TSTP Solution File: KLE093+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE093+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 02:15:14 EDT 2022
% Result : Theorem 0.71s 0.88s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 58
% Syntax : Number of formulae : 283 ( 165 unt; 0 def)
% Number of atoms : 450 ( 437 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 339 ( 172 ~; 163 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 525 ( 6 sgn 67 !; 1 ?)
% 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_idempotence,axiom,
! [A] : addition(A,A) = A ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(star_unfold_left,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)) ).
fof(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ).
fof(goals,conjecture,
! [X0] : domain(star(X0)) = one ).
fof(subgoal_0,plain,
! [X0] : domain(star(X0)) = one,
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : domain(star(X0)) = one,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : domain(star(X0)) != one,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
domain(star(skolemFOFtoCNF_X0)) != one,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[domain5]) ).
fof(normalize_0_3,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[domain2]) ).
fof(normalize_0_5,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_7,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(canonicalize,[],[star_unfold_left]) ).
fof(normalize_0_9,plain,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_11,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_15,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_17,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_19,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_21,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_23,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_25,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X0] : addition(domain(X0),one) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_27,plain,
! [X0] : addition(domain(X0),one) = one,
inference(specialize,[],[normalize_0_26]) ).
cnf(refute_0_0,plain,
domain(star(skolemFOFtoCNF_X0)) != one,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
domain(addition(domain(X_21),X_29)) = addition(domain(domain(X_21)),domain(X_29)),
inference(subst,[],[refute_0_1:[bind(X0,$fot(domain(X_21))),bind(X1,$fot(X_29))]]) ).
cnf(refute_0_3,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
domain(multiplication(one,X_21)) = domain(multiplication(one,domain(X_21))),
inference(subst,[],[refute_0_3:[bind(X0,$fot(one)),bind(X1,$fot(X_21))]]) ).
cnf(refute_0_5,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
multiplication(one,domain(X_21)) = domain(X_21),
inference(subst,[],[refute_0_5:[bind(A,$fot(domain(X_21)))]]) ).
cnf(refute_0_7,plain,
( domain(multiplication(one,X_21)) != domain(multiplication(one,domain(X_21)))
| multiplication(one,domain(X_21)) != domain(X_21)
| domain(multiplication(one,X_21)) = domain(domain(X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_21)),domain(multiplication(one,domain(X_21)))) ),[1,0],$fot(domain(X_21))]]) ).
cnf(refute_0_8,plain,
( domain(multiplication(one,X_21)) != domain(multiplication(one,domain(X_21)))
| domain(multiplication(one,X_21)) = domain(domain(X_21)) ),
inference(resolve,[$cnf( $equal(multiplication(one,domain(X_21)),domain(X_21)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
domain(multiplication(one,X_21)) = domain(domain(X_21)),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_21)),domain(multiplication(one,domain(X_21)))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
multiplication(one,X_21) = X_21,
inference(subst,[],[refute_0_5:[bind(A,$fot(X_21))]]) ).
cnf(refute_0_11,plain,
domain(multiplication(one,X_21)) = domain(multiplication(one,X_21)),
introduced(tautology,[refl,[$fot(domain(multiplication(one,X_21)))]]) ).
cnf(refute_0_12,plain,
( domain(multiplication(one,X_21)) != domain(multiplication(one,X_21))
| multiplication(one,X_21) != X_21
| domain(multiplication(one,X_21)) = domain(X_21) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_21)),domain(multiplication(one,X_21))) ),[1,0],$fot(X_21)]]) ).
cnf(refute_0_13,plain,
( multiplication(one,X_21) != X_21
| domain(multiplication(one,X_21)) = domain(X_21) ),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_21)),domain(multiplication(one,X_21))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
domain(multiplication(one,X_21)) = domain(X_21),
inference(resolve,[$cnf( $equal(multiplication(one,X_21),X_21) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( domain(multiplication(one,X_21)) != domain(X_21)
| domain(multiplication(one,X_21)) != domain(domain(X_21))
| domain(X_21) = domain(domain(X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_21)),domain(domain(X_21))) ),[0],$fot(domain(X_21))]]) ).
cnf(refute_0_16,plain,
( domain(multiplication(one,X_21)) != domain(domain(X_21))
| domain(X_21) = domain(domain(X_21)) ),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_21)),domain(X_21)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
domain(X_21) = domain(domain(X_21)),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_21)),domain(domain(X_21))) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_19,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_20,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( domain(X_21) != domain(domain(X_21))
| domain(domain(X_21)) = domain(X_21) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(domain(X_21))),bind(Y,$fot(domain(domain(X_21))))]]) ).
cnf(refute_0_22,plain,
domain(domain(X_21)) = domain(X_21),
inference(resolve,[$cnf( $equal(domain(X_21),domain(domain(X_21))) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
( domain(addition(domain(X_21),X_29)) != addition(domain(domain(X_21)),domain(X_29))
| domain(domain(X_21)) != domain(X_21)
| domain(addition(domain(X_21),X_29)) = addition(domain(X_21),domain(X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(domain(X_21),X_29)),addition(domain(domain(X_21)),domain(X_29))) ),[1,0],$fot(domain(X_21))]]) ).
cnf(refute_0_24,plain,
( domain(addition(domain(X_21),X_29)) != addition(domain(domain(X_21)),domain(X_29))
| domain(addition(domain(X_21),X_29)) = addition(domain(X_21),domain(X_29)) ),
inference(resolve,[$cnf( $equal(domain(domain(X_21)),domain(X_21)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
domain(addition(domain(X_21),X_29)) = addition(domain(X_21),domain(X_29)),
inference(resolve,[$cnf( $equal(domain(addition(domain(X_21),X_29)),addition(domain(domain(X_21)),domain(X_29))) )],[refute_0_2,refute_0_24]) ).
cnf(refute_0_26,plain,
( domain(addition(X0,X1)) != addition(domain(X0),domain(X1))
| addition(domain(X0),domain(X1)) = domain(addition(X0,X1)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(domain(addition(X0,X1)))),bind(Y,$fot(addition(domain(X0),domain(X1))))]]) ).
cnf(refute_0_27,plain,
addition(domain(X0),domain(X1)) = domain(addition(X0,X1)),
inference(resolve,[$cnf( $equal(domain(addition(X0,X1)),addition(domain(X0),domain(X1))) )],[refute_0_1,refute_0_26]) ).
cnf(refute_0_28,plain,
addition(domain(X_21),domain(X_29)) = domain(addition(X_21,X_29)),
inference(subst,[],[refute_0_27:[bind(X0,$fot(X_21)),bind(X1,$fot(X_29))]]) ).
cnf(refute_0_29,plain,
( addition(domain(X_21),domain(X_29)) != domain(addition(X_21,X_29))
| domain(addition(domain(X_21),X_29)) != addition(domain(X_21),domain(X_29))
| domain(addition(domain(X_21),X_29)) = domain(addition(X_21,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(domain(X_21),X_29)),addition(domain(X_21),domain(X_29))) ),[1],$fot(domain(addition(X_21,X_29)))]]) ).
cnf(refute_0_30,plain,
( domain(addition(domain(X_21),X_29)) != addition(domain(X_21),domain(X_29))
| domain(addition(domain(X_21),X_29)) = domain(addition(X_21,X_29)) ),
inference(resolve,[$cnf( $equal(addition(domain(X_21),domain(X_29)),domain(addition(X_21,X_29))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
domain(addition(domain(X_21),X_29)) = domain(addition(X_21,X_29)),
inference(resolve,[$cnf( $equal(domain(addition(domain(X_21),X_29)),addition(domain(X_21),domain(X_29))) )],[refute_0_25,refute_0_30]) ).
cnf(refute_0_32,plain,
domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) = domain(addition(one,multiplication(star(X_105),addition(X_105,one)))),
inference(subst,[],[refute_0_31:[bind(X_21,$fot(one)),bind(X_29,$fot(multiplication(star(X_105),addition(X_105,one))))]]) ).
cnf(refute_0_33,plain,
leq(addition(one,multiplication(star(A),A)),star(A)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_34,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_35,plain,
( ~ leq(addition(one,multiplication(star(A),A)),star(A))
| addition(addition(one,multiplication(star(A),A)),star(A)) = star(A) ),
inference(subst,[],[refute_0_34:[bind(A,$fot(addition(one,multiplication(star(A),A)))),bind(B,$fot(star(A)))]]) ).
cnf(refute_0_36,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = star(A),
inference(resolve,[$cnf( leq(addition(one,multiplication(star(A),A)),star(A)) )],[refute_0_33,refute_0_35]) ).
cnf(refute_0_37,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_38,plain,
addition(X_34,addition(X_35,multiplication(X_35,X_14))) = addition(addition(X_34,X_35),multiplication(X_35,X_14)),
inference(subst,[],[refute_0_37:[bind(A,$fot(X_34)),bind(B,$fot(X_35)),bind(C,$fot(multiplication(X_35,X_14)))]]) ).
cnf(refute_0_39,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_40,plain,
multiplication(X_13,addition(X_14,one)) = addition(multiplication(X_13,X_14),multiplication(X_13,one)),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_13)),bind(B,$fot(X_14)),bind(C,$fot(one))]]) ).
cnf(refute_0_41,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_42,plain,
multiplication(X_13,one) = X_13,
inference(subst,[],[refute_0_41:[bind(A,$fot(X_13))]]) ).
cnf(refute_0_43,plain,
( multiplication(X_13,addition(X_14,one)) != addition(multiplication(X_13,X_14),multiplication(X_13,one))
| multiplication(X_13,one) != X_13
| multiplication(X_13,addition(X_14,one)) = addition(multiplication(X_13,X_14),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_13,addition(X_14,one)),addition(multiplication(X_13,X_14),multiplication(X_13,one))) ),[1,1],$fot(X_13)]]) ).
cnf(refute_0_44,plain,
( multiplication(X_13,addition(X_14,one)) != addition(multiplication(X_13,X_14),multiplication(X_13,one))
| multiplication(X_13,addition(X_14,one)) = addition(multiplication(X_13,X_14),X_13) ),
inference(resolve,[$cnf( $equal(multiplication(X_13,one),X_13) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
multiplication(X_13,addition(X_14,one)) = addition(multiplication(X_13,X_14),X_13),
inference(resolve,[$cnf( $equal(multiplication(X_13,addition(X_14,one)),addition(multiplication(X_13,X_14),multiplication(X_13,one))) )],[refute_0_40,refute_0_44]) ).
cnf(refute_0_46,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_47,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_48,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
addition(multiplication(X_13,X_14),X_13) = addition(X_13,multiplication(X_13,X_14)),
inference(subst,[],[refute_0_48:[bind(A,$fot(X_13)),bind(B,$fot(multiplication(X_13,X_14)))]]) ).
cnf(refute_0_50,plain,
( addition(multiplication(X_13,X_14),X_13) != addition(X_13,multiplication(X_13,X_14))
| multiplication(X_13,addition(X_14,one)) != addition(multiplication(X_13,X_14),X_13)
| multiplication(X_13,addition(X_14,one)) = addition(X_13,multiplication(X_13,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_13,addition(X_14,one)),addition(multiplication(X_13,X_14),X_13)) ),[1],$fot(addition(X_13,multiplication(X_13,X_14)))]]) ).
cnf(refute_0_51,plain,
( multiplication(X_13,addition(X_14,one)) != addition(multiplication(X_13,X_14),X_13)
| multiplication(X_13,addition(X_14,one)) = addition(X_13,multiplication(X_13,X_14)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_13,X_14),X_13),addition(X_13,multiplication(X_13,X_14))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
multiplication(X_13,addition(X_14,one)) = addition(X_13,multiplication(X_13,X_14)),
inference(resolve,[$cnf( $equal(multiplication(X_13,addition(X_14,one)),addition(multiplication(X_13,X_14),X_13)) )],[refute_0_45,refute_0_51]) ).
cnf(refute_0_53,plain,
multiplication(X_35,addition(X_14,one)) = addition(X_35,multiplication(X_35,X_14)),
inference(subst,[],[refute_0_52:[bind(X_13,$fot(X_35))]]) ).
cnf(refute_0_54,plain,
( multiplication(X_35,addition(X_14,one)) != addition(X_35,multiplication(X_35,X_14))
| addition(X_35,multiplication(X_35,X_14)) = multiplication(X_35,addition(X_14,one)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(multiplication(X_35,addition(X_14,one)))),bind(Y,$fot(addition(X_35,multiplication(X_35,X_14))))]]) ).
cnf(refute_0_55,plain,
addition(X_35,multiplication(X_35,X_14)) = multiplication(X_35,addition(X_14,one)),
inference(resolve,[$cnf( $equal(multiplication(X_35,addition(X_14,one)),addition(X_35,multiplication(X_35,X_14))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( addition(X_34,addition(X_35,multiplication(X_35,X_14))) != addition(addition(X_34,X_35),multiplication(X_35,X_14))
| addition(X_35,multiplication(X_35,X_14)) != multiplication(X_35,addition(X_14,one))
| addition(X_34,multiplication(X_35,addition(X_14,one))) = addition(addition(X_34,X_35),multiplication(X_35,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_34,addition(X_35,multiplication(X_35,X_14))),addition(addition(X_34,X_35),multiplication(X_35,X_14))) ),[0,1],$fot(multiplication(X_35,addition(X_14,one)))]]) ).
cnf(refute_0_57,plain,
( addition(X_34,addition(X_35,multiplication(X_35,X_14))) != addition(addition(X_34,X_35),multiplication(X_35,X_14))
| addition(X_34,multiplication(X_35,addition(X_14,one))) = addition(addition(X_34,X_35),multiplication(X_35,X_14)) ),
inference(resolve,[$cnf( $equal(addition(X_35,multiplication(X_35,X_14)),multiplication(X_35,addition(X_14,one))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
addition(X_34,multiplication(X_35,addition(X_14,one))) = addition(addition(X_34,X_35),multiplication(X_35,X_14)),
inference(resolve,[$cnf( $equal(addition(X_34,addition(X_35,multiplication(X_35,X_14))),addition(addition(X_34,X_35),multiplication(X_35,X_14))) )],[refute_0_38,refute_0_57]) ).
cnf(refute_0_59,plain,
( addition(A,addition(B,C)) != addition(addition(A,B),C)
| addition(addition(A,B),C) = addition(A,addition(B,C)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(A,addition(B,C)))),bind(Y,$fot(addition(addition(A,B),C)))]]) ).
cnf(refute_0_60,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,C)),addition(addition(A,B),C)) )],[refute_0_37,refute_0_59]) ).
cnf(refute_0_61,plain,
addition(addition(X_34,X_35),multiplication(X_35,X_14)) = addition(X_34,addition(X_35,multiplication(X_35,X_14))),
inference(subst,[],[refute_0_60:[bind(A,$fot(X_34)),bind(B,$fot(X_35)),bind(C,$fot(multiplication(X_35,X_14)))]]) ).
cnf(refute_0_62,plain,
( addition(X_34,multiplication(X_35,addition(X_14,one))) != addition(addition(X_34,X_35),multiplication(X_35,X_14))
| addition(addition(X_34,X_35),multiplication(X_35,X_14)) != addition(X_34,addition(X_35,multiplication(X_35,X_14)))
| addition(X_34,multiplication(X_35,addition(X_14,one))) = addition(X_34,addition(X_35,multiplication(X_35,X_14))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_34,multiplication(X_35,addition(X_14,one))),addition(X_34,addition(X_35,multiplication(X_35,X_14)))) ),[0],$fot(addition(addition(X_34,X_35),multiplication(X_35,X_14)))]]) ).
cnf(refute_0_63,plain,
( addition(X_34,multiplication(X_35,addition(X_14,one))) != addition(addition(X_34,X_35),multiplication(X_35,X_14))
| addition(X_34,multiplication(X_35,addition(X_14,one))) = addition(X_34,addition(X_35,multiplication(X_35,X_14))) ),
inference(resolve,[$cnf( $equal(addition(addition(X_34,X_35),multiplication(X_35,X_14)),addition(X_34,addition(X_35,multiplication(X_35,X_14)))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
addition(X_34,multiplication(X_35,addition(X_14,one))) = addition(X_34,addition(X_35,multiplication(X_35,X_14))),
inference(resolve,[$cnf( $equal(addition(X_34,multiplication(X_35,addition(X_14,one))),addition(addition(X_34,X_35),multiplication(X_35,X_14))) )],[refute_0_58,refute_0_63]) ).
cnf(refute_0_65,plain,
( addition(X_34,multiplication(X_35,addition(X_14,one))) != addition(X_34,addition(X_35,multiplication(X_35,X_14)))
| addition(X_34,addition(X_35,multiplication(X_35,X_14))) = addition(X_34,multiplication(X_35,addition(X_14,one))) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(X_34,multiplication(X_35,addition(X_14,one))))),bind(Y,$fot(addition(X_34,addition(X_35,multiplication(X_35,X_14)))))]]) ).
cnf(refute_0_66,plain,
addition(X_34,addition(X_35,multiplication(X_35,X_14))) = addition(X_34,multiplication(X_35,addition(X_14,one))),
inference(resolve,[$cnf( $equal(addition(X_34,multiplication(X_35,addition(X_14,one))),addition(X_34,addition(X_35,multiplication(X_35,X_14)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
addition(one,addition(star(A),multiplication(star(A),A))) = addition(one,multiplication(star(A),addition(A,one))),
inference(subst,[],[refute_0_66:[bind(X_14,$fot(A)),bind(X_34,$fot(one)),bind(X_35,$fot(star(A)))]]) ).
cnf(refute_0_68,plain,
addition(A,addition(B,addition(X_76,B))) = addition(addition(A,B),addition(X_76,B)),
inference(subst,[],[refute_0_37:[bind(C,$fot(addition(X_76,B)))]]) ).
cnf(refute_0_69,plain,
addition(addition(X_35,X_36),addition(X_35,X_36)) = addition(addition(addition(X_35,X_36),X_35),X_36),
inference(subst,[],[refute_0_37:[bind(A,$fot(addition(X_35,X_36))),bind(B,$fot(X_35)),bind(C,$fot(X_36))]]) ).
cnf(refute_0_70,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_71,plain,
addition(addition(X_35,X_36),addition(X_35,X_36)) = addition(X_35,X_36),
inference(subst,[],[refute_0_70:[bind(A,$fot(addition(X_35,X_36)))]]) ).
cnf(refute_0_72,plain,
( addition(addition(X_35,X_36),addition(X_35,X_36)) != addition(X_35,X_36)
| addition(addition(X_35,X_36),addition(X_35,X_36)) != addition(addition(addition(X_35,X_36),X_35),X_36)
| addition(X_35,X_36) = addition(addition(addition(X_35,X_36),X_35),X_36) ),
introduced(tautology,[equality,[$cnf( $equal(addition(addition(X_35,X_36),addition(X_35,X_36)),addition(addition(addition(X_35,X_36),X_35),X_36)) ),[0],$fot(addition(X_35,X_36))]]) ).
cnf(refute_0_73,plain,
( addition(addition(X_35,X_36),addition(X_35,X_36)) != addition(addition(addition(X_35,X_36),X_35),X_36)
| addition(X_35,X_36) = addition(addition(addition(X_35,X_36),X_35),X_36) ),
inference(resolve,[$cnf( $equal(addition(addition(X_35,X_36),addition(X_35,X_36)),addition(X_35,X_36)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
addition(X_35,X_36) = addition(addition(addition(X_35,X_36),X_35),X_36),
inference(resolve,[$cnf( $equal(addition(addition(X_35,X_36),addition(X_35,X_36)),addition(addition(addition(X_35,X_36),X_35),X_36)) )],[refute_0_69,refute_0_73]) ).
cnf(refute_0_75,plain,
addition(X_34,addition(X_35,X_36)) = addition(addition(X_34,X_35),X_36),
inference(subst,[],[refute_0_37:[bind(A,$fot(X_34)),bind(B,$fot(X_35)),bind(C,$fot(X_36))]]) ).
cnf(refute_0_76,plain,
addition(X_36,X_35) = addition(X_35,X_36),
inference(subst,[],[refute_0_46:[bind(A,$fot(X_36)),bind(B,$fot(X_35))]]) ).
cnf(refute_0_77,plain,
( addition(X_36,X_35) != addition(X_35,X_36)
| addition(X_35,X_36) = addition(X_36,X_35) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(X_36,X_35))),bind(Y,$fot(addition(X_35,X_36)))]]) ).
cnf(refute_0_78,plain,
addition(X_35,X_36) = addition(X_36,X_35),
inference(resolve,[$cnf( $equal(addition(X_36,X_35),addition(X_35,X_36)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( addition(X_34,addition(X_35,X_36)) != addition(addition(X_34,X_35),X_36)
| addition(X_35,X_36) != addition(X_36,X_35)
| addition(X_34,addition(X_36,X_35)) = addition(addition(X_34,X_35),X_36) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_34,addition(X_35,X_36)),addition(addition(X_34,X_35),X_36)) ),[0,1],$fot(addition(X_36,X_35))]]) ).
cnf(refute_0_80,plain,
( addition(X_34,addition(X_35,X_36)) != addition(addition(X_34,X_35),X_36)
| addition(X_34,addition(X_36,X_35)) = addition(addition(X_34,X_35),X_36) ),
inference(resolve,[$cnf( $equal(addition(X_35,X_36),addition(X_36,X_35)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
addition(X_34,addition(X_36,X_35)) = addition(addition(X_34,X_35),X_36),
inference(resolve,[$cnf( $equal(addition(X_34,addition(X_35,X_36)),addition(addition(X_34,X_35),X_36)) )],[refute_0_75,refute_0_80]) ).
cnf(refute_0_82,plain,
addition(addition(X_34,X_35),X_36) = addition(X_34,addition(X_35,X_36)),
inference(subst,[],[refute_0_60:[bind(A,$fot(X_34)),bind(B,$fot(X_35)),bind(C,$fot(X_36))]]) ).
cnf(refute_0_83,plain,
( addition(X_34,addition(X_36,X_35)) != addition(addition(X_34,X_35),X_36)
| addition(addition(X_34,X_35),X_36) != addition(X_34,addition(X_35,X_36))
| addition(X_34,addition(X_36,X_35)) = addition(X_34,addition(X_35,X_36)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_34,addition(X_36,X_35)),addition(X_34,addition(X_35,X_36))) ),[0],$fot(addition(addition(X_34,X_35),X_36))]]) ).
cnf(refute_0_84,plain,
( addition(X_34,addition(X_36,X_35)) != addition(addition(X_34,X_35),X_36)
| addition(X_34,addition(X_36,X_35)) = addition(X_34,addition(X_35,X_36)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_34,X_35),X_36),addition(X_34,addition(X_35,X_36))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
addition(X_34,addition(X_36,X_35)) = addition(X_34,addition(X_35,X_36)),
inference(resolve,[$cnf( $equal(addition(X_34,addition(X_36,X_35)),addition(addition(X_34,X_35),X_36)) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( addition(X_34,addition(X_36,X_35)) != addition(X_34,addition(X_35,X_36))
| addition(X_34,addition(X_35,X_36)) = addition(X_34,addition(X_36,X_35)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(X_34,addition(X_36,X_35)))),bind(Y,$fot(addition(X_34,addition(X_35,X_36))))]]) ).
cnf(refute_0_87,plain,
addition(X_34,addition(X_35,X_36)) = addition(X_34,addition(X_36,X_35)),
inference(resolve,[$cnf( $equal(addition(X_34,addition(X_36,X_35)),addition(X_34,addition(X_35,X_36))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
addition(X_36,addition(addition(X_35,X_36),X_35)) = addition(X_36,addition(X_35,addition(X_35,X_36))),
inference(subst,[],[refute_0_87:[bind(X_34,$fot(X_36)),bind(X_35,$fot(addition(X_35,X_36))),bind(X_36,$fot(X_35))]]) ).
cnf(refute_0_89,plain,
addition(A,addition(X_34,X_35)) = addition(addition(X_34,X_35),A),
inference(subst,[],[refute_0_46:[bind(B,$fot(addition(X_34,X_35)))]]) ).
cnf(refute_0_90,plain,
addition(X_34,addition(X_35,A)) = addition(addition(X_34,X_35),A),
inference(subst,[],[refute_0_37:[bind(A,$fot(X_34)),bind(B,$fot(X_35)),bind(C,$fot(A))]]) ).
cnf(refute_0_91,plain,
( addition(X_34,addition(X_35,A)) != addition(addition(X_34,X_35),A)
| addition(addition(X_34,X_35),A) = addition(X_34,addition(X_35,A)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(X_34,addition(X_35,A)))),bind(Y,$fot(addition(addition(X_34,X_35),A)))]]) ).
cnf(refute_0_92,plain,
addition(addition(X_34,X_35),A) = addition(X_34,addition(X_35,A)),
inference(resolve,[$cnf( $equal(addition(X_34,addition(X_35,A)),addition(addition(X_34,X_35),A)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( addition(A,addition(X_34,X_35)) != addition(addition(X_34,X_35),A)
| addition(addition(X_34,X_35),A) != addition(X_34,addition(X_35,A))
| addition(A,addition(X_34,X_35)) = addition(X_34,addition(X_35,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_34,X_35)),addition(X_34,addition(X_35,A))) ),[0],$fot(addition(addition(X_34,X_35),A))]]) ).
cnf(refute_0_94,plain,
( addition(A,addition(X_34,X_35)) != addition(addition(X_34,X_35),A)
| addition(A,addition(X_34,X_35)) = addition(X_34,addition(X_35,A)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_34,X_35),A),addition(X_34,addition(X_35,A))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
addition(A,addition(X_34,X_35)) = addition(X_34,addition(X_35,A)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_34,X_35)),addition(addition(X_34,X_35),A)) )],[refute_0_89,refute_0_94]) ).
cnf(refute_0_96,plain,
( addition(A,addition(X_34,X_35)) != addition(X_34,addition(X_35,A))
| addition(X_34,addition(X_35,A)) = addition(A,addition(X_34,X_35)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(A,addition(X_34,X_35)))),bind(Y,$fot(addition(X_34,addition(X_35,A))))]]) ).
cnf(refute_0_97,plain,
addition(X_34,addition(X_35,A)) = addition(A,addition(X_34,X_35)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_34,X_35)),addition(X_34,addition(X_35,A))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
addition(addition(X_35,X_36),addition(X_35,X_36)) = addition(X_36,addition(addition(X_35,X_36),X_35)),
inference(subst,[],[refute_0_97:[bind(A,$fot(X_36)),bind(X_34,$fot(addition(X_35,X_36)))]]) ).
cnf(refute_0_99,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_100,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_20,refute_0_99]) ).
cnf(refute_0_101,plain,
( addition(X_36,addition(addition(X_35,X_36),X_35)) != addition(X_36,addition(X_35,addition(X_35,X_36)))
| addition(addition(X_35,X_36),addition(X_35,X_36)) != addition(X_36,addition(addition(X_35,X_36),X_35))
| addition(addition(X_35,X_36),addition(X_35,X_36)) = addition(X_36,addition(X_35,addition(X_35,X_36))) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(addition(addition(X_35,X_36),addition(X_35,X_36)))),bind(Y,$fot(addition(X_36,addition(addition(X_35,X_36),X_35)))),bind(Z,$fot(addition(X_36,addition(X_35,addition(X_35,X_36)))))]]) ).
cnf(refute_0_102,plain,
( addition(X_36,addition(addition(X_35,X_36),X_35)) != addition(X_36,addition(X_35,addition(X_35,X_36)))
| addition(addition(X_35,X_36),addition(X_35,X_36)) = addition(X_36,addition(X_35,addition(X_35,X_36))) ),
inference(resolve,[$cnf( $equal(addition(addition(X_35,X_36),addition(X_35,X_36)),addition(X_36,addition(addition(X_35,X_36),X_35))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
addition(addition(X_35,X_36),addition(X_35,X_36)) = addition(X_36,addition(X_35,addition(X_35,X_36))),
inference(resolve,[$cnf( $equal(addition(X_36,addition(addition(X_35,X_36),X_35)),addition(X_36,addition(X_35,addition(X_35,X_36)))) )],[refute_0_88,refute_0_102]) ).
cnf(refute_0_104,plain,
addition(addition(addition(X_35,X_36),X_35),X_36) = addition(addition(X_35,X_36),addition(X_35,X_36)),
inference(subst,[],[refute_0_60:[bind(A,$fot(addition(X_35,X_36))),bind(B,$fot(X_35)),bind(C,$fot(X_36))]]) ).
cnf(refute_0_105,plain,
( addition(addition(X_35,X_36),addition(X_35,X_36)) != addition(X_36,addition(X_35,addition(X_35,X_36)))
| addition(addition(addition(X_35,X_36),X_35),X_36) != addition(addition(X_35,X_36),addition(X_35,X_36))
| addition(addition(addition(X_35,X_36),X_35),X_36) = addition(X_36,addition(X_35,addition(X_35,X_36))) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(addition(addition(addition(X_35,X_36),X_35),X_36))),bind(Y,$fot(addition(addition(X_35,X_36),addition(X_35,X_36)))),bind(Z,$fot(addition(X_36,addition(X_35,addition(X_35,X_36)))))]]) ).
cnf(refute_0_106,plain,
( addition(addition(X_35,X_36),addition(X_35,X_36)) != addition(X_36,addition(X_35,addition(X_35,X_36)))
| addition(addition(addition(X_35,X_36),X_35),X_36) = addition(X_36,addition(X_35,addition(X_35,X_36))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(X_35,X_36),X_35),X_36),addition(addition(X_35,X_36),addition(X_35,X_36))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
addition(addition(addition(X_35,X_36),X_35),X_36) = addition(X_36,addition(X_35,addition(X_35,X_36))),
inference(resolve,[$cnf( $equal(addition(addition(X_35,X_36),addition(X_35,X_36)),addition(X_36,addition(X_35,addition(X_35,X_36)))) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
( addition(X_35,X_36) != addition(addition(addition(X_35,X_36),X_35),X_36)
| addition(addition(addition(X_35,X_36),X_35),X_36) != addition(X_36,addition(X_35,addition(X_35,X_36)))
| addition(X_35,X_36) = addition(X_36,addition(X_35,addition(X_35,X_36))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_35,X_36),addition(X_36,addition(X_35,addition(X_35,X_36)))) ),[0],$fot(addition(addition(addition(X_35,X_36),X_35),X_36))]]) ).
cnf(refute_0_109,plain,
( addition(X_35,X_36) != addition(addition(addition(X_35,X_36),X_35),X_36)
| addition(X_35,X_36) = addition(X_36,addition(X_35,addition(X_35,X_36))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(X_35,X_36),X_35),X_36),addition(X_36,addition(X_35,addition(X_35,X_36)))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
addition(X_35,X_36) = addition(X_36,addition(X_35,addition(X_35,X_36))),
inference(resolve,[$cnf( $equal(addition(X_35,X_36),addition(addition(addition(X_35,X_36),X_35),X_36)) )],[refute_0_74,refute_0_109]) ).
cnf(refute_0_111,plain,
addition(X_35,addition(X_35,X_36)) = addition(addition(X_35,X_35),X_36),
inference(subst,[],[refute_0_37:[bind(A,$fot(X_35)),bind(B,$fot(X_35)),bind(C,$fot(X_36))]]) ).
cnf(refute_0_112,plain,
addition(X_35,X_35) = X_35,
inference(subst,[],[refute_0_70:[bind(A,$fot(X_35))]]) ).
cnf(refute_0_113,plain,
( addition(X_35,X_35) != X_35
| addition(X_35,addition(X_35,X_36)) != addition(addition(X_35,X_35),X_36)
| addition(X_35,addition(X_35,X_36)) = addition(X_35,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_35,addition(X_35,X_36)),addition(addition(X_35,X_35),X_36)) ),[1,0],$fot(X_35)]]) ).
cnf(refute_0_114,plain,
( addition(X_35,addition(X_35,X_36)) != addition(addition(X_35,X_35),X_36)
| addition(X_35,addition(X_35,X_36)) = addition(X_35,X_36) ),
inference(resolve,[$cnf( $equal(addition(X_35,X_35),X_35) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
addition(X_35,addition(X_35,X_36)) = addition(X_35,X_36),
inference(resolve,[$cnf( $equal(addition(X_35,addition(X_35,X_36)),addition(addition(X_35,X_35),X_36)) )],[refute_0_111,refute_0_114]) ).
cnf(refute_0_116,plain,
addition(X_36,addition(X_35,addition(X_35,X_36))) = addition(X_36,addition(X_35,addition(X_35,X_36))),
introduced(tautology,[refl,[$fot(addition(X_36,addition(X_35,addition(X_35,X_36))))]]) ).
cnf(refute_0_117,plain,
( addition(X_35,addition(X_35,X_36)) != addition(X_35,X_36)
| addition(X_36,addition(X_35,addition(X_35,X_36))) != addition(X_36,addition(X_35,addition(X_35,X_36)))
| addition(X_36,addition(X_35,addition(X_35,X_36))) = addition(X_36,addition(X_35,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_36,addition(X_35,addition(X_35,X_36))),addition(X_36,addition(X_35,addition(X_35,X_36)))) ),[1,1],$fot(addition(X_35,X_36))]]) ).
cnf(refute_0_118,plain,
( addition(X_35,addition(X_35,X_36)) != addition(X_35,X_36)
| addition(X_36,addition(X_35,addition(X_35,X_36))) = addition(X_36,addition(X_35,X_36)) ),
inference(resolve,[$cnf( $equal(addition(X_36,addition(X_35,addition(X_35,X_36))),addition(X_36,addition(X_35,addition(X_35,X_36)))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
addition(X_36,addition(X_35,addition(X_35,X_36))) = addition(X_36,addition(X_35,X_36)),
inference(resolve,[$cnf( $equal(addition(X_35,addition(X_35,X_36)),addition(X_35,X_36)) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
( addition(X_35,X_36) != addition(X_36,addition(X_35,addition(X_35,X_36)))
| addition(X_36,addition(X_35,addition(X_35,X_36))) != addition(X_36,addition(X_35,X_36))
| addition(X_35,X_36) = addition(X_36,addition(X_35,X_36)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_35,X_36),addition(X_36,addition(X_35,X_36))) ),[0],$fot(addition(X_36,addition(X_35,addition(X_35,X_36))))]]) ).
cnf(refute_0_121,plain,
( addition(X_35,X_36) != addition(X_36,addition(X_35,addition(X_35,X_36)))
| addition(X_35,X_36) = addition(X_36,addition(X_35,X_36)) ),
inference(resolve,[$cnf( $equal(addition(X_36,addition(X_35,addition(X_35,X_36))),addition(X_36,addition(X_35,X_36))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
addition(X_35,X_36) = addition(X_36,addition(X_35,X_36)),
inference(resolve,[$cnf( $equal(addition(X_35,X_36),addition(X_36,addition(X_35,addition(X_35,X_36)))) )],[refute_0_110,refute_0_121]) ).
cnf(refute_0_123,plain,
addition(X_76,B) = addition(B,addition(X_76,B)),
inference(subst,[],[refute_0_122:[bind(X_35,$fot(X_76)),bind(X_36,$fot(B))]]) ).
cnf(refute_0_124,plain,
( addition(X_76,B) != addition(B,addition(X_76,B))
| addition(B,addition(X_76,B)) = addition(X_76,B) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(X_76,B))),bind(Y,$fot(addition(B,addition(X_76,B))))]]) ).
cnf(refute_0_125,plain,
addition(B,addition(X_76,B)) = addition(X_76,B),
inference(resolve,[$cnf( $equal(addition(X_76,B),addition(B,addition(X_76,B))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
( addition(A,addition(B,addition(X_76,B))) != addition(addition(A,B),addition(X_76,B))
| addition(B,addition(X_76,B)) != addition(X_76,B)
| addition(A,addition(X_76,B)) = addition(addition(A,B),addition(X_76,B)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(B,addition(X_76,B))),addition(addition(A,B),addition(X_76,B))) ),[0,1],$fot(addition(X_76,B))]]) ).
cnf(refute_0_127,plain,
( addition(A,addition(B,addition(X_76,B))) != addition(addition(A,B),addition(X_76,B))
| addition(A,addition(X_76,B)) = addition(addition(A,B),addition(X_76,B)) ),
inference(resolve,[$cnf( $equal(addition(B,addition(X_76,B)),addition(X_76,B)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
addition(A,addition(X_76,B)) = addition(addition(A,B),addition(X_76,B)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,addition(X_76,B))),addition(addition(A,B),addition(X_76,B))) )],[refute_0_68,refute_0_127]) ).
cnf(refute_0_129,plain,
addition(A,addition(addition(X_76,A),C)) = addition(addition(A,addition(X_76,A)),C),
inference(subst,[],[refute_0_37:[bind(B,$fot(addition(X_76,A)))]]) ).
cnf(refute_0_130,plain,
addition(X_76,A) = addition(A,addition(X_76,A)),
inference(subst,[],[refute_0_122:[bind(X_35,$fot(X_76)),bind(X_36,$fot(A))]]) ).
cnf(refute_0_131,plain,
( addition(X_76,A) != addition(A,addition(X_76,A))
| addition(A,addition(X_76,A)) = addition(X_76,A) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(X_76,A))),bind(Y,$fot(addition(A,addition(X_76,A))))]]) ).
cnf(refute_0_132,plain,
addition(A,addition(X_76,A)) = addition(X_76,A),
inference(resolve,[$cnf( $equal(addition(X_76,A),addition(A,addition(X_76,A))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
( addition(A,addition(X_76,A)) != addition(X_76,A)
| addition(A,addition(addition(X_76,A),C)) != addition(addition(A,addition(X_76,A)),C)
| addition(A,addition(addition(X_76,A),C)) = addition(addition(X_76,A),C) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(addition(X_76,A),C)),addition(addition(A,addition(X_76,A)),C)) ),[1,0],$fot(addition(X_76,A))]]) ).
cnf(refute_0_134,plain,
( addition(A,addition(addition(X_76,A),C)) != addition(addition(A,addition(X_76,A)),C)
| addition(A,addition(addition(X_76,A),C)) = addition(addition(X_76,A),C) ),
inference(resolve,[$cnf( $equal(addition(A,addition(X_76,A)),addition(X_76,A)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
addition(A,addition(addition(X_76,A),C)) = addition(addition(X_76,A),C),
inference(resolve,[$cnf( $equal(addition(A,addition(addition(X_76,A),C)),addition(addition(A,addition(X_76,A)),C)) )],[refute_0_129,refute_0_134]) ).
cnf(refute_0_136,plain,
addition(addition(X_76,A),C) = addition(X_76,addition(A,C)),
inference(subst,[],[refute_0_60:[bind(A,$fot(X_76)),bind(B,$fot(A))]]) ).
cnf(refute_0_137,plain,
addition(A,addition(addition(X_76,A),C)) = addition(A,addition(addition(X_76,A),C)),
introduced(tautology,[refl,[$fot(addition(A,addition(addition(X_76,A),C)))]]) ).
cnf(refute_0_138,plain,
( addition(A,addition(addition(X_76,A),C)) != addition(A,addition(addition(X_76,A),C))
| addition(addition(X_76,A),C) != addition(X_76,addition(A,C))
| addition(A,addition(addition(X_76,A),C)) = addition(A,addition(X_76,addition(A,C))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(addition(X_76,A),C)),addition(A,addition(addition(X_76,A),C))) ),[1,1],$fot(addition(X_76,addition(A,C)))]]) ).
cnf(refute_0_139,plain,
( addition(addition(X_76,A),C) != addition(X_76,addition(A,C))
| addition(A,addition(addition(X_76,A),C)) = addition(A,addition(X_76,addition(A,C))) ),
inference(resolve,[$cnf( $equal(addition(A,addition(addition(X_76,A),C)),addition(A,addition(addition(X_76,A),C))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
addition(A,addition(addition(X_76,A),C)) = addition(A,addition(X_76,addition(A,C))),
inference(resolve,[$cnf( $equal(addition(addition(X_76,A),C),addition(X_76,addition(A,C))) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
( addition(A,addition(addition(X_76,A),C)) != addition(A,addition(X_76,addition(A,C)))
| addition(A,addition(addition(X_76,A),C)) != addition(addition(X_76,A),C)
| addition(A,addition(X_76,addition(A,C))) = addition(addition(X_76,A),C) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(addition(X_76,A),C)),addition(addition(X_76,A),C)) ),[0],$fot(addition(A,addition(X_76,addition(A,C))))]]) ).
cnf(refute_0_142,plain,
( addition(A,addition(addition(X_76,A),C)) != addition(addition(X_76,A),C)
| addition(A,addition(X_76,addition(A,C))) = addition(addition(X_76,A),C) ),
inference(resolve,[$cnf( $equal(addition(A,addition(addition(X_76,A),C)),addition(A,addition(X_76,addition(A,C)))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
( addition(A,addition(X_76,addition(A,C))) != addition(addition(X_76,A),C)
| addition(addition(X_76,A),C) != addition(X_76,addition(A,C))
| addition(A,addition(X_76,addition(A,C))) = addition(X_76,addition(A,C)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_76,addition(A,C))),addition(X_76,addition(A,C))) ),[0],$fot(addition(addition(X_76,A),C))]]) ).
cnf(refute_0_144,plain,
( addition(A,addition(X_76,addition(A,C))) != addition(addition(X_76,A),C)
| addition(A,addition(X_76,addition(A,C))) = addition(X_76,addition(A,C)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_76,A),C),addition(X_76,addition(A,C))) )],[refute_0_136,refute_0_143]) ).
cnf(refute_0_145,plain,
( addition(A,addition(addition(X_76,A),C)) != addition(addition(X_76,A),C)
| addition(A,addition(X_76,addition(A,C))) = addition(X_76,addition(A,C)) ),
inference(resolve,[$cnf( $equal(addition(A,addition(X_76,addition(A,C))),addition(addition(X_76,A),C)) )],[refute_0_142,refute_0_144]) ).
cnf(refute_0_146,plain,
addition(A,addition(X_76,addition(A,C))) = addition(X_76,addition(A,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(addition(X_76,A),C)),addition(addition(X_76,A),C)) )],[refute_0_135,refute_0_145]) ).
cnf(refute_0_147,plain,
addition(B,addition(A,addition(B,X_76))) = addition(A,addition(B,X_76)),
inference(subst,[],[refute_0_146:[bind(A,$fot(B)),bind(C,$fot(X_76)),bind(X_76,$fot(A))]]) ).
cnf(refute_0_148,plain,
addition(addition(A,B),X_76) = addition(A,addition(B,X_76)),
inference(subst,[],[refute_0_60:[bind(C,$fot(X_76))]]) ).
cnf(refute_0_149,plain,
addition(B,addition(addition(A,B),X_76)) = addition(B,addition(addition(A,B),X_76)),
introduced(tautology,[refl,[$fot(addition(B,addition(addition(A,B),X_76)))]]) ).
cnf(refute_0_150,plain,
( addition(B,addition(addition(A,B),X_76)) != addition(B,addition(addition(A,B),X_76))
| addition(addition(A,B),X_76) != addition(A,addition(B,X_76))
| addition(B,addition(addition(A,B),X_76)) = addition(B,addition(A,addition(B,X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(B,addition(addition(A,B),X_76)),addition(B,addition(addition(A,B),X_76))) ),[1,1],$fot(addition(A,addition(B,X_76)))]]) ).
cnf(refute_0_151,plain,
( addition(addition(A,B),X_76) != addition(A,addition(B,X_76))
| addition(B,addition(addition(A,B),X_76)) = addition(B,addition(A,addition(B,X_76))) ),
inference(resolve,[$cnf( $equal(addition(B,addition(addition(A,B),X_76)),addition(B,addition(addition(A,B),X_76))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
addition(B,addition(addition(A,B),X_76)) = addition(B,addition(A,addition(B,X_76))),
inference(resolve,[$cnf( $equal(addition(addition(A,B),X_76),addition(A,addition(B,X_76))) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
( addition(B,addition(A,addition(B,X_76))) != addition(A,addition(B,X_76))
| addition(B,addition(addition(A,B),X_76)) != addition(B,addition(A,addition(B,X_76)))
| addition(B,addition(addition(A,B),X_76)) = addition(A,addition(B,X_76)) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(addition(B,addition(addition(A,B),X_76)))),bind(Y,$fot(addition(B,addition(A,addition(B,X_76))))),bind(Z,$fot(addition(A,addition(B,X_76))))]]) ).
cnf(refute_0_154,plain,
( addition(B,addition(A,addition(B,X_76))) != addition(A,addition(B,X_76))
| addition(B,addition(addition(A,B),X_76)) = addition(A,addition(B,X_76)) ),
inference(resolve,[$cnf( $equal(addition(B,addition(addition(A,B),X_76)),addition(B,addition(A,addition(B,X_76)))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
addition(B,addition(addition(A,B),X_76)) = addition(A,addition(B,X_76)),
inference(resolve,[$cnf( $equal(addition(B,addition(A,addition(B,X_76))),addition(A,addition(B,X_76))) )],[refute_0_147,refute_0_154]) ).
cnf(refute_0_156,plain,
addition(X_35,X_34) = addition(X_34,X_35),
inference(subst,[],[refute_0_46:[bind(A,$fot(X_35)),bind(B,$fot(X_34))]]) ).
cnf(refute_0_157,plain,
( addition(X_35,X_34) != addition(X_34,X_35)
| addition(X_34,X_35) = addition(X_35,X_34) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(X_35,X_34))),bind(Y,$fot(addition(X_34,X_35)))]]) ).
cnf(refute_0_158,plain,
addition(X_34,X_35) = addition(X_35,X_34),
inference(resolve,[$cnf( $equal(addition(X_35,X_34),addition(X_34,X_35)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
( addition(X_34,X_35) != addition(X_35,X_34)
| addition(X_34,addition(X_35,X_36)) != addition(addition(X_34,X_35),X_36)
| addition(X_34,addition(X_35,X_36)) = addition(addition(X_35,X_34),X_36) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_34,addition(X_35,X_36)),addition(addition(X_34,X_35),X_36)) ),[1,0],$fot(addition(X_35,X_34))]]) ).
cnf(refute_0_160,plain,
( addition(X_34,addition(X_35,X_36)) != addition(addition(X_34,X_35),X_36)
| addition(X_34,addition(X_35,X_36)) = addition(addition(X_35,X_34),X_36) ),
inference(resolve,[$cnf( $equal(addition(X_34,X_35),addition(X_35,X_34)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
addition(X_34,addition(X_35,X_36)) = addition(addition(X_35,X_34),X_36),
inference(resolve,[$cnf( $equal(addition(X_34,addition(X_35,X_36)),addition(addition(X_34,X_35),X_36)) )],[refute_0_75,refute_0_160]) ).
cnf(refute_0_162,plain,
addition(addition(X_35,X_34),X_36) = addition(X_35,addition(X_34,X_36)),
inference(subst,[],[refute_0_60:[bind(A,$fot(X_35)),bind(B,$fot(X_34)),bind(C,$fot(X_36))]]) ).
cnf(refute_0_163,plain,
( addition(X_34,addition(X_35,X_36)) != addition(addition(X_35,X_34),X_36)
| addition(addition(X_35,X_34),X_36) != addition(X_35,addition(X_34,X_36))
| addition(X_34,addition(X_35,X_36)) = addition(X_35,addition(X_34,X_36)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_34,addition(X_35,X_36)),addition(X_35,addition(X_34,X_36))) ),[0],$fot(addition(addition(X_35,X_34),X_36))]]) ).
cnf(refute_0_164,plain,
( addition(X_34,addition(X_35,X_36)) != addition(addition(X_35,X_34),X_36)
| addition(X_34,addition(X_35,X_36)) = addition(X_35,addition(X_34,X_36)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_35,X_34),X_36),addition(X_35,addition(X_34,X_36))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
addition(X_34,addition(X_35,X_36)) = addition(X_35,addition(X_34,X_36)),
inference(resolve,[$cnf( $equal(addition(X_34,addition(X_35,X_36)),addition(addition(X_35,X_34),X_36)) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
addition(X_61,addition(X_62,X_63)) = addition(X_62,addition(X_61,X_63)),
inference(subst,[],[refute_0_165:[bind(X_34,$fot(X_61)),bind(X_35,$fot(X_62)),bind(X_36,$fot(X_63))]]) ).
cnf(refute_0_167,plain,
addition(X_63,X_62) = addition(X_62,X_63),
inference(subst,[],[refute_0_46:[bind(A,$fot(X_63)),bind(B,$fot(X_62))]]) ).
cnf(refute_0_168,plain,
( addition(X_63,X_62) != addition(X_62,X_63)
| addition(X_62,X_63) = addition(X_63,X_62) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(X_63,X_62))),bind(Y,$fot(addition(X_62,X_63)))]]) ).
cnf(refute_0_169,plain,
addition(X_62,X_63) = addition(X_63,X_62),
inference(resolve,[$cnf( $equal(addition(X_63,X_62),addition(X_62,X_63)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
( addition(X_61,addition(X_62,X_63)) != addition(X_62,addition(X_61,X_63))
| addition(X_62,X_63) != addition(X_63,X_62)
| addition(X_61,addition(X_63,X_62)) = addition(X_62,addition(X_61,X_63)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_61,addition(X_62,X_63)),addition(X_62,addition(X_61,X_63))) ),[0,1],$fot(addition(X_63,X_62))]]) ).
cnf(refute_0_171,plain,
( addition(X_61,addition(X_62,X_63)) != addition(X_62,addition(X_61,X_63))
| addition(X_61,addition(X_63,X_62)) = addition(X_62,addition(X_61,X_63)) ),
inference(resolve,[$cnf( $equal(addition(X_62,X_63),addition(X_63,X_62)) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
addition(X_61,addition(X_63,X_62)) = addition(X_62,addition(X_61,X_63)),
inference(resolve,[$cnf( $equal(addition(X_61,addition(X_62,X_63)),addition(X_62,addition(X_61,X_63))) )],[refute_0_166,refute_0_171]) ).
cnf(refute_0_173,plain,
addition(addition(A,B),addition(X_76,B)) = addition(B,addition(addition(A,B),X_76)),
inference(subst,[],[refute_0_172:[bind(X_61,$fot(addition(A,B))),bind(X_62,$fot(B)),bind(X_63,$fot(X_76))]]) ).
cnf(refute_0_174,plain,
( addition(B,addition(addition(A,B),X_76)) != addition(A,addition(B,X_76))
| addition(addition(A,B),addition(X_76,B)) != addition(B,addition(addition(A,B),X_76))
| addition(addition(A,B),addition(X_76,B)) = addition(A,addition(B,X_76)) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(addition(addition(A,B),addition(X_76,B)))),bind(Y,$fot(addition(B,addition(addition(A,B),X_76)))),bind(Z,$fot(addition(A,addition(B,X_76))))]]) ).
cnf(refute_0_175,plain,
( addition(B,addition(addition(A,B),X_76)) != addition(A,addition(B,X_76))
| addition(addition(A,B),addition(X_76,B)) = addition(A,addition(B,X_76)) ),
inference(resolve,[$cnf( $equal(addition(addition(A,B),addition(X_76,B)),addition(B,addition(addition(A,B),X_76))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
addition(addition(A,B),addition(X_76,B)) = addition(A,addition(B,X_76)),
inference(resolve,[$cnf( $equal(addition(B,addition(addition(A,B),X_76)),addition(A,addition(B,X_76))) )],[refute_0_155,refute_0_175]) ).
cnf(refute_0_177,plain,
( addition(A,addition(X_76,B)) != addition(addition(A,B),addition(X_76,B))
| addition(addition(A,B),addition(X_76,B)) != addition(A,addition(B,X_76))
| addition(A,addition(X_76,B)) = addition(A,addition(B,X_76)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_76,B)),addition(A,addition(B,X_76))) ),[0],$fot(addition(addition(A,B),addition(X_76,B)))]]) ).
cnf(refute_0_178,plain,
( addition(A,addition(X_76,B)) != addition(addition(A,B),addition(X_76,B))
| addition(A,addition(X_76,B)) = addition(A,addition(B,X_76)) ),
inference(resolve,[$cnf( $equal(addition(addition(A,B),addition(X_76,B)),addition(A,addition(B,X_76))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
addition(A,addition(X_76,B)) = addition(A,addition(B,X_76)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_76,B)),addition(addition(A,B),addition(X_76,B))) )],[refute_0_128,refute_0_178]) ).
cnf(refute_0_180,plain,
( addition(A,addition(X_76,B)) != addition(A,addition(B,X_76))
| addition(A,addition(B,X_76)) = addition(A,addition(X_76,B)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(A,addition(X_76,B)))),bind(Y,$fot(addition(A,addition(B,X_76))))]]) ).
cnf(refute_0_181,plain,
addition(A,addition(B,X_76)) = addition(A,addition(X_76,B)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_76,B)),addition(A,addition(B,X_76))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,addition(star(A),multiplication(star(A),A))),
inference(subst,[],[refute_0_181:[bind(A,$fot(one)),bind(B,$fot(multiplication(star(A),A))),bind(X_76,$fot(star(A)))]]) ).
cnf(refute_0_183,plain,
( addition(one,addition(multiplication(star(A),A),star(A))) != addition(one,addition(star(A),multiplication(star(A),A)))
| addition(one,addition(star(A),multiplication(star(A),A))) != addition(one,multiplication(star(A),addition(A,one)))
| addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,multiplication(star(A),addition(A,one))) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(addition(one,addition(multiplication(star(A),A),star(A))))),bind(Y,$fot(addition(one,addition(star(A),multiplication(star(A),A))))),bind(Z,$fot(addition(one,multiplication(star(A),addition(A,one)))))]]) ).
cnf(refute_0_184,plain,
( addition(one,addition(star(A),multiplication(star(A),A))) != addition(one,multiplication(star(A),addition(A,one)))
| addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,multiplication(star(A),addition(A,one))) ),
inference(resolve,[$cnf( $equal(addition(one,addition(multiplication(star(A),A),star(A))),addition(one,addition(star(A),multiplication(star(A),A)))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,multiplication(star(A),addition(A,one))),
inference(resolve,[$cnf( $equal(addition(one,addition(star(A),multiplication(star(A),A))),addition(one,multiplication(star(A),addition(A,one)))) )],[refute_0_67,refute_0_184]) ).
cnf(refute_0_186,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,addition(multiplication(star(A),A),star(A))),
inference(subst,[],[refute_0_60:[bind(A,$fot(one)),bind(B,$fot(multiplication(star(A),A))),bind(C,$fot(star(A)))]]) ).
cnf(refute_0_187,plain,
( addition(addition(one,multiplication(star(A),A)),star(A)) != addition(one,addition(multiplication(star(A),A),star(A)))
| addition(one,addition(multiplication(star(A),A),star(A))) != addition(one,multiplication(star(A),addition(A,one)))
| addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,multiplication(star(A),addition(A,one))) ),
inference(subst,[],[refute_0_100:[bind(X,$fot(addition(addition(one,multiplication(star(A),A)),star(A)))),bind(Y,$fot(addition(one,addition(multiplication(star(A),A),star(A))))),bind(Z,$fot(addition(one,multiplication(star(A),addition(A,one)))))]]) ).
cnf(refute_0_188,plain,
( addition(one,addition(multiplication(star(A),A),star(A))) != addition(one,multiplication(star(A),addition(A,one)))
| addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,multiplication(star(A),addition(A,one))) ),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),addition(one,addition(multiplication(star(A),A),star(A)))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,multiplication(star(A),addition(A,one))),
inference(resolve,[$cnf( $equal(addition(one,addition(multiplication(star(A),A),star(A))),addition(one,multiplication(star(A),addition(A,one)))) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
( addition(addition(one,multiplication(star(A),A)),star(A)) != addition(one,multiplication(star(A),addition(A,one)))
| addition(addition(one,multiplication(star(A),A)),star(A)) != star(A)
| addition(one,multiplication(star(A),addition(A,one))) = star(A) ),
introduced(tautology,[equality,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),star(A)) ),[0],$fot(addition(one,multiplication(star(A),addition(A,one))))]]) ).
cnf(refute_0_191,plain,
( addition(addition(one,multiplication(star(A),A)),star(A)) != star(A)
| addition(one,multiplication(star(A),addition(A,one))) = star(A) ),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),addition(one,multiplication(star(A),addition(A,one)))) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
addition(one,multiplication(star(A),addition(A,one))) = star(A),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),star(A)) )],[refute_0_36,refute_0_191]) ).
cnf(refute_0_193,plain,
addition(one,multiplication(star(X_105),addition(X_105,one))) = star(X_105),
inference(subst,[],[refute_0_192:[bind(A,$fot(X_105))]]) ).
cnf(refute_0_194,plain,
( addition(one,multiplication(star(X_105),addition(X_105,one))) != star(X_105)
| domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) != domain(addition(one,multiplication(star(X_105),addition(X_105,one))))
| domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) = domain(star(X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))),domain(addition(one,multiplication(star(X_105),addition(X_105,one))))) ),[1,0],$fot(star(X_105))]]) ).
cnf(refute_0_195,plain,
( domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) != domain(addition(one,multiplication(star(X_105),addition(X_105,one))))
| domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) = domain(star(X_105)) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(star(X_105),addition(X_105,one))),star(X_105)) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) = domain(star(X_105)),
inference(resolve,[$cnf( $equal(domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))),domain(addition(one,multiplication(star(X_105),addition(X_105,one))))) )],[refute_0_32,refute_0_195]) ).
cnf(refute_0_197,plain,
domain(addition(one,X_29)) = addition(domain(one),domain(X_29)),
inference(subst,[],[refute_0_1:[bind(X0,$fot(one)),bind(X1,$fot(X_29))]]) ).
cnf(refute_0_198,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_199,plain,
addition(one,multiplication(domain(one),one)) = multiplication(domain(one),one),
inference(subst,[],[refute_0_198:[bind(X0,$fot(one))]]) ).
cnf(refute_0_200,plain,
multiplication(domain(one),one) = domain(one),
inference(subst,[],[refute_0_41:[bind(A,$fot(domain(one)))]]) ).
cnf(refute_0_201,plain,
( addition(one,multiplication(domain(one),one)) != multiplication(domain(one),one)
| multiplication(domain(one),one) != domain(one)
| addition(one,domain(one)) = multiplication(domain(one),one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,multiplication(domain(one),one)),multiplication(domain(one),one)) ),[0,1],$fot(domain(one))]]) ).
cnf(refute_0_202,plain,
( addition(one,multiplication(domain(one),one)) != multiplication(domain(one),one)
| addition(one,domain(one)) = multiplication(domain(one),one) ),
inference(resolve,[$cnf( $equal(multiplication(domain(one),one),domain(one)) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(resolve,[$cnf( $equal(addition(one,multiplication(domain(one),one)),multiplication(domain(one),one)) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
addition(domain(X0),one) = one,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_205,plain,
addition(domain(X0),one) = addition(one,domain(X0)),
inference(subst,[],[refute_0_48:[bind(A,$fot(one)),bind(B,$fot(domain(X0)))]]) ).
cnf(refute_0_206,plain,
( addition(domain(X0),one) != addition(one,domain(X0))
| addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X0),one),one) ),[0],$fot(addition(one,domain(X0)))]]) ).
cnf(refute_0_207,plain,
( addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X0),one),addition(one,domain(X0))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
addition(one,domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(domain(X0),one),one) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
addition(one,domain(one)) = one,
inference(subst,[],[refute_0_208:[bind(X0,$fot(one))]]) ).
cnf(refute_0_210,plain,
( addition(one,domain(one)) != multiplication(domain(one),one)
| addition(one,domain(one)) != one
| one = multiplication(domain(one),one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,domain(one)),multiplication(domain(one),one)) ),[0],$fot(one)]]) ).
cnf(refute_0_211,plain,
( addition(one,domain(one)) != multiplication(domain(one),one)
| one = multiplication(domain(one),one) ),
inference(resolve,[$cnf( $equal(addition(one,domain(one)),one) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
( multiplication(domain(one),one) != domain(one)
| one != multiplication(domain(one),one)
| one = domain(one) ),
introduced(tautology,[equality,[$cnf( $equal(one,multiplication(domain(one),one)) ),[1],$fot(domain(one))]]) ).
cnf(refute_0_213,plain,
( one != multiplication(domain(one),one)
| one = domain(one) ),
inference(resolve,[$cnf( $equal(multiplication(domain(one),one),domain(one)) )],[refute_0_200,refute_0_212]) ).
cnf(refute_0_214,plain,
( addition(one,domain(one)) != multiplication(domain(one),one)
| one = domain(one) ),
inference(resolve,[$cnf( $equal(one,multiplication(domain(one),one)) )],[refute_0_211,refute_0_213]) ).
cnf(refute_0_215,plain,
one = domain(one),
inference(resolve,[$cnf( $equal(addition(one,domain(one)),multiplication(domain(one),one)) )],[refute_0_203,refute_0_214]) ).
cnf(refute_0_216,plain,
( one != domain(one)
| domain(one) = one ),
inference(subst,[],[refute_0_20:[bind(X,$fot(one)),bind(Y,$fot(domain(one)))]]) ).
cnf(refute_0_217,plain,
domain(one) = one,
inference(resolve,[$cnf( $equal(one,domain(one)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
( domain(addition(one,X_29)) != addition(domain(one),domain(X_29))
| domain(one) != one
| domain(addition(one,X_29)) = addition(one,domain(X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(one,X_29)),addition(domain(one),domain(X_29))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_219,plain,
( domain(addition(one,X_29)) != addition(domain(one),domain(X_29))
| domain(addition(one,X_29)) = addition(one,domain(X_29)) ),
inference(resolve,[$cnf( $equal(domain(one),one) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
domain(addition(one,X_29)) = addition(one,domain(X_29)),
inference(resolve,[$cnf( $equal(domain(addition(one,X_29)),addition(domain(one),domain(X_29))) )],[refute_0_197,refute_0_219]) ).
cnf(refute_0_221,plain,
addition(one,domain(X_29)) = one,
inference(subst,[],[refute_0_208:[bind(X0,$fot(X_29))]]) ).
cnf(refute_0_222,plain,
( addition(one,domain(X_29)) != one
| domain(addition(one,X_29)) != addition(one,domain(X_29))
| domain(addition(one,X_29)) = one ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(one,X_29)),addition(one,domain(X_29))) ),[1],$fot(one)]]) ).
cnf(refute_0_223,plain,
( domain(addition(one,X_29)) != addition(one,domain(X_29))
| domain(addition(one,X_29)) = one ),
inference(resolve,[$cnf( $equal(addition(one,domain(X_29)),one) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
domain(addition(one,X_29)) = one,
inference(resolve,[$cnf( $equal(domain(addition(one,X_29)),addition(one,domain(X_29))) )],[refute_0_220,refute_0_223]) ).
cnf(refute_0_225,plain,
domain(addition(one,multiplication(star(X_105),addition(X_105,one)))) = one,
inference(subst,[],[refute_0_224:[bind(X_29,$fot(multiplication(star(X_105),addition(X_105,one))))]]) ).
cnf(refute_0_226,plain,
( domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) != domain(addition(one,multiplication(star(X_105),addition(X_105,one))))
| domain(addition(one,multiplication(star(X_105),addition(X_105,one)))) != one
| domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) = one ),
inference(subst,[],[refute_0_100:[bind(X,$fot(domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))))),bind(Y,$fot(domain(addition(one,multiplication(star(X_105),addition(X_105,one)))))),bind(Z,$fot(one))]]) ).
cnf(refute_0_227,plain,
( domain(addition(one,multiplication(star(X_105),addition(X_105,one)))) != one
| domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) = one ),
inference(resolve,[$cnf( $equal(domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))),domain(addition(one,multiplication(star(X_105),addition(X_105,one))))) )],[refute_0_32,refute_0_226]) ).
cnf(refute_0_228,plain,
domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) = one,
inference(resolve,[$cnf( $equal(domain(addition(one,multiplication(star(X_105),addition(X_105,one)))),one) )],[refute_0_225,refute_0_227]) ).
cnf(refute_0_229,plain,
( domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) != domain(star(X_105))
| domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) != one
| one = domain(star(X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))),domain(star(X_105))) ),[0],$fot(one)]]) ).
cnf(refute_0_230,plain,
( domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))) != domain(star(X_105))
| one = domain(star(X_105)) ),
inference(resolve,[$cnf( $equal(domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))),one) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
one = domain(star(X_105)),
inference(resolve,[$cnf( $equal(domain(addition(domain(one),multiplication(star(X_105),addition(X_105,one)))),domain(star(X_105))) )],[refute_0_196,refute_0_230]) ).
cnf(refute_0_232,plain,
( one != domain(star(X_105))
| domain(star(X_105)) = one ),
inference(subst,[],[refute_0_20:[bind(X,$fot(one)),bind(Y,$fot(domain(star(X_105))))]]) ).
cnf(refute_0_233,plain,
domain(star(X_105)) = one,
inference(resolve,[$cnf( $equal(one,domain(star(X_105))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
domain(star(skolemFOFtoCNF_X0)) = one,
inference(subst,[],[refute_0_233:[bind(X_105,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_235,plain,
( domain(star(skolemFOFtoCNF_X0)) != one
| one != one
| domain(star(skolemFOFtoCNF_X0)) = one ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(star(skolemFOFtoCNF_X0)),one) ),[0],$fot(one)]]) ).
cnf(refute_0_236,plain,
( one != one
| domain(star(skolemFOFtoCNF_X0)) = one ),
inference(resolve,[$cnf( $equal(domain(star(skolemFOFtoCNF_X0)),one) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
one != one,
inference(resolve,[$cnf( $equal(domain(star(skolemFOFtoCNF_X0)),one) )],[refute_0_236,refute_0_0]) ).
cnf(refute_0_238,plain,
one = one,
introduced(tautology,[refl,[$fot(one)]]) ).
cnf(refute_0_239,plain,
$false,
inference(resolve,[$cnf( $equal(one,one) )],[refute_0_238,refute_0_237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE093+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 12:51:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.71/0.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.71/0.88
% 0.71/0.88 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.74/0.90
%------------------------------------------------------------------------------