%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE028+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 : n002.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 07:44:08 AM UTC 2026
% Result : Theorem 82.13s 10.79s
% Output : CNFRefutation 82.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 14
% Syntax : Number of formulae : 233 ( 216 unt; 0 def)
% Number of atoms : 264 ( 223 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 29 ~; 14 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 241 ( 4 sgn 43 !; 8 ?)
% 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_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(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
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,X3,X4,X5] :
( ( test(X5)
& test(X4) )
=> addition(multiplication(X4,addition(multiplication(X5,X0),multiplication(c(X5),X1))),multiplication(c(X4),addition(multiplication(X5,X2),multiplication(c(X5),X3)))) = addition(multiplication(X5,addition(multiplication(X4,X0),multiplication(c(X4),X2))),multiplication(c(X5),addition(multiplication(X4,X1),multiplication(c(X4),X3)))) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( test(X5)
& test(X4) )
=> addition(multiplication(X4,addition(multiplication(X5,X0),multiplication(c(X5),X1))),multiplication(c(X4),addition(multiplication(X5,X2),multiplication(c(X5),X3)))) = addition(multiplication(X5,addition(multiplication(X4,X0),multiplication(c(X4),X2))),multiplication(c(X5),addition(multiplication(X4,X1),multiplication(c(X4),X3)))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1,X2,X3,X4,X5] :
( addition(multiplication(X5,addition(multiplication(X4,X0),multiplication(c(X4),X2))),multiplication(c(X5),addition(multiplication(X4,X1),multiplication(c(X4),X3)))) != addition(multiplication(X4,addition(multiplication(X5,X0),multiplication(c(X5),X1))),multiplication(c(X4),addition(multiplication(X5,X2),multiplication(c(X5),X3))))
& test(X5)
& test(X4) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( addition(multiplication(sK1,addition(multiplication(sK0,sK3),multiplication(c(sK0),sK4))),multiplication(c(sK1),addition(multiplication(sK0,sK5),multiplication(c(sK0),sK6)))) != addition(multiplication(sK0,addition(multiplication(sK1,sK3),multiplication(c(sK1),sK5))),multiplication(c(sK0),addition(multiplication(sK1,sK4),multiplication(c(sK1),sK6))))
& test(sK1)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK5),skolemize(X2,sK4),skolemize(X3,sK6),skolemize(X4,sK0),skolemize(X5,sK1)],[nnf_17]) ).
cnf(c_22,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_23,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_24,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
fof(nnf_13,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X6] : complement(X6,X0)
| ~ test(X0) ) ),
inference(fof_nnf,[status(thm)],[test_1]) ).
fof(sk_test_1_sk,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( complement(sK2(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X6,sK2(X0))],[nnf_13]) ).
fof(sk_test_1,plain,
( ! [VAR_0,VAR_1] :
( ~ complement(VAR_1,VAR_0)
| test(VAR_0) )
& ! [VAR_0] :
( complement(sK2(VAR_0),VAR_0)
| ~ test(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_test_1_sk]) ).
cnf(c_26,plain,
( complement(sK2(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_27,negated_conjecture,
complement(sK2(sK1),sK1),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_28,negated_conjecture,
complement(sK2(sK0),sK0),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_33,negated_conjecture,
( complement(sK1,A)
| c(sK1) != A ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_34,negated_conjecture,
( complement(sK0,A)
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_39,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_40,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_41,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_42,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_43,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_44,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_45,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
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(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_49,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_51,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_52,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_53,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_54,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_56,negated_conjecture,
addition(multiplication(sK1,addition(multiplication(sK0,sK3),multiplication(c(sK0),sK4))),multiplication(c(sK1),addition(multiplication(sK0,sK5),multiplication(c(sK0),sK6)))) != addition(multiplication(sK0,addition(multiplication(sK1,sK3),multiplication(c(sK1),sK5))),multiplication(c(sK0),addition(multiplication(sK1,sK4),multiplication(c(sK1),sK6)))),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_57,negated_conjecture,
addition(multiplication(sK0,addition(multiplication(sK1,sK3),multiplication(c(sK1),sK5))),multiplication(c(sK0),addition(multiplication(sK1,sK4),multiplication(c(sK1),sK6)))) != addition(multiplication(sK1,addition(multiplication(sK0,sK3),multiplication(c(sK0),sK4))),multiplication(c(sK1),addition(multiplication(sK0,sK5),multiplication(c(sK0),sK6)))),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_64,plain,
complement(sK1,c(sK1)),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_65,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_34]) ).
cnf(c_20993,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_39,c_40]) ).
cnf(c_72,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_40,c_20993]) ).
cnf(c_20994,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_41,c_39]) ).
cnf(c_76,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_20994]) ).
cnf(c_20995,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_77,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_20995]) ).
cnf(c_20996,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_79,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_39,c_20996]) ).
cnf(c_80,plain,
addition(multiplication(A,addition(B,C)),D) = addition(multiplication(A,B),addition(multiplication(A,C),D)),
inference(paramod,[status(thm)],[c_47,c_40]) ).
cnf(c_20997,negated_conjecture,
addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK0),addition(multiplication(sK1,sK4),multiplication(c(sK1),sK6))))) != addition(multiplication(sK1,addition(multiplication(sK0,sK3),multiplication(c(sK0),sK4))),multiplication(c(sK1),addition(multiplication(sK0,sK5),multiplication(c(sK0),sK6)))),
inference(paramod,[status(thm)],[c_80,c_57]) ).
cnf(c_83,negated_conjecture,
addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK0),addition(multiplication(sK1,sK4),multiplication(c(sK1),sK6))))) != addition(multiplication(sK1,multiplication(sK0,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),multiplication(c(sK1),addition(multiplication(sK0,sK5),multiplication(c(sK0),sK6))))),
inference(paramod,[status(thm)],[c_80,c_20997]) ).
cnf(c_84,plain,
addition(multiplication(addition(A,B),C),D) = addition(multiplication(A,C),addition(multiplication(B,C),D)),
inference(paramod,[status(thm)],[c_49,c_40]) ).
cnf(c_96,plain,
addition(sK0,sK2(sK0)) = one,
inference(resolve,[status(thm)],[c_54,c_28]) ).
cnf(c_97,plain,
addition(sK1,sK2(sK1)) = one,
inference(resolve,[status(thm)],[c_54,c_27]) ).
cnf(c_20998,plain,
addition(c(sK1),sK1) = one,
inference(resolve,[status(thm)],[c_64,c_54]) ).
cnf(c_112,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_39,c_20998]) ).
cnf(c_113,plain,
multiplication(sK1,c(sK1)) = zero,
inference(resolve,[status(thm)],[c_64,c_53]) ).
cnf(c_114,plain,
multiplication(c(sK1),sK1) = zero,
inference(resolve,[status(thm)],[c_64,c_52]) ).
cnf(c_20999,plain,
addition(c(sK0),sK0) = one,
inference(resolve,[status(thm)],[c_65,c_54]) ).
cnf(c_118,plain,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_39,c_20999]) ).
cnf(c_119,plain,
multiplication(sK0,c(sK0)) = zero,
inference(resolve,[status(thm)],[c_65,c_53]) ).
cnf(c_120,plain,
multiplication(c(sK0),sK0) = zero,
inference(resolve,[status(thm)],[c_65,c_52]) ).
cnf(c_21000,plain,
addition(multiplication(sK1,A),zero) = multiplication(sK1,addition(A,c(sK1))),
inference(paramod,[status(thm)],[c_113,c_47]) ).
cnf(c_21001,plain,
addition(zero,multiplication(sK1,A)) = multiplication(sK1,addition(A,c(sK1))),
inference(paramod,[status(thm)],[c_39,c_21000]) ).
cnf(c_21002,plain,
multiplication(sK1,A) = multiplication(sK1,addition(A,c(sK1))),
inference(paramod,[status(thm)],[c_76,c_21001]) ).
cnf(c_175,plain,
multiplication(sK1,addition(A,c(sK1))) = multiplication(sK1,A),
inference(copy,[status(thm)],[c_21002]) ).
cnf(c_21003,plain,
addition(zero,multiplication(A,c(sK1))) = multiplication(addition(sK1,A),c(sK1)),
inference(paramod,[status(thm)],[c_113,c_49]) ).
cnf(c_21004,plain,
multiplication(A,c(sK1)) = multiplication(addition(sK1,A),c(sK1)),
inference(paramod,[status(thm)],[c_76,c_21003]) ).
cnf(c_176,plain,
multiplication(addition(sK1,A),c(sK1)) = multiplication(A,c(sK1)),
inference(copy,[status(thm)],[c_21004]) ).
cnf(c_21005,plain,
addition(multiplication(A,c(sK1)),zero) = multiplication(addition(A,sK1),c(sK1)),
inference(paramod,[status(thm)],[c_113,c_49]) ).
cnf(c_21006,plain,
addition(zero,multiplication(A,c(sK1))) = multiplication(addition(A,sK1),c(sK1)),
inference(paramod,[status(thm)],[c_39,c_21005]) ).
cnf(c_21007,plain,
multiplication(A,c(sK1)) = multiplication(addition(A,sK1),c(sK1)),
inference(paramod,[status(thm)],[c_76,c_21006]) ).
cnf(c_177,plain,
multiplication(addition(A,sK1),c(sK1)) = multiplication(A,c(sK1)),
inference(copy,[status(thm)],[c_21007]) ).
cnf(c_21008,plain,
addition(zero,multiplication(c(sK1),A)) = multiplication(c(sK1),addition(sK1,A)),
inference(paramod,[status(thm)],[c_114,c_47]) ).
cnf(c_21009,plain,
multiplication(c(sK1),A) = multiplication(c(sK1),addition(sK1,A)),
inference(paramod,[status(thm)],[c_76,c_21008]) ).
cnf(c_179,plain,
multiplication(c(sK1),addition(sK1,A)) = multiplication(c(sK1),A),
inference(copy,[status(thm)],[c_21009]) ).
cnf(c_21010,plain,
addition(multiplication(c(sK1),A),zero) = multiplication(c(sK1),addition(A,sK1)),
inference(paramod,[status(thm)],[c_114,c_47]) ).
cnf(c_21011,plain,
addition(zero,multiplication(c(sK1),A)) = multiplication(c(sK1),addition(A,sK1)),
inference(paramod,[status(thm)],[c_39,c_21010]) ).
cnf(c_21012,plain,
multiplication(c(sK1),A) = multiplication(c(sK1),addition(A,sK1)),
inference(paramod,[status(thm)],[c_76,c_21011]) ).
cnf(c_180,plain,
multiplication(c(sK1),addition(A,sK1)) = multiplication(c(sK1),A),
inference(copy,[status(thm)],[c_21012]) ).
cnf(c_21013,plain,
addition(zero,multiplication(A,sK1)) = multiplication(addition(c(sK1),A),sK1),
inference(paramod,[status(thm)],[c_114,c_49]) ).
cnf(c_21014,plain,
multiplication(A,sK1) = multiplication(addition(c(sK1),A),sK1),
inference(paramod,[status(thm)],[c_76,c_21013]) ).
cnf(c_181,plain,
multiplication(addition(c(sK1),A),sK1) = multiplication(A,sK1),
inference(copy,[status(thm)],[c_21014]) ).
cnf(c_21015,plain,
addition(zero,multiplication(A,c(sK0))) = multiplication(addition(sK0,A),c(sK0)),
inference(paramod,[status(thm)],[c_119,c_49]) ).
cnf(c_21016,plain,
multiplication(A,c(sK0)) = multiplication(addition(sK0,A),c(sK0)),
inference(paramod,[status(thm)],[c_76,c_21015]) ).
cnf(c_196,plain,
multiplication(addition(sK0,A),c(sK0)) = multiplication(A,c(sK0)),
inference(copy,[status(thm)],[c_21016]) ).
cnf(c_21017,plain,
addition(zero,multiplication(c(sK0),A)) = multiplication(c(sK0),addition(sK0,A)),
inference(paramod,[status(thm)],[c_120,c_47]) ).
cnf(c_21018,plain,
multiplication(c(sK0),A) = multiplication(c(sK0),addition(sK0,A)),
inference(paramod,[status(thm)],[c_76,c_21017]) ).
cnf(c_199,plain,
multiplication(c(sK0),addition(sK0,A)) = multiplication(c(sK0),A),
inference(copy,[status(thm)],[c_21018]) ).
cnf(c_21019,plain,
addition(A,multiplication(B,addition(C,D))) = addition(multiplication(B,C),addition(A,multiplication(B,D))),
inference(paramod,[status(thm)],[c_47,c_72]) ).
cnf(c_208,plain,
addition(multiplication(A,B),addition(C,multiplication(A,D))) = addition(C,multiplication(A,addition(B,D))),
inference(copy,[status(thm)],[c_21019]) ).
cnf(c_21020,plain,
addition(sK0,one) = addition(sK0,sK2(sK0)),
inference(paramod,[status(thm)],[c_96,c_77]) ).
cnf(c_21021,plain,
addition(one,sK0) = addition(sK0,sK2(sK0)),
inference(paramod,[status(thm)],[c_39,c_21020]) ).
cnf(c_221,plain,
addition(one,sK0) = one,
inference(paramod,[status(thm)],[c_96,c_21021]) ).
cnf(c_21022,plain,
addition(sK1,one) = addition(sK1,sK2(sK1)),
inference(paramod,[status(thm)],[c_97,c_77]) ).
cnf(c_21023,plain,
addition(one,sK1) = addition(sK1,sK2(sK1)),
inference(paramod,[status(thm)],[c_39,c_21022]) ).
cnf(c_222,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_97,c_21023]) ).
cnf(c_21024,plain,
addition(multiplication(A,one),multiplication(A,sK0)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_221,c_47]) ).
cnf(c_21025,plain,
addition(A,multiplication(A,sK0)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_44,c_21024]) ).
cnf(c_226,plain,
addition(A,multiplication(A,sK0)) = A,
inference(paramod,[status(thm)],[c_44,c_21025]) ).
cnf(c_21026,plain,
addition(multiplication(one,A),multiplication(sK0,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_221,c_49]) ).
cnf(c_21027,plain,
addition(A,multiplication(sK0,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_45,c_21026]) ).
cnf(c_227,plain,
addition(A,multiplication(sK0,A)) = A,
inference(paramod,[status(thm)],[c_45,c_21027]) ).
cnf(c_21028,plain,
addition(multiplication(A,one),multiplication(A,sK1)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_222,c_47]) ).
cnf(c_21029,plain,
addition(A,multiplication(A,sK1)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_44,c_21028]) ).
cnf(c_232,plain,
addition(A,multiplication(A,sK1)) = A,
inference(paramod,[status(thm)],[c_44,c_21029]) ).
cnf(c_21030,plain,
addition(multiplication(one,A),multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_222,c_49]) ).
cnf(c_21031,plain,
addition(A,multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_45,c_21030]) ).
cnf(c_233,plain,
addition(A,multiplication(sK1,A)) = A,
inference(paramod,[status(thm)],[c_45,c_21031]) ).
cnf(c_21032,plain,
addition(A,addition(B,addition(C,A))) = addition(addition(B,C),A),
inference(paramod,[status(thm)],[c_40,c_79]) ).
cnf(c_236,plain,
addition(A,addition(B,addition(C,A))) = addition(B,addition(C,A)),
inference(paramod,[status(thm)],[c_40,c_21032]) ).
cnf(c_21033,plain,
addition(c(sK1),one) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_112,c_79]) ).
cnf(c_21034,plain,
addition(one,c(sK1)) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_39,c_21033]) ).
cnf(c_240,plain,
addition(one,c(sK1)) = one,
inference(paramod,[status(thm)],[c_112,c_21034]) ).
cnf(c_21035,plain,
addition(multiplication(A,one),B) = addition(multiplication(A,sK1),addition(multiplication(A,c(sK1)),B)),
inference(paramod,[status(thm)],[c_112,c_80]) ).
cnf(c_21036,plain,
addition(A,B) = addition(multiplication(A,sK1),addition(multiplication(A,c(sK1)),B)),
inference(paramod,[status(thm)],[c_44,c_21035]) ).
cnf(c_259,plain,
addition(multiplication(A,sK1),addition(multiplication(A,c(sK1)),B)) = addition(A,B),
inference(copy,[status(thm)],[c_21036]) ).
cnf(c_21037,plain,
addition(multiplication(A,one),B) = addition(multiplication(A,sK0),addition(multiplication(A,c(sK0)),B)),
inference(paramod,[status(thm)],[c_118,c_80]) ).
cnf(c_21038,plain,
addition(A,B) = addition(multiplication(A,sK0),addition(multiplication(A,c(sK0)),B)),
inference(paramod,[status(thm)],[c_44,c_21037]) ).
cnf(c_260,plain,
addition(multiplication(A,sK0),addition(multiplication(A,c(sK0)),B)) = addition(A,B),
inference(copy,[status(thm)],[c_21038]) ).
cnf(c_21039,plain,
addition(multiplication(A,one),multiplication(A,c(sK1))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_240,c_47]) ).
cnf(c_21040,plain,
addition(A,multiplication(A,c(sK1))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_44,c_21039]) ).
cnf(c_269,plain,
addition(A,multiplication(A,c(sK1))) = A,
inference(paramod,[status(thm)],[c_44,c_21040]) ).
cnf(c_21041,plain,
addition(multiplication(one,A),multiplication(c(sK1),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_240,c_49]) ).
cnf(c_21042,plain,
addition(A,multiplication(c(sK1),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_45,c_21041]) ).
cnf(c_270,plain,
addition(A,multiplication(c(sK1),A)) = A,
inference(paramod,[status(thm)],[c_45,c_21042]) ).
cnf(c_21043,plain,
addition(addition(A,B),multiplication(B,sK0)) = addition(A,B),
inference(paramod,[status(thm)],[c_226,c_40]) ).
cnf(c_280,plain,
addition(multiplication(A,sK0),addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_39,c_21043]) ).
cnf(c_21044,plain,
addition(addition(A,B),multiplication(sK0,B)) = addition(A,B),
inference(paramod,[status(thm)],[c_227,c_40]) ).
cnf(c_287,plain,
addition(multiplication(sK0,A),addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_39,c_21044]) ).
cnf(c_21045,plain,
addition(addition(A,B),multiplication(B,sK1)) = addition(A,B),
inference(paramod,[status(thm)],[c_232,c_40]) ).
cnf(c_309,plain,
addition(multiplication(A,sK1),addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_39,c_21045]) ).
cnf(c_21046,plain,
addition(addition(A,B),multiplication(sK1,B)) = addition(A,B),
inference(paramod,[status(thm)],[c_233,c_40]) ).
cnf(c_316,plain,
addition(multiplication(sK1,A),addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_39,c_21046]) ).
cnf(c_21047,plain,
addition(multiplication(one,A),B) = addition(multiplication(sK1,A),addition(multiplication(c(sK1),A),B)),
inference(paramod,[status(thm)],[c_112,c_84]) ).
cnf(c_21048,plain,
addition(A,B) = addition(multiplication(sK1,A),addition(multiplication(c(sK1),A),B)),
inference(paramod,[status(thm)],[c_45,c_21047]) ).
cnf(c_366,plain,
addition(multiplication(sK1,A),addition(multiplication(c(sK1),A),B)) = addition(A,B),
inference(copy,[status(thm)],[c_21048]) ).
cnf(c_21049,plain,
addition(multiplication(one,A),B) = addition(multiplication(sK0,A),addition(multiplication(c(sK0),A),B)),
inference(paramod,[status(thm)],[c_118,c_84]) ).
cnf(c_21050,plain,
addition(A,B) = addition(multiplication(sK0,A),addition(multiplication(c(sK0),A),B)),
inference(paramod,[status(thm)],[c_45,c_21049]) ).
cnf(c_367,plain,
addition(multiplication(sK0,A),addition(multiplication(c(sK0),A),B)) = addition(A,B),
inference(copy,[status(thm)],[c_21050]) ).
cnf(c_21051,plain,
multiplication(c(sK1),sK1) = multiplication(multiplication(c(sK1),sK0),sK1),
inference(paramod,[status(thm)],[c_226,c_181]) ).
cnf(c_21052,plain,
zero = multiplication(multiplication(c(sK1),sK0),sK1),
inference(paramod,[status(thm)],[c_114,c_21051]) ).
cnf(c_21053,plain,
zero = multiplication(c(sK1),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_43,c_21052]) ).
cnf(c_1577,plain,
multiplication(c(sK1),multiplication(sK0,sK1)) = zero,
inference(copy,[status(thm)],[c_21053]) ).
cnf(c_21054,plain,
multiplication(zero,A) = multiplication(c(sK1),multiplication(multiplication(sK0,sK1),A)),
inference(paramod,[status(thm)],[c_1577,c_43]) ).
cnf(c_21055,plain,
zero = multiplication(c(sK1),multiplication(multiplication(sK0,sK1),A)),
inference(paramod,[status(thm)],[c_51,c_21054]) ).
cnf(c_21056,plain,
zero = multiplication(c(sK1),multiplication(sK0,multiplication(sK1,A))),
inference(paramod,[status(thm)],[c_43,c_21055]) ).
cnf(c_1589,plain,
multiplication(c(sK1),multiplication(sK0,multiplication(sK1,A))) = zero,
inference(copy,[status(thm)],[c_21056]) ).
cnf(c_1978,plain,
addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(c(sK0),multiplication(sK1,sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK0),multiplication(c(sK1),sK6))))) != addition(multiplication(sK1,multiplication(sK0,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),multiplication(c(sK1),addition(multiplication(sK0,sK5),multiplication(c(sK0),sK6))))),
inference(paramod,[status(thm)],[c_208,c_83]) ).
cnf(c_21057,plain,
addition(multiplication(A,c(sK1)),addition(B,A)) = addition(B,addition(A,multiplication(A,c(sK1)))),
inference(paramod,[status(thm)],[c_269,c_236]) ).
cnf(c_2501,plain,
addition(multiplication(A,c(sK1)),addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_269,c_21057]) ).
cnf(c_21058,plain,
addition(multiplication(c(sK1),A),addition(B,A)) = addition(B,addition(A,multiplication(c(sK1),A))),
inference(paramod,[status(thm)],[c_270,c_236]) ).
cnf(c_2502,plain,
addition(multiplication(c(sK1),A),addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_270,c_21058]) ).
cnf(c_21059,plain,
addition(multiplication(sK0,c(sK1)),sK1) = addition(sK0,sK1),
inference(paramod,[status(thm)],[c_287,c_259]) ).
cnf(c_3978,plain,
addition(sK1,multiplication(sK0,c(sK1))) = addition(sK0,sK1),
inference(paramod,[status(thm)],[c_39,c_21059]) ).
cnf(c_21060,plain,
multiplication(c(sK1),addition(sK0,sK1)) = multiplication(c(sK1),multiplication(sK0,c(sK1))),
inference(paramod,[status(thm)],[c_3978,c_179]) ).
cnf(c_21061,plain,
multiplication(c(sK1),sK0) = multiplication(c(sK1),multiplication(sK0,c(sK1))),
inference(paramod,[status(thm)],[c_180,c_21060]) ).
cnf(c_3989,plain,
multiplication(c(sK1),multiplication(sK0,c(sK1))) = multiplication(c(sK1),sK0),
inference(copy,[status(thm)],[c_21061]) ).
cnf(c_21062,plain,
addition(multiplication(sK1,c(sK0)),sK0) = addition(sK1,sK0),
inference(paramod,[status(thm)],[c_316,c_260]) ).
cnf(c_21063,plain,
addition(sK0,multiplication(sK1,c(sK0))) = addition(sK1,sK0),
inference(paramod,[status(thm)],[c_39,c_21062]) ).
cnf(c_4209,plain,
addition(sK0,multiplication(sK1,c(sK0))) = addition(sK0,sK1),
inference(paramod,[status(thm)],[c_39,c_21063]) ).
cnf(c_21064,plain,
multiplication(c(sK0),addition(sK0,sK1)) = multiplication(c(sK0),multiplication(sK1,c(sK0))),
inference(paramod,[status(thm)],[c_4209,c_199]) ).
cnf(c_21065,plain,
multiplication(c(sK0),sK1) = multiplication(c(sK0),multiplication(sK1,c(sK0))),
inference(paramod,[status(thm)],[c_199,c_21064]) ).
cnf(c_4219,plain,
multiplication(c(sK0),multiplication(sK1,c(sK0))) = multiplication(c(sK0),sK1),
inference(copy,[status(thm)],[c_21065]) ).
cnf(c_21066,plain,
addition(multiplication(sK1,multiplication(sK0,multiplication(sK1,A))),addition(zero,B)) = addition(multiplication(sK0,multiplication(sK1,A)),B),
inference(paramod,[status(thm)],[c_1589,c_366]) ).
cnf(c_13108,plain,
addition(multiplication(sK1,multiplication(sK0,multiplication(sK1,A))),B) = addition(multiplication(sK0,multiplication(sK1,A)),B),
inference(paramod,[status(thm)],[c_76,c_21066]) ).
cnf(c_21067,plain,
addition(sK0,sK1) = addition(multiplication(c(sK1),sK0),sK1),
inference(paramod,[status(thm)],[c_366,c_280]) ).
cnf(c_21068,plain,
addition(sK0,sK1) = addition(sK1,multiplication(c(sK1),sK0)),
inference(paramod,[status(thm)],[c_39,c_21067]) ).
cnf(c_13113,plain,
addition(sK1,multiplication(c(sK1),sK0)) = addition(sK0,sK1),
inference(copy,[status(thm)],[c_21068]) ).
cnf(c_21069,plain,
multiplication(addition(sK0,sK1),c(sK1)) = multiplication(multiplication(c(sK1),sK0),c(sK1)),
inference(paramod,[status(thm)],[c_13113,c_176]) ).
cnf(c_21070,plain,
multiplication(sK0,c(sK1)) = multiplication(multiplication(c(sK1),sK0),c(sK1)),
inference(paramod,[status(thm)],[c_177,c_21069]) ).
cnf(c_21071,plain,
multiplication(sK0,c(sK1)) = multiplication(c(sK1),multiplication(sK0,c(sK1))),
inference(paramod,[status(thm)],[c_43,c_21070]) ).
cnf(c_21072,plain,
multiplication(sK0,c(sK1)) = multiplication(c(sK1),sK0),
inference(paramod,[status(thm)],[c_3989,c_21071]) ).
cnf(c_13163,plain,
multiplication(c(sK1),sK0) = multiplication(sK0,c(sK1)),
inference(copy,[status(thm)],[c_21072]) ).
cnf(c_21073,plain,
multiplication(multiplication(sK0,c(sK1)),A) = multiplication(c(sK1),multiplication(sK0,A)),
inference(paramod,[status(thm)],[c_13163,c_43]) ).
cnf(c_21074,plain,
multiplication(sK0,multiplication(c(sK1),A)) = multiplication(c(sK1),multiplication(sK0,A)),
inference(paramod,[status(thm)],[c_43,c_21073]) ).
cnf(c_13189,plain,
multiplication(c(sK1),multiplication(sK0,A)) = multiplication(sK0,multiplication(c(sK1),A)),
inference(copy,[status(thm)],[c_21074]) ).
cnf(c_21075,plain,
addition(sK1,sK0) = addition(multiplication(c(sK0),sK1),sK0),
inference(paramod,[status(thm)],[c_367,c_309]) ).
cnf(c_21076,plain,
addition(sK0,sK1) = addition(multiplication(c(sK0),sK1),sK0),
inference(paramod,[status(thm)],[c_39,c_21075]) ).
cnf(c_21077,plain,
addition(sK0,sK1) = addition(sK0,multiplication(c(sK0),sK1)),
inference(paramod,[status(thm)],[c_39,c_21076]) ).
cnf(c_13254,plain,
addition(sK0,multiplication(c(sK0),sK1)) = addition(sK0,sK1),
inference(copy,[status(thm)],[c_21077]) ).
cnf(c_21078,plain,
multiplication(addition(sK0,sK1),c(sK0)) = multiplication(multiplication(c(sK0),sK1),c(sK0)),
inference(paramod,[status(thm)],[c_13254,c_196]) ).
cnf(c_21079,plain,
multiplication(sK1,c(sK0)) = multiplication(multiplication(c(sK0),sK1),c(sK0)),
inference(paramod,[status(thm)],[c_196,c_21078]) ).
cnf(c_21080,plain,
multiplication(sK1,c(sK0)) = multiplication(c(sK0),multiplication(sK1,c(sK0))),
inference(paramod,[status(thm)],[c_43,c_21079]) ).
cnf(c_21081,plain,
multiplication(sK1,c(sK0)) = multiplication(c(sK0),sK1),
inference(paramod,[status(thm)],[c_4219,c_21080]) ).
cnf(c_13301,plain,
multiplication(c(sK0),sK1) = multiplication(sK1,c(sK0)),
inference(copy,[status(thm)],[c_21081]) ).
cnf(c_21082,plain,
multiplication(multiplication(sK1,c(sK0)),A) = multiplication(c(sK0),multiplication(sK1,A)),
inference(paramod,[status(thm)],[c_13301,c_43]) ).
cnf(c_21083,plain,
multiplication(sK1,multiplication(c(sK0),A)) = multiplication(c(sK0),multiplication(sK1,A)),
inference(paramod,[status(thm)],[c_43,c_21082]) ).
cnf(c_13327,plain,
multiplication(c(sK0),multiplication(sK1,A)) = multiplication(sK1,multiplication(c(sK0),A)),
inference(copy,[status(thm)],[c_21083]) ).
cnf(c_13361,plain,
addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK0),multiplication(c(sK1),sK6))))) != addition(multiplication(sK1,multiplication(sK0,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),multiplication(c(sK1),addition(multiplication(sK0,sK5),multiplication(c(sK0),sK6))))),
inference(paramod,[status(thm)],[c_13327,c_1978]) ).
cnf(c_21084,plain,
addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK0),multiplication(c(sK1),sK6))))) != addition(multiplication(sK1,multiplication(sK0,sK3)),addition(multiplication(c(sK1),multiplication(sK0,sK5)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),multiplication(c(sK1),multiplication(c(sK0),sK6))))),
inference(paramod,[status(thm)],[c_208,c_13361]) ).
cnf(c_21085,plain,
addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK0),multiplication(c(sK1),sK6))))) != addition(multiplication(sK1,multiplication(sK0,sK3)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),multiplication(c(sK1),multiplication(c(sK0),sK6))))),
inference(paramod,[status(thm)],[c_13189,c_21084]) ).
cnf(c_21086,plain,
addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK0),multiplication(c(sK1),sK6))))) != addition(multiplication(sK1,multiplication(sK0,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK1),multiplication(c(sK0),sK6))))),
inference(paramod,[status(thm)],[c_72,c_21085]) ).
cnf(c_13362,plain,
addition(multiplication(sK1,multiplication(sK0,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK1),multiplication(c(sK0),sK6))))) != addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK0),multiplication(c(sK1),sK6))))),
inference(copy,[status(thm)],[c_21086]) ).
cnf(c_21087,plain,
addition(multiplication(c(sK0),c(sK1)),sK0) = addition(c(sK1),sK0),
inference(paramod,[status(thm)],[c_2501,c_367]) ).
cnf(c_21088,plain,
addition(sK0,multiplication(c(sK0),c(sK1))) = addition(c(sK1),sK0),
inference(paramod,[status(thm)],[c_39,c_21087]) ).
cnf(c_15303,plain,
addition(sK0,multiplication(c(sK0),c(sK1))) = addition(sK0,c(sK1)),
inference(paramod,[status(thm)],[c_39,c_21088]) ).
cnf(c_21089,plain,
addition(multiplication(c(sK1),c(sK0)),sK0) = addition(c(sK1),sK0),
inference(paramod,[status(thm)],[c_2502,c_260]) ).
cnf(c_21090,plain,
addition(sK0,multiplication(c(sK1),c(sK0))) = addition(c(sK1),sK0),
inference(paramod,[status(thm)],[c_39,c_21089]) ).
cnf(c_15329,plain,
addition(sK0,multiplication(c(sK1),c(sK0))) = addition(sK0,c(sK1)),
inference(paramod,[status(thm)],[c_39,c_21090]) ).
cnf(c_21091,plain,
multiplication(addition(sK0,c(sK1)),c(sK0)) = multiplication(multiplication(c(sK0),c(sK1)),c(sK0)),
inference(paramod,[status(thm)],[c_15303,c_196]) ).
cnf(c_21092,plain,
multiplication(c(sK1),c(sK0)) = multiplication(multiplication(c(sK0),c(sK1)),c(sK0)),
inference(paramod,[status(thm)],[c_196,c_21091]) ).
cnf(c_21093,plain,
multiplication(c(sK1),c(sK0)) = multiplication(c(sK0),multiplication(c(sK1),c(sK0))),
inference(paramod,[status(thm)],[c_43,c_21092]) ).
cnf(c_20816,plain,
multiplication(c(sK0),multiplication(c(sK1),c(sK0))) = multiplication(c(sK1),c(sK0)),
inference(copy,[status(thm)],[c_21093]) ).
cnf(c_21094,plain,
addition(multiplication(sK0,sK1),addition(multiplication(sK0,c(sK1)),multiplication(c(sK0),c(sK1)))) = addition(sK0,c(sK1)),
inference(paramod,[status(thm)],[c_15303,c_259]) ).
cnf(c_21095,plain,
addition(multiplication(sK0,sK1),multiplication(addition(sK0,c(sK0)),c(sK1))) = addition(sK0,c(sK1)),
inference(paramod,[status(thm)],[c_49,c_21094]) ).
cnf(c_21096,plain,
addition(multiplication(sK0,sK1),multiplication(one,c(sK1))) = addition(sK0,c(sK1)),
inference(paramod,[status(thm)],[c_118,c_21095]) ).
cnf(c_20823,plain,
addition(multiplication(sK0,sK1),c(sK1)) = addition(sK0,c(sK1)),
inference(paramod,[status(thm)],[c_45,c_21096]) ).
cnf(c_21097,plain,
multiplication(sK1,addition(sK0,c(sK1))) = multiplication(sK1,multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_20823,c_175]) ).
cnf(c_21098,plain,
multiplication(sK1,sK0) = multiplication(sK1,multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_175,c_21097]) ).
cnf(c_20831,plain,
multiplication(sK1,multiplication(sK0,sK1)) = multiplication(sK1,sK0),
inference(copy,[status(thm)],[c_21098]) ).
cnf(c_21099,plain,
multiplication(multiplication(sK1,sK0),A) = multiplication(sK1,multiplication(multiplication(sK0,sK1),A)),
inference(paramod,[status(thm)],[c_20831,c_43]) ).
cnf(c_21100,plain,
multiplication(sK1,multiplication(sK0,A)) = multiplication(sK1,multiplication(multiplication(sK0,sK1),A)),
inference(paramod,[status(thm)],[c_43,c_21099]) ).
cnf(c_21101,plain,
multiplication(sK1,multiplication(sK0,A)) = multiplication(sK1,multiplication(sK0,multiplication(sK1,A))),
inference(paramod,[status(thm)],[c_43,c_21100]) ).
cnf(c_20851,plain,
multiplication(sK1,multiplication(sK0,multiplication(sK1,A))) = multiplication(sK1,multiplication(sK0,A)),
inference(copy,[status(thm)],[c_21101]) ).
cnf(c_20879,plain,
addition(multiplication(sK1,multiplication(sK0,A)),B) = addition(multiplication(sK0,multiplication(sK1,A)),B),
inference(paramod,[status(thm)],[c_20851,c_13108]) ).
cnf(c_20881,plain,
addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK1),multiplication(c(sK0),sK6))))) != addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK0),multiplication(c(sK1),sK6))))),
inference(paramod,[status(thm)],[c_20879,c_13362]) ).
cnf(c_21102,plain,
multiplication(c(sK0),addition(sK0,c(sK1))) = multiplication(c(sK0),multiplication(c(sK1),c(sK0))),
inference(paramod,[status(thm)],[c_15329,c_199]) ).
cnf(c_21103,plain,
multiplication(c(sK0),c(sK1)) = multiplication(c(sK0),multiplication(c(sK1),c(sK0))),
inference(paramod,[status(thm)],[c_199,c_21102]) ).
cnf(c_21104,plain,
multiplication(c(sK0),c(sK1)) = multiplication(c(sK1),c(sK0)),
inference(paramod,[status(thm)],[c_20816,c_21103]) ).
cnf(c_20958,plain,
multiplication(c(sK1),c(sK0)) = multiplication(c(sK0),c(sK1)),
inference(copy,[status(thm)],[c_21104]) ).
cnf(c_21105,plain,
multiplication(multiplication(c(sK0),c(sK1)),A) = multiplication(c(sK1),multiplication(c(sK0),A)),
inference(paramod,[status(thm)],[c_20958,c_43]) ).
cnf(c_21106,plain,
multiplication(c(sK0),multiplication(c(sK1),A)) = multiplication(c(sK1),multiplication(c(sK0),A)),
inference(paramod,[status(thm)],[c_43,c_21105]) ).
cnf(c_20972,plain,
multiplication(c(sK1),multiplication(c(sK0),A)) = multiplication(c(sK0),multiplication(c(sK1),A)),
inference(copy,[status(thm)],[c_21106]) ).
cnf(c_21107,plain,
addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK0),multiplication(c(sK1),sK6))))) != addition(multiplication(sK0,multiplication(sK1,sK3)),addition(multiplication(sK1,multiplication(c(sK0),sK4)),addition(multiplication(sK0,multiplication(c(sK1),sK5)),multiplication(c(sK0),multiplication(c(sK1),sK6))))),
inference(paramod,[status(thm)],[c_20972,c_20881]) ).
cnf(c_20992,plain,
$false,
inference(copy,[status(thm)],[c_21107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE028+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.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
% 0.08/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Sep 25 19:18:07 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 3916171 was started by sandbox2 on n002,
% 0.12/0.36 % Fri Sep 25 19:18:07 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 82.13/10.79
% 82.13/10.79 % given #500 (T,wt=11): 9351 multiplication(A,addition(B,one)) = A | complement(one,c(B)). [resolve(8611,a,133,a(flip))].
% 82.13/10.79
% 82.13/10.79 % SZS status Theorem for theBenchmark
% 82.13/10.79
% 82.13/10.79 % Proof 1 at 8.35 (+ 2.01) seconds.
% 82.13/10.79 % Length of proof is 112.
% 82.13/10.79 % Level of proof is 14.
% 82.13/10.79 % Maximum clause weight is 55.000.
% 82.13/10.79 % Given clauses 780.
% 82.13/10.79
% 82.13/10.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------