%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE131+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 : n009.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 07:44:22 AM UTC 2026
% Result : Theorem 83.14s 11.96s
% Output : CNFRefutation 83.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 15
% Syntax : Number of formulae : 135 ( 131 unt; 0 def)
% Number of atoms : 139 ( 138 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 20 ( 4 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 151 ( 2 sgn 27 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',right_distributivity) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_distributivity) ).
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('theBenchmark.p',right_annihilation) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(domain1,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('theBenchmark.p',domain1) ).
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(domain_difference,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('theBenchmark.p',domain_difference) ).
fof(forward_diamond,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('theBenchmark.p',forward_diamond) ).
fof(divergence1,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('theBenchmark.p',divergence1) ).
fof(goals,conjecture,
! [X0] :
( ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
=> divergence(X0) = zero ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
=> divergence(X0) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_29,plain,
? [X0] :
( ! [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) = addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))
& divergence(X0) != zero ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))))
& divergence(sK0) != zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_29]) ).
cnf(c_32,negated_conjecture,
forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))) = addition(domain(A),forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A))))),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_33,negated_conjecture,
addition(domain(A),forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_34,negated_conjecture,
divergence(sK0) != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_37,plain,
divergence(A) = forward_diamond(A,divergence(A)),
inference(clausify,[status(thm)],[divergence1]) ).
cnf(c_38,plain,
forward_diamond(A,divergence(A)) = divergence(A),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_42,plain,
forward_diamond(A,B) = domain(multiplication(A,domain(B))),
inference(clausify,[status(thm)],[forward_diamond]) ).
cnf(c_43,plain,
domain_difference(A,B) = multiplication(domain(A),antidomain(B)),
inference(clausify,[status(thm)],[domain_difference]) ).
cnf(c_50,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_51,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_54,plain,
multiplication(antidomain(A),A) = zero,
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_55,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_56,plain,
multiplication(A,zero) = zero,
inference(clausify,[status(thm)],[right_annihilation]) ).
cnf(c_57,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_58,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_59,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_60,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_61,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_62,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_65,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_67,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_6989,plain,
domain(multiplication(A,domain(divergence(A)))) = divergence(A),
inference(paramod,[status(thm)],[c_42,c_38]) ).
cnf(c_6990,plain,
domain(multiplication(A,antidomain(antidomain(divergence(A))))) = divergence(A),
inference(paramod,[status(thm)],[c_50,c_6989]) ).
cnf(c_70,plain,
antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))) = divergence(A),
inference(paramod,[status(thm)],[c_50,c_6990]) ).
cnf(c_6991,negated_conjecture,
addition(antidomain(antidomain(A)),forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_50,c_33]) ).
cnf(c_6992,negated_conjecture,
addition(antidomain(antidomain(A)),forward_diamond(star(sK0),domain_difference(antidomain(antidomain(A)),forward_diamond(sK0,domain(A))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_50,c_6991]) ).
cnf(c_6993,negated_conjecture,
addition(antidomain(antidomain(A)),forward_diamond(star(sK0),domain_difference(antidomain(antidomain(A)),forward_diamond(sK0,antidomain(antidomain(A)))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_50,c_6992]) ).
cnf(c_6994,negated_conjecture,
addition(antidomain(antidomain(A)),forward_diamond(star(sK0),domain_difference(antidomain(antidomain(A)),domain(multiplication(sK0,domain(antidomain(antidomain(A)))))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_42,c_6993]) ).
cnf(c_6995,negated_conjecture,
addition(antidomain(antidomain(A)),forward_diamond(star(sK0),domain_difference(antidomain(antidomain(A)),domain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_50,c_6994]) ).
cnf(c_6996,negated_conjecture,
addition(antidomain(antidomain(A)),forward_diamond(star(sK0),domain_difference(antidomain(antidomain(A)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_50,c_6995]) ).
cnf(c_6997,negated_conjecture,
addition(antidomain(antidomain(A)),forward_diamond(star(sK0),multiplication(domain(antidomain(antidomain(A))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_43,c_6996]) ).
cnf(c_6998,negated_conjecture,
addition(antidomain(antidomain(A)),forward_diamond(star(sK0),multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_50,c_6997]) ).
cnf(c_6999,negated_conjecture,
addition(antidomain(antidomain(A)),domain(multiplication(star(sK0),domain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_42,c_6998]) ).
cnf(c_7000,negated_conjecture,
addition(antidomain(antidomain(A)),domain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))))))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_50,c_6999]) ).
cnf(c_7001,negated_conjecture,
addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = forward_diamond(star(sK0),domain_difference(domain(A),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_50,c_7000]) ).
cnf(c_7002,negated_conjecture,
addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = forward_diamond(star(sK0),domain_difference(antidomain(antidomain(A)),forward_diamond(sK0,domain(A)))),
inference(paramod,[status(thm)],[c_50,c_7001]) ).
cnf(c_7003,negated_conjecture,
addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = forward_diamond(star(sK0),domain_difference(antidomain(antidomain(A)),forward_diamond(sK0,antidomain(antidomain(A))))),
inference(paramod,[status(thm)],[c_50,c_7002]) ).
cnf(c_7004,negated_conjecture,
addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = forward_diamond(star(sK0),domain_difference(antidomain(antidomain(A)),domain(multiplication(sK0,domain(antidomain(antidomain(A))))))),
inference(paramod,[status(thm)],[c_42,c_7003]) ).
cnf(c_7005,negated_conjecture,
addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = forward_diamond(star(sK0),domain_difference(antidomain(antidomain(A)),domain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))),
inference(paramod,[status(thm)],[c_50,c_7004]) ).
cnf(c_7006,negated_conjecture,
addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = forward_diamond(star(sK0),domain_difference(antidomain(antidomain(A)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))),
inference(paramod,[status(thm)],[c_50,c_7005]) ).
cnf(c_7007,negated_conjecture,
addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = forward_diamond(star(sK0),multiplication(domain(antidomain(antidomain(A))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))))),
inference(paramod,[status(thm)],[c_43,c_7006]) ).
cnf(c_7008,negated_conjecture,
addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = forward_diamond(star(sK0),multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))))),
inference(paramod,[status(thm)],[c_50,c_7007]) ).
cnf(c_7009,negated_conjecture,
addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = domain(multiplication(star(sK0),domain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))))))),
inference(paramod,[status(thm)],[c_42,c_7008]) ).
cnf(c_7010,negated_conjecture,
addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = domain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))),
inference(paramod,[status(thm)],[c_50,c_7009]) ).
cnf(c_72,negated_conjecture,
addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(A)))))))))))))),
inference(paramod,[status(thm)],[c_50,c_7010]) ).
cnf(c_77,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_67,c_51]) ).
cnf(c_7011,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(antidomain(B),A),B),
inference(paramod,[status(thm)],[c_54,c_58]) ).
cnf(c_89,plain,
multiplication(addition(antidomain(A),B),A) = addition(zero,multiplication(B,A)),
inference(copy,[status(thm)],[c_7011]) ).
cnf(c_91,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_55,c_58]) ).
cnf(c_7012,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_55,c_58]) ).
cnf(c_7013,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_67,c_7012]) ).
cnf(c_7014,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_91,c_7013]) ).
cnf(c_92,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_65,c_7014]) ).
cnf(c_7015,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(addition(zero,B),A),
inference(paramod,[status(thm)],[c_91,c_89]) ).
cnf(c_94,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(B,A),
inference(paramod,[status(thm)],[c_92,c_7015]) ).
cnf(c_97,plain,
addition(zero,multiplication(A,B)) = multiplication(A,B),
inference(paramod,[status(thm)],[c_92,c_91]) ).
cnf(c_7016,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(A,B)),
inference(paramod,[status(thm)],[c_54,c_60]) ).
cnf(c_7017,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(A,B)),
inference(paramod,[status(thm)],[c_97,c_7016]) ).
cnf(c_100,plain,
multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_7017]) ).
cnf(c_7018,plain,
addition(multiplication(antidomain(A),B),zero) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_54,c_60]) ).
cnf(c_7019,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_67,c_7018]) ).
cnf(c_7020,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_97,c_7019]) ).
cnf(c_101,plain,
multiplication(antidomain(A),addition(B,A)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_7020]) ).
cnf(c_111,plain,
antidomain(one) = zero,
inference(paramod,[status(thm)],[c_62,c_54]) ).
cnf(c_133,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_67,c_65]) ).
cnf(c_7021,plain,
addition(divergence(A),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A))))))))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))))))))))))))),
inference(paramod,[status(thm)],[c_70,c_72]) ).
cnf(c_7022,plain,
addition(divergence(A),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(A))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A))))))))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))))))))))))))),
inference(paramod,[status(thm)],[c_70,c_7021]) ).
cnf(c_7023,plain,
addition(divergence(A),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(A))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A)))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))))))))))))))),
inference(paramod,[status(thm)],[c_70,c_7022]) ).
cnf(c_7024,plain,
addition(divergence(A),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(A))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A)))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(A))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))))))))))))))),
inference(paramod,[status(thm)],[c_70,c_7023]) ).
cnf(c_141,plain,
addition(divergence(A),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(A))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A)))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(A))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A))))))))))))),
inference(paramod,[status(thm)],[c_70,c_7024]) ).
cnf(c_7025,plain,
addition(divergence(A),antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))))) = one,
inference(paramod,[status(thm)],[c_70,c_77]) ).
cnf(c_144,plain,
addition(divergence(A),antidomain(divergence(A))) = one,
inference(paramod,[status(thm)],[c_70,c_7025]) ).
cnf(c_7026,plain,
addition(antidomain(multiplication(A,antidomain(antidomain(divergence(A))))),divergence(A)) = one,
inference(paramod,[status(thm)],[c_70,c_77]) ).
cnf(c_145,plain,
addition(divergence(A),antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))) = one,
inference(paramod,[status(thm)],[c_67,c_7026]) ).
cnf(c_7027,plain,
addition(zero,antidomain(antidomain(one))) = one,
inference(paramod,[status(thm)],[c_111,c_77]) ).
cnf(c_7028,plain,
addition(zero,antidomain(zero)) = one,
inference(paramod,[status(thm)],[c_111,c_7027]) ).
cnf(c_161,plain,
antidomain(zero) = one,
inference(paramod,[status(thm)],[c_133,c_7028]) ).
cnf(c_7029,plain,
multiplication(one,A) = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_77,c_94]) ).
cnf(c_7030,plain,
A = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_61,c_7029]) ).
cnf(c_185,plain,
multiplication(antidomain(antidomain(A)),A) = A,
inference(copy,[status(thm)],[c_7030]) ).
cnf(c_7031,plain,
multiplication(antidomain(antidomain(antidomain(A))),one) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_77,c_101]) ).
cnf(c_7032,plain,
antidomain(antidomain(antidomain(A))) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_62,c_7031]) ).
cnf(c_282,plain,
antidomain(antidomain(antidomain(A))) = antidomain(A),
inference(paramod,[status(thm)],[c_185,c_7032]) ).
cnf(c_7033,plain,
multiplication(antidomain(antidomain(divergence(A))),one) = multiplication(antidomain(antidomain(divergence(A))),divergence(A)),
inference(paramod,[status(thm)],[c_144,c_101]) ).
cnf(c_7034,plain,
antidomain(antidomain(divergence(A))) = multiplication(antidomain(antidomain(divergence(A))),divergence(A)),
inference(paramod,[status(thm)],[c_62,c_7033]) ).
cnf(c_284,plain,
antidomain(antidomain(divergence(A))) = divergence(A),
inference(paramod,[status(thm)],[c_185,c_7034]) ).
cnf(c_7035,plain,
addition(divergence(A),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(A),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A)))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(A))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A))))))))))))),
inference(paramod,[status(thm)],[c_284,c_141]) ).
cnf(c_7036,plain,
addition(divergence(A),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(A),antidomain(antidomain(antidomain(multiplication(sK0,divergence(A)))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(A))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A))))))))))))),
inference(paramod,[status(thm)],[c_284,c_7035]) ).
cnf(c_7037,plain,
addition(divergence(A),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(A),antidomain(multiplication(sK0,divergence(A)))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(A))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A))))))))))))),
inference(paramod,[status(thm)],[c_282,c_7036]) ).
cnf(c_7038,plain,
addition(divergence(A),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(A),antidomain(multiplication(sK0,divergence(A)))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(A),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(A))))))))))))),
inference(paramod,[status(thm)],[c_284,c_7037]) ).
cnf(c_7039,plain,
addition(divergence(A),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(A),antidomain(multiplication(sK0,divergence(A)))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(A),antidomain(antidomain(antidomain(multiplication(sK0,divergence(A))))))))))),
inference(paramod,[status(thm)],[c_284,c_7038]) ).
cnf(c_288,plain,
addition(divergence(A),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(A),antidomain(multiplication(sK0,divergence(A)))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(A),antidomain(multiplication(sK0,divergence(A))))))))),
inference(paramod,[status(thm)],[c_282,c_7039]) ).
cnf(c_299,plain,
addition(divergence(A),antidomain(multiplication(A,divergence(A)))) = one,
inference(paramod,[status(thm)],[c_284,c_145]) ).
cnf(c_304,plain,
antidomain(antidomain(multiplication(A,divergence(A)))) = divergence(A),
inference(paramod,[status(thm)],[c_284,c_70]) ).
cnf(c_887,plain,
multiplication(divergence(A),antidomain(divergence(A))) = zero,
inference(paramod,[status(thm)],[c_284,c_54]) ).
cnf(c_7040,plain,
multiplication(antidomain(divergence(A)),one) = multiplication(antidomain(divergence(A)),antidomain(multiplication(A,divergence(A)))),
inference(paramod,[status(thm)],[c_299,c_100]) ).
cnf(c_7041,plain,
antidomain(divergence(A)) = multiplication(antidomain(divergence(A)),antidomain(multiplication(A,divergence(A)))),
inference(paramod,[status(thm)],[c_62,c_7040]) ).
cnf(c_1523,plain,
multiplication(antidomain(divergence(A)),antidomain(multiplication(A,divergence(A)))) = antidomain(divergence(A)),
inference(copy,[status(thm)],[c_7041]) ).
cnf(c_7042,plain,
multiplication(antidomain(divergence(A)),antidomain(multiplication(A,divergence(A)))) = antidomain(multiplication(A,divergence(A))),
inference(paramod,[status(thm)],[c_304,c_185]) ).
cnf(c_7043,plain,
antidomain(divergence(A)) = antidomain(multiplication(A,divergence(A))),
inference(paramod,[status(thm)],[c_1523,c_7042]) ).
cnf(c_3019,plain,
antidomain(multiplication(A,divergence(A))) = antidomain(divergence(A)),
inference(copy,[status(thm)],[c_7043]) ).
cnf(c_7044,plain,
addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(sK0),antidomain(divergence(sK0))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(sK0),antidomain(multiplication(sK0,divergence(sK0))))))))),
inference(paramod,[status(thm)],[c_3019,c_288]) ).
cnf(c_7045,plain,
addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero)))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(sK0),antidomain(multiplication(sK0,divergence(sK0))))))))),
inference(paramod,[status(thm)],[c_887,c_7044]) ).
cnf(c_7046,plain,
addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),antidomain(one))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(sK0),antidomain(multiplication(sK0,divergence(sK0))))))))),
inference(paramod,[status(thm)],[c_161,c_7045]) ).
cnf(c_7047,plain,
addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),zero)))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(sK0),antidomain(multiplication(sK0,divergence(sK0))))))))),
inference(paramod,[status(thm)],[c_111,c_7046]) ).
cnf(c_7048,plain,
addition(divergence(sK0),antidomain(antidomain(zero))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(sK0),antidomain(multiplication(sK0,divergence(sK0))))))))),
inference(paramod,[status(thm)],[c_56,c_7047]) ).
cnf(c_7049,plain,
addition(divergence(sK0),antidomain(one)) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(sK0),antidomain(multiplication(sK0,divergence(sK0))))))))),
inference(paramod,[status(thm)],[c_161,c_7048]) ).
cnf(c_7050,plain,
addition(divergence(sK0),zero) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(sK0),antidomain(multiplication(sK0,divergence(sK0))))))))),
inference(paramod,[status(thm)],[c_111,c_7049]) ).
cnf(c_7051,plain,
addition(zero,divergence(sK0)) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(sK0),antidomain(multiplication(sK0,divergence(sK0))))))))),
inference(paramod,[status(thm)],[c_67,c_7050]) ).
cnf(c_7052,plain,
divergence(sK0) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(sK0),antidomain(multiplication(sK0,divergence(sK0))))))))),
inference(paramod,[status(thm)],[c_133,c_7051]) ).
cnf(c_7053,plain,
divergence(sK0) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(divergence(sK0),antidomain(divergence(sK0)))))))),
inference(paramod,[status(thm)],[c_3019,c_7052]) ).
cnf(c_7054,plain,
divergence(sK0) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero))))),
inference(paramod,[status(thm)],[c_887,c_7053]) ).
cnf(c_7055,plain,
divergence(sK0) = antidomain(antidomain(multiplication(star(sK0),antidomain(one)))),
inference(paramod,[status(thm)],[c_161,c_7054]) ).
cnf(c_7056,plain,
divergence(sK0) = antidomain(antidomain(multiplication(star(sK0),zero))),
inference(paramod,[status(thm)],[c_111,c_7055]) ).
cnf(c_7057,plain,
divergence(sK0) = antidomain(antidomain(zero)),
inference(paramod,[status(thm)],[c_56,c_7056]) ).
cnf(c_7058,plain,
divergence(sK0) = antidomain(one),
inference(paramod,[status(thm)],[c_161,c_7057]) ).
cnf(c_6987,plain,
divergence(sK0) = zero,
inference(paramod,[status(thm)],[c_111,c_7058]) ).
cnf(c_6988,plain,
$false,
inference(resolve,[status(thm)],[c_6987,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE131+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 19:26:00 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2314274 was started by sandbox on n009,
% 0.11/0.37 % Fri Sep 25 19:26:00 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 83.14/11.96
% 83.14/11.96 % SZS status Theorem for theBenchmark
% 83.14/11.96
% 83.14/11.96 % Proof 1 at 2.66 (+ 0.79) seconds.
% 83.14/11.96 % Length of proof is 62.
% 83.14/11.96 % Level of proof is 12.
% 83.14/11.96 % Maximum clause weight is 125.000.
% 83.14/11.96 % Given clauses 302.
% 83.14/11.96
% 83.14/11.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------