%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE092+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 07:44:18 AM UTC 2026
% Result : Theorem 17.25s 2.95s
% Output : CNFRefutation 17.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 139 ( 139 unt; 0 def)
% Number of atoms : 139 ( 138 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 188 ( 6 sgn 25 !; 1 ?)
% 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(codomain3,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('theBenchmark.p',codomain3) ).
fof(goals,conjecture,
! [X0] : domain(coantidomain(X0)) = coantidomain(X0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : domain(coantidomain(X0)) = coantidomain(X0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_21,plain,
? [X0] : coantidomain(X0) != domain(coantidomain(X0)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
coantidomain(sK0) != domain(coantidomain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_21]) ).
cnf(c_24,negated_conjecture,
coantidomain(sK0) != domain(coantidomain(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_25,negated_conjecture,
domain(coantidomain(sK0)) != coantidomain(sK0),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_27,plain,
addition(coantidomain(coantidomain(A)),coantidomain(A)) = one,
inference(clausify,[status(thm)],[codomain3]) ).
cnf(c_30,plain,
multiplication(A,coantidomain(A)) = zero,
inference(clausify,[status(thm)],[codomain1]) ).
cnf(c_31,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_32,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_33,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_34,plain,
addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))),
inference(copy,[status(thm)],[c_33]) ).
cnf(c_35,plain,
multiplication(antidomain(A),A) = zero,
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_36,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_38,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_39,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_40,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_41,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_42,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_43,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_45,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_46,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_47,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_48,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_49,negated_conjecture,
antidomain(antidomain(coantidomain(sK0))) != coantidomain(sK0),
inference(paramod,[status(thm)],[c_31,c_25]) ).
cnf(c_50,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_48,c_32]) ).
cnf(c_51,plain,
addition(coantidomain(A),coantidomain(coantidomain(A))) = one,
inference(paramod,[status(thm)],[c_48,c_27]) ).
cnf(c_54,plain,
addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_30,c_34]) ).
cnf(c_6706,plain,
addition(multiplication(A,coantidomain(B)),zero) = multiplication(addition(A,B),coantidomain(B)),
inference(paramod,[status(thm)],[c_30,c_39]) ).
cnf(c_6707,plain,
addition(zero,multiplication(A,coantidomain(B))) = multiplication(addition(A,B),coantidomain(B)),
inference(paramod,[status(thm)],[c_48,c_6706]) ).
cnf(c_61,plain,
multiplication(addition(A,B),coantidomain(B)) = addition(zero,multiplication(A,coantidomain(B))),
inference(copy,[status(thm)],[c_6707]) ).
cnf(c_6708,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,antidomain(B)),B),
inference(paramod,[status(thm)],[c_35,c_39]) ).
cnf(c_6709,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,antidomain(B)),B),
inference(paramod,[status(thm)],[c_48,c_6708]) ).
cnf(c_63,plain,
multiplication(addition(A,antidomain(B)),B) = addition(zero,multiplication(A,B)),
inference(copy,[status(thm)],[c_6709]) ).
cnf(c_64,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_36,c_39]) ).
cnf(c_6710,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_36,c_39]) ).
cnf(c_6711,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_48,c_6710]) ).
cnf(c_6712,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_64,c_6711]) ).
cnf(c_65,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_46,c_6712]) ).
cnf(c_6713,plain,
multiplication(addition(A,antidomain(B)),B) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_64,c_63]) ).
cnf(c_66,plain,
multiplication(addition(A,antidomain(B)),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_65,c_6713]) ).
cnf(c_6714,plain,
multiplication(addition(A,B),coantidomain(B)) = multiplication(addition(zero,A),coantidomain(B)),
inference(paramod,[status(thm)],[c_64,c_61]) ).
cnf(c_68,plain,
multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)),
inference(paramod,[status(thm)],[c_65,c_6714]) ).
cnf(c_70,plain,
addition(zero,multiplication(A,B)) = multiplication(A,B),
inference(paramod,[status(thm)],[c_65,c_64]) ).
cnf(c_6715,plain,
addition(zero,multiplication(A,B)) = multiplication(A,addition(coantidomain(A),B)),
inference(paramod,[status(thm)],[c_30,c_41]) ).
cnf(c_6716,plain,
multiplication(A,B) = multiplication(A,addition(coantidomain(A),B)),
inference(paramod,[status(thm)],[c_70,c_6715]) ).
cnf(c_71,plain,
multiplication(A,addition(coantidomain(A),B)) = multiplication(A,B),
inference(copy,[status(thm)],[c_6716]) ).
cnf(c_6717,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(A,B)),
inference(paramod,[status(thm)],[c_35,c_41]) ).
cnf(c_6718,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(A,B)),
inference(paramod,[status(thm)],[c_70,c_6717]) ).
cnf(c_73,plain,
multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_6718]) ).
cnf(c_6719,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_42,c_39]) ).
cnf(c_79,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_6719]) ).
cnf(c_84,plain,
antidomain(one) = zero,
inference(paramod,[status(thm)],[c_43,c_35]) ).
cnf(c_6720,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_45,c_47]) ).
cnf(c_102,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_6720]) ).
cnf(c_106,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_48,c_46]) ).
cnf(c_6721,plain,
addition(addition(A,antidomain(B)),antidomain(antidomain(B))) = addition(A,one),
inference(paramod,[status(thm)],[c_50,c_47]) ).
cnf(c_109,plain,
addition(antidomain(antidomain(A)),addition(B,antidomain(A))) = addition(B,one),
inference(paramod,[status(thm)],[c_48,c_6721]) ).
cnf(c_6722,plain,
addition(zero,antidomain(antidomain(one))) = one,
inference(paramod,[status(thm)],[c_84,c_50]) ).
cnf(c_6723,plain,
addition(zero,antidomain(zero)) = one,
inference(paramod,[status(thm)],[c_84,c_6722]) ).
cnf(c_118,plain,
antidomain(zero) = one,
inference(paramod,[status(thm)],[c_106,c_6723]) ).
cnf(c_121,plain,
addition(one,antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_118,c_54]) ).
cnf(c_6724,plain,
multiplication(one,antidomain(A)) = multiplication(antidomain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_50,c_66]) ).
cnf(c_6725,plain,
antidomain(A) = multiplication(antidomain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_42,c_6724]) ).
cnf(c_130,plain,
multiplication(antidomain(A),antidomain(A)) = antidomain(A),
inference(copy,[status(thm)],[c_6725]) ).
cnf(c_6726,plain,
addition(antidomain(A),multiplication(B,antidomain(A))) = multiplication(addition(antidomain(A),B),antidomain(A)),
inference(paramod,[status(thm)],[c_130,c_39]) ).
cnf(c_6727,plain,
multiplication(addition(one,B),antidomain(A)) = multiplication(addition(antidomain(A),B),antidomain(A)),
inference(paramod,[status(thm)],[c_79,c_6726]) ).
cnf(c_149,plain,
multiplication(addition(antidomain(A),B),antidomain(A)) = multiplication(addition(one,B),antidomain(A)),
inference(copy,[status(thm)],[c_6727]) ).
cnf(c_6728,plain,
addition(antidomain(A),one) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_50,c_102]) ).
cnf(c_6729,plain,
addition(one,antidomain(A)) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_48,c_6728]) ).
cnf(c_176,plain,
addition(one,antidomain(A)) = one,
inference(paramod,[status(thm)],[c_50,c_6729]) ).
cnf(c_6730,plain,
addition(coantidomain(A),one) = addition(coantidomain(A),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_51,c_102]) ).
cnf(c_6731,plain,
addition(one,coantidomain(A)) = addition(coantidomain(A),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_48,c_6730]) ).
cnf(c_177,plain,
addition(one,coantidomain(A)) = one,
inference(paramod,[status(thm)],[c_51,c_6731]) ).
cnf(c_6732,plain,
one = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_176,c_121]) ).
cnf(c_180,plain,
antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one,
inference(copy,[status(thm)],[c_6732]) ).
cnf(c_6733,plain,
addition(multiplication(one,A),multiplication(antidomain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_176,c_39]) ).
cnf(c_6734,plain,
addition(A,multiplication(antidomain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_42,c_6733]) ).
cnf(c_187,plain,
addition(A,multiplication(antidomain(B),A)) = A,
inference(paramod,[status(thm)],[c_42,c_6734]) ).
cnf(c_6735,plain,
multiplication(one,coantidomain(coantidomain(coantidomain(A)))) = multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_51,c_68]) ).
cnf(c_6736,plain,
coantidomain(coantidomain(coantidomain(A))) = multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_42,c_6735]) ).
cnf(c_200,plain,
multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))),
inference(copy,[status(thm)],[c_6736]) ).
cnf(c_6737,plain,
multiplication(A,one) = multiplication(A,coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_51,c_71]) ).
cnf(c_6738,plain,
A = multiplication(A,coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_43,c_6737]) ).
cnf(c_256,plain,
multiplication(A,coantidomain(coantidomain(A))) = A,
inference(copy,[status(thm)],[c_6738]) ).
cnf(c_6739,plain,
coantidomain(A) = coantidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_256,c_200]) ).
cnf(c_259,plain,
coantidomain(coantidomain(coantidomain(A))) = coantidomain(A),
inference(copy,[status(thm)],[c_6739]) ).
cnf(c_6740,plain,
multiplication(antidomain(coantidomain(A)),one) = multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_51,c_73]) ).
cnf(c_6741,plain,
antidomain(coantidomain(A)) = multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_43,c_6740]) ).
cnf(c_314,plain,
multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)),
inference(copy,[status(thm)],[c_6741]) ).
cnf(c_6742,plain,
multiplication(one,multiplication(A,antidomain(antidomain(coantidomain(A))))) = zero,
inference(paramod,[status(thm)],[c_180,c_35]) ).
cnf(c_316,plain,
multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero,
inference(paramod,[status(thm)],[c_42,c_6742]) ).
cnf(c_6743,plain,
addition(zero,multiplication(A,B)) = multiplication(A,addition(antidomain(antidomain(coantidomain(A))),B)),
inference(paramod,[status(thm)],[c_316,c_41]) ).
cnf(c_6744,plain,
multiplication(A,B) = multiplication(A,addition(antidomain(antidomain(coantidomain(A))),B)),
inference(paramod,[status(thm)],[c_106,c_6743]) ).
cnf(c_321,plain,
multiplication(A,addition(antidomain(antidomain(coantidomain(A))),B)) = multiplication(A,B),
inference(copy,[status(thm)],[c_6744]) ).
cnf(c_6745,plain,
addition(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = coantidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_314,c_187]) ).
cnf(c_2137,plain,
addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_48,c_6745]) ).
cnf(c_6746,plain,
addition(antidomain(coantidomain(coantidomain(A))),coantidomain(A)) = coantidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_259,c_2137]) ).
cnf(c_6747,plain,
addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_48,c_6746]) ).
cnf(c_3362,plain,
addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = coantidomain(A),
inference(paramod,[status(thm)],[c_259,c_6747]) ).
cnf(c_6748,plain,
multiplication(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = multiplication(addition(one,coantidomain(coantidomain(A))),antidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_2137,c_149]) ).
cnf(c_6749,plain,
multiplication(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = multiplication(one,antidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_177,c_6748]) ).
cnf(c_3368,plain,
multiplication(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_42,c_6749]) ).
cnf(c_6750,plain,
addition(antidomain(antidomain(coantidomain(coantidomain(A)))),coantidomain(A)) = addition(coantidomain(A),one),
inference(paramod,[status(thm)],[c_3362,c_109]) ).
cnf(c_6751,plain,
addition(coantidomain(A),antidomain(antidomain(coantidomain(coantidomain(A))))) = addition(coantidomain(A),one),
inference(paramod,[status(thm)],[c_48,c_6750]) ).
cnf(c_6752,plain,
addition(coantidomain(A),antidomain(antidomain(coantidomain(coantidomain(A))))) = addition(one,coantidomain(A)),
inference(paramod,[status(thm)],[c_48,c_6751]) ).
cnf(c_3376,plain,
addition(coantidomain(A),antidomain(antidomain(coantidomain(coantidomain(A))))) = one,
inference(paramod,[status(thm)],[c_177,c_6752]) ).
cnf(c_6753,plain,
multiplication(one,antidomain(coantidomain(coantidomain(A)))) = multiplication(coantidomain(A),antidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_3376,c_66]) ).
cnf(c_6754,plain,
antidomain(coantidomain(coantidomain(A))) = multiplication(coantidomain(A),antidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_42,c_6753]) ).
cnf(c_3407,plain,
multiplication(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))),
inference(copy,[status(thm)],[c_6754]) ).
cnf(c_6755,plain,
multiplication(A,one) = multiplication(A,antidomain(antidomain(coantidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_3376,c_71]) ).
cnf(c_6756,plain,
A = multiplication(A,antidomain(antidomain(coantidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_43,c_6755]) ).
cnf(c_3409,plain,
multiplication(A,antidomain(antidomain(coantidomain(coantidomain(A))))) = A,
inference(copy,[status(thm)],[c_6756]) ).
cnf(c_3427,plain,
multiplication(coantidomain(A),antidomain(antidomain(coantidomain(A)))) = coantidomain(A),
inference(paramod,[status(thm)],[c_259,c_3409]) ).
cnf(c_6757,plain,
multiplication(coantidomain(coantidomain(A)),addition(antidomain(antidomain(coantidomain(coantidomain(coantidomain(A))))),antidomain(coantidomain(A)))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_3368,c_321]) ).
cnf(c_6758,plain,
multiplication(coantidomain(coantidomain(A)),addition(antidomain(antidomain(coantidomain(A))),antidomain(coantidomain(A)))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_259,c_6757]) ).
cnf(c_6759,plain,
multiplication(coantidomain(coantidomain(A)),addition(antidomain(coantidomain(A)),antidomain(antidomain(coantidomain(A))))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_48,c_6758]) ).
cnf(c_6760,plain,
multiplication(coantidomain(coantidomain(A)),one) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_50,c_6759]) ).
cnf(c_6680,plain,
coantidomain(coantidomain(A)) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_43,c_6760]) ).
cnf(c_6761,plain,
multiplication(coantidomain(A),antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_6680,c_3407]) ).
cnf(c_6762,plain,
coantidomain(A) = antidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_3427,c_6761]) ).
cnf(c_6763,plain,
coantidomain(A) = antidomain(antidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_6680,c_6762]) ).
cnf(c_6704,plain,
antidomain(antidomain(coantidomain(A))) = coantidomain(A),
inference(copy,[status(thm)],[c_6763]) ).
cnf(c_6705,plain,
$false,
inference(resolve,[status(thm)],[c_6704,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE092+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.72 % Computer : n008.cluster.edu
% 0.10/0.72 % Model : x86_64 x86_64
% 0.10/0.72 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.72 % Memory : 8046.5625MB
% 0.10/0.72 % OS : Linux 6.8.0-71-generic
% 0.10/0.72 % CPULimit : 300
% 0.10/0.72 % WCLimit : 300
% 0.10/0.72 % DateTime : Fri Sep 25 19:21:58 UTC 2026
% 0.10/0.72 % CPUTime :
% 0.10/0.72 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.72 % Process 1673307 was started by sandbox on n008,
% 0.10/0.72 % Fri Sep 25 19:21:58 2026
% 0.10/0.72 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.73
% 0.10/0.73 % From the command line: assign(max_seconds, 300).
% 17.25/2.95
% 17.25/2.95 % SZS status Theorem for theBenchmark
% 17.25/2.95
% 17.25/2.95 % Proof 1 at 1.64 (+ 0.54) seconds.
% 17.25/2.95 % Length of proof is 78.
% 17.25/2.95 % Level of proof is 14.
% 17.25/2.95 % Maximum clause weight is 18.000.
% 17.25/2.95 % Given clauses 327.
% 17.25/2.95
% 17.25/2.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------