%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE084-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:44:17 AM UTC 2026
% Result : Unsatisfiable 260.55s 34.43s
% Output : CNFRefutation 260.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 126 ( 126 unt; 0 def)
% Number of atoms : 126 ( 125 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 205 ( 15 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq2(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq2(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
fof(ifeq_axiom_001,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom_001) ).
cnf(c_2,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom_001]) ).
fof(additive_commutativity,axiom,
! [VAR_0,VAR_1] : addition(VAR_0,VAR_1) = addition(VAR_1,VAR_0),
file('theBenchmark.p',additive_commutativity) ).
cnf(c_3,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
fof(additive_associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : addition(VAR_0,addition(VAR_1,VAR_2)) = addition(addition(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',additive_associativity) ).
cnf(c_4,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_5,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(copy,[status(thm)],[c_4]) ).
fof(additive_identity,axiom,
! [VAR_0] : addition(VAR_0,zero) = VAR_0,
file('theBenchmark.p',additive_identity) ).
cnf(c_6,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
fof(additive_idempotence,axiom,
! [VAR_0] : addition(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',additive_idempotence) ).
cnf(c_7,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
fof(multiplicative_associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiplication(VAR_0,multiplication(VAR_1,VAR_2)) = multiplication(multiplication(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',multiplicative_associativity) ).
cnf(c_8,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_9,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(copy,[status(thm)],[c_8]) ).
fof(multiplicative_right_identity,axiom,
! [VAR_0] : multiplication(VAR_0,one) = VAR_0,
file('theBenchmark.p',multiplicative_right_identity) ).
cnf(c_10,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
fof(multiplicative_left_identity,axiom,
! [VAR_0] : multiplication(one,VAR_0) = VAR_0,
file('theBenchmark.p',multiplicative_left_identity) ).
cnf(c_11,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
fof(right_distributivity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiplication(VAR_0,addition(VAR_1,VAR_2)) = addition(multiplication(VAR_0,VAR_1),multiplication(VAR_0,VAR_2)),
file('theBenchmark.p',right_distributivity) ).
cnf(c_12,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_13,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_12]) ).
fof(left_distributivity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiplication(addition(VAR_0,VAR_1),VAR_2) = addition(multiplication(VAR_0,VAR_2),multiplication(VAR_1,VAR_2)),
file('theBenchmark.p',left_distributivity) ).
cnf(c_14,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_15,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_14]) ).
fof(left_annihilation,axiom,
! [VAR_0] : multiplication(zero,VAR_0) = zero,
file('theBenchmark.p',left_annihilation) ).
cnf(c_17,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
fof(order_1,axiom,
! [VAR_0,VAR_1] : ifeq(leq(VAR_0,VAR_1),true,addition(VAR_0,VAR_1),VAR_1) = VAR_1,
file('theBenchmark.p',order_1) ).
cnf(c_18,plain,
ifeq(leq(A,B),true,addition(A,B),B) = B,
inference(clausify,[status(thm)],[order_1]) ).
fof(order,axiom,
! [VAR_0,VAR_1] : ifeq2(addition(VAR_0,VAR_1),VAR_1,leq(VAR_0,VAR_1),true) = true,
file('theBenchmark.p',order) ).
cnf(c_19,plain,
ifeq2(addition(A,B),B,leq(A,B),true) = true,
inference(clausify,[status(thm)],[order]) ).
fof(domain1,axiom,
! [VAR_0] : multiplication(antidomain(VAR_0),VAR_0) = zero,
file('theBenchmark.p',domain1) ).
cnf(c_20,plain,
multiplication(antidomain(A),A) = zero,
inference(clausify,[status(thm)],[domain1]) ).
fof(domain2,axiom,
! [VAR_0,VAR_1] : addition(antidomain(multiplication(VAR_0,VAR_1)),antidomain(multiplication(VAR_0,antidomain(antidomain(VAR_1))))) = antidomain(multiplication(VAR_0,antidomain(antidomain(VAR_1)))),
file('theBenchmark.p',domain2) ).
cnf(c_21,plain,
addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))),
inference(clausify,[status(thm)],[domain2]) ).
fof(domain3,axiom,
! [VAR_0] : addition(antidomain(antidomain(VAR_0)),antidomain(VAR_0)) = one,
file('theBenchmark.p',domain3) ).
cnf(c_22,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_23,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_3,c_22]) ).
fof(domain4,axiom,
! [VAR_0] : domain(VAR_0) = antidomain(antidomain(VAR_0)),
file('theBenchmark.p',domain4) ).
cnf(c_24,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
fof(codomain1,axiom,
! [VAR_0] : multiplication(VAR_0,coantidomain(VAR_0)) = zero,
file('theBenchmark.p',codomain1) ).
cnf(c_25,plain,
multiplication(A,coantidomain(A)) = zero,
inference(clausify,[status(thm)],[codomain1]) ).
fof(codomain3,axiom,
! [VAR_0] : addition(coantidomain(coantidomain(VAR_0)),coantidomain(VAR_0)) = one,
file('theBenchmark.p',codomain3) ).
cnf(c_27,plain,
addition(coantidomain(coantidomain(A)),coantidomain(A)) = one,
inference(clausify,[status(thm)],[codomain3]) ).
cnf(c_28,plain,
addition(coantidomain(A),coantidomain(coantidomain(A))) = one,
inference(paramod,[status(thm)],[c_3,c_27]) ).
fof(goals,axiom,
domain(multiplication(sK2_goals_X0,sK1_goals_X1)) != domain(multiplication(sK2_goals_X0,domain(sK1_goals_X1))),
file('theBenchmark.p',goals) ).
cnf(c_30,plain,
domain(multiplication(sK2_goals_X0,sK1_goals_X1)) != domain(multiplication(sK2_goals_X0,domain(sK1_goals_X1))),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_38773,plain,
antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))) != domain(multiplication(sK2_goals_X0,domain(sK1_goals_X1))),
inference(paramod,[status(thm)],[c_24,c_30]) ).
cnf(c_38774,plain,
antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))) != domain(multiplication(sK2_goals_X0,antidomain(antidomain(sK1_goals_X1)))),
inference(paramod,[status(thm)],[c_24,c_38773]) ).
cnf(c_38775,plain,
antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))) != antidomain(antidomain(multiplication(sK2_goals_X0,antidomain(antidomain(sK1_goals_X1))))),
inference(paramod,[status(thm)],[c_24,c_38774]) ).
cnf(c_31,plain,
antidomain(antidomain(multiplication(sK2_goals_X0,antidomain(antidomain(sK1_goals_X1))))) != antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))),
inference(copy,[status(thm)],[c_38775]) ).
cnf(c_38776,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_34,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_38776]) ).
cnf(c_38777,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_7,c_5]) ).
cnf(c_35,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_38777]) ).
cnf(c_50,plain,
ifeq(leq(multiplication(A,B),multiplication(A,C)),true,multiplication(A,addition(B,C)),multiplication(A,C)) = multiplication(A,C),
inference(paramod,[status(thm)],[c_13,c_18]) ).
cnf(c_38778,plain,
multiplication(zero,A) = multiplication(antidomain(B),multiplication(B,A)),
inference(paramod,[status(thm)],[c_20,c_9]) ).
cnf(c_38779,plain,
zero = multiplication(antidomain(B),multiplication(B,A)),
inference(paramod,[status(thm)],[c_17,c_38778]) ).
cnf(c_58,plain,
multiplication(antidomain(A),multiplication(A,B)) = zero,
inference(copy,[status(thm)],[c_38779]) ).
cnf(c_38780,plain,
zero = antidomain(one),
inference(paramod,[status(thm)],[c_20,c_10]) ).
cnf(c_59,plain,
antidomain(one) = zero,
inference(copy,[status(thm)],[c_38780]) ).
cnf(c_38781,plain,
addition(multiplication(antidomain(A),B),zero) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_20,c_13]) ).
cnf(c_38782,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_3,c_38781]) ).
cnf(c_38783,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_34,c_38782]) ).
cnf(c_61,plain,
multiplication(antidomain(A),addition(B,A)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_38783]) ).
cnf(c_38784,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(antidomain(B),A),B),
inference(paramod,[status(thm)],[c_20,c_15]) ).
cnf(c_38785,plain,
multiplication(A,B) = multiplication(addition(antidomain(B),A),B),
inference(paramod,[status(thm)],[c_34,c_38784]) ).
cnf(c_62,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(B,A),
inference(copy,[status(thm)],[c_38785]) ).
cnf(c_38786,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,antidomain(B)),B),
inference(paramod,[status(thm)],[c_20,c_15]) ).
cnf(c_38787,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,antidomain(B)),B),
inference(paramod,[status(thm)],[c_3,c_38786]) ).
cnf(c_38788,plain,
multiplication(A,B) = multiplication(addition(A,antidomain(B)),B),
inference(paramod,[status(thm)],[c_34,c_38787]) ).
cnf(c_63,plain,
multiplication(addition(A,antidomain(B)),B) = multiplication(A,B),
inference(copy,[status(thm)],[c_38788]) ).
cnf(c_38789,plain,
zero = multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))),
inference(paramod,[status(thm)],[c_25,c_9]) ).
cnf(c_79,plain,
multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = zero,
inference(copy,[status(thm)],[c_38789]) ).
cnf(c_38790,plain,
zero = coantidomain(one),
inference(paramod,[status(thm)],[c_25,c_11]) ).
cnf(c_80,plain,
coantidomain(one) = zero,
inference(copy,[status(thm)],[c_38790]) ).
cnf(c_38791,plain,
addition(zero,antidomain(antidomain(one))) = one,
inference(paramod,[status(thm)],[c_59,c_23]) ).
cnf(c_38792,plain,
addition(zero,antidomain(zero)) = one,
inference(paramod,[status(thm)],[c_59,c_38791]) ).
cnf(c_109,plain,
antidomain(zero) = one,
inference(paramod,[status(thm)],[c_34,c_38792]) ).
cnf(c_38793,plain,
addition(zero,coantidomain(coantidomain(one))) = one,
inference(paramod,[status(thm)],[c_80,c_28]) ).
cnf(c_38794,plain,
addition(zero,coantidomain(zero)) = one,
inference(paramod,[status(thm)],[c_80,c_38793]) ).
cnf(c_113,plain,
coantidomain(zero) = one,
inference(paramod,[status(thm)],[c_34,c_38794]) ).
cnf(c_38795,plain,
ifeq2(A,A,leq(zero,A),true) = true,
inference(paramod,[status(thm)],[c_34,c_19]) ).
cnf(c_118,plain,
leq(zero,A) = true,
inference(paramod,[status(thm)],[c_1,c_38795]) ).
cnf(c_119,plain,
multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero,
inference(paramod,[status(thm)],[c_9,c_58]) ).
cnf(c_38796,plain,
multiplication(one,A) = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_23,c_62]) ).
cnf(c_38797,plain,
A = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_11,c_38796]) ).
cnf(c_541,plain,
multiplication(antidomain(antidomain(A)),A) = A,
inference(copy,[status(thm)],[c_38797]) ).
cnf(c_38798,plain,
ifeq(leq(multiplication(A,antidomain(B)),multiplication(A,antidomain(antidomain(B)))),true,multiplication(A,one),multiplication(A,antidomain(antidomain(B)))) = multiplication(A,antidomain(antidomain(B))),
inference(paramod,[status(thm)],[c_23,c_50]) ).
cnf(c_600,plain,
ifeq(leq(multiplication(A,antidomain(B)),multiplication(A,antidomain(antidomain(B)))),true,A,multiplication(A,antidomain(antidomain(B)))) = multiplication(A,antidomain(antidomain(B))),
inference(paramod,[status(thm)],[c_10,c_38798]) ).
cnf(c_38799,plain,
multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,antidomain(antidomain(B)))) = multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))),
inference(paramod,[status(thm)],[c_21,c_63]) ).
cnf(c_38800,plain,
zero = multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))),
inference(paramod,[status(thm)],[c_20,c_38799]) ).
cnf(c_650,plain,
multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))) = zero,
inference(copy,[status(thm)],[c_38800]) ).
cnf(c_38801,plain,
multiplication(antidomain(antidomain(antidomain(A))),one) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_23,c_61]) ).
cnf(c_38802,plain,
antidomain(antidomain(antidomain(A))) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_10,c_38801]) ).
cnf(c_1165,plain,
antidomain(antidomain(antidomain(A))) = antidomain(A),
inference(paramod,[status(thm)],[c_541,c_38802]) ).
cnf(c_38803,plain,
multiplication(antidomain(addition(A,B)),addition(A,B)) = multiplication(antidomain(addition(A,B)),A),
inference(paramod,[status(thm)],[c_35,c_61]) ).
cnf(c_38804,plain,
zero = multiplication(antidomain(addition(A,B)),A),
inference(paramod,[status(thm)],[c_20,c_38803]) ).
cnf(c_1169,plain,
multiplication(antidomain(addition(A,B)),A) = zero,
inference(copy,[status(thm)],[c_38804]) ).
cnf(c_38805,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(antidomain(addition(B,C)),A),B),
inference(paramod,[status(thm)],[c_1169,c_15]) ).
cnf(c_38806,plain,
multiplication(A,B) = multiplication(addition(antidomain(addition(B,C)),A),B),
inference(paramod,[status(thm)],[c_34,c_38805]) ).
cnf(c_1195,plain,
multiplication(addition(antidomain(addition(A,B)),C),A) = multiplication(C,A),
inference(copy,[status(thm)],[c_38806]) ).
cnf(c_3673,plain,
multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero,
inference(paramod,[status(thm)],[c_541,c_119]) ).
cnf(c_38807,plain,
multiplication(antidomain(zero),multiplication(A,antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B))))))) = zero,
inference(paramod,[status(thm)],[c_79,c_650]) ).
cnf(c_38808,plain,
multiplication(one,multiplication(A,antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B))))))) = zero,
inference(paramod,[status(thm)],[c_109,c_38807]) ).
cnf(c_10253,plain,
multiplication(A,antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B)))))) = zero,
inference(paramod,[status(thm)],[c_11,c_38808]) ).
cnf(c_38809,plain,
multiplication(one,A) = multiplication(antidomain(antidomain(addition(A,B))),A),
inference(paramod,[status(thm)],[c_23,c_1195]) ).
cnf(c_38810,plain,
A = multiplication(antidomain(antidomain(addition(A,B))),A),
inference(paramod,[status(thm)],[c_11,c_38809]) ).
cnf(c_11403,plain,
multiplication(antidomain(antidomain(addition(A,B))),A) = A,
inference(copy,[status(thm)],[c_38810]) ).
cnf(c_38811,plain,
multiplication(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(B)))))),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)),
inference(paramod,[status(thm)],[c_21,c_11403]) ).
cnf(c_11740,plain,
multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)),
inference(paramod,[status(thm)],[c_1165,c_38811]) ).
cnf(c_38812,plain,
ifeq(leq(zero,multiplication(A,antidomain(antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B)))))))),true,A,multiplication(A,antidomain(antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B)))))))) = multiplication(A,antidomain(antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B))))))),
inference(paramod,[status(thm)],[c_10253,c_600]) ).
cnf(c_38813,plain,
ifeq(leq(zero,multiplication(A,antidomain(multiplication(B,coantidomain(multiplication(A,B)))))),true,A,multiplication(A,antidomain(antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B)))))))) = multiplication(A,antidomain(antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B))))))),
inference(paramod,[status(thm)],[c_1165,c_38812]) ).
cnf(c_38814,plain,
ifeq(true,true,A,multiplication(A,antidomain(antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B)))))))) = multiplication(A,antidomain(antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B))))))),
inference(paramod,[status(thm)],[c_118,c_38813]) ).
cnf(c_38815,plain,
ifeq(true,true,A,multiplication(A,antidomain(multiplication(B,coantidomain(multiplication(A,B)))))) = multiplication(A,antidomain(antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B))))))),
inference(paramod,[status(thm)],[c_1165,c_38814]) ).
cnf(c_38816,plain,
A = multiplication(A,antidomain(antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B))))))),
inference(paramod,[status(thm)],[c_2,c_38815]) ).
cnf(c_38817,plain,
A = multiplication(A,antidomain(multiplication(B,coantidomain(multiplication(A,B))))),
inference(paramod,[status(thm)],[c_1165,c_38816]) ).
cnf(c_38454,plain,
multiplication(A,antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = A,
inference(copy,[status(thm)],[c_38817]) ).
cnf(c_38818,plain,
multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(multiplication(A,B),coantidomain(zero)))) = antidomain(multiplication(A,antidomain(antidomain(B)))),
inference(paramod,[status(thm)],[c_3673,c_38454]) ).
cnf(c_38819,plain,
multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(multiplication(A,B),one))) = antidomain(multiplication(A,antidomain(antidomain(B)))),
inference(paramod,[status(thm)],[c_113,c_38818]) ).
cnf(c_38820,plain,
multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(A,B))) = antidomain(multiplication(A,antidomain(antidomain(B)))),
inference(paramod,[status(thm)],[c_10,c_38819]) ).
cnf(c_38821,plain,
antidomain(multiplication(A,B)) = antidomain(multiplication(A,antidomain(antidomain(B)))),
inference(paramod,[status(thm)],[c_11740,c_38820]) ).
cnf(c_38632,plain,
antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)),
inference(copy,[status(thm)],[c_38821]) ).
cnf(c_38822,plain,
antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))) != antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))),
inference(paramod,[status(thm)],[c_38632,c_31]) ).
cnf(c_38772,plain,
$false,
inference(copy,[status(thm)],[c_38822]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE084-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.39 % Computer : n013.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8046.5625MB
% 0.15/0.39 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 19:19:51 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.40 % Process 993047 was started by sandbox on n013,
% 0.15/0.40 % Fri Sep 25 19:19:51 2026
% 0.15/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.41
% 0.18/0.41 % From the command line: assign(max_seconds, 300).
% 260.55/34.43
% 260.55/34.43 % given #500 (A,wt=19): 222 addition(A,addition(multiplication(A,B),multiplication(C,addition(one,B)))) = multiplication(addition(A,C),addition(one,B)). [para(39(a,1),15(a,1,1)),rewrite([5(6)])].
% 260.55/34.43
% 260.55/34.43 % given #1000 (A,wt=21): 416 multiplication(addition(one,A),multiplication(addition(B,C),D)) = multiplication(addition(B,addition(C,multiplication(A,addition(B,C)))),D). [para(44(a,2),41(a,1)),rewrite([43(11),15(11)])].
% 260.55/34.43
% 260.55/34.43 % SZS status Unsatisfiable for theBenchmark
% 260.55/34.43
% 260.55/34.43 % Proof 1 at 26.31 (+ 7.54) seconds.
% 260.55/34.43 % Length of proof is 55.
% 260.55/34.43 % Level of proof is 8.
% 260.55/34.43 % Maximum clause weight is 24.000.
% 260.55/34.43 % Given clauses 1398.
% 260.55/34.43
% 260.55/34.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------