TSTP Solution File: KLE089+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE089+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 02:15:10 EDT 2022
% Result : Theorem 0.86s 1.09s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 56
% Syntax : Number of formulae : 254 ( 151 unt; 0 def)
% Number of atoms : 400 ( 399 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 292 ( 146 ~; 141 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 365 ( 13 sgn 60 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = 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(goals,conjecture,
! [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
=> multiplication(domain(X0),X1) = zero ) ).
fof(subgoal_0,plain,
! [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
=> multiplication(domain(X0),X1) = zero ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
=> multiplication(domain(X0),X1) = zero ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[multiplicative_associativity]) ).
fof(normalize_0_1,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_3,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_0_5,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_7,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_9,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_11,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_13,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
? [X0,X1] :
( multiplication(domain(X0),X1) != zero
& addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_15,plain,
( multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != zero
& addition(domain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) = antidomain(skolemFOFtoCNF_X1) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
addition(domain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) = antidomain(skolemFOFtoCNF_X1),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_18,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[domain4]) ).
fof(normalize_0_20,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_22,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_24,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != zero,
inference(conjunct,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
multiplication(antidomain(X_73),multiplication(X_73,X_74)) = multiplication(multiplication(antidomain(X_73),X_73),X_74),
inference(subst,[],[refute_0_0:[bind(A,$fot(antidomain(X_73))),bind(B,$fot(X_73)),bind(C,$fot(X_74))]]) ).
cnf(refute_0_2,plain,
multiplication(antidomain(X0),X0) = zero,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
multiplication(antidomain(X_73),X_73) = zero,
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_73))]]) ).
cnf(refute_0_4,plain,
( multiplication(antidomain(X_73),X_73) != zero
| multiplication(antidomain(X_73),multiplication(X_73,X_74)) != multiplication(multiplication(antidomain(X_73),X_73),X_74)
| multiplication(antidomain(X_73),multiplication(X_73,X_74)) = multiplication(zero,X_74) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(antidomain(X_73),multiplication(X_73,X_74)),multiplication(multiplication(antidomain(X_73),X_73),X_74)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_5,plain,
( multiplication(antidomain(X_73),multiplication(X_73,X_74)) != multiplication(multiplication(antidomain(X_73),X_73),X_74)
| multiplication(antidomain(X_73),multiplication(X_73,X_74)) = multiplication(zero,X_74) ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(X_73),X_73),zero) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
multiplication(antidomain(X_73),multiplication(X_73,X_74)) = multiplication(zero,X_74),
inference(resolve,[$cnf( $equal(multiplication(antidomain(X_73),multiplication(X_73,X_74)),multiplication(multiplication(antidomain(X_73),X_73),X_74)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_8,plain,
multiplication(zero,X_74) = zero,
inference(subst,[],[refute_0_7:[bind(A,$fot(X_74))]]) ).
cnf(refute_0_9,plain,
( multiplication(antidomain(X_73),multiplication(X_73,X_74)) != multiplication(zero,X_74)
| multiplication(zero,X_74) != zero
| multiplication(antidomain(X_73),multiplication(X_73,X_74)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(antidomain(X_73),multiplication(X_73,X_74)),zero) ),[0],$fot(multiplication(zero,X_74))]]) ).
cnf(refute_0_10,plain,
( multiplication(antidomain(X_73),multiplication(X_73,X_74)) != multiplication(zero,X_74)
| multiplication(antidomain(X_73),multiplication(X_73,X_74)) = zero ),
inference(resolve,[$cnf( $equal(multiplication(zero,X_74),zero) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
multiplication(antidomain(X_73),multiplication(X_73,X_74)) = zero,
inference(resolve,[$cnf( $equal(multiplication(antidomain(X_73),multiplication(X_73,X_74)),multiplication(zero,X_74)) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) = zero,
inference(subst,[],[refute_0_11:[bind(X_73,$fot(antidomain(skolemFOFtoCNF_X0))),bind(X_74,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_13,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_14,plain,
multiplication(addition(X_38,antidomain(X_40)),X_40) = addition(multiplication(X_38,X_40),multiplication(antidomain(X_40),X_40)),
inference(subst,[],[refute_0_13:[bind(A,$fot(X_38)),bind(B,$fot(antidomain(X_40))),bind(C,$fot(X_40))]]) ).
cnf(refute_0_15,plain,
multiplication(antidomain(X_40),X_40) = zero,
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_40))]]) ).
cnf(refute_0_16,plain,
( multiplication(addition(X_38,antidomain(X_40)),X_40) != addition(multiplication(X_38,X_40),multiplication(antidomain(X_40),X_40))
| multiplication(antidomain(X_40),X_40) != zero
| multiplication(addition(X_38,antidomain(X_40)),X_40) = addition(multiplication(X_38,X_40),zero) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(X_38,antidomain(X_40)),X_40),addition(multiplication(X_38,X_40),multiplication(antidomain(X_40),X_40))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_17,plain,
( multiplication(addition(X_38,antidomain(X_40)),X_40) != addition(multiplication(X_38,X_40),multiplication(antidomain(X_40),X_40))
| multiplication(addition(X_38,antidomain(X_40)),X_40) = addition(multiplication(X_38,X_40),zero) ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(X_40),X_40),zero) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
multiplication(addition(X_38,antidomain(X_40)),X_40) = addition(multiplication(X_38,X_40),zero),
inference(resolve,[$cnf( $equal(multiplication(addition(X_38,antidomain(X_40)),X_40),addition(multiplication(X_38,X_40),multiplication(antidomain(X_40),X_40))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_20,plain,
addition(multiplication(X_38,X_40),zero) = multiplication(X_38,X_40),
inference(subst,[],[refute_0_19:[bind(A,$fot(multiplication(X_38,X_40)))]]) ).
cnf(refute_0_21,plain,
( addition(multiplication(X_38,X_40),zero) != multiplication(X_38,X_40)
| multiplication(addition(X_38,antidomain(X_40)),X_40) != addition(multiplication(X_38,X_40),zero)
| multiplication(addition(X_38,antidomain(X_40)),X_40) = multiplication(X_38,X_40) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(X_38,antidomain(X_40)),X_40),addition(multiplication(X_38,X_40),zero)) ),[1],$fot(multiplication(X_38,X_40))]]) ).
cnf(refute_0_22,plain,
( multiplication(addition(X_38,antidomain(X_40)),X_40) != addition(multiplication(X_38,X_40),zero)
| multiplication(addition(X_38,antidomain(X_40)),X_40) = multiplication(X_38,X_40) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_38,X_40),zero),multiplication(X_38,X_40)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiplication(addition(X_38,antidomain(X_40)),X_40) = multiplication(X_38,X_40),
inference(resolve,[$cnf( $equal(multiplication(addition(X_38,antidomain(X_40)),X_40),addition(multiplication(X_38,X_40),zero)) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
multiplication(addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X1) = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
inference(subst,[],[refute_0_23:[bind(X_38,$fot(antidomain(skolemFOFtoCNF_X0))),bind(X_40,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_25,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_26,plain,
addition(A,addition(X_21,X_22)) = addition(addition(X_21,X_22),A),
inference(subst,[],[refute_0_25:[bind(B,$fot(addition(X_21,X_22)))]]) ).
cnf(refute_0_27,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_28,plain,
addition(X_21,addition(X_22,A)) = addition(addition(X_21,X_22),A),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_21)),bind(B,$fot(X_22)),bind(C,$fot(A))]]) ).
cnf(refute_0_29,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_30,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_31,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( addition(X_21,addition(X_22,A)) != addition(addition(X_21,X_22),A)
| addition(addition(X_21,X_22),A) = addition(X_21,addition(X_22,A)) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(addition(X_21,addition(X_22,A)))),bind(Y,$fot(addition(addition(X_21,X_22),A)))]]) ).
cnf(refute_0_33,plain,
addition(addition(X_21,X_22),A) = addition(X_21,addition(X_22,A)),
inference(resolve,[$cnf( $equal(addition(X_21,addition(X_22,A)),addition(addition(X_21,X_22),A)) )],[refute_0_28,refute_0_32]) ).
cnf(refute_0_34,plain,
( addition(A,addition(X_21,X_22)) != addition(addition(X_21,X_22),A)
| addition(addition(X_21,X_22),A) != addition(X_21,addition(X_22,A))
| addition(A,addition(X_21,X_22)) = addition(X_21,addition(X_22,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_21,X_22)),addition(X_21,addition(X_22,A))) ),[0],$fot(addition(addition(X_21,X_22),A))]]) ).
cnf(refute_0_35,plain,
( addition(A,addition(X_21,X_22)) != addition(addition(X_21,X_22),A)
| addition(A,addition(X_21,X_22)) = addition(X_21,addition(X_22,A)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_21,X_22),A),addition(X_21,addition(X_22,A))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
addition(A,addition(X_21,X_22)) = addition(X_21,addition(X_22,A)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_21,X_22)),addition(addition(X_21,X_22),A)) )],[refute_0_26,refute_0_35]) ).
cnf(refute_0_37,plain,
addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))) = addition(X_97,addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0))),
inference(subst,[],[refute_0_36:[bind(A,$fot(domain(skolemFOFtoCNF_X0))),bind(X_21,$fot(X_97)),bind(X_22,$fot(antidomain(skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_38,plain,
addition(domain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) = antidomain(skolemFOFtoCNF_X1),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_39,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_40,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_25,refute_0_39]) ).
cnf(refute_0_41,plain,
addition(domain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) = addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_40:[bind(A,$fot(antidomain(skolemFOFtoCNF_X1))),bind(B,$fot(domain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_42,plain,
( addition(domain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) != addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0))
| addition(domain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) != antidomain(skolemFOFtoCNF_X1)
| addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0)) = antidomain(skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),antidomain(skolemFOFtoCNF_X1)) ),[0],$fot(addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_43,plain,
( addition(domain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) != antidomain(skolemFOFtoCNF_X1)
| addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0)) = antidomain(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0)) = antidomain(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),antidomain(skolemFOFtoCNF_X1)) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
( addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0)) != antidomain(skolemFOFtoCNF_X1)
| addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))) != addition(X_97,addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0)))
| addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))) = addition(X_97,antidomain(skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))),addition(X_97,addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0)))) ),[1,1],$fot(antidomain(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_46,plain,
( addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))) != addition(X_97,addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0)))
| addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))) = addition(X_97,antidomain(skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0)),antidomain(skolemFOFtoCNF_X1)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))) = addition(X_97,antidomain(skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))),addition(X_97,addition(antidomain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X0)))) )],[refute_0_37,refute_0_46]) ).
cnf(refute_0_48,plain,
addition(X_96,addition(X_97,X_98)) = addition(X_97,addition(X_98,X_96)),
inference(subst,[],[refute_0_36:[bind(A,$fot(X_96)),bind(X_21,$fot(X_97)),bind(X_22,$fot(X_98))]]) ).
cnf(refute_0_49,plain,
addition(X_98,X_97) = addition(X_97,X_98),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_98)),bind(B,$fot(X_97))]]) ).
cnf(refute_0_50,plain,
( addition(X_98,X_97) != addition(X_97,X_98)
| addition(X_97,X_98) = addition(X_98,X_97) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(addition(X_98,X_97))),bind(Y,$fot(addition(X_97,X_98)))]]) ).
cnf(refute_0_51,plain,
addition(X_97,X_98) = addition(X_98,X_97),
inference(resolve,[$cnf( $equal(addition(X_98,X_97),addition(X_97,X_98)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( addition(X_96,addition(X_97,X_98)) != addition(X_97,addition(X_98,X_96))
| addition(X_97,X_98) != addition(X_98,X_97)
| addition(X_96,addition(X_98,X_97)) = addition(X_97,addition(X_98,X_96)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_96,addition(X_97,X_98)),addition(X_97,addition(X_98,X_96))) ),[0,1],$fot(addition(X_98,X_97))]]) ).
cnf(refute_0_53,plain,
( addition(X_96,addition(X_97,X_98)) != addition(X_97,addition(X_98,X_96))
| addition(X_96,addition(X_98,X_97)) = addition(X_97,addition(X_98,X_96)) ),
inference(resolve,[$cnf( $equal(addition(X_97,X_98),addition(X_98,X_97)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
addition(X_96,addition(X_98,X_97)) = addition(X_97,addition(X_98,X_96)),
inference(resolve,[$cnf( $equal(addition(X_96,addition(X_97,X_98)),addition(X_97,addition(X_98,X_96))) )],[refute_0_48,refute_0_53]) ).
cnf(refute_0_55,plain,
( addition(X_96,addition(X_98,X_97)) != addition(X_97,addition(X_98,X_96))
| addition(X_97,addition(X_98,X_96)) = addition(X_96,addition(X_98,X_97)) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(addition(X_96,addition(X_98,X_97)))),bind(Y,$fot(addition(X_97,addition(X_98,X_96))))]]) ).
cnf(refute_0_56,plain,
addition(X_97,addition(X_98,X_96)) = addition(X_96,addition(X_98,X_97)),
inference(resolve,[$cnf( $equal(addition(X_96,addition(X_98,X_97)),addition(X_97,addition(X_98,X_96))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))) = addition(antidomain(skolemFOFtoCNF_X1),addition(X_97,domain(skolemFOFtoCNF_X0))),
inference(subst,[],[refute_0_56:[bind(X_96,$fot(antidomain(skolemFOFtoCNF_X1))),bind(X_97,$fot(domain(skolemFOFtoCNF_X0))),bind(X_98,$fot(X_97))]]) ).
cnf(refute_0_58,plain,
( addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))) != addition(X_97,antidomain(skolemFOFtoCNF_X1))
| addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))) != addition(antidomain(skolemFOFtoCNF_X1),addition(X_97,domain(skolemFOFtoCNF_X0)))
| addition(antidomain(skolemFOFtoCNF_X1),addition(X_97,domain(skolemFOFtoCNF_X0))) = addition(X_97,antidomain(skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))),addition(X_97,antidomain(skolemFOFtoCNF_X1))) ),[0],$fot(addition(antidomain(skolemFOFtoCNF_X1),addition(X_97,domain(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_59,plain,
( addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))) != addition(X_97,antidomain(skolemFOFtoCNF_X1))
| addition(antidomain(skolemFOFtoCNF_X1),addition(X_97,domain(skolemFOFtoCNF_X0))) = addition(X_97,antidomain(skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))),addition(antidomain(skolemFOFtoCNF_X1),addition(X_97,domain(skolemFOFtoCNF_X0)))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
addition(antidomain(skolemFOFtoCNF_X1),addition(X_97,domain(skolemFOFtoCNF_X0))) = addition(X_97,antidomain(skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),addition(X_97,antidomain(skolemFOFtoCNF_X1))),addition(X_97,antidomain(skolemFOFtoCNF_X1))) )],[refute_0_47,refute_0_59]) ).
cnf(refute_0_61,plain,
addition(antidomain(skolemFOFtoCNF_X1),addition(antidomain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0))) = addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_60:[bind(X_97,$fot(antidomain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_62,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_63,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(subst,[],[refute_0_40:[bind(A,$fot(antidomain(X0))),bind(B,$fot(antidomain(antidomain(X0))))]]) ).
cnf(refute_0_64,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_65,plain,
( addition(antidomain(antidomain(X0)),antidomain(X0)) != one
| addition(antidomain(X0),antidomain(antidomain(X0))) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),addition(antidomain(X0),antidomain(antidomain(X0)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),one) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_68,plain,
( domain(X0) != antidomain(antidomain(X0))
| antidomain(antidomain(X0)) = domain(X0) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(domain(X0))),bind(Y,$fot(antidomain(antidomain(X0))))]]) ).
cnf(refute_0_69,plain,
antidomain(antidomain(X0)) = domain(X0),
inference(resolve,[$cnf( $equal(domain(X0),antidomain(antidomain(X0))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),antidomain(antidomain(X0))),
introduced(tautology,[refl,[$fot(addition(antidomain(X0),antidomain(antidomain(X0))))]]) ).
cnf(refute_0_71,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_72,plain,
( antidomain(antidomain(X0)) != domain(X0)
| addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),antidomain(antidomain(X0)))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)),
inference(resolve,[$cnf( $equal(antidomain(antidomain(X0)),domain(X0)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != addition(antidomain(X0),domain(X0))
| addition(antidomain(X0),antidomain(antidomain(X0))) != one
| addition(antidomain(X0),domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),one) ),[0],$fot(addition(antidomain(X0),domain(X0)))]]) ).
cnf(refute_0_75,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != one
| addition(antidomain(X0),domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),domain(X0))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
addition(antidomain(X0),domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),one) )],[refute_0_66,refute_0_75]) ).
cnf(refute_0_77,plain,
addition(antidomain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) = one,
inference(subst,[],[refute_0_76:[bind(X0,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_78,plain,
( addition(antidomain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) != one
| addition(antidomain(skolemFOFtoCNF_X1),addition(antidomain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0))) != addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1))
| addition(antidomain(skolemFOFtoCNF_X1),one) = addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(skolemFOFtoCNF_X1),addition(antidomain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0))),addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1))) ),[0,1],$fot(one)]]) ).
cnf(refute_0_79,plain,
( addition(antidomain(skolemFOFtoCNF_X1),addition(antidomain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0))) != addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1))
| addition(antidomain(skolemFOFtoCNF_X1),one) = addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)),one) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
addition(antidomain(skolemFOFtoCNF_X1),one) = addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(addition(antidomain(skolemFOFtoCNF_X1),addition(antidomain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0))),addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1))) )],[refute_0_61,refute_0_79]) ).
cnf(refute_0_81,plain,
addition(X_22,addition(X_22,X_23)) = addition(addition(X_22,X_22),X_23),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_22)),bind(B,$fot(X_22)),bind(C,$fot(X_23))]]) ).
cnf(refute_0_82,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_83,plain,
addition(X_22,X_22) = X_22,
inference(subst,[],[refute_0_82:[bind(A,$fot(X_22))]]) ).
cnf(refute_0_84,plain,
( addition(X_22,X_22) != X_22
| addition(X_22,addition(X_22,X_23)) != addition(addition(X_22,X_22),X_23)
| addition(X_22,addition(X_22,X_23)) = addition(X_22,X_23) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_22,addition(X_22,X_23)),addition(addition(X_22,X_22),X_23)) ),[1,0],$fot(X_22)]]) ).
cnf(refute_0_85,plain,
( addition(X_22,addition(X_22,X_23)) != addition(addition(X_22,X_22),X_23)
| addition(X_22,addition(X_22,X_23)) = addition(X_22,X_23) ),
inference(resolve,[$cnf( $equal(addition(X_22,X_22),X_22) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
addition(X_22,addition(X_22,X_23)) = addition(X_22,X_23),
inference(resolve,[$cnf( $equal(addition(X_22,addition(X_22,X_23)),addition(addition(X_22,X_22),X_23)) )],[refute_0_81,refute_0_85]) ).
cnf(refute_0_87,plain,
addition(antidomain(X0),addition(antidomain(X0),domain(X0))) = addition(antidomain(X0),domain(X0)),
inference(subst,[],[refute_0_86:[bind(X_22,$fot(antidomain(X0))),bind(X_23,$fot(domain(X0)))]]) ).
cnf(refute_0_88,plain,
( addition(antidomain(X0),addition(antidomain(X0),domain(X0))) != addition(antidomain(X0),domain(X0))
| addition(antidomain(X0),domain(X0)) != one
| addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),addition(antidomain(X0),domain(X0))),addition(antidomain(X0),domain(X0))) ),[0,1],$fot(one)]]) ).
cnf(refute_0_89,plain,
( addition(antidomain(X0),addition(antidomain(X0),domain(X0))) != addition(antidomain(X0),domain(X0))
| addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),domain(X0)),one) )],[refute_0_76,refute_0_88]) ).
cnf(refute_0_90,plain,
addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),addition(antidomain(X0),domain(X0))),addition(antidomain(X0),domain(X0))) )],[refute_0_87,refute_0_89]) ).
cnf(refute_0_91,plain,
addition(antidomain(X0),one) = addition(one,antidomain(X0)),
inference(subst,[],[refute_0_40:[bind(A,$fot(one)),bind(B,$fot(antidomain(X0)))]]) ).
cnf(refute_0_92,plain,
( addition(antidomain(X0),one) != addition(antidomain(X0),domain(X0))
| addition(antidomain(X0),one) != addition(one,antidomain(X0))
| addition(one,antidomain(X0)) = addition(antidomain(X0),domain(X0)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),one),addition(antidomain(X0),domain(X0))) ),[0],$fot(addition(one,antidomain(X0)))]]) ).
cnf(refute_0_93,plain,
( addition(antidomain(X0),one) != addition(antidomain(X0),domain(X0))
| addition(one,antidomain(X0)) = addition(antidomain(X0),domain(X0)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),one),addition(one,antidomain(X0))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( addition(antidomain(X0),domain(X0)) != one
| addition(one,antidomain(X0)) != addition(antidomain(X0),domain(X0))
| addition(one,antidomain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,antidomain(X0)),addition(antidomain(X0),domain(X0))) ),[1],$fot(one)]]) ).
cnf(refute_0_95,plain,
( addition(one,antidomain(X0)) != addition(antidomain(X0),domain(X0))
| addition(one,antidomain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),domain(X0)),one) )],[refute_0_76,refute_0_94]) ).
cnf(refute_0_96,plain,
( addition(antidomain(X0),one) != addition(antidomain(X0),domain(X0))
| addition(one,antidomain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(one,antidomain(X0)),addition(antidomain(X0),domain(X0))) )],[refute_0_93,refute_0_95]) ).
cnf(refute_0_97,plain,
addition(one,antidomain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(X0),one),addition(antidomain(X0),domain(X0))) )],[refute_0_90,refute_0_96]) ).
cnf(refute_0_98,plain,
addition(one,antidomain(skolemFOFtoCNF_X1)) = one,
inference(subst,[],[refute_0_97:[bind(X0,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_99,plain,
addition(antidomain(X0),addition(domain(X0),X_23)) = addition(addition(antidomain(X0),domain(X0)),X_23),
inference(subst,[],[refute_0_27:[bind(A,$fot(antidomain(X0))),bind(B,$fot(domain(X0))),bind(C,$fot(X_23))]]) ).
cnf(refute_0_100,plain,
( addition(antidomain(X0),addition(domain(X0),X_23)) != addition(addition(antidomain(X0),domain(X0)),X_23)
| addition(antidomain(X0),domain(X0)) != one
| addition(antidomain(X0),addition(domain(X0),X_23)) = addition(one,X_23) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),addition(domain(X0),X_23)),addition(addition(antidomain(X0),domain(X0)),X_23)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_101,plain,
( addition(antidomain(X0),addition(domain(X0),X_23)) != addition(addition(antidomain(X0),domain(X0)),X_23)
| addition(antidomain(X0),addition(domain(X0),X_23)) = addition(one,X_23) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),domain(X0)),one) )],[refute_0_76,refute_0_100]) ).
cnf(refute_0_102,plain,
addition(antidomain(X0),addition(domain(X0),X_23)) = addition(one,X_23),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),addition(domain(X0),X_23)),addition(addition(antidomain(X0),domain(X0)),X_23)) )],[refute_0_99,refute_0_101]) ).
cnf(refute_0_103,plain,
addition(antidomain(X0),addition(domain(X0),addition(X_64,antidomain(domain(X0))))) = addition(one,addition(X_64,antidomain(domain(X0)))),
inference(subst,[],[refute_0_102:[bind(X_23,$fot(addition(X_64,antidomain(domain(X0)))))]]) ).
cnf(refute_0_104,plain,
addition(domain(X0),addition(antidomain(domain(X0)),X_23)) = addition(addition(domain(X0),antidomain(domain(X0))),X_23),
inference(subst,[],[refute_0_27:[bind(A,$fot(domain(X0))),bind(B,$fot(antidomain(domain(X0)))),bind(C,$fot(X_23))]]) ).
cnf(refute_0_105,plain,
addition(antidomain(antidomain(X0)),domain(antidomain(X0))) = one,
inference(subst,[],[refute_0_76:[bind(X0,$fot(antidomain(X0)))]]) ).
cnf(refute_0_106,plain,
( addition(antidomain(antidomain(X0)),domain(antidomain(X0))) != one
| antidomain(antidomain(X0)) != domain(X0)
| addition(domain(X0),domain(antidomain(X0))) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(antidomain(X0)),domain(antidomain(X0))),one) ),[0,0],$fot(domain(X0))]]) ).
cnf(refute_0_107,plain,
( addition(antidomain(antidomain(X0)),domain(antidomain(X0))) != one
| addition(domain(X0),domain(antidomain(X0))) = one ),
inference(resolve,[$cnf( $equal(antidomain(antidomain(X0)),domain(X0)) )],[refute_0_69,refute_0_106]) ).
cnf(refute_0_108,plain,
addition(domain(X0),domain(antidomain(X0))) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(antidomain(X0)),domain(antidomain(X0))),one) )],[refute_0_105,refute_0_107]) ).
cnf(refute_0_109,plain,
domain(antidomain(X_6)) = antidomain(antidomain(antidomain(X_6))),
inference(subst,[],[refute_0_67:[bind(X0,$fot(antidomain(X_6)))]]) ).
cnf(refute_0_110,plain,
domain(X_6) = antidomain(antidomain(X_6)),
inference(subst,[],[refute_0_67:[bind(X0,$fot(X_6))]]) ).
cnf(refute_0_111,plain,
( domain(X_6) != antidomain(antidomain(X_6))
| antidomain(antidomain(X_6)) = domain(X_6) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(domain(X_6))),bind(Y,$fot(antidomain(antidomain(X_6))))]]) ).
cnf(refute_0_112,plain,
antidomain(antidomain(X_6)) = domain(X_6),
inference(resolve,[$cnf( $equal(domain(X_6),antidomain(antidomain(X_6))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( antidomain(antidomain(X_6)) != domain(X_6)
| domain(antidomain(X_6)) != antidomain(antidomain(antidomain(X_6)))
| domain(antidomain(X_6)) = antidomain(domain(X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(antidomain(X_6)),antidomain(antidomain(antidomain(X_6)))) ),[1,0],$fot(domain(X_6))]]) ).
cnf(refute_0_114,plain,
( domain(antidomain(X_6)) != antidomain(antidomain(antidomain(X_6)))
| domain(antidomain(X_6)) = antidomain(domain(X_6)) ),
inference(resolve,[$cnf( $equal(antidomain(antidomain(X_6)),domain(X_6)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
domain(antidomain(X_6)) = antidomain(domain(X_6)),
inference(resolve,[$cnf( $equal(domain(antidomain(X_6)),antidomain(antidomain(antidomain(X_6)))) )],[refute_0_109,refute_0_114]) ).
cnf(refute_0_116,plain,
domain(antidomain(X0)) = antidomain(domain(X0)),
inference(subst,[],[refute_0_115:[bind(X_6,$fot(X0))]]) ).
cnf(refute_0_117,plain,
addition(domain(X0),domain(antidomain(X0))) = addition(domain(X0),domain(antidomain(X0))),
introduced(tautology,[refl,[$fot(addition(domain(X0),domain(antidomain(X0))))]]) ).
cnf(refute_0_118,plain,
( addition(domain(X0),domain(antidomain(X0))) != addition(domain(X0),domain(antidomain(X0)))
| domain(antidomain(X0)) != antidomain(domain(X0))
| addition(domain(X0),domain(antidomain(X0))) = addition(domain(X0),antidomain(domain(X0))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X0),domain(antidomain(X0))),addition(domain(X0),domain(antidomain(X0)))) ),[1,1],$fot(antidomain(domain(X0)))]]) ).
cnf(refute_0_119,plain,
( domain(antidomain(X0)) != antidomain(domain(X0))
| addition(domain(X0),domain(antidomain(X0))) = addition(domain(X0),antidomain(domain(X0))) ),
inference(resolve,[$cnf( $equal(addition(domain(X0),domain(antidomain(X0))),addition(domain(X0),domain(antidomain(X0)))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
addition(domain(X0),domain(antidomain(X0))) = addition(domain(X0),antidomain(domain(X0))),
inference(resolve,[$cnf( $equal(domain(antidomain(X0)),antidomain(domain(X0))) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
( addition(domain(X0),domain(antidomain(X0))) != addition(domain(X0),antidomain(domain(X0)))
| addition(domain(X0),domain(antidomain(X0))) != one
| addition(domain(X0),antidomain(domain(X0))) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X0),domain(antidomain(X0))),one) ),[0],$fot(addition(domain(X0),antidomain(domain(X0))))]]) ).
cnf(refute_0_122,plain,
( addition(domain(X0),domain(antidomain(X0))) != one
| addition(domain(X0),antidomain(domain(X0))) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X0),domain(antidomain(X0))),addition(domain(X0),antidomain(domain(X0)))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
addition(domain(X0),antidomain(domain(X0))) = one,
inference(resolve,[$cnf( $equal(addition(domain(X0),domain(antidomain(X0))),one) )],[refute_0_108,refute_0_122]) ).
cnf(refute_0_124,plain,
( addition(domain(X0),addition(antidomain(domain(X0)),X_23)) != addition(addition(domain(X0),antidomain(domain(X0))),X_23)
| addition(domain(X0),antidomain(domain(X0))) != one
| addition(domain(X0),addition(antidomain(domain(X0)),X_23)) = addition(one,X_23) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X0),addition(antidomain(domain(X0)),X_23)),addition(addition(domain(X0),antidomain(domain(X0))),X_23)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_125,plain,
( addition(domain(X0),addition(antidomain(domain(X0)),X_23)) != addition(addition(domain(X0),antidomain(domain(X0))),X_23)
| addition(domain(X0),addition(antidomain(domain(X0)),X_23)) = addition(one,X_23) ),
inference(resolve,[$cnf( $equal(addition(domain(X0),antidomain(domain(X0))),one) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
addition(domain(X0),addition(antidomain(domain(X0)),X_23)) = addition(one,X_23),
inference(resolve,[$cnf( $equal(addition(domain(X0),addition(antidomain(domain(X0)),X_23)),addition(addition(domain(X0),antidomain(domain(X0))),X_23)) )],[refute_0_104,refute_0_125]) ).
cnf(refute_0_127,plain,
addition(domain(X_36),addition(antidomain(domain(X_36)),X_37)) = addition(one,X_37),
inference(subst,[],[refute_0_126:[bind(X0,$fot(X_36)),bind(X_23,$fot(X_37))]]) ).
cnf(refute_0_128,plain,
addition(X_37,antidomain(domain(X_36))) = addition(antidomain(domain(X_36)),X_37),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_37)),bind(B,$fot(antidomain(domain(X_36))))]]) ).
cnf(refute_0_129,plain,
( addition(X_37,antidomain(domain(X_36))) != addition(antidomain(domain(X_36)),X_37)
| addition(antidomain(domain(X_36)),X_37) = addition(X_37,antidomain(domain(X_36))) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(addition(X_37,antidomain(domain(X_36))))),bind(Y,$fot(addition(antidomain(domain(X_36)),X_37)))]]) ).
cnf(refute_0_130,plain,
addition(antidomain(domain(X_36)),X_37) = addition(X_37,antidomain(domain(X_36))),
inference(resolve,[$cnf( $equal(addition(X_37,antidomain(domain(X_36))),addition(antidomain(domain(X_36)),X_37)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( addition(antidomain(domain(X_36)),X_37) != addition(X_37,antidomain(domain(X_36)))
| addition(domain(X_36),addition(antidomain(domain(X_36)),X_37)) != addition(one,X_37)
| addition(domain(X_36),addition(X_37,antidomain(domain(X_36)))) = addition(one,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X_36),addition(antidomain(domain(X_36)),X_37)),addition(one,X_37)) ),[0,1],$fot(addition(X_37,antidomain(domain(X_36))))]]) ).
cnf(refute_0_132,plain,
( addition(domain(X_36),addition(antidomain(domain(X_36)),X_37)) != addition(one,X_37)
| addition(domain(X_36),addition(X_37,antidomain(domain(X_36)))) = addition(one,X_37) ),
inference(resolve,[$cnf( $equal(addition(antidomain(domain(X_36)),X_37),addition(X_37,antidomain(domain(X_36)))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
addition(domain(X_36),addition(X_37,antidomain(domain(X_36)))) = addition(one,X_37),
inference(resolve,[$cnf( $equal(addition(domain(X_36),addition(antidomain(domain(X_36)),X_37)),addition(one,X_37)) )],[refute_0_127,refute_0_132]) ).
cnf(refute_0_134,plain,
addition(domain(X0),addition(X_64,antidomain(domain(X0)))) = addition(one,X_64),
inference(subst,[],[refute_0_133:[bind(X_36,$fot(X0)),bind(X_37,$fot(X_64))]]) ).
cnf(refute_0_135,plain,
( addition(antidomain(X0),addition(domain(X0),addition(X_64,antidomain(domain(X0))))) != addition(one,addition(X_64,antidomain(domain(X0))))
| addition(domain(X0),addition(X_64,antidomain(domain(X0)))) != addition(one,X_64)
| addition(antidomain(X0),addition(one,X_64)) = addition(one,addition(X_64,antidomain(domain(X0)))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),addition(domain(X0),addition(X_64,antidomain(domain(X0))))),addition(one,addition(X_64,antidomain(domain(X0))))) ),[0,1],$fot(addition(one,X_64))]]) ).
cnf(refute_0_136,plain,
( addition(antidomain(X0),addition(domain(X0),addition(X_64,antidomain(domain(X0))))) != addition(one,addition(X_64,antidomain(domain(X0))))
| addition(antidomain(X0),addition(one,X_64)) = addition(one,addition(X_64,antidomain(domain(X0)))) ),
inference(resolve,[$cnf( $equal(addition(domain(X0),addition(X_64,antidomain(domain(X0)))),addition(one,X_64)) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
addition(antidomain(X0),addition(one,X_64)) = addition(one,addition(X_64,antidomain(domain(X0)))),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),addition(domain(X0),addition(X_64,antidomain(domain(X0))))),addition(one,addition(X_64,antidomain(domain(X0))))) )],[refute_0_103,refute_0_136]) ).
cnf(refute_0_138,plain,
addition(one,addition(antidomain(X_26),C)) = addition(addition(one,antidomain(X_26)),C),
inference(subst,[],[refute_0_27:[bind(A,$fot(one)),bind(B,$fot(antidomain(X_26)))]]) ).
cnf(refute_0_139,plain,
addition(one,antidomain(X_26)) = one,
inference(subst,[],[refute_0_97:[bind(X0,$fot(X_26))]]) ).
cnf(refute_0_140,plain,
( addition(one,addition(antidomain(X_26),C)) != addition(addition(one,antidomain(X_26)),C)
| addition(one,antidomain(X_26)) != one
| addition(one,addition(antidomain(X_26),C)) = addition(one,C) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,addition(antidomain(X_26),C)),addition(addition(one,antidomain(X_26)),C)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_141,plain,
( addition(one,addition(antidomain(X_26),C)) != addition(addition(one,antidomain(X_26)),C)
| addition(one,addition(antidomain(X_26),C)) = addition(one,C) ),
inference(resolve,[$cnf( $equal(addition(one,antidomain(X_26)),one) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
addition(one,addition(antidomain(X_26),C)) = addition(one,C),
inference(resolve,[$cnf( $equal(addition(one,addition(antidomain(X_26),C)),addition(addition(one,antidomain(X_26)),C)) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
addition(one,addition(antidomain(X0),X_64)) = addition(one,X_64),
inference(subst,[],[refute_0_142:[bind(C,$fot(X_64)),bind(X_26,$fot(X0))]]) ).
cnf(refute_0_144,plain,
addition(X_21,addition(X_22,X_23)) = addition(addition(X_21,X_22),X_23),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_21)),bind(B,$fot(X_22)),bind(C,$fot(X_23))]]) ).
cnf(refute_0_145,plain,
addition(X_22,X_21) = addition(X_21,X_22),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_22)),bind(B,$fot(X_21))]]) ).
cnf(refute_0_146,plain,
( addition(X_22,X_21) != addition(X_21,X_22)
| addition(X_21,X_22) = addition(X_22,X_21) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(addition(X_22,X_21))),bind(Y,$fot(addition(X_21,X_22)))]]) ).
cnf(refute_0_147,plain,
addition(X_21,X_22) = addition(X_22,X_21),
inference(resolve,[$cnf( $equal(addition(X_22,X_21),addition(X_21,X_22)) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
( addition(X_21,X_22) != addition(X_22,X_21)
| addition(X_21,addition(X_22,X_23)) != addition(addition(X_21,X_22),X_23)
| addition(X_21,addition(X_22,X_23)) = addition(addition(X_22,X_21),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_21,addition(X_22,X_23)),addition(addition(X_21,X_22),X_23)) ),[1,0],$fot(addition(X_22,X_21))]]) ).
cnf(refute_0_149,plain,
( addition(X_21,addition(X_22,X_23)) != addition(addition(X_21,X_22),X_23)
| addition(X_21,addition(X_22,X_23)) = addition(addition(X_22,X_21),X_23) ),
inference(resolve,[$cnf( $equal(addition(X_21,X_22),addition(X_22,X_21)) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
addition(X_21,addition(X_22,X_23)) = addition(addition(X_22,X_21),X_23),
inference(resolve,[$cnf( $equal(addition(X_21,addition(X_22,X_23)),addition(addition(X_21,X_22),X_23)) )],[refute_0_144,refute_0_149]) ).
cnf(refute_0_151,plain,
( addition(A,addition(B,C)) != addition(addition(A,B),C)
| addition(addition(A,B),C) = addition(A,addition(B,C)) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(addition(A,addition(B,C)))),bind(Y,$fot(addition(addition(A,B),C)))]]) ).
cnf(refute_0_152,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,C)),addition(addition(A,B),C)) )],[refute_0_27,refute_0_151]) ).
cnf(refute_0_153,plain,
addition(addition(X_22,X_21),X_23) = addition(X_22,addition(X_21,X_23)),
inference(subst,[],[refute_0_152:[bind(A,$fot(X_22)),bind(B,$fot(X_21)),bind(C,$fot(X_23))]]) ).
cnf(refute_0_154,plain,
( addition(X_21,addition(X_22,X_23)) != addition(addition(X_22,X_21),X_23)
| addition(addition(X_22,X_21),X_23) != addition(X_22,addition(X_21,X_23))
| addition(X_21,addition(X_22,X_23)) = addition(X_22,addition(X_21,X_23)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_21,addition(X_22,X_23)),addition(X_22,addition(X_21,X_23))) ),[0],$fot(addition(addition(X_22,X_21),X_23))]]) ).
cnf(refute_0_155,plain,
( addition(X_21,addition(X_22,X_23)) != addition(addition(X_22,X_21),X_23)
| addition(X_21,addition(X_22,X_23)) = addition(X_22,addition(X_21,X_23)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_22,X_21),X_23),addition(X_22,addition(X_21,X_23))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
addition(X_21,addition(X_22,X_23)) = addition(X_22,addition(X_21,X_23)),
inference(resolve,[$cnf( $equal(addition(X_21,addition(X_22,X_23)),addition(addition(X_22,X_21),X_23)) )],[refute_0_150,refute_0_155]) ).
cnf(refute_0_157,plain,
( addition(X_21,addition(X_22,X_23)) != addition(X_22,addition(X_21,X_23))
| addition(X_22,addition(X_21,X_23)) = addition(X_21,addition(X_22,X_23)) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(addition(X_21,addition(X_22,X_23)))),bind(Y,$fot(addition(X_22,addition(X_21,X_23))))]]) ).
cnf(refute_0_158,plain,
addition(X_22,addition(X_21,X_23)) = addition(X_21,addition(X_22,X_23)),
inference(resolve,[$cnf( $equal(addition(X_21,addition(X_22,X_23)),addition(X_22,addition(X_21,X_23))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
addition(antidomain(X0),addition(one,X_64)) = addition(one,addition(antidomain(X0),X_64)),
inference(subst,[],[refute_0_158:[bind(X_21,$fot(one)),bind(X_22,$fot(antidomain(X0))),bind(X_23,$fot(X_64))]]) ).
cnf(refute_0_160,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_161,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_31,refute_0_160]) ).
cnf(refute_0_162,plain,
( addition(antidomain(X0),addition(one,X_64)) != addition(one,addition(antidomain(X0),X_64))
| addition(one,addition(antidomain(X0),X_64)) != addition(one,X_64)
| addition(antidomain(X0),addition(one,X_64)) = addition(one,X_64) ),
inference(subst,[],[refute_0_161:[bind(X,$fot(addition(antidomain(X0),addition(one,X_64)))),bind(Y,$fot(addition(one,addition(antidomain(X0),X_64)))),bind(Z,$fot(addition(one,X_64)))]]) ).
cnf(refute_0_163,plain,
( addition(one,addition(antidomain(X0),X_64)) != addition(one,X_64)
| addition(antidomain(X0),addition(one,X_64)) = addition(one,X_64) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),addition(one,X_64)),addition(one,addition(antidomain(X0),X_64))) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
addition(antidomain(X0),addition(one,X_64)) = addition(one,X_64),
inference(resolve,[$cnf( $equal(addition(one,addition(antidomain(X0),X_64)),addition(one,X_64)) )],[refute_0_143,refute_0_163]) ).
cnf(refute_0_165,plain,
( addition(antidomain(X0),addition(one,X_64)) != addition(one,X_64)
| addition(antidomain(X0),addition(one,X_64)) != addition(one,addition(X_64,antidomain(domain(X0))))
| addition(one,X_64) = addition(one,addition(X_64,antidomain(domain(X0)))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),addition(one,X_64)),addition(one,addition(X_64,antidomain(domain(X0))))) ),[0],$fot(addition(one,X_64))]]) ).
cnf(refute_0_166,plain,
( addition(antidomain(X0),addition(one,X_64)) != addition(one,addition(X_64,antidomain(domain(X0))))
| addition(one,X_64) = addition(one,addition(X_64,antidomain(domain(X0)))) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),addition(one,X_64)),addition(one,X_64)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
addition(one,X_64) = addition(one,addition(X_64,antidomain(domain(X0)))),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),addition(one,X_64)),addition(one,addition(X_64,antidomain(domain(X0))))) )],[refute_0_137,refute_0_166]) ).
cnf(refute_0_168,plain,
addition(antidomain(X0),addition(X_97,one)) = addition(X_97,addition(one,antidomain(X0))),
inference(subst,[],[refute_0_36:[bind(A,$fot(antidomain(X0))),bind(X_21,$fot(X_97)),bind(X_22,$fot(one))]]) ).
cnf(refute_0_169,plain,
( addition(antidomain(X0),addition(X_97,one)) != addition(X_97,addition(one,antidomain(X0)))
| addition(one,antidomain(X0)) != one
| addition(antidomain(X0),addition(X_97,one)) = addition(X_97,one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),addition(X_97,one)),addition(X_97,addition(one,antidomain(X0)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_170,plain,
( addition(antidomain(X0),addition(X_97,one)) != addition(X_97,addition(one,antidomain(X0)))
| addition(antidomain(X0),addition(X_97,one)) = addition(X_97,one) ),
inference(resolve,[$cnf( $equal(addition(one,antidomain(X0)),one) )],[refute_0_97,refute_0_169]) ).
cnf(refute_0_171,plain,
addition(antidomain(X0),addition(X_97,one)) = addition(X_97,one),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),addition(X_97,one)),addition(X_97,addition(one,antidomain(X0)))) )],[refute_0_168,refute_0_170]) ).
cnf(refute_0_172,plain,
addition(antidomain(X0),addition(X_97,one)) = addition(one,addition(X_97,antidomain(X0))),
inference(subst,[],[refute_0_56:[bind(X_96,$fot(one)),bind(X_97,$fot(antidomain(X0))),bind(X_98,$fot(X_97))]]) ).
cnf(refute_0_173,plain,
( addition(antidomain(X0),addition(X_97,one)) != addition(X_97,one)
| addition(antidomain(X0),addition(X_97,one)) != addition(one,addition(X_97,antidomain(X0)))
| addition(one,addition(X_97,antidomain(X0))) = addition(X_97,one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),addition(X_97,one)),addition(X_97,one)) ),[0],$fot(addition(one,addition(X_97,antidomain(X0))))]]) ).
cnf(refute_0_174,plain,
( addition(antidomain(X0),addition(X_97,one)) != addition(X_97,one)
| addition(one,addition(X_97,antidomain(X0))) = addition(X_97,one) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),addition(X_97,one)),addition(one,addition(X_97,antidomain(X0)))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
addition(one,addition(X_97,antidomain(X0))) = addition(X_97,one),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),addition(X_97,one)),addition(X_97,one)) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
addition(one,addition(X_64,antidomain(domain(X0)))) = addition(X_64,one),
inference(subst,[],[refute_0_175:[bind(X0,$fot(domain(X0))),bind(X_97,$fot(X_64))]]) ).
cnf(refute_0_177,plain,
( addition(one,X_64) != addition(one,addition(X_64,antidomain(domain(X0))))
| addition(one,addition(X_64,antidomain(domain(X0)))) != addition(X_64,one)
| addition(one,X_64) = addition(X_64,one) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(one,X_64),addition(X_64,one)) ),[0],$fot(addition(one,addition(X_64,antidomain(domain(X0)))))]]) ).
cnf(refute_0_178,plain,
( addition(one,X_64) != addition(one,addition(X_64,antidomain(domain(X0))))
| addition(one,X_64) = addition(X_64,one) ),
inference(resolve,[$cnf( $equal(addition(one,addition(X_64,antidomain(domain(X0)))),addition(X_64,one)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
addition(one,X_64) = addition(X_64,one),
inference(resolve,[$cnf( $equal(addition(one,X_64),addition(one,addition(X_64,antidomain(domain(X0))))) )],[refute_0_167,refute_0_178]) ).
cnf(refute_0_180,plain,
( addition(one,X_64) != addition(X_64,one)
| addition(X_64,one) = addition(one,X_64) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(addition(one,X_64))),bind(Y,$fot(addition(X_64,one)))]]) ).
cnf(refute_0_181,plain,
addition(X_64,one) = addition(one,X_64),
inference(resolve,[$cnf( $equal(addition(one,X_64),addition(X_64,one)) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
addition(antidomain(skolemFOFtoCNF_X1),one) = addition(one,antidomain(skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_181:[bind(X_64,$fot(antidomain(skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_183,plain,
( addition(antidomain(skolemFOFtoCNF_X1),one) != addition(one,antidomain(skolemFOFtoCNF_X1))
| addition(one,antidomain(skolemFOFtoCNF_X1)) != one
| addition(antidomain(skolemFOFtoCNF_X1),one) = one ),
inference(subst,[],[refute_0_161:[bind(X,$fot(addition(antidomain(skolemFOFtoCNF_X1),one))),bind(Y,$fot(addition(one,antidomain(skolemFOFtoCNF_X1)))),bind(Z,$fot(one))]]) ).
cnf(refute_0_184,plain,
( addition(one,antidomain(skolemFOFtoCNF_X1)) != one
| addition(antidomain(skolemFOFtoCNF_X1),one) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(skolemFOFtoCNF_X1),one),addition(one,antidomain(skolemFOFtoCNF_X1))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
addition(antidomain(skolemFOFtoCNF_X1),one) = one,
inference(resolve,[$cnf( $equal(addition(one,antidomain(skolemFOFtoCNF_X1)),one) )],[refute_0_98,refute_0_184]) ).
cnf(refute_0_186,plain,
( addition(antidomain(skolemFOFtoCNF_X1),one) != addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1))
| addition(antidomain(skolemFOFtoCNF_X1),one) != one
| one = addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(skolemFOFtoCNF_X1),one),addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1))) ),[0],$fot(one)]]) ).
cnf(refute_0_187,plain,
( addition(antidomain(skolemFOFtoCNF_X1),one) != addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1))
| one = addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(skolemFOFtoCNF_X1),one),one) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
one = addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(addition(antidomain(skolemFOFtoCNF_X1),one),addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1))) )],[refute_0_80,refute_0_187]) ).
cnf(refute_0_189,plain,
( one != addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1))
| addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) = one ),
inference(subst,[],[refute_0_31:[bind(X,$fot(one)),bind(Y,$fot(addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_190,plain,
addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) = one,
inference(resolve,[$cnf( $equal(one,addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
( addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)) != one
| multiplication(addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X1) != multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| multiplication(one,skolemFOFtoCNF_X1) = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X1),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) ),[0,0],$fot(one)]]) ).
cnf(refute_0_192,plain,
( multiplication(addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X1) != multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| multiplication(one,skolemFOFtoCNF_X1) = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),one) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
multiplication(one,skolemFOFtoCNF_X1) = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(multiplication(addition(antidomain(skolemFOFtoCNF_X0),antidomain(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X1),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_24,refute_0_192]) ).
cnf(refute_0_194,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_195,plain,
multiplication(one,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(subst,[],[refute_0_194:[bind(A,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_196,plain,
( multiplication(one,skolemFOFtoCNF_X1) != multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| multiplication(one,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| skolemFOFtoCNF_X1 = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) ),[0],$fot(skolemFOFtoCNF_X1)]]) ).
cnf(refute_0_197,plain,
( multiplication(one,skolemFOFtoCNF_X1) != multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| skolemFOFtoCNF_X1 = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
skolemFOFtoCNF_X1 = multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_193,refute_0_197]) ).
cnf(refute_0_199,plain,
( skolemFOFtoCNF_X1 != multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
inference(subst,[],[refute_0_31:[bind(X,$fot(skolemFOFtoCNF_X1)),bind(Y,$fot(multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_200,plain,
multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1,multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
( multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) != zero
| multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)),zero) ),[0,1],$fot(skolemFOFtoCNF_X1)]]) ).
cnf(refute_0_202,plain,
( multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) != zero
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = zero ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = zero,
inference(resolve,[$cnf( $equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),multiplication(antidomain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)),zero) )],[refute_0_12,refute_0_202]) ).
cnf(refute_0_204,plain,
antidomain(antidomain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_69:[bind(X0,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_205,plain,
multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),
introduced(tautology,[refl,[$fot(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_206,plain,
( antidomain(antidomain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0)
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) != multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1)
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1)) ),[1,0],$fot(domain(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_207,plain,
( antidomain(antidomain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0)
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(antidomain(antidomain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
( multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)
| multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) != zero
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),zero) ),[0],$fot(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_210,plain,
( multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1) != zero
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = zero ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1)) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) = zero,
inference(resolve,[$cnf( $equal(multiplication(antidomain(antidomain(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1),zero) )],[refute_0_203,refute_0_210]) ).
cnf(refute_0_212,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1) != zero,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_213,plain,
$false,
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1),zero) )],[refute_0_211,refute_0_212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE089+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n003.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 10:01:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.86/1.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.86/1.09
% 0.86/1.09 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.93/1.11
%------------------------------------------------------------------------------