TSTP Solution File: KLE119+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE119+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 02:15:22 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 47
% Syntax : Number of formulae : 184 ( 109 unt; 0 def)
% Number of atoms : 295 ( 294 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 229 ( 118 ~; 111 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 116 ( 3 sgn 36 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero ).
fof(codomain1,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero ).
fof(codomain3,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one ).
fof(codomain4,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)) ).
fof(backward_diamond,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)) ).
fof(goals,conjecture,
! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1) ).
fof(subgoal_0,plain,
! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) != domain(X1),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
addition(backward_diamond(zero,domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_3,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(canonicalize,[],[backward_diamond]) ).
fof(normalize_0_5,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : multiplication(A,zero) = zero,
inference(canonicalize,[],[right_annihilation]) ).
fof(normalize_0_7,plain,
! [A] : multiplication(A,zero) = zero,
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,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
inference(canonicalize,[],[codomain1]) ).
fof(normalize_0_11,plain,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
inference(canonicalize,[],[codomain4]) ).
fof(normalize_0_13,plain,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_15,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(canonicalize,[],[codomain3]) ).
fof(normalize_0_17,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(specialize,[],[normalize_0_16]) ).
cnf(refute_0_0,plain,
addition(backward_diamond(zero,domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_6,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
addition(backward_diamond(zero,domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X1)) = addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))),
inference(subst,[],[refute_0_6:[bind(A,$fot(domain(skolemFOFtoCNF_X1))),bind(B,$fot(backward_diamond(zero,domain(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_8,plain,
( addition(backward_diamond(zero,domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X1)) != addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0)))
| addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) != domain(skolemFOFtoCNF_X1)
| addition(backward_diamond(zero,domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(backward_diamond(zero,domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) ),[0],$fot(addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_9,plain,
( addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) != domain(skolemFOFtoCNF_X1)
| addition(backward_diamond(zero,domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(addition(backward_diamond(zero,domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X1)),addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0)))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) != domain(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(addition(backward_diamond(zero,domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
addition(domain(skolemFOFtoCNF_X1),codomain(zero)) = addition(codomain(zero),domain(skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_6:[bind(A,$fot(codomain(zero))),bind(B,$fot(domain(skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_12,plain,
backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_13,plain,
backward_diamond(zero,X_39) = codomain(multiplication(codomain(X_39),zero)),
inference(subst,[],[refute_0_12:[bind(X0,$fot(zero)),bind(X1,$fot(X_39))]]) ).
cnf(refute_0_14,plain,
multiplication(A,zero) = zero,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_15,plain,
multiplication(codomain(X_39),zero) = zero,
inference(subst,[],[refute_0_14:[bind(A,$fot(codomain(X_39)))]]) ).
cnf(refute_0_16,plain,
( backward_diamond(zero,X_39) != codomain(multiplication(codomain(X_39),zero))
| multiplication(codomain(X_39),zero) != zero
| backward_diamond(zero,X_39) = codomain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(backward_diamond(zero,X_39),codomain(multiplication(codomain(X_39),zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_17,plain,
( backward_diamond(zero,X_39) != codomain(multiplication(codomain(X_39),zero))
| backward_diamond(zero,X_39) = codomain(zero) ),
inference(resolve,[$cnf( $equal(multiplication(codomain(X_39),zero),zero) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
backward_diamond(zero,X_39) = codomain(zero),
inference(resolve,[$cnf( $equal(backward_diamond(zero,X_39),codomain(multiplication(codomain(X_39),zero))) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
backward_diamond(zero,domain(skolemFOFtoCNF_X0)) = codomain(zero),
inference(subst,[],[refute_0_18:[bind(X_39,$fot(domain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_20,plain,
addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) = addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))),
introduced(tautology,[refl,[$fot(addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))))]]) ).
cnf(refute_0_21,plain,
( addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) != addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0)))
| backward_diamond(zero,domain(skolemFOFtoCNF_X0)) != codomain(zero)
| addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) = addition(domain(skolemFOFtoCNF_X1),codomain(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))),addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0)))) ),[1,1],$fot(codomain(zero))]]) ).
cnf(refute_0_22,plain,
( backward_diamond(zero,domain(skolemFOFtoCNF_X0)) != codomain(zero)
| addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) = addition(domain(skolemFOFtoCNF_X1),codomain(zero)) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))),addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) = addition(domain(skolemFOFtoCNF_X1),codomain(zero)),
inference(resolve,[$cnf( $equal(backward_diamond(zero,domain(skolemFOFtoCNF_X0)),codomain(zero)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_25,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_24]) ).
cnf(refute_0_26,plain,
( addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) != addition(domain(skolemFOFtoCNF_X1),codomain(zero))
| addition(domain(skolemFOFtoCNF_X1),codomain(zero)) != addition(codomain(zero),domain(skolemFOFtoCNF_X1))
| addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) = addition(codomain(zero),domain(skolemFOFtoCNF_X1)) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))))),bind(Y,$fot(addition(domain(skolemFOFtoCNF_X1),codomain(zero)))),bind(Z,$fot(addition(codomain(zero),domain(skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_27,plain,
( addition(domain(skolemFOFtoCNF_X1),codomain(zero)) != addition(codomain(zero),domain(skolemFOFtoCNF_X1))
| addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) = addition(codomain(zero),domain(skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))),addition(domain(skolemFOFtoCNF_X1),codomain(zero))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) = addition(codomain(zero),domain(skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X1),codomain(zero)),addition(codomain(zero),domain(skolemFOFtoCNF_X1))) )],[refute_0_11,refute_0_27]) ).
cnf(refute_0_29,plain,
( addition(codomain(zero),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
| addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) != addition(codomain(zero),domain(skolemFOFtoCNF_X1))
| addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) = domain(skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))),addition(codomain(zero),domain(skolemFOFtoCNF_X1))) ),[1],$fot(domain(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_30,plain,
( addition(codomain(zero),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
| addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))) = domain(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))),addition(codomain(zero),domain(skolemFOFtoCNF_X1))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
addition(codomain(zero),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X1),backward_diamond(zero,domain(skolemFOFtoCNF_X0))),domain(skolemFOFtoCNF_X1)) )],[refute_0_30,refute_0_10]) ).
cnf(refute_0_32,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_33,plain,
addition(A,zero) = addition(zero,A),
inference(subst,[],[refute_0_1:[bind(B,$fot(zero))]]) ).
cnf(refute_0_34,plain,
( addition(A,zero) != A
| addition(A,zero) != addition(zero,A)
| addition(zero,A) = A ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,zero),A) ),[0],$fot(addition(zero,A))]]) ).
cnf(refute_0_35,plain,
( addition(A,zero) != A
| addition(zero,A) = A ),
inference(resolve,[$cnf( $equal(addition(A,zero),addition(zero,A)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
addition(zero,A) = A,
inference(resolve,[$cnf( $equal(addition(A,zero),A) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
addition(zero,domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1),
inference(subst,[],[refute_0_36:[bind(A,$fot(domain(skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_38,plain,
backward_diamond(coantidomain(codomain(X_39)),X_39) = codomain(multiplication(codomain(X_39),coantidomain(codomain(X_39)))),
inference(subst,[],[refute_0_12:[bind(X0,$fot(coantidomain(codomain(X_39)))),bind(X1,$fot(X_39))]]) ).
cnf(refute_0_39,plain,
multiplication(X0,coantidomain(X0)) = zero,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_40,plain,
multiplication(codomain(X_39),coantidomain(codomain(X_39))) = zero,
inference(subst,[],[refute_0_39:[bind(X0,$fot(codomain(X_39)))]]) ).
cnf(refute_0_41,plain,
( backward_diamond(coantidomain(codomain(X_39)),X_39) != codomain(multiplication(codomain(X_39),coantidomain(codomain(X_39))))
| multiplication(codomain(X_39),coantidomain(codomain(X_39))) != zero
| backward_diamond(coantidomain(codomain(X_39)),X_39) = codomain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(backward_diamond(coantidomain(codomain(X_39)),X_39),codomain(multiplication(codomain(X_39),coantidomain(codomain(X_39))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_42,plain,
( backward_diamond(coantidomain(codomain(X_39)),X_39) != codomain(multiplication(codomain(X_39),coantidomain(codomain(X_39))))
| backward_diamond(coantidomain(codomain(X_39)),X_39) = codomain(zero) ),
inference(resolve,[$cnf( $equal(multiplication(codomain(X_39),coantidomain(codomain(X_39))),zero) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
backward_diamond(coantidomain(codomain(X_39)),X_39) = codomain(zero),
inference(resolve,[$cnf( $equal(backward_diamond(coantidomain(codomain(X_39)),X_39),codomain(multiplication(codomain(X_39),coantidomain(codomain(X_39))))) )],[refute_0_38,refute_0_42]) ).
cnf(refute_0_44,plain,
backward_diamond(coantidomain(codomain(one)),one) = codomain(zero),
inference(subst,[],[refute_0_43:[bind(X_39,$fot(one))]]) ).
cnf(refute_0_45,plain,
codomain(X0) = coantidomain(coantidomain(X0)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_46,plain,
codomain(one) = coantidomain(coantidomain(one)),
inference(subst,[],[refute_0_45:[bind(X0,$fot(one))]]) ).
cnf(refute_0_47,plain,
multiplication(one,coantidomain(one)) = zero,
inference(subst,[],[refute_0_39:[bind(X0,$fot(one))]]) ).
cnf(refute_0_48,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_49,plain,
multiplication(one,coantidomain(one)) = coantidomain(one),
inference(subst,[],[refute_0_48:[bind(A,$fot(coantidomain(one)))]]) ).
cnf(refute_0_50,plain,
( multiplication(one,coantidomain(one)) != coantidomain(one)
| multiplication(one,coantidomain(one)) != zero
| coantidomain(one) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,coantidomain(one)),zero) ),[0],$fot(coantidomain(one))]]) ).
cnf(refute_0_51,plain,
( multiplication(one,coantidomain(one)) != zero
| coantidomain(one) = zero ),
inference(resolve,[$cnf( $equal(multiplication(one,coantidomain(one)),coantidomain(one)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
coantidomain(one) = zero,
inference(resolve,[$cnf( $equal(multiplication(one,coantidomain(one)),zero) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
( coantidomain(one) != zero
| codomain(one) != coantidomain(coantidomain(one))
| codomain(one) = coantidomain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(one),coantidomain(coantidomain(one))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_54,plain,
( codomain(one) != coantidomain(coantidomain(one))
| codomain(one) = coantidomain(zero) ),
inference(resolve,[$cnf( $equal(coantidomain(one),zero) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
codomain(one) = coantidomain(zero),
inference(resolve,[$cnf( $equal(codomain(one),coantidomain(coantidomain(one))) )],[refute_0_46,refute_0_54]) ).
cnf(refute_0_56,plain,
addition(zero,coantidomain(zero)) = addition(coantidomain(zero),zero),
inference(subst,[],[refute_0_1:[bind(A,$fot(zero)),bind(B,$fot(coantidomain(zero)))]]) ).
cnf(refute_0_57,plain,
addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_58,plain,
addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = addition(coantidomain(X0),coantidomain(coantidomain(X0))),
inference(subst,[],[refute_0_6:[bind(A,$fot(coantidomain(X0))),bind(B,$fot(coantidomain(coantidomain(X0))))]]) ).
cnf(refute_0_59,plain,
( addition(coantidomain(coantidomain(X0)),coantidomain(X0)) != addition(coantidomain(X0),coantidomain(coantidomain(X0)))
| addition(coantidomain(coantidomain(X0)),coantidomain(X0)) != one
| addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(coantidomain(coantidomain(X0)),coantidomain(X0)),one) ),[0],$fot(addition(coantidomain(X0),coantidomain(coantidomain(X0))))]]) ).
cnf(refute_0_60,plain,
( addition(coantidomain(coantidomain(X0)),coantidomain(X0)) != one
| addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one ),
inference(resolve,[$cnf( $equal(addition(coantidomain(coantidomain(X0)),coantidomain(X0)),addition(coantidomain(X0),coantidomain(coantidomain(X0)))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(resolve,[$cnf( $equal(addition(coantidomain(coantidomain(X0)),coantidomain(X0)),one) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
( codomain(X0) != coantidomain(coantidomain(X0))
| coantidomain(coantidomain(X0)) = codomain(X0) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(codomain(X0))),bind(Y,$fot(coantidomain(coantidomain(X0))))]]) ).
cnf(refute_0_63,plain,
coantidomain(coantidomain(X0)) = codomain(X0),
inference(resolve,[$cnf( $equal(codomain(X0),coantidomain(coantidomain(X0))) )],[refute_0_45,refute_0_62]) ).
cnf(refute_0_64,plain,
addition(coantidomain(X0),coantidomain(coantidomain(X0))) = addition(coantidomain(X0),coantidomain(coantidomain(X0))),
introduced(tautology,[refl,[$fot(addition(coantidomain(X0),coantidomain(coantidomain(X0))))]]) ).
cnf(refute_0_65,plain,
( addition(coantidomain(X0),coantidomain(coantidomain(X0))) != addition(coantidomain(X0),coantidomain(coantidomain(X0)))
| coantidomain(coantidomain(X0)) != codomain(X0)
| addition(coantidomain(X0),coantidomain(coantidomain(X0))) = addition(coantidomain(X0),codomain(X0)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(coantidomain(X0),coantidomain(coantidomain(X0))),addition(coantidomain(X0),coantidomain(coantidomain(X0)))) ),[1,1],$fot(codomain(X0))]]) ).
cnf(refute_0_66,plain,
( coantidomain(coantidomain(X0)) != codomain(X0)
| addition(coantidomain(X0),coantidomain(coantidomain(X0))) = addition(coantidomain(X0),codomain(X0)) ),
inference(resolve,[$cnf( $equal(addition(coantidomain(X0),coantidomain(coantidomain(X0))),addition(coantidomain(X0),coantidomain(coantidomain(X0)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
addition(coantidomain(X0),coantidomain(coantidomain(X0))) = addition(coantidomain(X0),codomain(X0)),
inference(resolve,[$cnf( $equal(coantidomain(coantidomain(X0)),codomain(X0)) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
( addition(coantidomain(X0),coantidomain(coantidomain(X0))) != addition(coantidomain(X0),codomain(X0))
| addition(coantidomain(X0),coantidomain(coantidomain(X0))) != one
| addition(coantidomain(X0),codomain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(coantidomain(X0),coantidomain(coantidomain(X0))),one) ),[0],$fot(addition(coantidomain(X0),codomain(X0)))]]) ).
cnf(refute_0_69,plain,
( addition(coantidomain(X0),coantidomain(coantidomain(X0))) != one
| addition(coantidomain(X0),codomain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(coantidomain(X0),coantidomain(coantidomain(X0))),addition(coantidomain(X0),codomain(X0))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
addition(coantidomain(X0),codomain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(coantidomain(X0),coantidomain(coantidomain(X0))),one) )],[refute_0_61,refute_0_69]) ).
cnf(refute_0_71,plain,
addition(coantidomain(one),codomain(one)) = one,
inference(subst,[],[refute_0_70:[bind(X0,$fot(one))]]) ).
cnf(refute_0_72,plain,
( addition(coantidomain(one),codomain(one)) != one
| codomain(one) != coantidomain(zero)
| addition(coantidomain(one),coantidomain(zero)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(coantidomain(one),codomain(one)),one) ),[0,1],$fot(coantidomain(zero))]]) ).
cnf(refute_0_73,plain,
( addition(coantidomain(one),codomain(one)) != one
| addition(coantidomain(one),coantidomain(zero)) = one ),
inference(resolve,[$cnf( $equal(codomain(one),coantidomain(zero)) )],[refute_0_55,refute_0_72]) ).
cnf(refute_0_74,plain,
addition(coantidomain(one),coantidomain(zero)) = one,
inference(resolve,[$cnf( $equal(addition(coantidomain(one),codomain(one)),one) )],[refute_0_71,refute_0_73]) ).
cnf(refute_0_75,plain,
addition(coantidomain(one),coantidomain(zero)) = addition(coantidomain(one),coantidomain(zero)),
introduced(tautology,[refl,[$fot(addition(coantidomain(one),coantidomain(zero)))]]) ).
cnf(refute_0_76,plain,
( addition(coantidomain(one),coantidomain(zero)) != addition(coantidomain(one),coantidomain(zero))
| coantidomain(one) != zero
| addition(coantidomain(one),coantidomain(zero)) = addition(zero,coantidomain(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(coantidomain(one),coantidomain(zero)),addition(coantidomain(one),coantidomain(zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_77,plain,
( coantidomain(one) != zero
| addition(coantidomain(one),coantidomain(zero)) = addition(zero,coantidomain(zero)) ),
inference(resolve,[$cnf( $equal(addition(coantidomain(one),coantidomain(zero)),addition(coantidomain(one),coantidomain(zero))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
addition(coantidomain(one),coantidomain(zero)) = addition(zero,coantidomain(zero)),
inference(resolve,[$cnf( $equal(coantidomain(one),zero) )],[refute_0_52,refute_0_77]) ).
cnf(refute_0_79,plain,
( addition(coantidomain(one),coantidomain(zero)) != addition(zero,coantidomain(zero))
| addition(coantidomain(one),coantidomain(zero)) != one
| addition(zero,coantidomain(zero)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(coantidomain(one),coantidomain(zero)),one) ),[0],$fot(addition(zero,coantidomain(zero)))]]) ).
cnf(refute_0_80,plain,
( addition(coantidomain(one),coantidomain(zero)) != one
| addition(zero,coantidomain(zero)) = one ),
inference(resolve,[$cnf( $equal(addition(coantidomain(one),coantidomain(zero)),addition(zero,coantidomain(zero))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
addition(zero,coantidomain(zero)) = one,
inference(resolve,[$cnf( $equal(addition(coantidomain(one),coantidomain(zero)),one) )],[refute_0_74,refute_0_80]) ).
cnf(refute_0_82,plain,
( addition(zero,coantidomain(zero)) != addition(coantidomain(zero),zero)
| addition(zero,coantidomain(zero)) != one
| one = addition(coantidomain(zero),zero) ),
introduced(tautology,[equality,[$cnf( $equal(addition(zero,coantidomain(zero)),addition(coantidomain(zero),zero)) ),[0],$fot(one)]]) ).
cnf(refute_0_83,plain,
( addition(zero,coantidomain(zero)) != addition(coantidomain(zero),zero)
| one = addition(coantidomain(zero),zero) ),
inference(resolve,[$cnf( $equal(addition(zero,coantidomain(zero)),one) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
one = addition(coantidomain(zero),zero),
inference(resolve,[$cnf( $equal(addition(zero,coantidomain(zero)),addition(coantidomain(zero),zero)) )],[refute_0_56,refute_0_83]) ).
cnf(refute_0_85,plain,
addition(coantidomain(zero),zero) = coantidomain(zero),
inference(subst,[],[refute_0_32:[bind(A,$fot(coantidomain(zero)))]]) ).
cnf(refute_0_86,plain,
( addition(coantidomain(zero),zero) != coantidomain(zero)
| one != addition(coantidomain(zero),zero)
| one = coantidomain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(one,addition(coantidomain(zero),zero)) ),[1],$fot(coantidomain(zero))]]) ).
cnf(refute_0_87,plain,
( one != addition(coantidomain(zero),zero)
| one = coantidomain(zero) ),
inference(resolve,[$cnf( $equal(addition(coantidomain(zero),zero),coantidomain(zero)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
one = coantidomain(zero),
inference(resolve,[$cnf( $equal(one,addition(coantidomain(zero),zero)) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( one != coantidomain(zero)
| coantidomain(zero) = one ),
inference(subst,[],[refute_0_4:[bind(X,$fot(one)),bind(Y,$fot(coantidomain(zero)))]]) ).
cnf(refute_0_90,plain,
coantidomain(zero) = one,
inference(resolve,[$cnf( $equal(one,coantidomain(zero)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( coantidomain(zero) != one
| codomain(one) != coantidomain(zero)
| codomain(one) = one ),
introduced(tautology,[equality,[$cnf( $equal(codomain(one),coantidomain(zero)) ),[1],$fot(one)]]) ).
cnf(refute_0_92,plain,
( codomain(one) != coantidomain(zero)
| codomain(one) = one ),
inference(resolve,[$cnf( $equal(coantidomain(zero),one) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
codomain(one) = one,
inference(resolve,[$cnf( $equal(codomain(one),coantidomain(zero)) )],[refute_0_55,refute_0_92]) ).
cnf(refute_0_94,plain,
( backward_diamond(coantidomain(codomain(one)),one) != codomain(zero)
| codomain(one) != one
| backward_diamond(coantidomain(one),one) = codomain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(backward_diamond(coantidomain(codomain(one)),one),codomain(zero)) ),[0,0,0],$fot(one)]]) ).
cnf(refute_0_95,plain,
( backward_diamond(coantidomain(codomain(one)),one) != codomain(zero)
| backward_diamond(coantidomain(one),one) = codomain(zero) ),
inference(resolve,[$cnf( $equal(codomain(one),one) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
backward_diamond(coantidomain(one),one) = codomain(zero),
inference(resolve,[$cnf( $equal(backward_diamond(coantidomain(codomain(one)),one),codomain(zero)) )],[refute_0_44,refute_0_95]) ).
cnf(refute_0_97,plain,
coantidomain(codomain(one)) = coantidomain(codomain(one)),
introduced(tautology,[refl,[$fot(coantidomain(codomain(one)))]]) ).
cnf(refute_0_98,plain,
( coantidomain(codomain(one)) != coantidomain(codomain(one))
| codomain(one) != one
| coantidomain(codomain(one)) = coantidomain(one) ),
introduced(tautology,[equality,[$cnf( $equal(coantidomain(codomain(one)),coantidomain(codomain(one))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_99,plain,
( codomain(one) != one
| coantidomain(codomain(one)) = coantidomain(one) ),
inference(resolve,[$cnf( $equal(coantidomain(codomain(one)),coantidomain(codomain(one))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
coantidomain(codomain(one)) = coantidomain(one),
inference(resolve,[$cnf( $equal(codomain(one),one) )],[refute_0_93,refute_0_99]) ).
cnf(refute_0_101,plain,
( coantidomain(codomain(one)) != coantidomain(one)
| coantidomain(one) != zero
| coantidomain(codomain(one)) = zero ),
inference(subst,[],[refute_0_25:[bind(X,$fot(coantidomain(codomain(one)))),bind(Y,$fot(coantidomain(one))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_102,plain,
( coantidomain(one) != zero
| coantidomain(codomain(one)) = zero ),
inference(resolve,[$cnf( $equal(coantidomain(codomain(one)),coantidomain(one)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
coantidomain(codomain(one)) = zero,
inference(resolve,[$cnf( $equal(coantidomain(one),zero) )],[refute_0_52,refute_0_102]) ).
cnf(refute_0_104,plain,
codomain(coantidomain(X_8)) = coantidomain(coantidomain(coantidomain(X_8))),
inference(subst,[],[refute_0_45:[bind(X0,$fot(coantidomain(X_8)))]]) ).
cnf(refute_0_105,plain,
codomain(X_8) = coantidomain(coantidomain(X_8)),
inference(subst,[],[refute_0_45:[bind(X0,$fot(X_8))]]) ).
cnf(refute_0_106,plain,
( codomain(X_8) != coantidomain(coantidomain(X_8))
| coantidomain(coantidomain(X_8)) = codomain(X_8) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(codomain(X_8))),bind(Y,$fot(coantidomain(coantidomain(X_8))))]]) ).
cnf(refute_0_107,plain,
coantidomain(coantidomain(X_8)) = codomain(X_8),
inference(resolve,[$cnf( $equal(codomain(X_8),coantidomain(coantidomain(X_8))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
( coantidomain(coantidomain(X_8)) != codomain(X_8)
| codomain(coantidomain(X_8)) != coantidomain(coantidomain(coantidomain(X_8)))
| codomain(coantidomain(X_8)) = coantidomain(codomain(X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(coantidomain(X_8)),coantidomain(coantidomain(coantidomain(X_8)))) ),[1,0],$fot(codomain(X_8))]]) ).
cnf(refute_0_109,plain,
( codomain(coantidomain(X_8)) != coantidomain(coantidomain(coantidomain(X_8)))
| codomain(coantidomain(X_8)) = coantidomain(codomain(X_8)) ),
inference(resolve,[$cnf( $equal(coantidomain(coantidomain(X_8)),codomain(X_8)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
codomain(coantidomain(X_8)) = coantidomain(codomain(X_8)),
inference(resolve,[$cnf( $equal(codomain(coantidomain(X_8)),coantidomain(coantidomain(coantidomain(X_8)))) )],[refute_0_104,refute_0_109]) ).
cnf(refute_0_111,plain,
codomain(coantidomain(one)) = coantidomain(codomain(one)),
inference(subst,[],[refute_0_110:[bind(X_8,$fot(one))]]) ).
cnf(refute_0_112,plain,
backward_diamond(X_38,one) = codomain(multiplication(codomain(one),X_38)),
inference(subst,[],[refute_0_12:[bind(X0,$fot(X_38)),bind(X1,$fot(one))]]) ).
cnf(refute_0_113,plain,
( backward_diamond(X_38,one) != codomain(multiplication(codomain(one),X_38))
| codomain(one) != coantidomain(zero)
| backward_diamond(X_38,one) = codomain(multiplication(coantidomain(zero),X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(backward_diamond(X_38,one),codomain(multiplication(codomain(one),X_38))) ),[1,0,0],$fot(coantidomain(zero))]]) ).
cnf(refute_0_114,plain,
( backward_diamond(X_38,one) != codomain(multiplication(codomain(one),X_38))
| backward_diamond(X_38,one) = codomain(multiplication(coantidomain(zero),X_38)) ),
inference(resolve,[$cnf( $equal(codomain(one),coantidomain(zero)) )],[refute_0_55,refute_0_113]) ).
cnf(refute_0_115,plain,
backward_diamond(X_38,one) = codomain(multiplication(coantidomain(zero),X_38)),
inference(resolve,[$cnf( $equal(backward_diamond(X_38,one),codomain(multiplication(codomain(one),X_38))) )],[refute_0_112,refute_0_114]) ).
cnf(refute_0_116,plain,
multiplication(one,X_38) = X_38,
inference(subst,[],[refute_0_48:[bind(A,$fot(X_38))]]) ).
cnf(refute_0_117,plain,
multiplication(coantidomain(zero),X_38) = multiplication(coantidomain(zero),X_38),
introduced(tautology,[refl,[$fot(multiplication(coantidomain(zero),X_38))]]) ).
cnf(refute_0_118,plain,
( coantidomain(zero) != one
| multiplication(coantidomain(zero),X_38) != multiplication(coantidomain(zero),X_38)
| multiplication(coantidomain(zero),X_38) = multiplication(one,X_38) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(coantidomain(zero),X_38),multiplication(coantidomain(zero),X_38)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_119,plain,
( coantidomain(zero) != one
| multiplication(coantidomain(zero),X_38) = multiplication(one,X_38) ),
inference(resolve,[$cnf( $equal(multiplication(coantidomain(zero),X_38),multiplication(coantidomain(zero),X_38)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
multiplication(coantidomain(zero),X_38) = multiplication(one,X_38),
inference(resolve,[$cnf( $equal(coantidomain(zero),one) )],[refute_0_90,refute_0_119]) ).
cnf(refute_0_121,plain,
( multiplication(coantidomain(zero),X_38) != multiplication(one,X_38)
| multiplication(one,X_38) != X_38
| multiplication(coantidomain(zero),X_38) = X_38 ),
inference(subst,[],[refute_0_25:[bind(X,$fot(multiplication(coantidomain(zero),X_38))),bind(Y,$fot(multiplication(one,X_38))),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_122,plain,
( multiplication(one,X_38) != X_38
| multiplication(coantidomain(zero),X_38) = X_38 ),
inference(resolve,[$cnf( $equal(multiplication(coantidomain(zero),X_38),multiplication(one,X_38)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
multiplication(coantidomain(zero),X_38) = X_38,
inference(resolve,[$cnf( $equal(multiplication(one,X_38),X_38) )],[refute_0_116,refute_0_122]) ).
cnf(refute_0_124,plain,
codomain(multiplication(coantidomain(zero),X_38)) = codomain(multiplication(coantidomain(zero),X_38)),
introduced(tautology,[refl,[$fot(codomain(multiplication(coantidomain(zero),X_38)))]]) ).
cnf(refute_0_125,plain,
( codomain(multiplication(coantidomain(zero),X_38)) != codomain(multiplication(coantidomain(zero),X_38))
| multiplication(coantidomain(zero),X_38) != X_38
| codomain(multiplication(coantidomain(zero),X_38)) = codomain(X_38) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(multiplication(coantidomain(zero),X_38)),codomain(multiplication(coantidomain(zero),X_38))) ),[1,0],$fot(X_38)]]) ).
cnf(refute_0_126,plain,
( multiplication(coantidomain(zero),X_38) != X_38
| codomain(multiplication(coantidomain(zero),X_38)) = codomain(X_38) ),
inference(resolve,[$cnf( $equal(codomain(multiplication(coantidomain(zero),X_38)),codomain(multiplication(coantidomain(zero),X_38))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
codomain(multiplication(coantidomain(zero),X_38)) = codomain(X_38),
inference(resolve,[$cnf( $equal(multiplication(coantidomain(zero),X_38),X_38) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
( backward_diamond(X_38,one) != codomain(multiplication(coantidomain(zero),X_38))
| codomain(multiplication(coantidomain(zero),X_38)) != codomain(X_38)
| backward_diamond(X_38,one) = codomain(X_38) ),
introduced(tautology,[equality,[$cnf( ~ $equal(backward_diamond(X_38,one),codomain(X_38)) ),[0],$fot(codomain(multiplication(coantidomain(zero),X_38)))]]) ).
cnf(refute_0_129,plain,
( backward_diamond(X_38,one) != codomain(multiplication(coantidomain(zero),X_38))
| backward_diamond(X_38,one) = codomain(X_38) ),
inference(resolve,[$cnf( $equal(codomain(multiplication(coantidomain(zero),X_38)),codomain(X_38)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
backward_diamond(X_38,one) = codomain(X_38),
inference(resolve,[$cnf( $equal(backward_diamond(X_38,one),codomain(multiplication(coantidomain(zero),X_38))) )],[refute_0_115,refute_0_129]) ).
cnf(refute_0_131,plain,
backward_diamond(coantidomain(one),one) = codomain(coantidomain(one)),
inference(subst,[],[refute_0_130:[bind(X_38,$fot(coantidomain(one)))]]) ).
cnf(refute_0_132,plain,
( backward_diamond(coantidomain(one),one) != codomain(coantidomain(one))
| codomain(coantidomain(one)) != coantidomain(codomain(one))
| backward_diamond(coantidomain(one),one) = coantidomain(codomain(one)) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(backward_diamond(coantidomain(one),one))),bind(Y,$fot(codomain(coantidomain(one)))),bind(Z,$fot(coantidomain(codomain(one))))]]) ).
cnf(refute_0_133,plain,
( codomain(coantidomain(one)) != coantidomain(codomain(one))
| backward_diamond(coantidomain(one),one) = coantidomain(codomain(one)) ),
inference(resolve,[$cnf( $equal(backward_diamond(coantidomain(one),one),codomain(coantidomain(one))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
backward_diamond(coantidomain(one),one) = coantidomain(codomain(one)),
inference(resolve,[$cnf( $equal(codomain(coantidomain(one)),coantidomain(codomain(one))) )],[refute_0_111,refute_0_133]) ).
cnf(refute_0_135,plain,
( backward_diamond(coantidomain(one),one) != coantidomain(codomain(one))
| coantidomain(codomain(one)) != zero
| backward_diamond(coantidomain(one),one) = zero ),
inference(subst,[],[refute_0_25:[bind(X,$fot(backward_diamond(coantidomain(one),one))),bind(Y,$fot(coantidomain(codomain(one)))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_136,plain,
( coantidomain(codomain(one)) != zero
| backward_diamond(coantidomain(one),one) = zero ),
inference(resolve,[$cnf( $equal(backward_diamond(coantidomain(one),one),coantidomain(codomain(one))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
backward_diamond(coantidomain(one),one) = zero,
inference(resolve,[$cnf( $equal(coantidomain(codomain(one)),zero) )],[refute_0_103,refute_0_136]) ).
cnf(refute_0_138,plain,
( backward_diamond(coantidomain(one),one) != codomain(zero)
| backward_diamond(coantidomain(one),one) != zero
| zero = codomain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(backward_diamond(coantidomain(one),one),codomain(zero)) ),[0],$fot(zero)]]) ).
cnf(refute_0_139,plain,
( backward_diamond(coantidomain(one),one) != codomain(zero)
| zero = codomain(zero) ),
inference(resolve,[$cnf( $equal(backward_diamond(coantidomain(one),one),zero) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
zero = codomain(zero),
inference(resolve,[$cnf( $equal(backward_diamond(coantidomain(one),one),codomain(zero)) )],[refute_0_96,refute_0_139]) ).
cnf(refute_0_141,plain,
( zero != codomain(zero)
| codomain(zero) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(codomain(zero)))]]) ).
cnf(refute_0_142,plain,
codomain(zero) = zero,
inference(resolve,[$cnf( $equal(zero,codomain(zero)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
addition(codomain(zero),domain(skolemFOFtoCNF_X1)) = addition(codomain(zero),domain(skolemFOFtoCNF_X1)),
introduced(tautology,[refl,[$fot(addition(codomain(zero),domain(skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_144,plain,
( addition(codomain(zero),domain(skolemFOFtoCNF_X1)) != addition(codomain(zero),domain(skolemFOFtoCNF_X1))
| codomain(zero) != zero
| addition(codomain(zero),domain(skolemFOFtoCNF_X1)) = addition(zero,domain(skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(codomain(zero),domain(skolemFOFtoCNF_X1)),addition(codomain(zero),domain(skolemFOFtoCNF_X1))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_145,plain,
( codomain(zero) != zero
| addition(codomain(zero),domain(skolemFOFtoCNF_X1)) = addition(zero,domain(skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(addition(codomain(zero),domain(skolemFOFtoCNF_X1)),addition(codomain(zero),domain(skolemFOFtoCNF_X1))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
addition(codomain(zero),domain(skolemFOFtoCNF_X1)) = addition(zero,domain(skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(codomain(zero),zero) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
( addition(codomain(zero),domain(skolemFOFtoCNF_X1)) != addition(zero,domain(skolemFOFtoCNF_X1))
| addition(zero,domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
| addition(codomain(zero),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(addition(codomain(zero),domain(skolemFOFtoCNF_X1)))),bind(Y,$fot(addition(zero,domain(skolemFOFtoCNF_X1)))),bind(Z,$fot(domain(skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_148,plain,
( addition(zero,domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
| addition(codomain(zero),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(addition(codomain(zero),domain(skolemFOFtoCNF_X1)),addition(zero,domain(skolemFOFtoCNF_X1))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
addition(codomain(zero),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(addition(zero,domain(skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) )],[refute_0_37,refute_0_148]) ).
cnf(refute_0_150,plain,
( addition(codomain(zero),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
| domain(skolemFOFtoCNF_X1) != domain(skolemFOFtoCNF_X1)
| addition(codomain(zero),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(codomain(zero),domain(skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) ),[0],$fot(domain(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_151,plain,
( domain(skolemFOFtoCNF_X1) != domain(skolemFOFtoCNF_X1)
| addition(codomain(zero),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(addition(codomain(zero),domain(skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
domain(skolemFOFtoCNF_X1) != domain(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(addition(codomain(zero),domain(skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) )],[refute_0_151,refute_0_31]) ).
cnf(refute_0_153,plain,
domain(skolemFOFtoCNF_X1) = domain(skolemFOFtoCNF_X1),
introduced(tautology,[refl,[$fot(domain(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_154,plain,
$false,
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X1)) )],[refute_0_153,refute_0_152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE119+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 13:04:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43
% 0.20/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.45
%------------------------------------------------------------------------------