%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE088+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 07:44:17 AM UTC 2026
% Result : Theorem 86.63s 17.33s
% Output : CNFRefutation 86.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 17
% Syntax : Number of formulae : 247 ( 243 unt; 0 def)
% Number of atoms : 251 ( 250 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 308 ( 12 sgn 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('theBenchmark.p',additive_associativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(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(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(domain1,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('theBenchmark.p',domain1) ).
fof(domain2,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('theBenchmark.p',domain2) ).
fof(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('theBenchmark.p',domain3) ).
fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('theBenchmark.p',domain4) ).
fof(codomain1,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('theBenchmark.p',codomain1) ).
fof(codomain2,axiom,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
file('theBenchmark.p',codomain2) ).
fof(codomain3,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('theBenchmark.p',codomain3) ).
fof(goals,conjecture,
! [X0,X1] :
( multiplication(domain(X0),X1) = zero
=> addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( multiplication(domain(X0),X1) = zero
=> addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_21,plain,
? [X0,X1] :
( antidomain(X1) != addition(domain(X0),antidomain(X1))
& multiplication(domain(X0),X1) = zero ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( antidomain(sK0) != addition(domain(sK1),antidomain(sK0))
& multiplication(domain(sK1),sK0) = zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_21]) ).
cnf(c_24,negated_conjecture,
antidomain(sK0) != addition(domain(sK1),antidomain(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_25,negated_conjecture,
addition(domain(sK1),antidomain(sK0)) != antidomain(sK0),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_26,negated_conjecture,
multiplication(domain(sK1),sK0) = zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_28,plain,
addition(coantidomain(coantidomain(A)),coantidomain(A)) = one,
inference(clausify,[status(thm)],[codomain3]) ).
cnf(c_29,plain,
coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))),
inference(clausify,[status(thm)],[codomain2]) ).
cnf(c_30,plain,
addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_31,plain,
multiplication(A,coantidomain(A)) = zero,
inference(clausify,[status(thm)],[codomain1]) ).
cnf(c_32,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_33,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_34,plain,
antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))),
inference(clausify,[status(thm)],[domain2]) ).
cnf(c_35,plain,
addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_36,plain,
multiplication(antidomain(A),A) = zero,
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_37,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_39,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_40,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_41,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_42,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_43,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_44,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_46,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_47,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_48,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_49,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_50,negated_conjecture,
multiplication(antidomain(antidomain(sK1)),sK0) = zero,
inference(paramod,[status(thm)],[c_32,c_26]) ).
cnf(c_28105,negated_conjecture,
addition(antidomain(antidomain(sK1)),antidomain(sK0)) != antidomain(sK0),
inference(paramod,[status(thm)],[c_32,c_25]) ).
cnf(c_51,negated_conjecture,
addition(antidomain(sK0),antidomain(antidomain(sK1))) != antidomain(sK0),
inference(paramod,[status(thm)],[c_49,c_28105]) ).
cnf(c_52,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_49,c_33]) ).
cnf(c_53,plain,
addition(coantidomain(A),coantidomain(coantidomain(A))) = one,
inference(paramod,[status(thm)],[c_49,c_28]) ).
cnf(c_56,plain,
addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_31,c_35]) ).
cnf(c_57,plain,
addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)),
inference(paramod,[status(thm)],[c_36,c_30]) ).
cnf(c_28106,plain,
addition(zero,multiplication(A,coantidomain(B))) = multiplication(addition(B,A),coantidomain(B)),
inference(paramod,[status(thm)],[c_31,c_40]) ).
cnf(c_62,plain,
multiplication(addition(A,B),coantidomain(A)) = addition(zero,multiplication(B,coantidomain(A))),
inference(copy,[status(thm)],[c_28106]) ).
cnf(c_28107,plain,
addition(multiplication(A,coantidomain(B)),zero) = multiplication(addition(A,B),coantidomain(B)),
inference(paramod,[status(thm)],[c_31,c_40]) ).
cnf(c_28108,plain,
addition(zero,multiplication(A,coantidomain(B))) = multiplication(addition(A,B),coantidomain(B)),
inference(paramod,[status(thm)],[c_49,c_28107]) ).
cnf(c_63,plain,
multiplication(addition(A,B),coantidomain(B)) = addition(zero,multiplication(A,coantidomain(B))),
inference(copy,[status(thm)],[c_28108]) ).
cnf(c_28109,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(antidomain(B),A),B),
inference(paramod,[status(thm)],[c_36,c_40]) ).
cnf(c_64,plain,
multiplication(addition(antidomain(A),B),A) = addition(zero,multiplication(B,A)),
inference(copy,[status(thm)],[c_28109]) ).
cnf(c_28110,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,antidomain(B)),B),
inference(paramod,[status(thm)],[c_36,c_40]) ).
cnf(c_28111,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,antidomain(B)),B),
inference(paramod,[status(thm)],[c_49,c_28110]) ).
cnf(c_65,plain,
multiplication(addition(A,antidomain(B)),B) = addition(zero,multiplication(A,B)),
inference(copy,[status(thm)],[c_28111]) ).
cnf(c_66,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_37,c_40]) ).
cnf(c_28112,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_37,c_40]) ).
cnf(c_28113,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_49,c_28112]) ).
cnf(c_28114,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_66,c_28113]) ).
cnf(c_67,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_47,c_28114]) ).
cnf(c_28115,plain,
multiplication(addition(A,antidomain(B)),B) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_66,c_65]) ).
cnf(c_68,plain,
multiplication(addition(A,antidomain(B)),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_67,c_28115]) ).
cnf(c_28116,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(addition(zero,B),A),
inference(paramod,[status(thm)],[c_66,c_64]) ).
cnf(c_69,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(B,A),
inference(paramod,[status(thm)],[c_67,c_28116]) ).
cnf(c_28117,plain,
multiplication(addition(A,B),coantidomain(B)) = multiplication(addition(zero,A),coantidomain(B)),
inference(paramod,[status(thm)],[c_66,c_63]) ).
cnf(c_70,plain,
multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)),
inference(paramod,[status(thm)],[c_67,c_28117]) ).
cnf(c_28118,plain,
multiplication(addition(A,B),coantidomain(A)) = multiplication(addition(zero,B),coantidomain(A)),
inference(paramod,[status(thm)],[c_66,c_62]) ).
cnf(c_71,plain,
multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)),
inference(paramod,[status(thm)],[c_67,c_28118]) ).
cnf(c_72,plain,
addition(zero,multiplication(A,B)) = multiplication(A,B),
inference(paramod,[status(thm)],[c_67,c_66]) ).
cnf(c_28119,plain,
addition(zero,multiplication(A,B)) = multiplication(A,addition(coantidomain(A),B)),
inference(paramod,[status(thm)],[c_31,c_42]) ).
cnf(c_28120,plain,
multiplication(A,B) = multiplication(A,addition(coantidomain(A),B)),
inference(paramod,[status(thm)],[c_72,c_28119]) ).
cnf(c_73,plain,
multiplication(A,addition(coantidomain(A),B)) = multiplication(A,B),
inference(copy,[status(thm)],[c_28120]) ).
cnf(c_28121,plain,
addition(multiplication(A,B),zero) = multiplication(A,addition(B,coantidomain(A))),
inference(paramod,[status(thm)],[c_31,c_42]) ).
cnf(c_28122,plain,
addition(zero,multiplication(A,B)) = multiplication(A,addition(B,coantidomain(A))),
inference(paramod,[status(thm)],[c_49,c_28121]) ).
cnf(c_28123,plain,
multiplication(A,B) = multiplication(A,addition(B,coantidomain(A))),
inference(paramod,[status(thm)],[c_72,c_28122]) ).
cnf(c_74,plain,
multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B),
inference(copy,[status(thm)],[c_28123]) ).
cnf(c_28124,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(A,B)),
inference(paramod,[status(thm)],[c_36,c_42]) ).
cnf(c_28125,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(A,B)),
inference(paramod,[status(thm)],[c_72,c_28124]) ).
cnf(c_75,plain,
multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_28125]) ).
cnf(c_28126,plain,
addition(multiplication(antidomain(A),B),zero) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_36,c_42]) ).
cnf(c_28127,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_49,c_28126]) ).
cnf(c_28128,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_72,c_28127]) ).
cnf(c_76,plain,
multiplication(antidomain(A),addition(B,A)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_28128]) ).
cnf(c_79,plain,
coantidomain(one) = zero,
inference(paramod,[status(thm)],[c_43,c_31]) ).
cnf(c_28129,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_43,c_40]) ).
cnf(c_81,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_28129]) ).
cnf(c_86,plain,
antidomain(one) = zero,
inference(paramod,[status(thm)],[c_44,c_36]) ).
cnf(c_28130,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_44,c_42]) ).
cnf(c_87,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_28130]) ).
cnf(c_28131,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_46,c_48]) ).
cnf(c_104,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_28131]) ).
cnf(c_108,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_49,c_47]) ).
cnf(c_28132,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_49,c_48]) ).
cnf(c_109,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_48,c_28132]) ).
cnf(c_111,plain,
addition(antidomain(zero),antidomain(multiplication(antidomain(antidomain(sK1)),antidomain(antidomain(sK0))))) = antidomain(multiplication(antidomain(antidomain(sK1)),antidomain(antidomain(sK0)))),
inference(paramod,[status(thm)],[c_50,c_35]) ).
cnf(c_28133,plain,
addition(addition(A,antidomain(B)),antidomain(antidomain(B))) = addition(A,one),
inference(paramod,[status(thm)],[c_52,c_48]) ).
cnf(c_118,plain,
addition(antidomain(antidomain(A)),addition(B,antidomain(A))) = addition(B,one),
inference(paramod,[status(thm)],[c_49,c_28133]) ).
cnf(c_28134,plain,
addition(addition(A,coantidomain(B)),coantidomain(coantidomain(B))) = addition(A,one),
inference(paramod,[status(thm)],[c_53,c_48]) ).
cnf(c_120,plain,
addition(coantidomain(coantidomain(A)),addition(B,coantidomain(A))) = addition(B,one),
inference(paramod,[status(thm)],[c_49,c_28134]) ).
cnf(c_28135,plain,
addition(zero,coantidomain(coantidomain(one))) = one,
inference(paramod,[status(thm)],[c_79,c_53]) ).
cnf(c_28136,plain,
addition(zero,coantidomain(zero)) = one,
inference(paramod,[status(thm)],[c_79,c_28135]) ).
cnf(c_122,plain,
coantidomain(zero) = one,
inference(paramod,[status(thm)],[c_108,c_28136]) ).
cnf(c_125,plain,
addition(one,coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)),
inference(paramod,[status(thm)],[c_122,c_57]) ).
cnf(c_28137,plain,
addition(zero,antidomain(antidomain(one))) = one,
inference(paramod,[status(thm)],[c_86,c_52]) ).
cnf(c_28138,plain,
addition(zero,antidomain(zero)) = one,
inference(paramod,[status(thm)],[c_86,c_28137]) ).
cnf(c_128,plain,
antidomain(zero) = one,
inference(paramod,[status(thm)],[c_108,c_28138]) ).
cnf(c_129,plain,
addition(one,antidomain(multiplication(antidomain(antidomain(sK1)),antidomain(antidomain(sK0))))) = antidomain(multiplication(antidomain(antidomain(sK1)),antidomain(antidomain(sK0)))),
inference(paramod,[status(thm)],[c_128,c_111]) ).
cnf(c_132,plain,
addition(one,antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_128,c_56]) ).
cnf(c_28139,plain,
multiplication(one,antidomain(A)) = multiplication(antidomain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_52,c_68]) ).
cnf(c_28140,plain,
antidomain(A) = multiplication(antidomain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_43,c_28139]) ).
cnf(c_141,plain,
multiplication(antidomain(A),antidomain(A)) = antidomain(A),
inference(copy,[status(thm)],[c_28140]) ).
cnf(c_28141,plain,
addition(antidomain(A),multiplication(B,antidomain(A))) = multiplication(addition(antidomain(A),B),antidomain(A)),
inference(paramod,[status(thm)],[c_141,c_40]) ).
cnf(c_28142,plain,
multiplication(addition(one,B),antidomain(A)) = multiplication(addition(antidomain(A),B),antidomain(A)),
inference(paramod,[status(thm)],[c_81,c_28141]) ).
cnf(c_160,plain,
multiplication(addition(antidomain(A),B),antidomain(A)) = multiplication(addition(one,B),antidomain(A)),
inference(copy,[status(thm)],[c_28142]) ).
cnf(c_28143,plain,
multiplication(one,A) = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_52,c_69]) ).
cnf(c_28144,plain,
A = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_43,c_28143]) ).
cnf(c_169,plain,
multiplication(antidomain(antidomain(A)),A) = A,
inference(copy,[status(thm)],[c_28144]) ).
cnf(c_28145,plain,
addition(antidomain(A),one) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_52,c_104]) ).
cnf(c_28146,plain,
addition(one,antidomain(A)) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_49,c_28145]) ).
cnf(c_187,plain,
addition(one,antidomain(A)) = one,
inference(paramod,[status(thm)],[c_52,c_28146]) ).
cnf(c_28147,plain,
addition(coantidomain(A),one) = addition(coantidomain(A),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_53,c_104]) ).
cnf(c_28148,plain,
addition(one,coantidomain(A)) = addition(coantidomain(A),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_49,c_28147]) ).
cnf(c_188,plain,
addition(one,coantidomain(A)) = one,
inference(paramod,[status(thm)],[c_53,c_28148]) ).
cnf(c_28149,plain,
one = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_187,c_132]) ).
cnf(c_191,plain,
antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one,
inference(copy,[status(thm)],[c_28149]) ).
cnf(c_28150,plain,
one = antidomain(multiplication(antidomain(antidomain(sK1)),antidomain(antidomain(sK0)))),
inference(paramod,[status(thm)],[c_187,c_129]) ).
cnf(c_193,plain,
antidomain(multiplication(antidomain(antidomain(sK1)),antidomain(antidomain(sK0)))) = one,
inference(copy,[status(thm)],[c_28150]) ).
cnf(c_28151,plain,
one = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)),
inference(paramod,[status(thm)],[c_188,c_125]) ).
cnf(c_198,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one,
inference(copy,[status(thm)],[c_28151]) ).
cnf(c_28152,plain,
addition(multiplication(one,A),multiplication(antidomain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_187,c_40]) ).
cnf(c_28153,plain,
addition(A,multiplication(antidomain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_43,c_28152]) ).
cnf(c_200,plain,
addition(A,multiplication(antidomain(B),A)) = A,
inference(paramod,[status(thm)],[c_43,c_28153]) ).
cnf(c_28154,plain,
addition(multiplication(A,one),multiplication(A,antidomain(B))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_187,c_42]) ).
cnf(c_28155,plain,
addition(A,multiplication(A,antidomain(B))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_44,c_28154]) ).
cnf(c_201,plain,
addition(A,multiplication(A,antidomain(B))) = A,
inference(paramod,[status(thm)],[c_44,c_28155]) ).
cnf(c_28156,plain,
multiplication(one,coantidomain(coantidomain(coantidomain(A)))) = multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_53,c_70]) ).
cnf(c_28157,plain,
coantidomain(coantidomain(coantidomain(A))) = multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_43,c_28156]) ).
cnf(c_213,plain,
multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))),
inference(copy,[status(thm)],[c_28157]) ).
cnf(c_28158,plain,
addition(multiplication(A,one),multiplication(A,coantidomain(B))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_188,c_42]) ).
cnf(c_28159,plain,
addition(A,multiplication(A,coantidomain(B))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_44,c_28158]) ).
cnf(c_217,plain,
addition(A,multiplication(A,coantidomain(B))) = A,
inference(paramod,[status(thm)],[c_44,c_28159]) ).
cnf(c_28160,plain,
multiplication(one,coantidomain(antidomain(A))) = multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_52,c_71]) ).
cnf(c_28161,plain,
coantidomain(antidomain(A)) = multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_43,c_28160]) ).
cnf(c_244,plain,
multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)),
inference(copy,[status(thm)],[c_28161]) ).
cnf(c_28162,plain,
multiplication(A,one) = multiplication(A,coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_53,c_73]) ).
cnf(c_28163,plain,
A = multiplication(A,coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_44,c_28162]) ).
cnf(c_269,plain,
multiplication(A,coantidomain(coantidomain(A))) = A,
inference(copy,[status(thm)],[c_28163]) ).
cnf(c_28164,plain,
coantidomain(A) = coantidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_269,c_213]) ).
cnf(c_272,plain,
coantidomain(coantidomain(coantidomain(A))) = coantidomain(A),
inference(copy,[status(thm)],[c_28164]) ).
cnf(c_28165,plain,
multiplication(antidomain(coantidomain(A)),one) = multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_53,c_75]) ).
cnf(c_28166,plain,
antidomain(coantidomain(A)) = multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_44,c_28165]) ).
cnf(c_327,plain,
multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)),
inference(copy,[status(thm)],[c_28166]) ).
cnf(c_28167,plain,
multiplication(one,multiplication(A,antidomain(antidomain(coantidomain(A))))) = zero,
inference(paramod,[status(thm)],[c_191,c_36]) ).
cnf(c_335,plain,
multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero,
inference(paramod,[status(thm)],[c_43,c_28167]) ).
cnf(c_28168,plain,
addition(zero,multiplication(A,B)) = multiplication(A,addition(antidomain(antidomain(coantidomain(A))),B)),
inference(paramod,[status(thm)],[c_335,c_42]) ).
cnf(c_28169,plain,
multiplication(A,B) = multiplication(A,addition(antidomain(antidomain(coantidomain(A))),B)),
inference(paramod,[status(thm)],[c_108,c_28168]) ).
cnf(c_340,plain,
multiplication(A,addition(antidomain(antidomain(coantidomain(A))),B)) = multiplication(A,B),
inference(copy,[status(thm)],[c_28169]) ).
cnf(c_28170,plain,
multiplication(antidomain(antidomain(antidomain(A))),one) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_52,c_76]) ).
cnf(c_28171,plain,
antidomain(antidomain(antidomain(A))) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_44,c_28170]) ).
cnf(c_356,plain,
antidomain(antidomain(antidomain(A))) = antidomain(A),
inference(paramod,[status(thm)],[c_169,c_28171]) ).
cnf(c_28172,plain,
multiplication(multiplication(coantidomain(coantidomain(antidomain(A))),A),one) = zero,
inference(paramod,[status(thm)],[c_198,c_31]) ).
cnf(c_433,plain,
multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero,
inference(paramod,[status(thm)],[c_44,c_28172]) ).
cnf(c_28173,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B),
inference(paramod,[status(thm)],[c_433,c_40]) ).
cnf(c_28174,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B),
inference(paramod,[status(thm)],[c_49,c_28173]) ).
cnf(c_28175,plain,
multiplication(A,B) = multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B),
inference(paramod,[status(thm)],[c_108,c_28174]) ).
cnf(c_436,plain,
multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B),
inference(copy,[status(thm)],[c_28175]) ).
cnf(c_28176,plain,
multiplication(addition(A,antidomain(B)),addition(one,B)) = addition(addition(A,antidomain(B)),multiplication(A,B)),
inference(paramod,[status(thm)],[c_68,c_87]) ).
cnf(c_28177,plain,
multiplication(addition(A,antidomain(B)),addition(one,B)) = addition(multiplication(A,B),addition(A,antidomain(B))),
inference(paramod,[status(thm)],[c_49,c_28176]) ).
cnf(c_28178,plain,
multiplication(addition(A,antidomain(B)),addition(one,B)) = addition(A,addition(multiplication(A,B),antidomain(B))),
inference(paramod,[status(thm)],[c_109,c_28177]) ).
cnf(c_474,plain,
addition(A,addition(multiplication(A,B),antidomain(B))) = multiplication(addition(A,antidomain(B)),addition(one,B)),
inference(copy,[status(thm)],[c_28178]) ).
cnf(c_28179,plain,
multiplication(one,multiplication(antidomain(antidomain(sK1)),antidomain(antidomain(sK0)))) = zero,
inference(paramod,[status(thm)],[c_193,c_36]) ).
cnf(c_533,plain,
multiplication(antidomain(antidomain(sK1)),antidomain(antidomain(sK0))) = zero,
inference(paramod,[status(thm)],[c_43,c_28179]) ).
cnf(c_28180,plain,
addition(zero,multiplication(A,antidomain(antidomain(sK0)))) = multiplication(addition(antidomain(antidomain(sK1)),A),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_533,c_40]) ).
cnf(c_28181,plain,
multiplication(A,antidomain(antidomain(sK0))) = multiplication(addition(antidomain(antidomain(sK1)),A),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_108,c_28180]) ).
cnf(c_535,plain,
multiplication(addition(antidomain(antidomain(sK1)),A),antidomain(antidomain(sK0))) = multiplication(A,antidomain(antidomain(sK0))),
inference(copy,[status(thm)],[c_28181]) ).
cnf(c_1958,plain,
addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)),
inference(paramod,[status(thm)],[c_244,c_217]) ).
cnf(c_28182,plain,
addition(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = coantidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_327,c_200]) ).
cnf(c_2378,plain,
addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_49,c_28182]) ).
cnf(c_28183,plain,
addition(coantidomain(coantidomain(antidomain(A))),antidomain(antidomain(A))) = addition(antidomain(antidomain(A)),one),
inference(paramod,[status(thm)],[c_1958,c_120]) ).
cnf(c_28184,plain,
addition(antidomain(antidomain(A)),coantidomain(coantidomain(antidomain(A)))) = addition(antidomain(antidomain(A)),one),
inference(paramod,[status(thm)],[c_49,c_28183]) ).
cnf(c_28185,plain,
addition(antidomain(antidomain(A)),coantidomain(coantidomain(antidomain(A)))) = addition(one,antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_49,c_28184]) ).
cnf(c_3869,plain,
addition(antidomain(antidomain(A)),coantidomain(coantidomain(antidomain(A)))) = one,
inference(paramod,[status(thm)],[c_187,c_28185]) ).
cnf(c_28186,plain,
multiplication(coantidomain(antidomain(A)),one) = multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_3869,c_74]) ).
cnf(c_28187,plain,
coantidomain(antidomain(A)) = multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_44,c_28186]) ).
cnf(c_3886,plain,
multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)),
inference(copy,[status(thm)],[c_28187]) ).
cnf(c_28188,plain,
addition(antidomain(coantidomain(coantidomain(A))),coantidomain(A)) = coantidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_272,c_2378]) ).
cnf(c_28189,plain,
addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_49,c_28188]) ).
cnf(c_4209,plain,
addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = coantidomain(A),
inference(paramod,[status(thm)],[c_272,c_28189]) ).
cnf(c_28190,plain,
multiplication(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = multiplication(addition(one,coantidomain(coantidomain(A))),antidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_2378,c_160]) ).
cnf(c_28191,plain,
multiplication(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = multiplication(one,antidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_188,c_28190]) ).
cnf(c_4215,plain,
multiplication(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_43,c_28191]) ).
cnf(c_28192,plain,
addition(antidomain(antidomain(coantidomain(coantidomain(A)))),coantidomain(A)) = addition(coantidomain(A),one),
inference(paramod,[status(thm)],[c_4209,c_118]) ).
cnf(c_28193,plain,
addition(coantidomain(A),antidomain(antidomain(coantidomain(coantidomain(A))))) = addition(coantidomain(A),one),
inference(paramod,[status(thm)],[c_49,c_28192]) ).
cnf(c_28194,plain,
addition(coantidomain(A),antidomain(antidomain(coantidomain(coantidomain(A))))) = addition(one,coantidomain(A)),
inference(paramod,[status(thm)],[c_49,c_28193]) ).
cnf(c_4246,plain,
addition(coantidomain(A),antidomain(antidomain(coantidomain(coantidomain(A))))) = one,
inference(paramod,[status(thm)],[c_188,c_28194]) ).
cnf(c_28195,plain,
multiplication(one,antidomain(coantidomain(coantidomain(A)))) = multiplication(coantidomain(A),antidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_4246,c_68]) ).
cnf(c_28196,plain,
antidomain(coantidomain(coantidomain(A))) = multiplication(coantidomain(A),antidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_43,c_28195]) ).
cnf(c_4252,plain,
multiplication(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))),
inference(copy,[status(thm)],[c_28196]) ).
cnf(c_28197,plain,
multiplication(A,one) = multiplication(A,antidomain(antidomain(coantidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_4246,c_73]) ).
cnf(c_28198,plain,
A = multiplication(A,antidomain(antidomain(coantidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_44,c_28197]) ).
cnf(c_4254,plain,
multiplication(A,antidomain(antidomain(coantidomain(coantidomain(A))))) = A,
inference(copy,[status(thm)],[c_28198]) ).
cnf(c_28199,plain,
addition(coantidomain(coantidomain(A)),antidomain(antidomain(coantidomain(A)))) = one,
inference(paramod,[status(thm)],[c_272,c_4246]) ).
cnf(c_4255,plain,
addition(antidomain(antidomain(coantidomain(A))),coantidomain(coantidomain(A))) = one,
inference(paramod,[status(thm)],[c_49,c_28199]) ).
cnf(c_4272,plain,
multiplication(coantidomain(A),antidomain(antidomain(coantidomain(A)))) = coantidomain(A),
inference(paramod,[status(thm)],[c_272,c_4254]) ).
cnf(c_28200,plain,
multiplication(coantidomain(coantidomain(A)),addition(antidomain(antidomain(coantidomain(coantidomain(coantidomain(A))))),antidomain(coantidomain(A)))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_4215,c_340]) ).
cnf(c_28201,plain,
multiplication(coantidomain(coantidomain(A)),addition(antidomain(antidomain(coantidomain(A))),antidomain(coantidomain(A)))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_272,c_28200]) ).
cnf(c_28202,plain,
multiplication(coantidomain(coantidomain(A)),addition(antidomain(coantidomain(A)),antidomain(antidomain(coantidomain(A))))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_49,c_28201]) ).
cnf(c_28203,plain,
multiplication(coantidomain(coantidomain(A)),one) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_52,c_28202]) ).
cnf(c_8450,plain,
coantidomain(coantidomain(A)) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_44,c_28203]) ).
cnf(c_28204,plain,
multiplication(coantidomain(A),antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_8450,c_4252]) ).
cnf(c_28205,plain,
coantidomain(A) = antidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_4272,c_28204]) ).
cnf(c_28206,plain,
coantidomain(A) = antidomain(antidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_8450,c_28205]) ).
cnf(c_8478,plain,
antidomain(antidomain(coantidomain(A))) = coantidomain(A),
inference(copy,[status(thm)],[c_28206]) ).
cnf(c_28207,plain,
addition(coantidomain(A),coantidomain(coantidomain(A))) = one,
inference(paramod,[status(thm)],[c_8478,c_4255]) ).
cnf(c_9722,plain,
addition(coantidomain(A),antidomain(coantidomain(A))) = one,
inference(paramod,[status(thm)],[c_8450,c_28207]) ).
cnf(c_10466,plain,
multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_8450,c_436]) ).
cnf(c_28208,plain,
multiplication(addition(coantidomain(antidomain(A)),antidomain(coantidomain(antidomain(antidomain(antidomain(A)))))),antidomain(antidomain(A))) = coantidomain(antidomain(A)),
inference(paramod,[status(thm)],[c_3886,c_10466]) ).
cnf(c_28209,plain,
multiplication(addition(coantidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))),antidomain(antidomain(A))) = coantidomain(antidomain(A)),
inference(paramod,[status(thm)],[c_356,c_28208]) ).
cnf(c_28210,plain,
multiplication(one,antidomain(antidomain(A))) = coantidomain(antidomain(A)),
inference(paramod,[status(thm)],[c_9722,c_28209]) ).
cnf(c_28211,plain,
antidomain(antidomain(A)) = coantidomain(antidomain(A)),
inference(paramod,[status(thm)],[c_43,c_28210]) ).
cnf(c_24809,plain,
coantidomain(antidomain(A)) = antidomain(antidomain(A)),
inference(copy,[status(thm)],[c_28211]) ).
cnf(c_28212,plain,
multiplication(one,antidomain(antidomain(sK0))) = multiplication(antidomain(antidomain(antidomain(sK1))),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_52,c_535]) ).
cnf(c_28213,plain,
antidomain(antidomain(sK0)) = multiplication(antidomain(antidomain(antidomain(sK1))),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_43,c_28212]) ).
cnf(c_28214,plain,
antidomain(antidomain(sK0)) = multiplication(antidomain(sK1),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_356,c_28213]) ).
cnf(c_27830,plain,
multiplication(antidomain(sK1),antidomain(antidomain(sK0))) = antidomain(antidomain(sK0)),
inference(copy,[status(thm)],[c_28214]) ).
cnf(c_28215,plain,
addition(antidomain(sK1),addition(antidomain(antidomain(sK0)),antidomain(antidomain(antidomain(sK0))))) = multiplication(addition(antidomain(sK1),antidomain(antidomain(antidomain(sK0)))),addition(one,antidomain(antidomain(sK0)))),
inference(paramod,[status(thm)],[c_27830,c_474]) ).
cnf(c_28216,plain,
addition(antidomain(sK1),addition(antidomain(antidomain(sK0)),antidomain(sK0))) = multiplication(addition(antidomain(sK1),antidomain(antidomain(antidomain(sK0)))),addition(one,antidomain(antidomain(sK0)))),
inference(paramod,[status(thm)],[c_356,c_28215]) ).
cnf(c_28217,plain,
addition(antidomain(sK1),addition(antidomain(sK0),antidomain(antidomain(sK0)))) = multiplication(addition(antidomain(sK1),antidomain(antidomain(antidomain(sK0)))),addition(one,antidomain(antidomain(sK0)))),
inference(paramod,[status(thm)],[c_49,c_28216]) ).
cnf(c_28218,plain,
addition(antidomain(sK1),one) = multiplication(addition(antidomain(sK1),antidomain(antidomain(antidomain(sK0)))),addition(one,antidomain(antidomain(sK0)))),
inference(paramod,[status(thm)],[c_52,c_28217]) ).
cnf(c_28219,plain,
addition(one,antidomain(sK1)) = multiplication(addition(antidomain(sK1),antidomain(antidomain(antidomain(sK0)))),addition(one,antidomain(antidomain(sK0)))),
inference(paramod,[status(thm)],[c_49,c_28218]) ).
cnf(c_28220,plain,
one = multiplication(addition(antidomain(sK1),antidomain(antidomain(antidomain(sK0)))),addition(one,antidomain(antidomain(sK0)))),
inference(paramod,[status(thm)],[c_187,c_28219]) ).
cnf(c_28221,plain,
one = multiplication(addition(antidomain(sK1),antidomain(sK0)),addition(one,antidomain(antidomain(sK0)))),
inference(paramod,[status(thm)],[c_356,c_28220]) ).
cnf(c_28222,plain,
one = multiplication(addition(antidomain(sK1),antidomain(sK0)),one),
inference(paramod,[status(thm)],[c_187,c_28221]) ).
cnf(c_28223,plain,
one = addition(antidomain(sK1),antidomain(sK0)),
inference(paramod,[status(thm)],[c_44,c_28222]) ).
cnf(c_27886,plain,
addition(antidomain(sK1),antidomain(sK0)) = one,
inference(copy,[status(thm)],[c_28223]) ).
cnf(c_28224,plain,
multiplication(one,coantidomain(antidomain(sK1))) = multiplication(antidomain(sK0),coantidomain(antidomain(sK1))),
inference(paramod,[status(thm)],[c_27886,c_71]) ).
cnf(c_28225,plain,
multiplication(one,antidomain(antidomain(sK1))) = multiplication(antidomain(sK0),coantidomain(antidomain(sK1))),
inference(paramod,[status(thm)],[c_24809,c_28224]) ).
cnf(c_28226,plain,
antidomain(antidomain(sK1)) = multiplication(antidomain(sK0),coantidomain(antidomain(sK1))),
inference(paramod,[status(thm)],[c_43,c_28225]) ).
cnf(c_28227,plain,
antidomain(antidomain(sK1)) = multiplication(antidomain(sK0),antidomain(antidomain(sK1))),
inference(paramod,[status(thm)],[c_24809,c_28226]) ).
cnf(c_27895,plain,
multiplication(antidomain(sK0),antidomain(antidomain(sK1))) = antidomain(antidomain(sK1)),
inference(copy,[status(thm)],[c_28227]) ).
cnf(c_28103,plain,
addition(antidomain(sK0),antidomain(antidomain(sK1))) = antidomain(sK0),
inference(paramod,[status(thm)],[c_27895,c_201]) ).
cnf(c_28104,plain,
$false,
inference(resolve,[status(thm)],[c_28103,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE088+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n002.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 19:23:45 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 3928065 was started by sandbox2 on n002,
% 0.09/5.37 % Fri Sep 25 19:23:45 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 86.63/17.33
% 86.63/17.33 % given #500 (T,wt=12): 407 multiplication(antidomain(multiplication(addition(A,B),C)),multiplication(B,C)) = zero. [para(40(a,1),360(a,1,1,1))].
% 86.63/17.33
% 86.63/17.33 % SZS status Theorem for theBenchmark
% 86.63/17.33
% 86.63/17.33 % Proof 1 at 9.05 (+ 2.47) seconds.
% 86.63/17.33 % Length of proof is 121.
% 86.63/17.33 % Level of proof is 18.
% 86.63/17.33 % Maximum clause weight is 20.000.
% 86.63/17.33 % Given clauses 998.
% 86.63/17.33
% 86.63/17.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------