjecture,
( ~ leq(addition(multiplication(sK0,c(sK1)),addition(c(addition(sK1,sK0)),sK1)),one)
| ~ leq(one,addition(sK1,addition(multiplication(sK0,c(sK1)),c(addition(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_55,c_646]) ).
cnf(c_648,negated_conjecture,
( ~ leq(addition(multiplication(sK0,c(sK1)),addition(sK1,c(addition(sK1,sK0)))),one)
| ~ leq(one,addition(sK1,addition(multiplication(sK0,c(sK1)),c(addition(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_60,c_647]) ).
cnf(c_493,negated_conjecture,
( ~ leq(addition(sK1,addition(multiplication(sK0,c(sK1)),c(addition(sK1,sK0)))),one)
| ~ leq(one,addition(sK1,addition(multiplication(sK0,c(sK1)),c(addition(sK1,sK0))))) ),
inference(paramod,[status(thm)],[c_189,c_648]) ).
cnf(c_577,plain,
addition(multiplication(A,c(sK1)),c(addition(sK1,sK0))) = multiplication(addition(A,c(sK0)),c(sK1)),
inference(paramod,[status(thm)],[c_107,c_51]) ).
cnf(c_649,negated_conjecture,
( ~ leq(addition(sK1,addition(multiplication(sK0,c(sK1)),c(addition(sK1,sK0)))),one)
| ~ leq(one,addition(sK1,multiplication(addition(sK0,c(sK0)),c(sK1)))) ),
inference(paramod,[status(thm)],[c_577,c_493]) ).
cnf(c_650,negated_conjecture,
( ~ leq(addition(sK1,addition(multiplication(sK0,c(sK1)),c(addition(sK1,sK0)))),one)
| ~ leq(one,addition(sK1,multiplication(one,c(sK1)))) ),
inference(paramod,[status(thm)],[c_87,c_649]) ).
cnf(c_651,negated_conjecture,
( ~ leq(addition(sK1,addition(multiplication(sK0,c(sK1)),c(addition(sK1,sK0)))),one)
| ~ leq(one,addition(sK1,c(sK1))) ),
inference(paramod,[status(thm)],[c_54,c_650]) ).
cnf(c_652,negated_conjecture,
( ~ leq(addition(sK1,addition(multiplication(sK0,c(sK1)),c(addition(sK1,sK0)))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_74,c_651]) ).
cnf(c_653,negated_conjecture,
( ~ leq(addition(sK1,multiplication(addition(sK0,c(sK0)),c(sK1))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_577,c_652]) ).
cnf(c_654,negated_conjecture,
( ~ leq(addition(sK1,multiplication(one,c(sK1))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_87,c_653]) ).
cnf(c_655,negated_conjecture,
( ~ leq(addition(sK1,c(sK1)),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_54,c_654]) ).
cnf(c_656,negated_conjecture,
( ~ leq(one,one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_74,c_655]) ).
cnf(c_657,negated_conjecture,
~ leq(one,one),
inference(copy,[status(thm)],[c_656]) ).
cnf(c_581,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_164,c_657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE010+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n004.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Fri Sep 25 19:12:27 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.44 % Process 3841881 was started by sandbox2 on n004,
% 0.16/5.44 % Fri Sep 25 19:12:27 2026
% 0.16/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.46
% 0.16/5.46 % From the command line: assign(max_seconds, 300).
% 0.22/5.64
% 0.22/5.64 % SZS status Theorem for theBenchmark
% 0.22/5.64
% 0.22/5.64 % Proof 1 at 0.11 (+ 0.05) seconds.
% 0.22/5.64 % Length of proof is 80.
% 0.22/5.64 % Level of proof is 10.
% 0.22/5.64 % Maximum clause weight is 115.000.
% 0.22/5.64 % Given clauses 150.
% 0.22/5.64
% 0.22/5.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------