%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE113+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 02:15:20 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 59
% Syntax : Number of formulae : 238 ( 139 unt; 0 def)
% Number of atoms : 382 ( 381 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 293 ( 149 ~; 144 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 150 ( 6 sgn 45 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero ).
fof(domain1,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero ).
fof(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one ).
fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)) ).
fof(complement,axiom,
! [X0] : c(X0) = antidomain(domain(X0)) ).
fof(domain_difference,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)) ).
fof(forward_diamond,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))) ).
fof(goals,conjecture,
! [X0] : forward_diamond(X0,zero) = zero ).
fof(subgoal_0,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : forward_diamond(X0,zero) = zero,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : forward_diamond(X0,zero) != zero,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
forward_diamond(skolemFOFtoCNF_X0,zero) != zero,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[forward_diamond]) ).
fof(normalize_0_3,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(canonicalize,[],[complement]) ).
fof(normalize_0_5,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[domain4]) ).
fof(normalize_0_7,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_9,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_11,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_13,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(canonicalize,[],[domain_difference]) ).
fof(normalize_0_15,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_17,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_19,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_21,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A] : multiplication(A,zero) = zero,
inference(canonicalize,[],[right_annihilation]) ).
fof(normalize_0_23,plain,
! [A] : multiplication(A,zero) = zero,
inference(specialize,[],[normalize_0_22]) ).
cnf(refute_0_0,plain,
forward_diamond(skolemFOFtoCNF_X0,zero) != zero,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
forward_diamond(X0,zero) = domain(multiplication(X0,domain(zero))),
inference(subst,[],[refute_0_1:[bind(X1,$fot(zero))]]) ).
cnf(refute_0_3,plain,
c(X0) = antidomain(domain(X0)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
c(one) = antidomain(domain(one)),
inference(subst,[],[refute_0_3:[bind(X0,$fot(one))]]) ).
cnf(refute_0_5,plain,
domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
domain(one) = antidomain(antidomain(one)),
inference(subst,[],[refute_0_5:[bind(X0,$fot(one))]]) ).
cnf(refute_0_7,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
multiplication(antidomain(one),one) = antidomain(one),
inference(subst,[],[refute_0_7:[bind(A,$fot(antidomain(one)))]]) ).
cnf(refute_0_9,plain,
multiplication(antidomain(X0),X0) = zero,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
multiplication(antidomain(one),one) = zero,
inference(subst,[],[refute_0_9:[bind(X0,$fot(one))]]) ).
cnf(refute_0_11,plain,
( multiplication(antidomain(one),one) != antidomain(one)
| multiplication(antidomain(one),one) != zero
| zero = antidomain(one) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(antidomain(one),one),antidomain(one)) ),[0],$fot(zero)]]) ).
cnf(refute_0_12,plain,
( multiplication(antidomain(one),one) != antidomain(one)
| zero = antidomain(one) ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(one),one),zero) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
zero = antidomain(one),
inference(resolve,[$cnf( $equal(multiplication(antidomain(one),one),antidomain(one)) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_15,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_16,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( zero != antidomain(one)
| antidomain(one) = zero ),
inference(subst,[],[refute_0_16:[bind(X,$fot(zero)),bind(Y,$fot(antidomain(one)))]]) ).
cnf(refute_0_18,plain,
antidomain(one) = zero,
inference(resolve,[$cnf( $equal(zero,antidomain(one)) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( antidomain(one) != zero
| domain(one) != antidomain(antidomain(one))
| domain(one) = antidomain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(domain(one),antidomain(antidomain(one))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_20,plain,
( domain(one) != antidomain(antidomain(one))
| domain(one) = antidomain(zero) ),
inference(resolve,[$cnf( $equal(antidomain(one),zero) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
domain(one) = antidomain(zero),
inference(resolve,[$cnf( $equal(domain(one),antidomain(antidomain(one))) )],[refute_0_6,refute_0_20]) ).
cnf(refute_0_22,plain,
( c(one) != antidomain(domain(one))
| domain(one) != antidomain(zero)
| c(one) = antidomain(antidomain(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(c(one),antidomain(domain(one))) ),[1,0],$fot(antidomain(zero))]]) ).
cnf(refute_0_23,plain,
( c(one) != antidomain(domain(one))
| c(one) = antidomain(antidomain(zero)) ),
inference(resolve,[$cnf( $equal(domain(one),antidomain(zero)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
c(one) = antidomain(antidomain(zero)),
inference(resolve,[$cnf( $equal(c(one),antidomain(domain(one))) )],[refute_0_4,refute_0_23]) ).
cnf(refute_0_25,plain,
( domain(X0) != antidomain(antidomain(X0))
| antidomain(antidomain(X0)) = domain(X0) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(domain(X0))),bind(Y,$fot(antidomain(antidomain(X0))))]]) ).
cnf(refute_0_26,plain,
antidomain(antidomain(X0)) = domain(X0),
inference(resolve,[$cnf( $equal(domain(X0),antidomain(antidomain(X0))) )],[refute_0_5,refute_0_25]) ).
cnf(refute_0_27,plain,
antidomain(antidomain(zero)) = domain(zero),
inference(subst,[],[refute_0_26:[bind(X0,$fot(zero))]]) ).
cnf(refute_0_28,plain,
( antidomain(antidomain(zero)) != domain(zero)
| c(one) != antidomain(antidomain(zero))
| c(one) = domain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(c(one),antidomain(antidomain(zero))) ),[1],$fot(domain(zero))]]) ).
cnf(refute_0_29,plain,
( c(one) != antidomain(antidomain(zero))
| c(one) = domain(zero) ),
inference(resolve,[$cnf( $equal(antidomain(antidomain(zero)),domain(zero)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
c(one) = domain(zero),
inference(resolve,[$cnf( $equal(c(one),antidomain(antidomain(zero))) )],[refute_0_24,refute_0_29]) ).
cnf(refute_0_31,plain,
multiplication(antidomain(c(one)),c(one)) = zero,
inference(subst,[],[refute_0_9:[bind(X0,$fot(c(one)))]]) ).
cnf(refute_0_32,plain,
c(zero) = antidomain(domain(zero)),
inference(subst,[],[refute_0_3:[bind(X0,$fot(zero))]]) ).
cnf(refute_0_33,plain,
( c(one) != domain(zero)
| domain(zero) = c(one) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(c(one))),bind(Y,$fot(domain(zero)))]]) ).
cnf(refute_0_34,plain,
domain(zero) = c(one),
inference(resolve,[$cnf( $equal(c(one),domain(zero)) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( c(zero) != antidomain(domain(zero))
| domain(zero) != c(one)
| c(zero) = antidomain(c(one)) ),
introduced(tautology,[equality,[$cnf( $equal(c(zero),antidomain(domain(zero))) ),[1,0],$fot(c(one))]]) ).
cnf(refute_0_36,plain,
( c(zero) != antidomain(domain(zero))
| c(zero) = antidomain(c(one)) ),
inference(resolve,[$cnf( $equal(domain(zero),c(one)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
c(zero) = antidomain(c(one)),
inference(resolve,[$cnf( $equal(c(zero),antidomain(domain(zero))) )],[refute_0_32,refute_0_36]) ).
cnf(refute_0_38,plain,
( c(zero) != antidomain(c(one))
| antidomain(c(one)) = c(zero) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(c(zero))),bind(Y,$fot(antidomain(c(one))))]]) ).
cnf(refute_0_39,plain,
antidomain(c(one)) = c(zero),
inference(resolve,[$cnf( $equal(c(zero),antidomain(c(one))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( antidomain(c(one)) != c(zero)
| multiplication(antidomain(c(one)),c(one)) != zero
| multiplication(c(zero),c(one)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(antidomain(c(one)),c(one)),zero) ),[0,0],$fot(c(zero))]]) ).
cnf(refute_0_41,plain,
( multiplication(antidomain(c(one)),c(one)) != zero
| multiplication(c(zero),c(one)) = zero ),
inference(resolve,[$cnf( $equal(antidomain(c(one)),c(zero)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
multiplication(c(zero),c(one)) = zero,
inference(resolve,[$cnf( $equal(multiplication(antidomain(c(one)),c(one)),zero) )],[refute_0_31,refute_0_41]) ).
cnf(refute_0_43,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_44,plain,
multiplication(one,c(one)) = c(one),
inference(subst,[],[refute_0_43:[bind(A,$fot(c(one)))]]) ).
cnf(refute_0_45,plain,
forward_diamond(X_34,one) = domain(multiplication(X_34,domain(one))),
inference(subst,[],[refute_0_1:[bind(X0,$fot(X_34)),bind(X1,$fot(one))]]) ).
cnf(refute_0_46,plain,
( domain(one) != antidomain(zero)
| forward_diamond(X_34,one) != domain(multiplication(X_34,domain(one)))
| forward_diamond(X_34,one) = domain(multiplication(X_34,antidomain(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(forward_diamond(X_34,one),domain(multiplication(X_34,domain(one)))) ),[1,0,1],$fot(antidomain(zero))]]) ).
cnf(refute_0_47,plain,
( forward_diamond(X_34,one) != domain(multiplication(X_34,domain(one)))
| forward_diamond(X_34,one) = domain(multiplication(X_34,antidomain(zero))) ),
inference(resolve,[$cnf( $equal(domain(one),antidomain(zero)) )],[refute_0_21,refute_0_46]) ).
cnf(refute_0_48,plain,
forward_diamond(X_34,one) = domain(multiplication(X_34,antidomain(zero))),
inference(resolve,[$cnf( $equal(forward_diamond(X_34,one),domain(multiplication(X_34,domain(one)))) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
forward_diamond(antidomain(zero),one) = domain(multiplication(antidomain(zero),antidomain(zero))),
inference(subst,[],[refute_0_48:[bind(X_34,$fot(antidomain(zero)))]]) ).
cnf(refute_0_50,plain,
domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_51,plain,
domain_difference(one,X_25) = multiplication(domain(one),antidomain(X_25)),
inference(subst,[],[refute_0_50:[bind(X0,$fot(one)),bind(X1,$fot(X_25))]]) ).
cnf(refute_0_52,plain,
( domain(one) != antidomain(zero)
| domain_difference(one,X_25) != multiplication(domain(one),antidomain(X_25))
| domain_difference(one,X_25) = multiplication(antidomain(zero),antidomain(X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(domain_difference(one,X_25),multiplication(domain(one),antidomain(X_25))) ),[1,0],$fot(antidomain(zero))]]) ).
cnf(refute_0_53,plain,
( domain_difference(one,X_25) != multiplication(domain(one),antidomain(X_25))
| domain_difference(one,X_25) = multiplication(antidomain(zero),antidomain(X_25)) ),
inference(resolve,[$cnf( $equal(domain(one),antidomain(zero)) )],[refute_0_21,refute_0_52]) ).
cnf(refute_0_54,plain,
domain_difference(one,X_25) = multiplication(antidomain(zero),antidomain(X_25)),
inference(resolve,[$cnf( $equal(domain_difference(one,X_25),multiplication(domain(one),antidomain(X_25))) )],[refute_0_51,refute_0_53]) ).
cnf(refute_0_55,plain,
domain_difference(one,zero) = multiplication(antidomain(zero),antidomain(zero)),
inference(subst,[],[refute_0_54:[bind(X_25,$fot(zero))]]) ).
cnf(refute_0_56,plain,
( domain_difference(one,zero) != multiplication(antidomain(zero),antidomain(zero))
| multiplication(antidomain(zero),antidomain(zero)) = domain_difference(one,zero) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(domain_difference(one,zero))),bind(Y,$fot(multiplication(antidomain(zero),antidomain(zero))))]]) ).
cnf(refute_0_57,plain,
multiplication(antidomain(zero),antidomain(zero)) = domain_difference(one,zero),
inference(resolve,[$cnf( $equal(domain_difference(one,zero),multiplication(antidomain(zero),antidomain(zero))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( forward_diamond(antidomain(zero),one) != domain(multiplication(antidomain(zero),antidomain(zero)))
| multiplication(antidomain(zero),antidomain(zero)) != domain_difference(one,zero)
| forward_diamond(antidomain(zero),one) = domain(domain_difference(one,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(forward_diamond(antidomain(zero),one),domain(multiplication(antidomain(zero),antidomain(zero)))) ),[1,0],$fot(domain_difference(one,zero))]]) ).
cnf(refute_0_59,plain,
( forward_diamond(antidomain(zero),one) != domain(multiplication(antidomain(zero),antidomain(zero)))
| forward_diamond(antidomain(zero),one) = domain(domain_difference(one,zero)) ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(zero),antidomain(zero)),domain_difference(one,zero)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
forward_diamond(antidomain(zero),one) = domain(domain_difference(one,zero)),
inference(resolve,[$cnf( $equal(forward_diamond(antidomain(zero),one),domain(multiplication(antidomain(zero),antidomain(zero)))) )],[refute_0_49,refute_0_59]) ).
cnf(refute_0_61,plain,
domain(antidomain(X_4)) = antidomain(antidomain(antidomain(X_4))),
inference(subst,[],[refute_0_5:[bind(X0,$fot(antidomain(X_4)))]]) ).
cnf(refute_0_62,plain,
domain(X_4) = antidomain(antidomain(X_4)),
inference(subst,[],[refute_0_5:[bind(X0,$fot(X_4))]]) ).
cnf(refute_0_63,plain,
( domain(X_4) != antidomain(antidomain(X_4))
| antidomain(antidomain(X_4)) = domain(X_4) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(domain(X_4))),bind(Y,$fot(antidomain(antidomain(X_4))))]]) ).
cnf(refute_0_64,plain,
antidomain(antidomain(X_4)) = domain(X_4),
inference(resolve,[$cnf( $equal(domain(X_4),antidomain(antidomain(X_4))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( antidomain(antidomain(X_4)) != domain(X_4)
| domain(antidomain(X_4)) != antidomain(antidomain(antidomain(X_4)))
| domain(antidomain(X_4)) = antidomain(domain(X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(antidomain(X_4)),antidomain(antidomain(antidomain(X_4)))) ),[1,0],$fot(domain(X_4))]]) ).
cnf(refute_0_66,plain,
( domain(antidomain(X_4)) != antidomain(antidomain(antidomain(X_4)))
| domain(antidomain(X_4)) = antidomain(domain(X_4)) ),
inference(resolve,[$cnf( $equal(antidomain(antidomain(X_4)),domain(X_4)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
domain(antidomain(X_4)) = antidomain(domain(X_4)),
inference(resolve,[$cnf( $equal(domain(antidomain(X_4)),antidomain(antidomain(antidomain(X_4)))) )],[refute_0_61,refute_0_66]) ).
cnf(refute_0_68,plain,
( c(X0) != antidomain(domain(X0))
| antidomain(domain(X0)) = c(X0) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(c(X0))),bind(Y,$fot(antidomain(domain(X0))))]]) ).
cnf(refute_0_69,plain,
antidomain(domain(X0)) = c(X0),
inference(resolve,[$cnf( $equal(c(X0),antidomain(domain(X0))) )],[refute_0_3,refute_0_68]) ).
cnf(refute_0_70,plain,
antidomain(domain(X_4)) = c(X_4),
inference(subst,[],[refute_0_69:[bind(X0,$fot(X_4))]]) ).
cnf(refute_0_71,plain,
( antidomain(domain(X_4)) != c(X_4)
| domain(antidomain(X_4)) != antidomain(domain(X_4))
| domain(antidomain(X_4)) = c(X_4) ),
introduced(tautology,[equality,[$cnf( $equal(domain(antidomain(X_4)),antidomain(domain(X_4))) ),[1],$fot(c(X_4))]]) ).
cnf(refute_0_72,plain,
( domain(antidomain(X_4)) != antidomain(domain(X_4))
| domain(antidomain(X_4)) = c(X_4) ),
inference(resolve,[$cnf( $equal(antidomain(domain(X_4)),c(X_4)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
domain(antidomain(X_4)) = c(X_4),
inference(resolve,[$cnf( $equal(domain(antidomain(X_4)),antidomain(domain(X_4))) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
domain(antidomain(zero)) = c(zero),
inference(subst,[],[refute_0_73:[bind(X_4,$fot(zero))]]) ).
cnf(refute_0_75,plain,
multiplication(X_34,one) = X_34,
inference(subst,[],[refute_0_7:[bind(A,$fot(X_34))]]) ).
cnf(refute_0_76,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_77,plain,
addition(zero,antidomain(zero)) = addition(antidomain(zero),zero),
inference(subst,[],[refute_0_76:[bind(A,$fot(zero)),bind(B,$fot(antidomain(zero)))]]) ).
cnf(refute_0_78,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_79,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_80,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(subst,[],[refute_0_80:[bind(A,$fot(antidomain(X0))),bind(B,$fot(antidomain(antidomain(X0))))]]) ).
cnf(refute_0_82,plain,
( addition(antidomain(antidomain(X0)),antidomain(X0)) != addition(antidomain(X0),antidomain(antidomain(X0)))
| addition(antidomain(antidomain(X0)),antidomain(X0)) != one
| addition(antidomain(X0),antidomain(antidomain(X0))) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),one) ),[0],$fot(addition(antidomain(X0),antidomain(antidomain(X0))))]]) ).
cnf(refute_0_83,plain,
( addition(antidomain(antidomain(X0)),antidomain(X0)) != one
| addition(antidomain(X0),antidomain(antidomain(X0))) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),addition(antidomain(X0),antidomain(antidomain(X0)))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),one) )],[refute_0_78,refute_0_83]) ).
cnf(refute_0_85,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),antidomain(antidomain(X0))),
introduced(tautology,[refl,[$fot(addition(antidomain(X0),antidomain(antidomain(X0))))]]) ).
cnf(refute_0_86,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != addition(antidomain(X0),antidomain(antidomain(X0)))
| antidomain(antidomain(X0)) != domain(X0)
| addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),antidomain(antidomain(X0)))) ),[1,1],$fot(domain(X0))]]) ).
cnf(refute_0_87,plain,
( antidomain(antidomain(X0)) != domain(X0)
| addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),antidomain(antidomain(X0)))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)),
inference(resolve,[$cnf( $equal(antidomain(antidomain(X0)),domain(X0)) )],[refute_0_26,refute_0_87]) ).
cnf(refute_0_89,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != addition(antidomain(X0),domain(X0))
| addition(antidomain(X0),antidomain(antidomain(X0))) != one
| addition(antidomain(X0),domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),one) ),[0],$fot(addition(antidomain(X0),domain(X0)))]]) ).
cnf(refute_0_90,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != one
| addition(antidomain(X0),domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),domain(X0))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
addition(antidomain(X0),domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),one) )],[refute_0_84,refute_0_90]) ).
cnf(refute_0_92,plain,
addition(antidomain(one),domain(one)) = one,
inference(subst,[],[refute_0_91:[bind(X0,$fot(one))]]) ).
cnf(refute_0_93,plain,
( addition(antidomain(one),domain(one)) != one
| domain(one) != antidomain(zero)
| addition(antidomain(one),antidomain(zero)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(one),domain(one)),one) ),[0,1],$fot(antidomain(zero))]]) ).
cnf(refute_0_94,plain,
( addition(antidomain(one),domain(one)) != one
| addition(antidomain(one),antidomain(zero)) = one ),
inference(resolve,[$cnf( $equal(domain(one),antidomain(zero)) )],[refute_0_21,refute_0_93]) ).
cnf(refute_0_95,plain,
addition(antidomain(one),antidomain(zero)) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(one),domain(one)),one) )],[refute_0_92,refute_0_94]) ).
cnf(refute_0_96,plain,
addition(antidomain(one),antidomain(zero)) = addition(antidomain(one),antidomain(zero)),
introduced(tautology,[refl,[$fot(addition(antidomain(one),antidomain(zero)))]]) ).
cnf(refute_0_97,plain,
( addition(antidomain(one),antidomain(zero)) != addition(antidomain(one),antidomain(zero))
| antidomain(one) != zero
| addition(antidomain(one),antidomain(zero)) = addition(zero,antidomain(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(one),antidomain(zero)),addition(antidomain(one),antidomain(zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_98,plain,
( antidomain(one) != zero
| addition(antidomain(one),antidomain(zero)) = addition(zero,antidomain(zero)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(one),antidomain(zero)),addition(antidomain(one),antidomain(zero))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
addition(antidomain(one),antidomain(zero)) = addition(zero,antidomain(zero)),
inference(resolve,[$cnf( $equal(antidomain(one),zero) )],[refute_0_18,refute_0_98]) ).
cnf(refute_0_100,plain,
( addition(antidomain(one),antidomain(zero)) != addition(zero,antidomain(zero))
| addition(antidomain(one),antidomain(zero)) != one
| addition(zero,antidomain(zero)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(one),antidomain(zero)),one) ),[0],$fot(addition(zero,antidomain(zero)))]]) ).
cnf(refute_0_101,plain,
( addition(antidomain(one),antidomain(zero)) != one
| addition(zero,antidomain(zero)) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(one),antidomain(zero)),addition(zero,antidomain(zero))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
addition(zero,antidomain(zero)) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(one),antidomain(zero)),one) )],[refute_0_95,refute_0_101]) ).
cnf(refute_0_103,plain,
( addition(zero,antidomain(zero)) != addition(antidomain(zero),zero)
| addition(zero,antidomain(zero)) != one
| one = addition(antidomain(zero),zero) ),
introduced(tautology,[equality,[$cnf( $equal(addition(zero,antidomain(zero)),addition(antidomain(zero),zero)) ),[0],$fot(one)]]) ).
cnf(refute_0_104,plain,
( addition(zero,antidomain(zero)) != addition(antidomain(zero),zero)
| one = addition(antidomain(zero),zero) ),
inference(resolve,[$cnf( $equal(addition(zero,antidomain(zero)),one) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
one = addition(antidomain(zero),zero),
inference(resolve,[$cnf( $equal(addition(zero,antidomain(zero)),addition(antidomain(zero),zero)) )],[refute_0_77,refute_0_104]) ).
cnf(refute_0_106,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_107,plain,
addition(antidomain(zero),zero) = antidomain(zero),
inference(subst,[],[refute_0_106:[bind(A,$fot(antidomain(zero)))]]) ).
cnf(refute_0_108,plain,
( addition(antidomain(zero),zero) != antidomain(zero)
| one != addition(antidomain(zero),zero)
| one = antidomain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(one,addition(antidomain(zero),zero)) ),[1],$fot(antidomain(zero))]]) ).
cnf(refute_0_109,plain,
( one != addition(antidomain(zero),zero)
| one = antidomain(zero) ),
inference(resolve,[$cnf( $equal(addition(antidomain(zero),zero),antidomain(zero)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
one = antidomain(zero),
inference(resolve,[$cnf( $equal(one,addition(antidomain(zero),zero)) )],[refute_0_105,refute_0_109]) ).
cnf(refute_0_111,plain,
( one != antidomain(zero)
| antidomain(zero) = one ),
inference(subst,[],[refute_0_16:[bind(X,$fot(one)),bind(Y,$fot(antidomain(zero)))]]) ).
cnf(refute_0_112,plain,
antidomain(zero) = one,
inference(resolve,[$cnf( $equal(one,antidomain(zero)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
multiplication(X_34,antidomain(zero)) = multiplication(X_34,antidomain(zero)),
introduced(tautology,[refl,[$fot(multiplication(X_34,antidomain(zero)))]]) ).
cnf(refute_0_114,plain,
( antidomain(zero) != one
| multiplication(X_34,antidomain(zero)) != multiplication(X_34,antidomain(zero))
| multiplication(X_34,antidomain(zero)) = multiplication(X_34,one) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_34,antidomain(zero)),multiplication(X_34,antidomain(zero))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_115,plain,
( antidomain(zero) != one
| multiplication(X_34,antidomain(zero)) = multiplication(X_34,one) ),
inference(resolve,[$cnf( $equal(multiplication(X_34,antidomain(zero)),multiplication(X_34,antidomain(zero))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
multiplication(X_34,antidomain(zero)) = multiplication(X_34,one),
inference(resolve,[$cnf( $equal(antidomain(zero),one) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_118,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_16,refute_0_117]) ).
cnf(refute_0_119,plain,
( multiplication(X_34,antidomain(zero)) != multiplication(X_34,one)
| multiplication(X_34,one) != X_34
| multiplication(X_34,antidomain(zero)) = X_34 ),
inference(subst,[],[refute_0_118:[bind(X,$fot(multiplication(X_34,antidomain(zero)))),bind(Y,$fot(multiplication(X_34,one))),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_120,plain,
( multiplication(X_34,one) != X_34
| multiplication(X_34,antidomain(zero)) = X_34 ),
inference(resolve,[$cnf( $equal(multiplication(X_34,antidomain(zero)),multiplication(X_34,one)) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
multiplication(X_34,antidomain(zero)) = X_34,
inference(resolve,[$cnf( $equal(multiplication(X_34,one),X_34) )],[refute_0_75,refute_0_120]) ).
cnf(refute_0_122,plain,
domain(multiplication(X_34,antidomain(zero))) = domain(multiplication(X_34,antidomain(zero))),
introduced(tautology,[refl,[$fot(domain(multiplication(X_34,antidomain(zero))))]]) ).
cnf(refute_0_123,plain,
( domain(multiplication(X_34,antidomain(zero))) != domain(multiplication(X_34,antidomain(zero)))
| multiplication(X_34,antidomain(zero)) != X_34
| domain(multiplication(X_34,antidomain(zero))) = domain(X_34) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(X_34,antidomain(zero))),domain(multiplication(X_34,antidomain(zero)))) ),[1,0],$fot(X_34)]]) ).
cnf(refute_0_124,plain,
( multiplication(X_34,antidomain(zero)) != X_34
| domain(multiplication(X_34,antidomain(zero))) = domain(X_34) ),
inference(resolve,[$cnf( $equal(domain(multiplication(X_34,antidomain(zero))),domain(multiplication(X_34,antidomain(zero)))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
domain(multiplication(X_34,antidomain(zero))) = domain(X_34),
inference(resolve,[$cnf( $equal(multiplication(X_34,antidomain(zero)),X_34) )],[refute_0_121,refute_0_124]) ).
cnf(refute_0_126,plain,
( domain(multiplication(X_34,antidomain(zero))) != domain(X_34)
| forward_diamond(X_34,one) != domain(multiplication(X_34,antidomain(zero)))
| forward_diamond(X_34,one) = domain(X_34) ),
introduced(tautology,[equality,[$cnf( $equal(forward_diamond(X_34,one),domain(multiplication(X_34,antidomain(zero)))) ),[1],$fot(domain(X_34))]]) ).
cnf(refute_0_127,plain,
( forward_diamond(X_34,one) != domain(multiplication(X_34,antidomain(zero)))
| forward_diamond(X_34,one) = domain(X_34) ),
inference(resolve,[$cnf( $equal(domain(multiplication(X_34,antidomain(zero))),domain(X_34)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
forward_diamond(X_34,one) = domain(X_34),
inference(resolve,[$cnf( $equal(forward_diamond(X_34,one),domain(multiplication(X_34,antidomain(zero)))) )],[refute_0_48,refute_0_127]) ).
cnf(refute_0_129,plain,
forward_diamond(antidomain(zero),one) = domain(antidomain(zero)),
inference(subst,[],[refute_0_128:[bind(X_34,$fot(antidomain(zero)))]]) ).
cnf(refute_0_130,plain,
( domain(antidomain(zero)) != c(zero)
| forward_diamond(antidomain(zero),one) != domain(antidomain(zero))
| forward_diamond(antidomain(zero),one) = c(zero) ),
inference(subst,[],[refute_0_118:[bind(X,$fot(forward_diamond(antidomain(zero),one))),bind(Y,$fot(domain(antidomain(zero)))),bind(Z,$fot(c(zero)))]]) ).
cnf(refute_0_131,plain,
( domain(antidomain(zero)) != c(zero)
| forward_diamond(antidomain(zero),one) = c(zero) ),
inference(resolve,[$cnf( $equal(forward_diamond(antidomain(zero),one),domain(antidomain(zero))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
forward_diamond(antidomain(zero),one) = c(zero),
inference(resolve,[$cnf( $equal(domain(antidomain(zero)),c(zero)) )],[refute_0_74,refute_0_131]) ).
cnf(refute_0_133,plain,
( forward_diamond(antidomain(zero),one) != c(zero)
| forward_diamond(antidomain(zero),one) != domain(domain_difference(one,zero))
| c(zero) = domain(domain_difference(one,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(forward_diamond(antidomain(zero),one),domain(domain_difference(one,zero))) ),[0],$fot(c(zero))]]) ).
cnf(refute_0_134,plain,
( forward_diamond(antidomain(zero),one) != domain(domain_difference(one,zero))
| c(zero) = domain(domain_difference(one,zero)) ),
inference(resolve,[$cnf( $equal(forward_diamond(antidomain(zero),one),c(zero)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
( antidomain(zero) != one
| domain(one) != antidomain(zero)
| domain(one) = one ),
introduced(tautology,[equality,[$cnf( $equal(domain(one),antidomain(zero)) ),[1],$fot(one)]]) ).
cnf(refute_0_136,plain,
( domain(one) != antidomain(zero)
| domain(one) = one ),
inference(resolve,[$cnf( $equal(antidomain(zero),one) )],[refute_0_112,refute_0_135]) ).
cnf(refute_0_137,plain,
domain(one) = one,
inference(resolve,[$cnf( $equal(domain(one),antidomain(zero)) )],[refute_0_21,refute_0_136]) ).
cnf(refute_0_138,plain,
multiplication(one,antidomain(X_25)) = antidomain(X_25),
inference(subst,[],[refute_0_43:[bind(A,$fot(antidomain(X_25)))]]) ).
cnf(refute_0_139,plain,
multiplication(antidomain(zero),antidomain(X_25)) = multiplication(antidomain(zero),antidomain(X_25)),
introduced(tautology,[refl,[$fot(multiplication(antidomain(zero),antidomain(X_25)))]]) ).
cnf(refute_0_140,plain,
( antidomain(zero) != one
| multiplication(antidomain(zero),antidomain(X_25)) != multiplication(antidomain(zero),antidomain(X_25))
| multiplication(antidomain(zero),antidomain(X_25)) = multiplication(one,antidomain(X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(antidomain(zero),antidomain(X_25)),multiplication(antidomain(zero),antidomain(X_25))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_141,plain,
( antidomain(zero) != one
| multiplication(antidomain(zero),antidomain(X_25)) = multiplication(one,antidomain(X_25)) ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(zero),antidomain(X_25)),multiplication(antidomain(zero),antidomain(X_25))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
multiplication(antidomain(zero),antidomain(X_25)) = multiplication(one,antidomain(X_25)),
inference(resolve,[$cnf( $equal(antidomain(zero),one) )],[refute_0_112,refute_0_141]) ).
cnf(refute_0_143,plain,
( multiplication(antidomain(zero),antidomain(X_25)) != multiplication(one,antidomain(X_25))
| multiplication(one,antidomain(X_25)) != antidomain(X_25)
| multiplication(antidomain(zero),antidomain(X_25)) = antidomain(X_25) ),
inference(subst,[],[refute_0_118:[bind(X,$fot(multiplication(antidomain(zero),antidomain(X_25)))),bind(Y,$fot(multiplication(one,antidomain(X_25)))),bind(Z,$fot(antidomain(X_25)))]]) ).
cnf(refute_0_144,plain,
( multiplication(one,antidomain(X_25)) != antidomain(X_25)
| multiplication(antidomain(zero),antidomain(X_25)) = antidomain(X_25) ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(zero),antidomain(X_25)),multiplication(one,antidomain(X_25))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
multiplication(antidomain(zero),antidomain(X_25)) = antidomain(X_25),
inference(resolve,[$cnf( $equal(multiplication(one,antidomain(X_25)),antidomain(X_25)) )],[refute_0_138,refute_0_144]) ).
cnf(refute_0_146,plain,
( domain_difference(one,X_25) != multiplication(antidomain(zero),antidomain(X_25))
| multiplication(antidomain(zero),antidomain(X_25)) != antidomain(X_25)
| domain_difference(one,X_25) = antidomain(X_25) ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain_difference(one,X_25),antidomain(X_25)) ),[0],$fot(multiplication(antidomain(zero),antidomain(X_25)))]]) ).
cnf(refute_0_147,plain,
( domain_difference(one,X_25) != multiplication(antidomain(zero),antidomain(X_25))
| domain_difference(one,X_25) = antidomain(X_25) ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(zero),antidomain(X_25)),antidomain(X_25)) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
domain_difference(one,X_25) = antidomain(X_25),
inference(resolve,[$cnf( $equal(domain_difference(one,X_25),multiplication(antidomain(zero),antidomain(X_25))) )],[refute_0_54,refute_0_147]) ).
cnf(refute_0_149,plain,
domain_difference(one,zero) = antidomain(zero),
inference(subst,[],[refute_0_148:[bind(X_25,$fot(zero))]]) ).
cnf(refute_0_150,plain,
( antidomain(zero) != one
| domain_difference(one,zero) != antidomain(zero)
| domain_difference(one,zero) = one ),
inference(subst,[],[refute_0_118:[bind(X,$fot(domain_difference(one,zero))),bind(Y,$fot(antidomain(zero))),bind(Z,$fot(one))]]) ).
cnf(refute_0_151,plain,
( antidomain(zero) != one
| domain_difference(one,zero) = one ),
inference(resolve,[$cnf( $equal(domain_difference(one,zero),antidomain(zero)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
domain_difference(one,zero) = one,
inference(resolve,[$cnf( $equal(antidomain(zero),one) )],[refute_0_112,refute_0_151]) ).
cnf(refute_0_153,plain,
domain(domain_difference(one,zero)) = domain(domain_difference(one,zero)),
introduced(tautology,[refl,[$fot(domain(domain_difference(one,zero)))]]) ).
cnf(refute_0_154,plain,
( domain(domain_difference(one,zero)) != domain(domain_difference(one,zero))
| domain_difference(one,zero) != one
| domain(domain_difference(one,zero)) = domain(one) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain_difference(one,zero)),domain(domain_difference(one,zero))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_155,plain,
( domain_difference(one,zero) != one
| domain(domain_difference(one,zero)) = domain(one) ),
inference(resolve,[$cnf( $equal(domain(domain_difference(one,zero)),domain(domain_difference(one,zero))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
domain(domain_difference(one,zero)) = domain(one),
inference(resolve,[$cnf( $equal(domain_difference(one,zero),one) )],[refute_0_152,refute_0_155]) ).
cnf(refute_0_157,plain,
( domain(domain_difference(one,zero)) != domain(one)
| domain(one) != one
| domain(domain_difference(one,zero)) = one ),
inference(subst,[],[refute_0_118:[bind(X,$fot(domain(domain_difference(one,zero)))),bind(Y,$fot(domain(one))),bind(Z,$fot(one))]]) ).
cnf(refute_0_158,plain,
( domain(one) != one
| domain(domain_difference(one,zero)) = one ),
inference(resolve,[$cnf( $equal(domain(domain_difference(one,zero)),domain(one)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
domain(domain_difference(one,zero)) = one,
inference(resolve,[$cnf( $equal(domain(one),one) )],[refute_0_137,refute_0_158]) ).
cnf(refute_0_160,plain,
( c(zero) != domain(domain_difference(one,zero))
| domain(domain_difference(one,zero)) != one
| c(zero) = one ),
introduced(tautology,[equality,[$cnf( ~ $equal(c(zero),one) ),[0],$fot(domain(domain_difference(one,zero)))]]) ).
cnf(refute_0_161,plain,
( c(zero) != domain(domain_difference(one,zero))
| c(zero) = one ),
inference(resolve,[$cnf( $equal(domain(domain_difference(one,zero)),one) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( forward_diamond(antidomain(zero),one) != domain(domain_difference(one,zero))
| c(zero) = one ),
inference(resolve,[$cnf( $equal(c(zero),domain(domain_difference(one,zero))) )],[refute_0_134,refute_0_161]) ).
cnf(refute_0_163,plain,
c(zero) = one,
inference(resolve,[$cnf( $equal(forward_diamond(antidomain(zero),one),domain(domain_difference(one,zero))) )],[refute_0_60,refute_0_162]) ).
cnf(refute_0_164,plain,
multiplication(c(zero),c(one)) = multiplication(c(zero),c(one)),
introduced(tautology,[refl,[$fot(multiplication(c(zero),c(one)))]]) ).
cnf(refute_0_165,plain,
( c(zero) != one
| multiplication(c(zero),c(one)) != multiplication(c(zero),c(one))
| multiplication(c(zero),c(one)) = multiplication(one,c(one)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(zero),c(one)),multiplication(c(zero),c(one))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_166,plain,
( c(zero) != one
| multiplication(c(zero),c(one)) = multiplication(one,c(one)) ),
inference(resolve,[$cnf( $equal(multiplication(c(zero),c(one)),multiplication(c(zero),c(one))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
multiplication(c(zero),c(one)) = multiplication(one,c(one)),
inference(resolve,[$cnf( $equal(c(zero),one) )],[refute_0_163,refute_0_166]) ).
cnf(refute_0_168,plain,
( multiplication(c(zero),c(one)) != multiplication(one,c(one))
| multiplication(one,c(one)) != c(one)
| multiplication(c(zero),c(one)) = c(one) ),
inference(subst,[],[refute_0_118:[bind(X,$fot(multiplication(c(zero),c(one)))),bind(Y,$fot(multiplication(one,c(one)))),bind(Z,$fot(c(one)))]]) ).
cnf(refute_0_169,plain,
( multiplication(one,c(one)) != c(one)
| multiplication(c(zero),c(one)) = c(one) ),
inference(resolve,[$cnf( $equal(multiplication(c(zero),c(one)),multiplication(one,c(one))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
multiplication(c(zero),c(one)) = c(one),
inference(resolve,[$cnf( $equal(multiplication(one,c(one)),c(one)) )],[refute_0_44,refute_0_169]) ).
cnf(refute_0_171,plain,
( multiplication(c(zero),c(one)) != c(one)
| multiplication(c(zero),c(one)) != zero
| c(one) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(zero),c(one)),zero) ),[0],$fot(c(one))]]) ).
cnf(refute_0_172,plain,
( multiplication(c(zero),c(one)) != zero
| c(one) = zero ),
inference(resolve,[$cnf( $equal(multiplication(c(zero),c(one)),c(one)) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
c(one) = zero,
inference(resolve,[$cnf( $equal(multiplication(c(zero),c(one)),zero) )],[refute_0_42,refute_0_172]) ).
cnf(refute_0_174,plain,
( c(one) != domain(zero)
| c(one) != zero
| zero = domain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(c(one),domain(zero)) ),[0],$fot(zero)]]) ).
cnf(refute_0_175,plain,
( c(one) != domain(zero)
| zero = domain(zero) ),
inference(resolve,[$cnf( $equal(c(one),zero) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
zero = domain(zero),
inference(resolve,[$cnf( $equal(c(one),domain(zero)) )],[refute_0_30,refute_0_175]) ).
cnf(refute_0_177,plain,
( zero != domain(zero)
| domain(zero) = zero ),
inference(subst,[],[refute_0_16:[bind(X,$fot(zero)),bind(Y,$fot(domain(zero)))]]) ).
cnf(refute_0_178,plain,
domain(zero) = zero,
inference(resolve,[$cnf( $equal(zero,domain(zero)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( domain(zero) != zero
| forward_diamond(X0,zero) != domain(multiplication(X0,domain(zero)))
| forward_diamond(X0,zero) = domain(multiplication(X0,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(forward_diamond(X0,zero),domain(multiplication(X0,domain(zero)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_180,plain,
( forward_diamond(X0,zero) != domain(multiplication(X0,domain(zero)))
| forward_diamond(X0,zero) = domain(multiplication(X0,zero)) ),
inference(resolve,[$cnf( $equal(domain(zero),zero) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(resolve,[$cnf( $equal(forward_diamond(X0,zero),domain(multiplication(X0,domain(zero)))) )],[refute_0_2,refute_0_180]) ).
cnf(refute_0_182,plain,
multiplication(A,zero) = zero,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_183,plain,
multiplication(X0,zero) = zero,
inference(subst,[],[refute_0_182:[bind(A,$fot(X0))]]) ).
cnf(refute_0_184,plain,
domain(multiplication(X0,zero)) = domain(multiplication(X0,zero)),
introduced(tautology,[refl,[$fot(domain(multiplication(X0,zero)))]]) ).
cnf(refute_0_185,plain,
( domain(multiplication(X0,zero)) != domain(multiplication(X0,zero))
| multiplication(X0,zero) != zero
| domain(multiplication(X0,zero)) = domain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(X0,zero)),domain(multiplication(X0,zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_186,plain,
( multiplication(X0,zero) != zero
| domain(multiplication(X0,zero)) = domain(zero) ),
inference(resolve,[$cnf( $equal(domain(multiplication(X0,zero)),domain(multiplication(X0,zero))) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
domain(multiplication(X0,zero)) = domain(zero),
inference(resolve,[$cnf( $equal(multiplication(X0,zero),zero) )],[refute_0_183,refute_0_186]) ).
cnf(refute_0_188,plain,
( domain(multiplication(X0,zero)) != domain(zero)
| domain(zero) != zero
| domain(multiplication(X0,zero)) = zero ),
inference(subst,[],[refute_0_118:[bind(X,$fot(domain(multiplication(X0,zero)))),bind(Y,$fot(domain(zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_189,plain,
( domain(zero) != zero
| domain(multiplication(X0,zero)) = zero ),
inference(resolve,[$cnf( $equal(domain(multiplication(X0,zero)),domain(zero)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
domain(multiplication(X0,zero)) = zero,
inference(resolve,[$cnf( $equal(domain(zero),zero) )],[refute_0_178,refute_0_189]) ).
cnf(refute_0_191,plain,
( domain(multiplication(X0,zero)) != zero
| forward_diamond(X0,zero) != domain(multiplication(X0,zero))
| forward_diamond(X0,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(forward_diamond(X0,zero),domain(multiplication(X0,zero))) ),[1],$fot(zero)]]) ).
cnf(refute_0_192,plain,
( forward_diamond(X0,zero) != domain(multiplication(X0,zero))
| forward_diamond(X0,zero) = zero ),
inference(resolve,[$cnf( $equal(domain(multiplication(X0,zero)),zero) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
forward_diamond(X0,zero) = zero,
inference(resolve,[$cnf( $equal(forward_diamond(X0,zero),domain(multiplication(X0,zero))) )],[refute_0_181,refute_0_192]) ).
cnf(refute_0_194,plain,
forward_diamond(skolemFOFtoCNF_X0,zero) = zero,
inference(subst,[],[refute_0_193:[bind(X0,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_195,plain,
( forward_diamond(skolemFOFtoCNF_X0,zero) != zero
| zero != zero
| forward_diamond(skolemFOFtoCNF_X0,zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(forward_diamond(skolemFOFtoCNF_X0,zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_196,plain,
( zero != zero
| forward_diamond(skolemFOFtoCNF_X0,zero) = zero ),
inference(resolve,[$cnf( $equal(forward_diamond(skolemFOFtoCNF_X0,zero),zero) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
zero != zero,
inference(resolve,[$cnf( $equal(forward_diamond(skolemFOFtoCNF_X0,zero),zero) )],[refute_0_196,refute_0_0]) ).
cnf(refute_0_198,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_199,plain,
$false,
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_198,refute_0_197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE113+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 11:11:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46
% 0.19/0.46 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.48
%------------------------------------------------------------------------------