TSTP Solution File: KLE037+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE037+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 02:14:50 EDT 2022
% Result : Theorem 0.40s 0.61s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 42
% Syntax : Number of formulae : 224 ( 127 unt; 0 def)
% Number of atoms : 361 ( 330 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 278 ( 141 ~; 133 |; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 533 ( 2 sgn 48 !; 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(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(goals,conjecture,
! [X0] : leq(one,star(X0)) ).
fof(subgoal_0,plain,
! [X0] : leq(one,star(X0)),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : leq(one,star(X0)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : ~ leq(one,star(X0)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ leq(one,star(skolemFOFtoCNF_X0)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_3,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_7,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_9,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(canonicalize,[],[star_unfold_left]) ).
fof(normalize_0_11,plain,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_13,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_14,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_16,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_18,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_17]) ).
cnf(refute_0_0,plain,
~ leq(one,star(skolemFOFtoCNF_X0)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( addition(X_39,addition(X_39,X_13)) != addition(X_39,X_13)
| leq(X_39,addition(X_39,X_13)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_39)),bind(B,$fot(addition(X_39,X_13)))]]) ).
cnf(refute_0_3,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
addition(X_12,addition(X_12,X_13)) = addition(addition(X_12,X_12),X_13),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_12)),bind(B,$fot(X_12)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_5,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
addition(X_12,X_12) = X_12,
inference(subst,[],[refute_0_5:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_7,plain,
( addition(X_12,X_12) != X_12
| addition(X_12,addition(X_12,X_13)) != addition(addition(X_12,X_12),X_13)
| addition(X_12,addition(X_12,X_13)) = addition(X_12,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_12,addition(X_12,X_13)),addition(addition(X_12,X_12),X_13)) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_8,plain,
( addition(X_12,addition(X_12,X_13)) != addition(addition(X_12,X_12),X_13)
| addition(X_12,addition(X_12,X_13)) = addition(X_12,X_13) ),
inference(resolve,[$cnf( $equal(addition(X_12,X_12),X_12) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
addition(X_12,addition(X_12,X_13)) = addition(X_12,X_13),
inference(resolve,[$cnf( $equal(addition(X_12,addition(X_12,X_13)),addition(addition(X_12,X_12),X_13)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
addition(X_39,addition(X_39,X_13)) = addition(X_39,X_13),
inference(subst,[],[refute_0_9:[bind(X_12,$fot(X_39))]]) ).
cnf(refute_0_11,plain,
( addition(X_39,X_13) != addition(X_39,X_13)
| addition(X_39,addition(X_39,X_13)) != addition(X_39,X_13)
| addition(X_39,addition(X_39,X_13)) = addition(X_39,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_39,addition(X_39,X_13)),addition(X_39,X_13)) ),[0,1],$fot(addition(X_39,X_13))]]) ).
cnf(refute_0_12,plain,
( addition(X_39,X_13) != addition(X_39,X_13)
| addition(X_39,addition(X_39,X_13)) = addition(X_39,X_13) ),
inference(resolve,[$cnf( $equal(addition(X_39,addition(X_39,X_13)),addition(X_39,X_13)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( addition(X_39,X_13) != addition(X_39,X_13)
| leq(X_39,addition(X_39,X_13)) ),
inference(resolve,[$cnf( $equal(addition(X_39,addition(X_39,X_13)),addition(X_39,X_13)) )],[refute_0_12,refute_0_2]) ).
cnf(refute_0_14,plain,
addition(X_39,X_13) = addition(X_39,X_13),
introduced(tautology,[refl,[$fot(addition(X_39,X_13))]]) ).
cnf(refute_0_15,plain,
leq(X_39,addition(X_39,X_13)),
inference(resolve,[$cnf( $equal(addition(X_39,X_13),addition(X_39,X_13)) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
leq(one,addition(one,multiplication(star(X_54),addition(one,X_54)))),
inference(subst,[],[refute_0_15:[bind(X_13,$fot(multiplication(star(X_54),addition(one,X_54)))),bind(X_39,$fot(one))]]) ).
cnf(refute_0_17,plain,
leq(addition(one,multiplication(star(A),A)),star(A)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_18,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_19,plain,
( ~ leq(addition(one,multiplication(star(A),A)),star(A))
| addition(addition(one,multiplication(star(A),A)),star(A)) = star(A) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(addition(one,multiplication(star(A),A)))),bind(B,$fot(star(A)))]]) ).
cnf(refute_0_20,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = star(A),
inference(resolve,[$cnf( leq(addition(one,multiplication(star(A),A)),star(A)) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
addition(A,addition(B,multiplication(B,X_28))) = addition(addition(A,B),multiplication(B,X_28)),
inference(subst,[],[refute_0_3:[bind(C,$fot(multiplication(B,X_28)))]]) ).
cnf(refute_0_22,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_23,plain,
multiplication(X_22,addition(one,X_24)) = addition(multiplication(X_22,one),multiplication(X_22,X_24)),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_22)),bind(B,$fot(one)),bind(C,$fot(X_24))]]) ).
cnf(refute_0_24,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_25,plain,
multiplication(X_22,one) = X_22,
inference(subst,[],[refute_0_24:[bind(A,$fot(X_22))]]) ).
cnf(refute_0_26,plain,
( multiplication(X_22,addition(one,X_24)) != addition(multiplication(X_22,one),multiplication(X_22,X_24))
| multiplication(X_22,one) != X_22
| multiplication(X_22,addition(one,X_24)) = addition(X_22,multiplication(X_22,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_22,addition(one,X_24)),addition(multiplication(X_22,one),multiplication(X_22,X_24))) ),[1,0],$fot(X_22)]]) ).
cnf(refute_0_27,plain,
( multiplication(X_22,addition(one,X_24)) != addition(multiplication(X_22,one),multiplication(X_22,X_24))
| multiplication(X_22,addition(one,X_24)) = addition(X_22,multiplication(X_22,X_24)) ),
inference(resolve,[$cnf( $equal(multiplication(X_22,one),X_22) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiplication(X_22,addition(one,X_24)) = addition(X_22,multiplication(X_22,X_24)),
inference(resolve,[$cnf( $equal(multiplication(X_22,addition(one,X_24)),addition(multiplication(X_22,one),multiplication(X_22,X_24))) )],[refute_0_23,refute_0_27]) ).
cnf(refute_0_29,plain,
multiplication(B,addition(one,X_28)) = addition(B,multiplication(B,X_28)),
inference(subst,[],[refute_0_28:[bind(X_22,$fot(B)),bind(X_24,$fot(X_28))]]) ).
cnf(refute_0_30,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_31,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_32,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( multiplication(B,addition(one,X_28)) != addition(B,multiplication(B,X_28))
| addition(B,multiplication(B,X_28)) = multiplication(B,addition(one,X_28)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(multiplication(B,addition(one,X_28)))),bind(Y,$fot(addition(B,multiplication(B,X_28))))]]) ).
cnf(refute_0_34,plain,
addition(B,multiplication(B,X_28)) = multiplication(B,addition(one,X_28)),
inference(resolve,[$cnf( $equal(multiplication(B,addition(one,X_28)),addition(B,multiplication(B,X_28))) )],[refute_0_29,refute_0_33]) ).
cnf(refute_0_35,plain,
( addition(A,addition(B,multiplication(B,X_28))) != addition(addition(A,B),multiplication(B,X_28))
| addition(B,multiplication(B,X_28)) != multiplication(B,addition(one,X_28))
| addition(A,multiplication(B,addition(one,X_28))) = addition(addition(A,B),multiplication(B,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(B,multiplication(B,X_28))),addition(addition(A,B),multiplication(B,X_28))) ),[0,1],$fot(multiplication(B,addition(one,X_28)))]]) ).
cnf(refute_0_36,plain,
( addition(A,addition(B,multiplication(B,X_28))) != addition(addition(A,B),multiplication(B,X_28))
| addition(A,multiplication(B,addition(one,X_28))) = addition(addition(A,B),multiplication(B,X_28)) ),
inference(resolve,[$cnf( $equal(addition(B,multiplication(B,X_28)),multiplication(B,addition(one,X_28))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
addition(A,multiplication(B,addition(one,X_28))) = addition(addition(A,B),multiplication(B,X_28)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,multiplication(B,X_28))),addition(addition(A,B),multiplication(B,X_28))) )],[refute_0_21,refute_0_36]) ).
cnf(refute_0_38,plain,
( addition(A,addition(B,C)) != addition(addition(A,B),C)
| addition(addition(A,B),C) = addition(A,addition(B,C)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(addition(A,addition(B,C)))),bind(Y,$fot(addition(addition(A,B),C)))]]) ).
cnf(refute_0_39,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,C)),addition(addition(A,B),C)) )],[refute_0_3,refute_0_38]) ).
cnf(refute_0_40,plain,
addition(addition(A,B),multiplication(B,X_28)) = addition(A,addition(B,multiplication(B,X_28))),
inference(subst,[],[refute_0_39:[bind(C,$fot(multiplication(B,X_28)))]]) ).
cnf(refute_0_41,plain,
( addition(A,multiplication(B,addition(one,X_28))) != addition(addition(A,B),multiplication(B,X_28))
| addition(addition(A,B),multiplication(B,X_28)) != addition(A,addition(B,multiplication(B,X_28)))
| addition(A,multiplication(B,addition(one,X_28))) = addition(A,addition(B,multiplication(B,X_28))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,multiplication(B,addition(one,X_28))),addition(A,addition(B,multiplication(B,X_28)))) ),[0],$fot(addition(addition(A,B),multiplication(B,X_28)))]]) ).
cnf(refute_0_42,plain,
( addition(A,multiplication(B,addition(one,X_28))) != addition(addition(A,B),multiplication(B,X_28))
| addition(A,multiplication(B,addition(one,X_28))) = addition(A,addition(B,multiplication(B,X_28))) ),
inference(resolve,[$cnf( $equal(addition(addition(A,B),multiplication(B,X_28)),addition(A,addition(B,multiplication(B,X_28)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
addition(A,multiplication(B,addition(one,X_28))) = addition(A,addition(B,multiplication(B,X_28))),
inference(resolve,[$cnf( $equal(addition(A,multiplication(B,addition(one,X_28))),addition(addition(A,B),multiplication(B,X_28))) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
( addition(A,multiplication(B,addition(one,X_28))) != addition(A,addition(B,multiplication(B,X_28)))
| addition(A,addition(B,multiplication(B,X_28))) = addition(A,multiplication(B,addition(one,X_28))) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(addition(A,multiplication(B,addition(one,X_28))))),bind(Y,$fot(addition(A,addition(B,multiplication(B,X_28)))))]]) ).
cnf(refute_0_45,plain,
addition(A,addition(B,multiplication(B,X_28))) = addition(A,multiplication(B,addition(one,X_28))),
inference(resolve,[$cnf( $equal(addition(A,multiplication(B,addition(one,X_28))),addition(A,addition(B,multiplication(B,X_28)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
addition(one,addition(star(A),multiplication(star(A),A))) = addition(one,multiplication(star(A),addition(one,A))),
inference(subst,[],[refute_0_45:[bind(A,$fot(one)),bind(B,$fot(star(A))),bind(X_28,$fot(A))]]) ).
cnf(refute_0_47,plain,
addition(addition(X_12,X_13),addition(X_12,X_13)) = addition(addition(addition(X_12,X_13),X_12),X_13),
inference(subst,[],[refute_0_3:[bind(A,$fot(addition(X_12,X_13))),bind(B,$fot(X_12)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_48,plain,
addition(addition(X_12,X_13),addition(X_12,X_13)) = addition(X_12,X_13),
inference(subst,[],[refute_0_5:[bind(A,$fot(addition(X_12,X_13)))]]) ).
cnf(refute_0_49,plain,
( addition(addition(X_12,X_13),addition(X_12,X_13)) != addition(X_12,X_13)
| addition(addition(X_12,X_13),addition(X_12,X_13)) != addition(addition(addition(X_12,X_13),X_12),X_13)
| addition(X_12,X_13) = addition(addition(addition(X_12,X_13),X_12),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(addition(addition(X_12,X_13),addition(X_12,X_13)),addition(addition(addition(X_12,X_13),X_12),X_13)) ),[0],$fot(addition(X_12,X_13))]]) ).
cnf(refute_0_50,plain,
( addition(addition(X_12,X_13),addition(X_12,X_13)) != addition(addition(addition(X_12,X_13),X_12),X_13)
| addition(X_12,X_13) = addition(addition(addition(X_12,X_13),X_12),X_13) ),
inference(resolve,[$cnf( $equal(addition(addition(X_12,X_13),addition(X_12,X_13)),addition(X_12,X_13)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
addition(X_12,X_13) = addition(addition(addition(X_12,X_13),X_12),X_13),
inference(resolve,[$cnf( $equal(addition(addition(X_12,X_13),addition(X_12,X_13)),addition(addition(addition(X_12,X_13),X_12),X_13)) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
addition(X_11,addition(X_12,X_13)) = addition(addition(X_11,X_12),X_13),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_11)),bind(B,$fot(X_12)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_53,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_54,plain,
addition(X_13,X_12) = addition(X_12,X_13),
inference(subst,[],[refute_0_53:[bind(A,$fot(X_13)),bind(B,$fot(X_12))]]) ).
cnf(refute_0_55,plain,
( addition(X_13,X_12) != addition(X_12,X_13)
| addition(X_12,X_13) = addition(X_13,X_12) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(addition(X_13,X_12))),bind(Y,$fot(addition(X_12,X_13)))]]) ).
cnf(refute_0_56,plain,
addition(X_12,X_13) = addition(X_13,X_12),
inference(resolve,[$cnf( $equal(addition(X_13,X_12),addition(X_12,X_13)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( addition(X_11,addition(X_12,X_13)) != addition(addition(X_11,X_12),X_13)
| addition(X_12,X_13) != addition(X_13,X_12)
| addition(X_11,addition(X_13,X_12)) = addition(addition(X_11,X_12),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_11,addition(X_12,X_13)),addition(addition(X_11,X_12),X_13)) ),[0,1],$fot(addition(X_13,X_12))]]) ).
cnf(refute_0_58,plain,
( addition(X_11,addition(X_12,X_13)) != addition(addition(X_11,X_12),X_13)
| addition(X_11,addition(X_13,X_12)) = addition(addition(X_11,X_12),X_13) ),
inference(resolve,[$cnf( $equal(addition(X_12,X_13),addition(X_13,X_12)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
addition(X_11,addition(X_13,X_12)) = addition(addition(X_11,X_12),X_13),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_12,X_13)),addition(addition(X_11,X_12),X_13)) )],[refute_0_52,refute_0_58]) ).
cnf(refute_0_60,plain,
addition(addition(X_11,X_12),X_13) = addition(X_11,addition(X_12,X_13)),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_11)),bind(B,$fot(X_12)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_61,plain,
( addition(X_11,addition(X_13,X_12)) != addition(addition(X_11,X_12),X_13)
| addition(addition(X_11,X_12),X_13) != addition(X_11,addition(X_12,X_13))
| addition(X_11,addition(X_13,X_12)) = addition(X_11,addition(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_11,addition(X_13,X_12)),addition(X_11,addition(X_12,X_13))) ),[0],$fot(addition(addition(X_11,X_12),X_13))]]) ).
cnf(refute_0_62,plain,
( addition(X_11,addition(X_13,X_12)) != addition(addition(X_11,X_12),X_13)
| addition(X_11,addition(X_13,X_12)) = addition(X_11,addition(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_11,X_12),X_13),addition(X_11,addition(X_12,X_13))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
addition(X_11,addition(X_13,X_12)) = addition(X_11,addition(X_12,X_13)),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_13,X_12)),addition(addition(X_11,X_12),X_13)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( addition(X_11,addition(X_13,X_12)) != addition(X_11,addition(X_12,X_13))
| addition(X_11,addition(X_12,X_13)) = addition(X_11,addition(X_13,X_12)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(addition(X_11,addition(X_13,X_12)))),bind(Y,$fot(addition(X_11,addition(X_12,X_13))))]]) ).
cnf(refute_0_65,plain,
addition(X_11,addition(X_12,X_13)) = addition(X_11,addition(X_13,X_12)),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_13,X_12)),addition(X_11,addition(X_12,X_13))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
addition(X_13,addition(addition(X_12,X_13),X_12)) = addition(X_13,addition(X_12,addition(X_12,X_13))),
inference(subst,[],[refute_0_65:[bind(X_11,$fot(X_13)),bind(X_12,$fot(addition(X_12,X_13))),bind(X_13,$fot(X_12))]]) ).
cnf(refute_0_67,plain,
addition(A,addition(X_11,X_12)) = addition(addition(X_11,X_12),A),
inference(subst,[],[refute_0_53:[bind(B,$fot(addition(X_11,X_12)))]]) ).
cnf(refute_0_68,plain,
addition(X_11,addition(X_12,A)) = addition(addition(X_11,X_12),A),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_11)),bind(B,$fot(X_12)),bind(C,$fot(A))]]) ).
cnf(refute_0_69,plain,
( addition(X_11,addition(X_12,A)) != addition(addition(X_11,X_12),A)
| addition(addition(X_11,X_12),A) = addition(X_11,addition(X_12,A)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(addition(X_11,addition(X_12,A)))),bind(Y,$fot(addition(addition(X_11,X_12),A)))]]) ).
cnf(refute_0_70,plain,
addition(addition(X_11,X_12),A) = addition(X_11,addition(X_12,A)),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_12,A)),addition(addition(X_11,X_12),A)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( addition(A,addition(X_11,X_12)) != addition(addition(X_11,X_12),A)
| addition(addition(X_11,X_12),A) != addition(X_11,addition(X_12,A))
| addition(A,addition(X_11,X_12)) = addition(X_11,addition(X_12,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_11,X_12)),addition(X_11,addition(X_12,A))) ),[0],$fot(addition(addition(X_11,X_12),A))]]) ).
cnf(refute_0_72,plain,
( addition(A,addition(X_11,X_12)) != addition(addition(X_11,X_12),A)
| addition(A,addition(X_11,X_12)) = addition(X_11,addition(X_12,A)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_11,X_12),A),addition(X_11,addition(X_12,A))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
addition(A,addition(X_11,X_12)) = addition(X_11,addition(X_12,A)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_11,X_12)),addition(addition(X_11,X_12),A)) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
( addition(A,addition(X_11,X_12)) != addition(X_11,addition(X_12,A))
| addition(X_11,addition(X_12,A)) = addition(A,addition(X_11,X_12)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(addition(A,addition(X_11,X_12)))),bind(Y,$fot(addition(X_11,addition(X_12,A))))]]) ).
cnf(refute_0_75,plain,
addition(X_11,addition(X_12,A)) = addition(A,addition(X_11,X_12)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_11,X_12)),addition(X_11,addition(X_12,A))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
addition(addition(X_12,X_13),addition(X_12,X_13)) = addition(X_13,addition(addition(X_12,X_13),X_12)),
inference(subst,[],[refute_0_75:[bind(A,$fot(X_13)),bind(X_11,$fot(addition(X_12,X_13)))]]) ).
cnf(refute_0_77,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_78,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_32,refute_0_77]) ).
cnf(refute_0_79,plain,
( addition(X_13,addition(addition(X_12,X_13),X_12)) != addition(X_13,addition(X_12,addition(X_12,X_13)))
| addition(addition(X_12,X_13),addition(X_12,X_13)) != addition(X_13,addition(addition(X_12,X_13),X_12))
| addition(addition(X_12,X_13),addition(X_12,X_13)) = addition(X_13,addition(X_12,addition(X_12,X_13))) ),
inference(subst,[],[refute_0_78:[bind(X,$fot(addition(addition(X_12,X_13),addition(X_12,X_13)))),bind(Y,$fot(addition(X_13,addition(addition(X_12,X_13),X_12)))),bind(Z,$fot(addition(X_13,addition(X_12,addition(X_12,X_13)))))]]) ).
cnf(refute_0_80,plain,
( addition(X_13,addition(addition(X_12,X_13),X_12)) != addition(X_13,addition(X_12,addition(X_12,X_13)))
| addition(addition(X_12,X_13),addition(X_12,X_13)) = addition(X_13,addition(X_12,addition(X_12,X_13))) ),
inference(resolve,[$cnf( $equal(addition(addition(X_12,X_13),addition(X_12,X_13)),addition(X_13,addition(addition(X_12,X_13),X_12))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
addition(addition(X_12,X_13),addition(X_12,X_13)) = addition(X_13,addition(X_12,addition(X_12,X_13))),
inference(resolve,[$cnf( $equal(addition(X_13,addition(addition(X_12,X_13),X_12)),addition(X_13,addition(X_12,addition(X_12,X_13)))) )],[refute_0_66,refute_0_80]) ).
cnf(refute_0_82,plain,
addition(addition(addition(X_12,X_13),X_12),X_13) = addition(addition(X_12,X_13),addition(X_12,X_13)),
inference(subst,[],[refute_0_39:[bind(A,$fot(addition(X_12,X_13))),bind(B,$fot(X_12)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_83,plain,
( addition(addition(X_12,X_13),addition(X_12,X_13)) != addition(X_13,addition(X_12,addition(X_12,X_13)))
| addition(addition(addition(X_12,X_13),X_12),X_13) != addition(addition(X_12,X_13),addition(X_12,X_13))
| addition(addition(addition(X_12,X_13),X_12),X_13) = addition(X_13,addition(X_12,addition(X_12,X_13))) ),
inference(subst,[],[refute_0_78:[bind(X,$fot(addition(addition(addition(X_12,X_13),X_12),X_13))),bind(Y,$fot(addition(addition(X_12,X_13),addition(X_12,X_13)))),bind(Z,$fot(addition(X_13,addition(X_12,addition(X_12,X_13)))))]]) ).
cnf(refute_0_84,plain,
( addition(addition(X_12,X_13),addition(X_12,X_13)) != addition(X_13,addition(X_12,addition(X_12,X_13)))
| addition(addition(addition(X_12,X_13),X_12),X_13) = addition(X_13,addition(X_12,addition(X_12,X_13))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(X_12,X_13),X_12),X_13),addition(addition(X_12,X_13),addition(X_12,X_13))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
addition(addition(addition(X_12,X_13),X_12),X_13) = addition(X_13,addition(X_12,addition(X_12,X_13))),
inference(resolve,[$cnf( $equal(addition(addition(X_12,X_13),addition(X_12,X_13)),addition(X_13,addition(X_12,addition(X_12,X_13)))) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( addition(X_12,X_13) != addition(addition(addition(X_12,X_13),X_12),X_13)
| addition(addition(addition(X_12,X_13),X_12),X_13) != addition(X_13,addition(X_12,addition(X_12,X_13)))
| addition(X_12,X_13) = addition(X_13,addition(X_12,addition(X_12,X_13))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_12,X_13),addition(X_13,addition(X_12,addition(X_12,X_13)))) ),[0],$fot(addition(addition(addition(X_12,X_13),X_12),X_13))]]) ).
cnf(refute_0_87,plain,
( addition(X_12,X_13) != addition(addition(addition(X_12,X_13),X_12),X_13)
| addition(X_12,X_13) = addition(X_13,addition(X_12,addition(X_12,X_13))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(X_12,X_13),X_12),X_13),addition(X_13,addition(X_12,addition(X_12,X_13)))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
addition(X_12,X_13) = addition(X_13,addition(X_12,addition(X_12,X_13))),
inference(resolve,[$cnf( $equal(addition(X_12,X_13),addition(addition(addition(X_12,X_13),X_12),X_13)) )],[refute_0_51,refute_0_87]) ).
cnf(refute_0_89,plain,
addition(X_13,addition(X_12,addition(X_12,X_13))) = addition(X_13,addition(X_12,addition(X_12,X_13))),
introduced(tautology,[refl,[$fot(addition(X_13,addition(X_12,addition(X_12,X_13))))]]) ).
cnf(refute_0_90,plain,
( addition(X_12,addition(X_12,X_13)) != addition(X_12,X_13)
| addition(X_13,addition(X_12,addition(X_12,X_13))) != addition(X_13,addition(X_12,addition(X_12,X_13)))
| addition(X_13,addition(X_12,addition(X_12,X_13))) = addition(X_13,addition(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_13,addition(X_12,addition(X_12,X_13))),addition(X_13,addition(X_12,addition(X_12,X_13)))) ),[1,1],$fot(addition(X_12,X_13))]]) ).
cnf(refute_0_91,plain,
( addition(X_12,addition(X_12,X_13)) != addition(X_12,X_13)
| addition(X_13,addition(X_12,addition(X_12,X_13))) = addition(X_13,addition(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(addition(X_13,addition(X_12,addition(X_12,X_13))),addition(X_13,addition(X_12,addition(X_12,X_13)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
addition(X_13,addition(X_12,addition(X_12,X_13))) = addition(X_13,addition(X_12,X_13)),
inference(resolve,[$cnf( $equal(addition(X_12,addition(X_12,X_13)),addition(X_12,X_13)) )],[refute_0_9,refute_0_91]) ).
cnf(refute_0_93,plain,
( addition(X_12,X_13) != addition(X_13,addition(X_12,addition(X_12,X_13)))
| addition(X_13,addition(X_12,addition(X_12,X_13))) != addition(X_13,addition(X_12,X_13))
| addition(X_12,X_13) = addition(X_13,addition(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_12,X_13),addition(X_13,addition(X_12,X_13))) ),[0],$fot(addition(X_13,addition(X_12,addition(X_12,X_13))))]]) ).
cnf(refute_0_94,plain,
( addition(X_12,X_13) != addition(X_13,addition(X_12,addition(X_12,X_13)))
| addition(X_12,X_13) = addition(X_13,addition(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(addition(X_13,addition(X_12,addition(X_12,X_13))),addition(X_13,addition(X_12,X_13))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
addition(X_12,X_13) = addition(X_13,addition(X_12,X_13)),
inference(resolve,[$cnf( $equal(addition(X_12,X_13),addition(X_13,addition(X_12,addition(X_12,X_13)))) )],[refute_0_88,refute_0_94]) ).
cnf(refute_0_96,plain,
addition(X_32,addition(X_11,X_13)) = addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))),
inference(subst,[],[refute_0_95:[bind(X_12,$fot(X_32)),bind(X_13,$fot(addition(X_11,X_13)))]]) ).
cnf(refute_0_97,plain,
addition(X_12,X_11) = addition(X_11,X_12),
inference(subst,[],[refute_0_53:[bind(A,$fot(X_12)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_98,plain,
( addition(X_12,X_11) != addition(X_11,X_12)
| addition(X_11,X_12) = addition(X_12,X_11) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(addition(X_12,X_11))),bind(Y,$fot(addition(X_11,X_12)))]]) ).
cnf(refute_0_99,plain,
addition(X_11,X_12) = addition(X_12,X_11),
inference(resolve,[$cnf( $equal(addition(X_12,X_11),addition(X_11,X_12)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( addition(X_11,X_12) != addition(X_12,X_11)
| addition(X_11,addition(X_12,X_13)) != addition(addition(X_11,X_12),X_13)
| addition(X_11,addition(X_12,X_13)) = addition(addition(X_12,X_11),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_11,addition(X_12,X_13)),addition(addition(X_11,X_12),X_13)) ),[1,0],$fot(addition(X_12,X_11))]]) ).
cnf(refute_0_101,plain,
( addition(X_11,addition(X_12,X_13)) != addition(addition(X_11,X_12),X_13)
| addition(X_11,addition(X_12,X_13)) = addition(addition(X_12,X_11),X_13) ),
inference(resolve,[$cnf( $equal(addition(X_11,X_12),addition(X_12,X_11)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
addition(X_11,addition(X_12,X_13)) = addition(addition(X_12,X_11),X_13),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_12,X_13)),addition(addition(X_11,X_12),X_13)) )],[refute_0_52,refute_0_101]) ).
cnf(refute_0_103,plain,
addition(addition(X_12,X_11),X_13) = addition(X_12,addition(X_11,X_13)),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_12)),bind(B,$fot(X_11)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_104,plain,
( addition(X_11,addition(X_12,X_13)) != addition(addition(X_12,X_11),X_13)
| addition(addition(X_12,X_11),X_13) != addition(X_12,addition(X_11,X_13))
| addition(X_11,addition(X_12,X_13)) = addition(X_12,addition(X_11,X_13)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_11,addition(X_12,X_13)),addition(X_12,addition(X_11,X_13))) ),[0],$fot(addition(addition(X_12,X_11),X_13))]]) ).
cnf(refute_0_105,plain,
( addition(X_11,addition(X_12,X_13)) != addition(addition(X_12,X_11),X_13)
| addition(X_11,addition(X_12,X_13)) = addition(X_12,addition(X_11,X_13)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_12,X_11),X_13),addition(X_12,addition(X_11,X_13))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
addition(X_11,addition(X_12,X_13)) = addition(X_12,addition(X_11,X_13)),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_12,X_13)),addition(addition(X_12,X_11),X_13)) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
addition(X_11,addition(X_32,X_13)) = addition(X_32,addition(X_11,X_13)),
inference(subst,[],[refute_0_106:[bind(X_12,$fot(X_32))]]) ).
cnf(refute_0_108,plain,
( addition(X_11,addition(X_32,X_13)) != addition(X_32,addition(X_11,X_13))
| addition(X_32,addition(X_11,X_13)) = addition(X_11,addition(X_32,X_13)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(addition(X_11,addition(X_32,X_13)))),bind(Y,$fot(addition(X_32,addition(X_11,X_13))))]]) ).
cnf(refute_0_109,plain,
addition(X_32,addition(X_11,X_13)) = addition(X_11,addition(X_32,X_13)),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_32,X_13)),addition(X_32,addition(X_11,X_13))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
( addition(X_32,addition(X_11,X_13)) != addition(X_11,addition(X_32,X_13))
| addition(X_32,addition(X_11,X_13)) != addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13)))
| addition(X_11,addition(X_32,X_13)) = addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_32,addition(X_11,X_13)),addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13)))) ),[0],$fot(addition(X_11,addition(X_32,X_13)))]]) ).
cnf(refute_0_111,plain,
( addition(X_32,addition(X_11,X_13)) != addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13)))
| addition(X_11,addition(X_32,X_13)) = addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) ),
inference(resolve,[$cnf( $equal(addition(X_32,addition(X_11,X_13)),addition(X_11,addition(X_32,X_13))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
addition(X_11,addition(X_32,X_13)) = addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))),
inference(resolve,[$cnf( $equal(addition(X_32,addition(X_11,X_13)),addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13)))) )],[refute_0_96,refute_0_111]) ).
cnf(refute_0_113,plain,
addition(A,addition(B,addition(B,X_15))) = addition(addition(A,B),addition(B,X_15)),
inference(subst,[],[refute_0_3:[bind(C,$fot(addition(B,X_15)))]]) ).
cnf(refute_0_114,plain,
addition(B,addition(B,X_15)) = addition(B,X_15),
inference(subst,[],[refute_0_9:[bind(X_12,$fot(B)),bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_115,plain,
( addition(A,addition(B,addition(B,X_15))) != addition(addition(A,B),addition(B,X_15))
| addition(B,addition(B,X_15)) != addition(B,X_15)
| addition(A,addition(B,X_15)) = addition(addition(A,B),addition(B,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(B,addition(B,X_15))),addition(addition(A,B),addition(B,X_15))) ),[0,1],$fot(addition(B,X_15))]]) ).
cnf(refute_0_116,plain,
( addition(A,addition(B,addition(B,X_15))) != addition(addition(A,B),addition(B,X_15))
| addition(A,addition(B,X_15)) = addition(addition(A,B),addition(B,X_15)) ),
inference(resolve,[$cnf( $equal(addition(B,addition(B,X_15)),addition(B,X_15)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
addition(A,addition(B,X_15)) = addition(addition(A,B),addition(B,X_15)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,addition(B,X_15))),addition(addition(A,B),addition(B,X_15))) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
addition(addition(A,B),X_15) = addition(A,addition(B,X_15)),
inference(subst,[],[refute_0_39:[bind(C,$fot(X_15))]]) ).
cnf(refute_0_119,plain,
addition(B,addition(addition(A,B),X_15)) = addition(B,addition(addition(A,B),X_15)),
introduced(tautology,[refl,[$fot(addition(B,addition(addition(A,B),X_15)))]]) ).
cnf(refute_0_120,plain,
( addition(B,addition(addition(A,B),X_15)) != addition(B,addition(addition(A,B),X_15))
| addition(addition(A,B),X_15) != addition(A,addition(B,X_15))
| addition(B,addition(addition(A,B),X_15)) = addition(B,addition(A,addition(B,X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(B,addition(addition(A,B),X_15)),addition(B,addition(addition(A,B),X_15))) ),[1,1],$fot(addition(A,addition(B,X_15)))]]) ).
cnf(refute_0_121,plain,
( addition(addition(A,B),X_15) != addition(A,addition(B,X_15))
| addition(B,addition(addition(A,B),X_15)) = addition(B,addition(A,addition(B,X_15))) ),
inference(resolve,[$cnf( $equal(addition(B,addition(addition(A,B),X_15)),addition(B,addition(addition(A,B),X_15))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
addition(B,addition(addition(A,B),X_15)) = addition(B,addition(A,addition(B,X_15))),
inference(resolve,[$cnf( $equal(addition(addition(A,B),X_15),addition(A,addition(B,X_15))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
( addition(X_11,addition(X_12,X_13)) != addition(X_12,addition(X_11,X_13))
| addition(X_12,addition(X_11,X_13)) = addition(X_11,addition(X_12,X_13)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(addition(X_11,addition(X_12,X_13)))),bind(Y,$fot(addition(X_12,addition(X_11,X_13))))]]) ).
cnf(refute_0_124,plain,
addition(X_12,addition(X_11,X_13)) = addition(X_11,addition(X_12,X_13)),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_12,X_13)),addition(X_12,addition(X_11,X_13))) )],[refute_0_106,refute_0_123]) ).
cnf(refute_0_125,plain,
addition(addition(A,B),addition(B,X_15)) = addition(B,addition(addition(A,B),X_15)),
inference(subst,[],[refute_0_124:[bind(X_11,$fot(B)),bind(X_12,$fot(addition(A,B))),bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_126,plain,
( addition(B,addition(addition(A,B),X_15)) != addition(B,addition(A,addition(B,X_15)))
| addition(addition(A,B),addition(B,X_15)) != addition(B,addition(addition(A,B),X_15))
| addition(addition(A,B),addition(B,X_15)) = addition(B,addition(A,addition(B,X_15))) ),
inference(subst,[],[refute_0_78:[bind(X,$fot(addition(addition(A,B),addition(B,X_15)))),bind(Y,$fot(addition(B,addition(addition(A,B),X_15)))),bind(Z,$fot(addition(B,addition(A,addition(B,X_15)))))]]) ).
cnf(refute_0_127,plain,
( addition(B,addition(addition(A,B),X_15)) != addition(B,addition(A,addition(B,X_15)))
| addition(addition(A,B),addition(B,X_15)) = addition(B,addition(A,addition(B,X_15))) ),
inference(resolve,[$cnf( $equal(addition(addition(A,B),addition(B,X_15)),addition(B,addition(addition(A,B),X_15))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
addition(addition(A,B),addition(B,X_15)) = addition(B,addition(A,addition(B,X_15))),
inference(resolve,[$cnf( $equal(addition(B,addition(addition(A,B),X_15)),addition(B,addition(A,addition(B,X_15)))) )],[refute_0_122,refute_0_127]) ).
cnf(refute_0_129,plain,
( addition(A,addition(B,X_15)) != addition(addition(A,B),addition(B,X_15))
| addition(addition(A,B),addition(B,X_15)) != addition(B,addition(A,addition(B,X_15)))
| addition(A,addition(B,X_15)) = addition(B,addition(A,addition(B,X_15))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(B,X_15)),addition(B,addition(A,addition(B,X_15)))) ),[0],$fot(addition(addition(A,B),addition(B,X_15)))]]) ).
cnf(refute_0_130,plain,
( addition(A,addition(B,X_15)) != addition(addition(A,B),addition(B,X_15))
| addition(A,addition(B,X_15)) = addition(B,addition(A,addition(B,X_15))) ),
inference(resolve,[$cnf( $equal(addition(addition(A,B),addition(B,X_15)),addition(B,addition(A,addition(B,X_15)))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
addition(A,addition(B,X_15)) = addition(B,addition(A,addition(B,X_15))),
inference(resolve,[$cnf( $equal(addition(A,addition(B,X_15)),addition(addition(A,B),addition(B,X_15))) )],[refute_0_117,refute_0_130]) ).
cnf(refute_0_132,plain,
( addition(A,addition(B,X_15)) != addition(B,addition(A,addition(B,X_15)))
| addition(B,addition(A,addition(B,X_15))) = addition(A,addition(B,X_15)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(addition(A,addition(B,X_15)))),bind(Y,$fot(addition(B,addition(A,addition(B,X_15)))))]]) ).
cnf(refute_0_133,plain,
addition(B,addition(A,addition(B,X_15))) = addition(A,addition(B,X_15)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,X_15)),addition(B,addition(A,addition(B,X_15)))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
addition(X_13,addition(X_11,addition(X_13,X_32))) = addition(X_11,addition(X_13,X_32)),
inference(subst,[],[refute_0_133:[bind(A,$fot(X_11)),bind(B,$fot(X_13)),bind(X_15,$fot(X_32))]]) ).
cnf(refute_0_135,plain,
addition(X_11,addition(X_11,addition(X_13,X_32))) = addition(X_11,addition(X_13,X_32)),
inference(subst,[],[refute_0_9:[bind(X_12,$fot(X_11)),bind(X_13,$fot(addition(X_13,X_32)))]]) ).
cnf(refute_0_136,plain,
addition(addition(X_11,X_13),X_32) = addition(X_11,addition(X_13,X_32)),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_11)),bind(B,$fot(X_13)),bind(C,$fot(X_32))]]) ).
cnf(refute_0_137,plain,
addition(X_11,addition(addition(X_11,X_13),X_32)) = addition(X_11,addition(addition(X_11,X_13),X_32)),
introduced(tautology,[refl,[$fot(addition(X_11,addition(addition(X_11,X_13),X_32)))]]) ).
cnf(refute_0_138,plain,
( addition(X_11,addition(addition(X_11,X_13),X_32)) != addition(X_11,addition(addition(X_11,X_13),X_32))
| addition(addition(X_11,X_13),X_32) != addition(X_11,addition(X_13,X_32))
| addition(X_11,addition(addition(X_11,X_13),X_32)) = addition(X_11,addition(X_11,addition(X_13,X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_11,addition(addition(X_11,X_13),X_32)),addition(X_11,addition(addition(X_11,X_13),X_32))) ),[1,1],$fot(addition(X_11,addition(X_13,X_32)))]]) ).
cnf(refute_0_139,plain,
( addition(addition(X_11,X_13),X_32) != addition(X_11,addition(X_13,X_32))
| addition(X_11,addition(addition(X_11,X_13),X_32)) = addition(X_11,addition(X_11,addition(X_13,X_32))) ),
inference(resolve,[$cnf( $equal(addition(X_11,addition(addition(X_11,X_13),X_32)),addition(X_11,addition(addition(X_11,X_13),X_32))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
addition(X_11,addition(addition(X_11,X_13),X_32)) = addition(X_11,addition(X_11,addition(X_13,X_32))),
inference(resolve,[$cnf( $equal(addition(addition(X_11,X_13),X_32),addition(X_11,addition(X_13,X_32))) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
( addition(X_11,addition(X_11,addition(X_13,X_32))) != addition(X_11,addition(X_13,X_32))
| addition(X_11,addition(addition(X_11,X_13),X_32)) != addition(X_11,addition(X_11,addition(X_13,X_32)))
| addition(X_11,addition(addition(X_11,X_13),X_32)) = addition(X_11,addition(X_13,X_32)) ),
inference(subst,[],[refute_0_78:[bind(X,$fot(addition(X_11,addition(addition(X_11,X_13),X_32)))),bind(Y,$fot(addition(X_11,addition(X_11,addition(X_13,X_32))))),bind(Z,$fot(addition(X_11,addition(X_13,X_32))))]]) ).
cnf(refute_0_142,plain,
( addition(X_11,addition(X_11,addition(X_13,X_32))) != addition(X_11,addition(X_13,X_32))
| addition(X_11,addition(addition(X_11,X_13),X_32)) = addition(X_11,addition(X_13,X_32)) ),
inference(resolve,[$cnf( $equal(addition(X_11,addition(addition(X_11,X_13),X_32)),addition(X_11,addition(X_11,addition(X_13,X_32)))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
addition(X_11,addition(addition(X_11,X_13),X_32)) = addition(X_11,addition(X_13,X_32)),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_11,addition(X_13,X_32))),addition(X_11,addition(X_13,X_32))) )],[refute_0_135,refute_0_142]) ).
cnf(refute_0_144,plain,
addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) = addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))),
introduced(tautology,[refl,[$fot(addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))))]]) ).
cnf(refute_0_145,plain,
( addition(X_11,addition(addition(X_11,X_13),X_32)) != addition(X_11,addition(X_13,X_32))
| addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) != addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32)))
| addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) = addition(X_13,addition(X_11,addition(X_13,X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))),addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32)))) ),[1,1],$fot(addition(X_11,addition(X_13,X_32)))]]) ).
cnf(refute_0_146,plain,
( addition(X_11,addition(addition(X_11,X_13),X_32)) != addition(X_11,addition(X_13,X_32))
| addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) = addition(X_13,addition(X_11,addition(X_13,X_32))) ),
inference(resolve,[$cnf( $equal(addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))),addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32)))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) = addition(X_13,addition(X_11,addition(X_13,X_32))),
inference(resolve,[$cnf( $equal(addition(X_11,addition(addition(X_11,X_13),X_32)),addition(X_11,addition(X_13,X_32))) )],[refute_0_143,refute_0_146]) ).
cnf(refute_0_148,plain,
( addition(X_13,addition(X_11,addition(X_13,X_32))) != addition(X_11,addition(X_13,X_32))
| addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) != addition(X_13,addition(X_11,addition(X_13,X_32)))
| addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) = addition(X_11,addition(X_13,X_32)) ),
inference(subst,[],[refute_0_78:[bind(X,$fot(addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))))),bind(Y,$fot(addition(X_13,addition(X_11,addition(X_13,X_32))))),bind(Z,$fot(addition(X_11,addition(X_13,X_32))))]]) ).
cnf(refute_0_149,plain,
( addition(X_13,addition(X_11,addition(X_13,X_32))) != addition(X_11,addition(X_13,X_32))
| addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) = addition(X_11,addition(X_13,X_32)) ),
inference(resolve,[$cnf( $equal(addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))),addition(X_13,addition(X_11,addition(X_13,X_32)))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) = addition(X_11,addition(X_13,X_32)),
inference(resolve,[$cnf( $equal(addition(X_13,addition(X_11,addition(X_13,X_32))),addition(X_11,addition(X_13,X_32))) )],[refute_0_134,refute_0_149]) ).
cnf(refute_0_151,plain,
addition(A,addition(B,addition(X_17,X_18))) = addition(addition(A,B),addition(X_17,X_18)),
inference(subst,[],[refute_0_3:[bind(C,$fot(addition(X_17,X_18)))]]) ).
cnf(refute_0_152,plain,
addition(B,addition(X_17,X_18)) = addition(X_17,addition(X_18,B)),
inference(subst,[],[refute_0_73:[bind(A,$fot(B)),bind(X_11,$fot(X_17)),bind(X_12,$fot(X_18))]]) ).
cnf(refute_0_153,plain,
( addition(A,addition(B,addition(X_17,X_18))) != addition(addition(A,B),addition(X_17,X_18))
| addition(B,addition(X_17,X_18)) != addition(X_17,addition(X_18,B))
| addition(A,addition(X_17,addition(X_18,B))) = addition(addition(A,B),addition(X_17,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(B,addition(X_17,X_18))),addition(addition(A,B),addition(X_17,X_18))) ),[0,1],$fot(addition(X_17,addition(X_18,B)))]]) ).
cnf(refute_0_154,plain,
( addition(A,addition(B,addition(X_17,X_18))) != addition(addition(A,B),addition(X_17,X_18))
| addition(A,addition(X_17,addition(X_18,B))) = addition(addition(A,B),addition(X_17,X_18)) ),
inference(resolve,[$cnf( $equal(addition(B,addition(X_17,X_18)),addition(X_17,addition(X_18,B))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
addition(A,addition(X_17,addition(X_18,B))) = addition(addition(A,B),addition(X_17,X_18)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,addition(X_17,X_18))),addition(addition(A,B),addition(X_17,X_18))) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
addition(addition(A,B),addition(X_17,X_18)) = addition(A,addition(B,addition(X_17,X_18))),
inference(subst,[],[refute_0_39:[bind(C,$fot(addition(X_17,X_18)))]]) ).
cnf(refute_0_157,plain,
( addition(A,addition(X_17,addition(X_18,B))) != addition(addition(A,B),addition(X_17,X_18))
| addition(addition(A,B),addition(X_17,X_18)) != addition(A,addition(B,addition(X_17,X_18)))
| addition(A,addition(X_17,addition(X_18,B))) = addition(A,addition(B,addition(X_17,X_18))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_17,addition(X_18,B))),addition(A,addition(B,addition(X_17,X_18)))) ),[0],$fot(addition(addition(A,B),addition(X_17,X_18)))]]) ).
cnf(refute_0_158,plain,
( addition(A,addition(X_17,addition(X_18,B))) != addition(addition(A,B),addition(X_17,X_18))
| addition(A,addition(X_17,addition(X_18,B))) = addition(A,addition(B,addition(X_17,X_18))) ),
inference(resolve,[$cnf( $equal(addition(addition(A,B),addition(X_17,X_18)),addition(A,addition(B,addition(X_17,X_18)))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
addition(A,addition(X_17,addition(X_18,B))) = addition(A,addition(B,addition(X_17,X_18))),
inference(resolve,[$cnf( $equal(addition(A,addition(X_17,addition(X_18,B))),addition(addition(A,B),addition(X_17,X_18))) )],[refute_0_155,refute_0_158]) ).
cnf(refute_0_160,plain,
addition(X_13,addition(addition(X_11,X_13),addition(X_32,X_11))) = addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))),
inference(subst,[],[refute_0_159:[bind(A,$fot(X_13)),bind(B,$fot(X_11)),bind(X_17,$fot(addition(X_11,X_13))),bind(X_18,$fot(X_32))]]) ).
cnf(refute_0_161,plain,
addition(X_19,addition(X_20,addition(X_11,X_12))) = addition(X_20,addition(X_19,addition(X_11,X_12))),
inference(subst,[],[refute_0_106:[bind(X_11,$fot(X_19)),bind(X_12,$fot(X_20)),bind(X_13,$fot(addition(X_11,X_12)))]]) ).
cnf(refute_0_162,plain,
addition(X_20,addition(X_11,X_12)) = addition(X_11,addition(X_12,X_20)),
inference(subst,[],[refute_0_73:[bind(A,$fot(X_20))]]) ).
cnf(refute_0_163,plain,
( addition(X_19,addition(X_20,addition(X_11,X_12))) != addition(X_20,addition(X_19,addition(X_11,X_12)))
| addition(X_20,addition(X_11,X_12)) != addition(X_11,addition(X_12,X_20))
| addition(X_19,addition(X_11,addition(X_12,X_20))) = addition(X_20,addition(X_19,addition(X_11,X_12))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_19,addition(X_20,addition(X_11,X_12))),addition(X_20,addition(X_19,addition(X_11,X_12)))) ),[0,1],$fot(addition(X_11,addition(X_12,X_20)))]]) ).
cnf(refute_0_164,plain,
( addition(X_19,addition(X_20,addition(X_11,X_12))) != addition(X_20,addition(X_19,addition(X_11,X_12)))
| addition(X_19,addition(X_11,addition(X_12,X_20))) = addition(X_20,addition(X_19,addition(X_11,X_12))) ),
inference(resolve,[$cnf( $equal(addition(X_20,addition(X_11,X_12)),addition(X_11,addition(X_12,X_20))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
addition(X_19,addition(X_11,addition(X_12,X_20))) = addition(X_20,addition(X_19,addition(X_11,X_12))),
inference(resolve,[$cnf( $equal(addition(X_19,addition(X_20,addition(X_11,X_12))),addition(X_20,addition(X_19,addition(X_11,X_12)))) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) = addition(X_13,addition(addition(X_11,X_13),addition(X_32,X_11))),
inference(subst,[],[refute_0_165:[bind(X_11,$fot(X_32)),bind(X_12,$fot(X_11)),bind(X_19,$fot(addition(X_11,X_13))),bind(X_20,$fot(X_13))]]) ).
cnf(refute_0_167,plain,
( addition(X_13,addition(addition(X_11,X_13),addition(X_32,X_11))) != addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32)))
| addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) != addition(X_13,addition(addition(X_11,X_13),addition(X_32,X_11)))
| addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) = addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) ),
inference(subst,[],[refute_0_78:[bind(X,$fot(addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))))),bind(Y,$fot(addition(X_13,addition(addition(X_11,X_13),addition(X_32,X_11))))),bind(Z,$fot(addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32)))))]]) ).
cnf(refute_0_168,plain,
( addition(X_13,addition(addition(X_11,X_13),addition(X_32,X_11))) != addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32)))
| addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) = addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) ),
inference(resolve,[$cnf( $equal(addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))),addition(X_13,addition(addition(X_11,X_13),addition(X_32,X_11)))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) = addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))),
inference(resolve,[$cnf( $equal(addition(X_13,addition(addition(X_11,X_13),addition(X_32,X_11))),addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32)))) )],[refute_0_160,refute_0_168]) ).
cnf(refute_0_170,plain,
( addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) != addition(X_11,addition(X_13,X_32))
| addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) != addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32)))
| addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) = addition(X_11,addition(X_13,X_32)) ),
inference(subst,[],[refute_0_78:[bind(X,$fot(addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))))),bind(Y,$fot(addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))))),bind(Z,$fot(addition(X_11,addition(X_13,X_32))))]]) ).
cnf(refute_0_171,plain,
( addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))) != addition(X_11,addition(X_13,X_32))
| addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) = addition(X_11,addition(X_13,X_32)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))),addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32)))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) = addition(X_11,addition(X_13,X_32)),
inference(resolve,[$cnf( $equal(addition(X_13,addition(X_11,addition(addition(X_11,X_13),X_32))),addition(X_11,addition(X_13,X_32))) )],[refute_0_150,refute_0_171]) ).
cnf(refute_0_173,plain,
( addition(X_11,addition(X_32,X_13)) != addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13)))
| addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))) != addition(X_11,addition(X_13,X_32))
| addition(X_11,addition(X_32,X_13)) = addition(X_11,addition(X_13,X_32)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_11,addition(X_32,X_13)),addition(X_11,addition(X_13,X_32))) ),[0],$fot(addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))))]]) ).
cnf(refute_0_174,plain,
( addition(X_11,addition(X_32,X_13)) != addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13)))
| addition(X_11,addition(X_32,X_13)) = addition(X_11,addition(X_13,X_32)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13))),addition(X_11,addition(X_13,X_32))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
addition(X_11,addition(X_32,X_13)) = addition(X_11,addition(X_13,X_32)),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_32,X_13)),addition(addition(X_11,X_13),addition(X_32,addition(X_11,X_13)))) )],[refute_0_112,refute_0_174]) ).
cnf(refute_0_176,plain,
( addition(X_11,addition(X_32,X_13)) != addition(X_11,addition(X_13,X_32))
| addition(X_11,addition(X_13,X_32)) = addition(X_11,addition(X_32,X_13)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(addition(X_11,addition(X_32,X_13)))),bind(Y,$fot(addition(X_11,addition(X_13,X_32))))]]) ).
cnf(refute_0_177,plain,
addition(X_11,addition(X_13,X_32)) = addition(X_11,addition(X_32,X_13)),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_32,X_13)),addition(X_11,addition(X_13,X_32))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,addition(star(A),multiplication(star(A),A))),
inference(subst,[],[refute_0_177:[bind(X_11,$fot(one)),bind(X_13,$fot(multiplication(star(A),A))),bind(X_32,$fot(star(A)))]]) ).
cnf(refute_0_179,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(one,A)))
| addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,multiplication(star(A),addition(one,A))) ),
inference(subst,[],[refute_0_78:[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,$fot(addition(one,multiplication(star(A),addition(one,A)))))]]) ).
cnf(refute_0_180,plain,
( addition(one,addition(star(A),multiplication(star(A),A))) != addition(one,multiplication(star(A),addition(one,A)))
| addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,multiplication(star(A),addition(one,A))) ),
inference(resolve,[$cnf( $equal(addition(one,addition(multiplication(star(A),A),star(A))),addition(one,addition(star(A),multiplication(star(A),A)))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,multiplication(star(A),addition(one,A))),
inference(resolve,[$cnf( $equal(addition(one,addition(star(A),multiplication(star(A),A))),addition(one,multiplication(star(A),addition(one,A)))) )],[refute_0_46,refute_0_180]) ).
cnf(refute_0_182,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,addition(multiplication(star(A),A),star(A))),
inference(subst,[],[refute_0_39:[bind(A,$fot(one)),bind(B,$fot(multiplication(star(A),A))),bind(C,$fot(star(A)))]]) ).
cnf(refute_0_183,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(one,A)))
| addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,multiplication(star(A),addition(one,A))) ),
inference(subst,[],[refute_0_78:[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,$fot(addition(one,multiplication(star(A),addition(one,A)))))]]) ).
cnf(refute_0_184,plain,
( addition(one,addition(multiplication(star(A),A),star(A))) != addition(one,multiplication(star(A),addition(one,A)))
| addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,multiplication(star(A),addition(one,A))) ),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),addition(one,addition(multiplication(star(A),A),star(A)))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,multiplication(star(A),addition(one,A))),
inference(resolve,[$cnf( $equal(addition(one,addition(multiplication(star(A),A),star(A))),addition(one,multiplication(star(A),addition(one,A)))) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
( addition(addition(one,multiplication(star(A),A)),star(A)) != addition(one,multiplication(star(A),addition(one,A)))
| addition(addition(one,multiplication(star(A),A)),star(A)) != star(A)
| addition(one,multiplication(star(A),addition(one,A))) = star(A) ),
introduced(tautology,[equality,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),star(A)) ),[0],$fot(addition(one,multiplication(star(A),addition(one,A))))]]) ).
cnf(refute_0_187,plain,
( addition(addition(one,multiplication(star(A),A)),star(A)) != star(A)
| addition(one,multiplication(star(A),addition(one,A))) = star(A) ),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),addition(one,multiplication(star(A),addition(one,A)))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
addition(one,multiplication(star(A),addition(one,A))) = star(A),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),star(A)) )],[refute_0_20,refute_0_187]) ).
cnf(refute_0_189,plain,
addition(one,multiplication(star(X_54),addition(one,X_54))) = star(X_54),
inference(subst,[],[refute_0_188:[bind(A,$fot(X_54))]]) ).
cnf(refute_0_190,plain,
( addition(one,multiplication(star(X_54),addition(one,X_54))) != star(X_54)
| ~ leq(one,addition(one,multiplication(star(X_54),addition(one,X_54))))
| leq(one,star(X_54)) ),
introduced(tautology,[equality,[$cnf( leq(one,addition(one,multiplication(star(X_54),addition(one,X_54)))) ),[1],$fot(star(X_54))]]) ).
cnf(refute_0_191,plain,
( ~ leq(one,addition(one,multiplication(star(X_54),addition(one,X_54))))
| leq(one,star(X_54)) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(star(X_54),addition(one,X_54))),star(X_54)) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
leq(one,star(X_54)),
inference(resolve,[$cnf( leq(one,addition(one,multiplication(star(X_54),addition(one,X_54)))) )],[refute_0_16,refute_0_191]) ).
cnf(refute_0_193,plain,
leq(one,star(skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_192:[bind(X_54,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_194,plain,
$false,
inference(resolve,[$cnf( leq(one,star(skolemFOFtoCNF_X0)) )],[refute_0_193,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE037+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n009.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 09:23:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.40/0.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.61
% 0.40/0.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.48/0.64
%------------------------------------------------------------------------------