%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE120+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 07:44:21 AM UTC 2026
% Result : Theorem 79.08s 21.70s
% Output : CNFRefutation 79.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 19
% Syntax : Number of formulae : 222 ( 222 unt; 0 def)
% Number of atoms : 222 ( 221 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 18 ( 18 ~; 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 : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 286 ( 9 sgn 30 !; 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(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(codomain4,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('theBenchmark.p',codomain4) ).
fof(backward_diamond,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('theBenchmark.p',backward_diamond) ).
fof(goals,conjecture,
! [X0] : addition(backward_diamond(one,domain(X0)),domain(X0)) = domain(X0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : addition(backward_diamond(one,domain(X0)),domain(X0)) = domain(X0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_27,plain,
? [X0] : domain(X0) != addition(backward_diamond(one,domain(X0)),domain(X0)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
domain(sK0) != addition(backward_diamond(one,domain(sK0)),domain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_27]) ).
cnf(c_30,negated_conjecture,
domain(sK0) != addition(backward_diamond(one,domain(sK0)),domain(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_31,negated_conjecture,
addition(backward_diamond(one,domain(sK0)),domain(sK0)) != domain(sK0),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_34,plain,
backward_diamond(A,B) = codomain(multiplication(codomain(B),A)),
inference(clausify,[status(thm)],[backward_diamond]) ).
cnf(c_38,plain,
codomain(A) = coantidomain(coantidomain(A)),
inference(clausify,[status(thm)],[codomain4]) ).
cnf(c_39,plain,
addition(coantidomain(coantidomain(A)),coantidomain(A)) = one,
inference(clausify,[status(thm)],[codomain3]) ).
cnf(c_40,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_41,plain,
addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_42,plain,
multiplication(A,coantidomain(A)) = zero,
inference(clausify,[status(thm)],[codomain1]) ).
cnf(c_43,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_44,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_45,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_46,plain,
addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))),
inference(copy,[status(thm)],[c_45]) ).
cnf(c_47,plain,
multiplication(antidomain(A),A) = zero,
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_48,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_50,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_51,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_52,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_53,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_54,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_55,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_57,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_58,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_59,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_60,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_22639,negated_conjecture,
addition(backward_diamond(one,antidomain(antidomain(sK0))),domain(sK0)) != domain(sK0),
inference(paramod,[status(thm)],[c_43,c_31]) ).
cnf(c_22640,negated_conjecture,
addition(codomain(multiplication(codomain(antidomain(antidomain(sK0))),one)),domain(sK0)) != domain(sK0),
inference(paramod,[status(thm)],[c_34,c_22639]) ).
cnf(c_22641,negated_conjecture,
addition(codomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),one)),domain(sK0)) != domain(sK0),
inference(paramod,[status(thm)],[c_38,c_22640]) ).
cnf(c_22642,negated_conjecture,
addition(codomain(coantidomain(coantidomain(antidomain(antidomain(sK0))))),domain(sK0)) != domain(sK0),
inference(paramod,[status(thm)],[c_55,c_22641]) ).
cnf(c_22643,negated_conjecture,
addition(coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(sK0)))))),domain(sK0)) != domain(sK0),
inference(paramod,[status(thm)],[c_38,c_22642]) ).
cnf(c_22644,negated_conjecture,
addition(coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(sK0)))))),antidomain(antidomain(sK0))) != domain(sK0),
inference(paramod,[status(thm)],[c_43,c_22643]) ).
cnf(c_22645,negated_conjecture,
addition(antidomain(antidomain(sK0)),coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(sK0))))))) != domain(sK0),
inference(paramod,[status(thm)],[c_60,c_22644]) ).
cnf(c_62,negated_conjecture,
addition(antidomain(antidomain(sK0)),coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(sK0))))))) != antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_43,c_22645]) ).
cnf(c_68,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_60,c_44]) ).
cnf(c_69,plain,
addition(coantidomain(A),coantidomain(coantidomain(A))) = one,
inference(paramod,[status(thm)],[c_60,c_39]) ).
cnf(c_72,plain,
addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_42,c_46]) ).
cnf(c_73,plain,
addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)),
inference(paramod,[status(thm)],[c_47,c_41]) ).
cnf(c_22646,plain,
addition(zero,multiplication(A,coantidomain(B))) = multiplication(addition(B,A),coantidomain(B)),
inference(paramod,[status(thm)],[c_42,c_51]) ).
cnf(c_78,plain,
multiplication(addition(A,B),coantidomain(A)) = addition(zero,multiplication(B,coantidomain(A))),
inference(copy,[status(thm)],[c_22646]) ).
cnf(c_22647,plain,
addition(multiplication(A,coantidomain(B)),zero) = multiplication(addition(A,B),coantidomain(B)),
inference(paramod,[status(thm)],[c_42,c_51]) ).
cnf(c_22648,plain,
addition(zero,multiplication(A,coantidomain(B))) = multiplication(addition(A,B),coantidomain(B)),
inference(paramod,[status(thm)],[c_60,c_22647]) ).
cnf(c_79,plain,
multiplication(addition(A,B),coantidomain(B)) = addition(zero,multiplication(A,coantidomain(B))),
inference(copy,[status(thm)],[c_22648]) ).
cnf(c_22649,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(antidomain(B),A),B),
inference(paramod,[status(thm)],[c_47,c_51]) ).
cnf(c_80,plain,
multiplication(addition(antidomain(A),B),A) = addition(zero,multiplication(B,A)),
inference(copy,[status(thm)],[c_22649]) ).
cnf(c_22650,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,antidomain(B)),B),
inference(paramod,[status(thm)],[c_47,c_51]) ).
cnf(c_22651,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,antidomain(B)),B),
inference(paramod,[status(thm)],[c_60,c_22650]) ).
cnf(c_81,plain,
multiplication(addition(A,antidomain(B)),B) = addition(zero,multiplication(A,B)),
inference(copy,[status(thm)],[c_22651]) ).
cnf(c_82,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_48,c_51]) ).
cnf(c_22652,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_48,c_51]) ).
cnf(c_22653,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_60,c_22652]) ).
cnf(c_22654,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_82,c_22653]) ).
cnf(c_83,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_58,c_22654]) ).
cnf(c_22655,plain,
multiplication(addition(A,antidomain(B)),B) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_82,c_81]) ).
cnf(c_84,plain,
multiplication(addition(A,antidomain(B)),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_83,c_22655]) ).
cnf(c_22656,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(addition(zero,B),A),
inference(paramod,[status(thm)],[c_82,c_80]) ).
cnf(c_85,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(B,A),
inference(paramod,[status(thm)],[c_83,c_22656]) ).
cnf(c_22657,plain,
multiplication(addition(A,B),coantidomain(B)) = multiplication(addition(zero,A),coantidomain(B)),
inference(paramod,[status(thm)],[c_82,c_79]) ).
cnf(c_86,plain,
multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)),
inference(paramod,[status(thm)],[c_83,c_22657]) ).
cnf(c_22658,plain,
multiplication(addition(A,B),coantidomain(A)) = multiplication(addition(zero,B),coantidomain(A)),
inference(paramod,[status(thm)],[c_82,c_78]) ).
cnf(c_87,plain,
multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)),
inference(paramod,[status(thm)],[c_83,c_22658]) ).
cnf(c_88,plain,
addition(zero,multiplication(A,B)) = multiplication(A,B),
inference(paramod,[status(thm)],[c_83,c_82]) ).
cnf(c_22659,plain,
addition(zero,multiplication(A,B)) = multiplication(A,addition(coantidomain(A),B)),
inference(paramod,[status(thm)],[c_42,c_53]) ).
cnf(c_22660,plain,
multiplication(A,B) = multiplication(A,addition(coantidomain(A),B)),
inference(paramod,[status(thm)],[c_88,c_22659]) ).
cnf(c_89,plain,
multiplication(A,addition(coantidomain(A),B)) = multiplication(A,B),
inference(copy,[status(thm)],[c_22660]) ).
cnf(c_22661,plain,
addition(multiplication(A,B),zero) = multiplication(A,addition(B,coantidomain(A))),
inference(paramod,[status(thm)],[c_42,c_53]) ).
cnf(c_22662,plain,
addition(zero,multiplication(A,B)) = multiplication(A,addition(B,coantidomain(A))),
inference(paramod,[status(thm)],[c_60,c_22661]) ).
cnf(c_22663,plain,
multiplication(A,B) = multiplication(A,addition(B,coantidomain(A))),
inference(paramod,[status(thm)],[c_88,c_22662]) ).
cnf(c_90,plain,
multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B),
inference(copy,[status(thm)],[c_22663]) ).
cnf(c_22664,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(A,B)),
inference(paramod,[status(thm)],[c_47,c_53]) ).
cnf(c_22665,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(A,B)),
inference(paramod,[status(thm)],[c_88,c_22664]) ).
cnf(c_91,plain,
multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_22665]) ).
cnf(c_22666,plain,
addition(multiplication(antidomain(A),B),zero) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_47,c_53]) ).
cnf(c_22667,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_60,c_22666]) ).
cnf(c_22668,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_88,c_22667]) ).
cnf(c_92,plain,
multiplication(antidomain(A),addition(B,A)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_22668]) ).
cnf(c_95,plain,
coantidomain(one) = zero,
inference(paramod,[status(thm)],[c_54,c_42]) ).
cnf(c_22669,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_54,c_51]) ).
cnf(c_97,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_22669]) ).
cnf(c_102,plain,
antidomain(one) = zero,
inference(paramod,[status(thm)],[c_55,c_47]) ).
cnf(c_22670,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_57,c_59]) ).
cnf(c_120,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_22670]) ).
cnf(c_124,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_60,c_58]) ).
cnf(c_22671,plain,
addition(addition(A,antidomain(B)),antidomain(antidomain(B))) = addition(A,one),
inference(paramod,[status(thm)],[c_68,c_59]) ).
cnf(c_127,plain,
addition(antidomain(antidomain(A)),addition(B,antidomain(A))) = addition(B,one),
inference(paramod,[status(thm)],[c_60,c_22671]) ).
cnf(c_22672,plain,
addition(addition(A,coantidomain(B)),coantidomain(coantidomain(B))) = addition(A,one),
inference(paramod,[status(thm)],[c_69,c_59]) ).
cnf(c_129,plain,
addition(coantidomain(coantidomain(A)),addition(B,coantidomain(A))) = addition(B,one),
inference(paramod,[status(thm)],[c_60,c_22672]) ).
cnf(c_22673,plain,
addition(zero,coantidomain(coantidomain(one))) = one,
inference(paramod,[status(thm)],[c_95,c_69]) ).
cnf(c_22674,plain,
addition(zero,coantidomain(zero)) = one,
inference(paramod,[status(thm)],[c_95,c_22673]) ).
cnf(c_131,plain,
coantidomain(zero) = one,
inference(paramod,[status(thm)],[c_124,c_22674]) ).
cnf(c_133,plain,
addition(one,coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)),
inference(paramod,[status(thm)],[c_131,c_73]) ).
cnf(c_22675,plain,
addition(zero,antidomain(antidomain(one))) = one,
inference(paramod,[status(thm)],[c_102,c_68]) ).
cnf(c_22676,plain,
addition(zero,antidomain(zero)) = one,
inference(paramod,[status(thm)],[c_102,c_22675]) ).
cnf(c_136,plain,
antidomain(zero) = one,
inference(paramod,[status(thm)],[c_124,c_22676]) ).
cnf(c_139,plain,
addition(one,antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_136,c_72]) ).
cnf(c_22677,plain,
multiplication(one,antidomain(A)) = multiplication(antidomain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_68,c_84]) ).
cnf(c_22678,plain,
antidomain(A) = multiplication(antidomain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_54,c_22677]) ).
cnf(c_148,plain,
multiplication(antidomain(A),antidomain(A)) = antidomain(A),
inference(copy,[status(thm)],[c_22678]) ).
cnf(c_22679,plain,
addition(antidomain(A),multiplication(B,antidomain(A))) = multiplication(addition(antidomain(A),B),antidomain(A)),
inference(paramod,[status(thm)],[c_148,c_51]) ).
cnf(c_22680,plain,
multiplication(addition(one,B),antidomain(A)) = multiplication(addition(antidomain(A),B),antidomain(A)),
inference(paramod,[status(thm)],[c_97,c_22679]) ).
cnf(c_167,plain,
multiplication(addition(antidomain(A),B),antidomain(A)) = multiplication(addition(one,B),antidomain(A)),
inference(copy,[status(thm)],[c_22680]) ).
cnf(c_22681,plain,
multiplication(one,A) = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_68,c_85]) ).
cnf(c_22682,plain,
A = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_54,c_22681]) ).
cnf(c_176,plain,
multiplication(antidomain(antidomain(A)),A) = A,
inference(copy,[status(thm)],[c_22682]) ).
cnf(c_22683,plain,
addition(antidomain(A),one) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_68,c_120]) ).
cnf(c_22684,plain,
addition(one,antidomain(A)) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_60,c_22683]) ).
cnf(c_194,plain,
addition(one,antidomain(A)) = one,
inference(paramod,[status(thm)],[c_68,c_22684]) ).
cnf(c_22685,plain,
addition(coantidomain(A),one) = addition(coantidomain(A),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_69,c_120]) ).
cnf(c_22686,plain,
addition(one,coantidomain(A)) = addition(coantidomain(A),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_60,c_22685]) ).
cnf(c_195,plain,
addition(one,coantidomain(A)) = one,
inference(paramod,[status(thm)],[c_69,c_22686]) ).
cnf(c_22687,plain,
one = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_194,c_139]) ).
cnf(c_198,plain,
antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one,
inference(copy,[status(thm)],[c_22687]) ).
cnf(c_22688,plain,
one = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)),
inference(paramod,[status(thm)],[c_195,c_133]) ).
cnf(c_204,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one,
inference(copy,[status(thm)],[c_22688]) ).
cnf(c_22689,plain,
addition(multiplication(one,A),multiplication(antidomain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_194,c_51]) ).
cnf(c_22690,plain,
addition(A,multiplication(antidomain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_54,c_22689]) ).
cnf(c_205,plain,
addition(A,multiplication(antidomain(B),A)) = A,
inference(paramod,[status(thm)],[c_54,c_22690]) ).
cnf(c_22691,plain,
multiplication(one,coantidomain(coantidomain(coantidomain(A)))) = multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_69,c_86]) ).
cnf(c_22692,plain,
coantidomain(coantidomain(coantidomain(A))) = multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_54,c_22691]) ).
cnf(c_218,plain,
multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))),
inference(copy,[status(thm)],[c_22692]) ).
cnf(c_22693,plain,
addition(multiplication(A,one),multiplication(A,coantidomain(B))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_195,c_53]) ).
cnf(c_22694,plain,
addition(A,multiplication(A,coantidomain(B))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_55,c_22693]) ).
cnf(c_222,plain,
addition(A,multiplication(A,coantidomain(B))) = A,
inference(paramod,[status(thm)],[c_55,c_22694]) ).
cnf(c_22695,plain,
multiplication(one,coantidomain(antidomain(A))) = multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_68,c_87]) ).
cnf(c_22696,plain,
coantidomain(antidomain(A)) = multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_54,c_22695]) ).
cnf(c_249,plain,
multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)),
inference(copy,[status(thm)],[c_22696]) ).
cnf(c_22697,plain,
multiplication(A,one) = multiplication(A,coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_69,c_89]) ).
cnf(c_22698,plain,
A = multiplication(A,coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_55,c_22697]) ).
cnf(c_274,plain,
multiplication(A,coantidomain(coantidomain(A))) = A,
inference(copy,[status(thm)],[c_22698]) ).
cnf(c_22699,plain,
coantidomain(A) = coantidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_274,c_218]) ).
cnf(c_277,plain,
coantidomain(coantidomain(coantidomain(A))) = coantidomain(A),
inference(copy,[status(thm)],[c_22699]) ).
cnf(c_278,negated_conjecture,
addition(antidomain(antidomain(sK0)),coantidomain(coantidomain(antidomain(antidomain(sK0))))) != antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_277,c_62]) ).
cnf(c_22700,plain,
addition(coantidomain(coantidomain(antidomain(A))),antidomain(A)) = coantidomain(coantidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_274,c_205]) ).
cnf(c_285,plain,
addition(antidomain(A),coantidomain(coantidomain(antidomain(A)))) = coantidomain(coantidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_60,c_22700]) ).
cnf(c_286,negated_conjecture,
coantidomain(coantidomain(antidomain(antidomain(sK0)))) != antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_285,c_278]) ).
cnf(c_22701,plain,
multiplication(antidomain(coantidomain(A)),one) = multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_69,c_91]) ).
cnf(c_22702,plain,
antidomain(coantidomain(A)) = multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_55,c_22701]) ).
cnf(c_334,plain,
multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)),
inference(copy,[status(thm)],[c_22702]) ).
cnf(c_22703,plain,
multiplication(one,multiplication(A,antidomain(antidomain(coantidomain(A))))) = zero,
inference(paramod,[status(thm)],[c_198,c_47]) ).
cnf(c_336,plain,
multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero,
inference(paramod,[status(thm)],[c_54,c_22703]) ).
cnf(c_22704,plain,
addition(zero,multiplication(A,B)) = multiplication(A,addition(antidomain(antidomain(coantidomain(A))),B)),
inference(paramod,[status(thm)],[c_336,c_53]) ).
cnf(c_22705,plain,
multiplication(A,B) = multiplication(A,addition(antidomain(antidomain(coantidomain(A))),B)),
inference(paramod,[status(thm)],[c_124,c_22704]) ).
cnf(c_341,plain,
multiplication(A,addition(antidomain(antidomain(coantidomain(A))),B)) = multiplication(A,B),
inference(copy,[status(thm)],[c_22705]) ).
cnf(c_22706,plain,
multiplication(antidomain(antidomain(antidomain(A))),one) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_68,c_92]) ).
cnf(c_22707,plain,
antidomain(antidomain(antidomain(A))) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_55,c_22706]) ).
cnf(c_363,plain,
antidomain(antidomain(antidomain(A))) = antidomain(A),
inference(paramod,[status(thm)],[c_176,c_22707]) ).
cnf(c_22708,plain,
multiplication(multiplication(coantidomain(coantidomain(antidomain(A))),A),one) = zero,
inference(paramod,[status(thm)],[c_204,c_42]) ).
cnf(c_437,plain,
multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero,
inference(paramod,[status(thm)],[c_55,c_22708]) ).
cnf(c_22709,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B),
inference(paramod,[status(thm)],[c_437,c_51]) ).
cnf(c_22710,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B),
inference(paramod,[status(thm)],[c_60,c_22709]) ).
cnf(c_22711,plain,
multiplication(A,B) = multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B),
inference(paramod,[status(thm)],[c_124,c_22710]) ).
cnf(c_440,plain,
multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B),
inference(copy,[status(thm)],[c_22711]) ).
cnf(c_1840,plain,
addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)),
inference(paramod,[status(thm)],[c_249,c_222]) ).
cnf(c_22712,plain,
addition(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = coantidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_334,c_205]) ).
cnf(c_2265,plain,
addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_60,c_22712]) ).
cnf(c_22713,plain,
addition(coantidomain(coantidomain(antidomain(A))),antidomain(antidomain(A))) = addition(antidomain(antidomain(A)),one),
inference(paramod,[status(thm)],[c_1840,c_129]) ).
cnf(c_22714,plain,
addition(antidomain(antidomain(A)),coantidomain(coantidomain(antidomain(A)))) = addition(antidomain(antidomain(A)),one),
inference(paramod,[status(thm)],[c_60,c_22713]) ).
cnf(c_22715,plain,
addition(antidomain(antidomain(A)),coantidomain(coantidomain(antidomain(A)))) = addition(one,antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_60,c_22714]) ).
cnf(c_3190,plain,
addition(antidomain(antidomain(A)),coantidomain(coantidomain(antidomain(A)))) = one,
inference(paramod,[status(thm)],[c_194,c_22715]) ).
cnf(c_22716,plain,
multiplication(coantidomain(antidomain(A)),one) = multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_3190,c_90]) ).
cnf(c_22717,plain,
coantidomain(antidomain(A)) = multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_55,c_22716]) ).
cnf(c_3207,plain,
multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)),
inference(copy,[status(thm)],[c_22717]) ).
cnf(c_22718,plain,
addition(antidomain(coantidomain(coantidomain(A))),coantidomain(A)) = coantidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_277,c_2265]) ).
cnf(c_22719,plain,
addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_60,c_22718]) ).
cnf(c_3414,plain,
addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = coantidomain(A),
inference(paramod,[status(thm)],[c_277,c_22719]) ).
cnf(c_22720,plain,
multiplication(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = multiplication(addition(one,coantidomain(coantidomain(A))),antidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_2265,c_167]) ).
cnf(c_22721,plain,
multiplication(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = multiplication(one,antidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_195,c_22720]) ).
cnf(c_3420,plain,
multiplication(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_54,c_22721]) ).
cnf(c_22722,plain,
addition(antidomain(antidomain(coantidomain(coantidomain(A)))),coantidomain(A)) = addition(coantidomain(A),one),
inference(paramod,[status(thm)],[c_3414,c_127]) ).
cnf(c_22723,plain,
addition(coantidomain(A),antidomain(antidomain(coantidomain(coantidomain(A))))) = addition(coantidomain(A),one),
inference(paramod,[status(thm)],[c_60,c_22722]) ).
cnf(c_22724,plain,
addition(coantidomain(A),antidomain(antidomain(coantidomain(coantidomain(A))))) = addition(one,coantidomain(A)),
inference(paramod,[status(thm)],[c_60,c_22723]) ).
cnf(c_3428,plain,
addition(coantidomain(A),antidomain(antidomain(coantidomain(coantidomain(A))))) = one,
inference(paramod,[status(thm)],[c_195,c_22724]) ).
cnf(c_22725,plain,
multiplication(one,antidomain(coantidomain(coantidomain(A)))) = multiplication(coantidomain(A),antidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_3428,c_84]) ).
cnf(c_22726,plain,
antidomain(coantidomain(coantidomain(A))) = multiplication(coantidomain(A),antidomain(coantidomain(coantidomain(A)))),
inference(paramod,[status(thm)],[c_54,c_22725]) ).
cnf(c_3434,plain,
multiplication(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))),
inference(copy,[status(thm)],[c_22726]) ).
cnf(c_22727,plain,
multiplication(A,one) = multiplication(A,antidomain(antidomain(coantidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_3428,c_89]) ).
cnf(c_22728,plain,
A = multiplication(A,antidomain(antidomain(coantidomain(coantidomain(A))))),
inference(paramod,[status(thm)],[c_55,c_22727]) ).
cnf(c_3436,plain,
multiplication(A,antidomain(antidomain(coantidomain(coantidomain(A))))) = A,
inference(copy,[status(thm)],[c_22728]) ).
cnf(c_22729,plain,
addition(coantidomain(coantidomain(A)),antidomain(antidomain(coantidomain(A)))) = one,
inference(paramod,[status(thm)],[c_277,c_3428]) ).
cnf(c_3437,plain,
addition(antidomain(antidomain(coantidomain(A))),coantidomain(coantidomain(A))) = one,
inference(paramod,[status(thm)],[c_60,c_22729]) ).
cnf(c_3454,plain,
multiplication(coantidomain(A),antidomain(antidomain(coantidomain(A)))) = coantidomain(A),
inference(paramod,[status(thm)],[c_277,c_3436]) ).
cnf(c_22730,plain,
multiplication(coantidomain(coantidomain(A)),addition(antidomain(antidomain(coantidomain(coantidomain(coantidomain(A))))),antidomain(coantidomain(A)))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_3420,c_341]) ).
cnf(c_22731,plain,
multiplication(coantidomain(coantidomain(A)),addition(antidomain(antidomain(coantidomain(A))),antidomain(coantidomain(A)))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_277,c_22730]) ).
cnf(c_22732,plain,
multiplication(coantidomain(coantidomain(A)),addition(antidomain(coantidomain(A)),antidomain(antidomain(coantidomain(A))))) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_60,c_22731]) ).
cnf(c_22733,plain,
multiplication(coantidomain(coantidomain(A)),one) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_68,c_22732]) ).
cnf(c_6707,plain,
coantidomain(coantidomain(A)) = antidomain(coantidomain(A)),
inference(paramod,[status(thm)],[c_55,c_22733]) ).
cnf(c_22734,plain,
multiplication(coantidomain(A),antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_6707,c_3434]) ).
cnf(c_22735,plain,
coantidomain(A) = antidomain(coantidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_3454,c_22734]) ).
cnf(c_22736,plain,
coantidomain(A) = antidomain(antidomain(coantidomain(A))),
inference(paramod,[status(thm)],[c_6707,c_22735]) ).
cnf(c_6731,plain,
antidomain(antidomain(coantidomain(A))) = coantidomain(A),
inference(copy,[status(thm)],[c_22736]) ).
cnf(c_22737,plain,
addition(coantidomain(A),coantidomain(coantidomain(A))) = one,
inference(paramod,[status(thm)],[c_6731,c_3437]) ).
cnf(c_7742,plain,
addition(coantidomain(A),antidomain(coantidomain(A))) = one,
inference(paramod,[status(thm)],[c_6707,c_22737]) ).
cnf(c_8306,plain,
multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_6707,c_440]) ).
cnf(c_8310,negated_conjecture,
antidomain(coantidomain(antidomain(antidomain(sK0)))) != antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_6707,c_286]) ).
cnf(c_22738,plain,
multiplication(addition(coantidomain(antidomain(A)),antidomain(coantidomain(antidomain(antidomain(antidomain(A)))))),antidomain(antidomain(A))) = coantidomain(antidomain(A)),
inference(paramod,[status(thm)],[c_3207,c_8306]) ).
cnf(c_22739,plain,
multiplication(addition(coantidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))),antidomain(antidomain(A))) = coantidomain(antidomain(A)),
inference(paramod,[status(thm)],[c_363,c_22738]) ).
cnf(c_22740,plain,
multiplication(one,antidomain(antidomain(A))) = coantidomain(antidomain(A)),
inference(paramod,[status(thm)],[c_7742,c_22739]) ).
cnf(c_22741,plain,
antidomain(antidomain(A)) = coantidomain(antidomain(A)),
inference(paramod,[status(thm)],[c_54,c_22740]) ).
cnf(c_22433,plain,
coantidomain(antidomain(A)) = antidomain(antidomain(A)),
inference(copy,[status(thm)],[c_22741]) ).
cnf(c_22742,negated_conjecture,
antidomain(antidomain(antidomain(antidomain(sK0)))) != antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_22433,c_8310]) ).
cnf(c_22743,negated_conjecture,
antidomain(antidomain(sK0)) != antidomain(antidomain(sK0)),
inference(paramod,[status(thm)],[c_363,c_22742]) ).
cnf(c_22638,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_22743]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE120+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.42 % Computer : n009.cluster.edu
% 0.09/5.42 % Model : x86_64 x86_64
% 0.09/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.42 % Memory : 8046.5625MB
% 0.09/5.42 % OS : Linux 6.8.0-71-generic
% 0.09/5.42 % CPULimit : 300
% 0.09/5.42 % WCLimit : 300
% 0.09/5.42 % DateTime : Fri Sep 25 19:24:34 UTC 2026
% 0.09/5.43 % CPUTime :
% 0.09/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.43 % Process 2311373 was started by sandbox on n009,
% 0.09/5.43 % Fri Sep 25 19:24:34 2026
% 0.09/5.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.44
% 0.09/5.44 % From the command line: assign(max_seconds, 300).
% 79.08/21.70
% 79.08/21.70 % given #500 (A,wt=13): 352 multiplication(antidomain(A),addition(B,antidomain(antidomain(A)))) = multiplication(antidomain(A),B). [para(347(a,1),53(a,1,2)),rewrite([60(4),124(4)]),flip(a)].
% 79.08/21.70
% 79.08/21.70 % SZS status Theorem for theBenchmark
% 79.08/21.70
% 79.08/21.70 % Proof 1 at 8.05 (+ 2.19) seconds.
% 79.08/21.70 % Length of proof is 114.
% 79.08/21.70 % Level of proof is 16.
% 79.08/21.70 % Maximum clause weight is 18.000.
% 79.08/21.70 % Given clauses 741.
% 79.08/21.70
% 79.08/21.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
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