TSTP Solution File: KLE170+1.002 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE170+1.002 : TPTP v8.1.0. Released v5.2.0.
% 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 02:15:41 EDT 2022
% Result : Theorem 1.31s 1.46s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 46
% Syntax : Number of formulae : 240 ( 141 unt; 0 def)
% Number of atoms : 378 ( 311 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 279 ( 141 ~; 134 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 396 ( 20 sgn 60 !; 0 ?)
% 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(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(star_unfold_right,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)) ).
fof(star_unfold_left,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)) ).
fof(a,conjecture,
leq(multiplication(a,a),star(a)) ).
fof(subgoal_0,plain,
leq(multiplication(a,a),star(a)),
inference(strip,[],[a]) ).
fof(negate_0_0,plain,
~ leq(multiplication(a,a),star(a)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
~ leq(multiplication(a,a),star(a)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_2,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_6,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_8,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_10,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_12,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_14,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(canonicalize,[],[star_unfold_left]) ).
fof(normalize_0_16,plain,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_0_3]) ).
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] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(canonicalize,[],[star_unfold_right]) ).
fof(normalize_0_21,plain,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_23,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_22]) ).
cnf(refute_0_0,plain,
~ leq(multiplication(a,a),star(a)),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( addition(X_21,addition(X_21,X_13)) != addition(X_21,X_13)
| leq(X_21,addition(X_21,X_13)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_21)),bind(B,$fot(addition(X_21,X_13)))]]) ).
cnf(refute_0_3,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_6]) ).
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,$fot(X_13))]]) ).
cnf(refute_0_5,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
addition(X_12,X_12) = X_12,
inference(subst,[],[refute_0_5:[bind(A,$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( $equal(addition(X_12,addition(X_12,X_13)),addition(addition(X_12,X_12),X_13)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
addition(X_21,addition(X_21,X_13)) = addition(X_21,X_13),
inference(subst,[],[refute_0_9:[bind(X_12,$fot(X_21))]]) ).
cnf(refute_0_11,plain,
( addition(X_21,X_13) != addition(X_21,X_13)
| addition(X_21,addition(X_21,X_13)) != addition(X_21,X_13)
| addition(X_21,addition(X_21,X_13)) = addition(X_21,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_21,addition(X_21,X_13)),addition(X_21,X_13)) ),[0,1],$fot(addition(X_21,X_13))]]) ).
cnf(refute_0_12,plain,
( addition(X_21,X_13) != addition(X_21,X_13)
| addition(X_21,addition(X_21,X_13)) = addition(X_21,X_13) ),
inference(resolve,[$cnf( $equal(addition(X_21,addition(X_21,X_13)),addition(X_21,X_13)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( addition(X_21,X_13) != addition(X_21,X_13)
| leq(X_21,addition(X_21,X_13)) ),
inference(resolve,[$cnf( $equal(addition(X_21,addition(X_21,X_13)),addition(X_21,X_13)) )],[refute_0_12,refute_0_2]) ).
cnf(refute_0_14,plain,
addition(X_21,X_13) = addition(X_21,X_13),
introduced(tautology,[refl,[$fot(addition(X_21,X_13))]]) ).
cnf(refute_0_15,plain,
leq(X_21,addition(X_21,X_13)),
inference(resolve,[$cnf( $equal(addition(X_21,X_13),addition(X_21,X_13)) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
leq(X_26,addition(X_26,X_25)),
inference(subst,[],[refute_0_15:[bind(X_13,$fot(X_25)),bind(X_21,$fot(X_26))]]) ).
cnf(refute_0_17,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_18,plain,
addition(X_25,X_26) = addition(X_26,X_25),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_25)),bind(B,$fot(X_26))]]) ).
cnf(refute_0_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( addition(X_25,X_26) != addition(X_26,X_25)
| addition(X_26,X_25) = addition(X_25,X_26) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(X_25,X_26))),bind(Y,$fot(addition(X_26,X_25)))]]) ).
cnf(refute_0_23,plain,
addition(X_26,X_25) = addition(X_25,X_26),
inference(resolve,[$cnf( $equal(addition(X_25,X_26),addition(X_26,X_25)) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( addition(X_26,X_25) != addition(X_25,X_26)
| ~ leq(X_26,addition(X_26,X_25))
| leq(X_26,addition(X_25,X_26)) ),
introduced(tautology,[equality,[$cnf( leq(X_26,addition(X_26,X_25)) ),[1],$fot(addition(X_25,X_26))]]) ).
cnf(refute_0_25,plain,
( ~ leq(X_26,addition(X_26,X_25))
| leq(X_26,addition(X_25,X_26)) ),
inference(resolve,[$cnf( $equal(addition(X_26,X_25),addition(X_25,X_26)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
leq(X_26,addition(X_25,X_26)),
inference(resolve,[$cnf( leq(X_26,addition(X_26,X_25)) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
leq(X_28,addition(addition(A,B),X_28)),
inference(subst,[],[refute_0_26:[bind(X_25,$fot(addition(A,B))),bind(X_26,$fot(X_28))]]) ).
cnf(refute_0_28,plain,
addition(A,addition(B,X_28)) = addition(addition(A,B),X_28),
inference(subst,[],[refute_0_3:[bind(C,$fot(X_28))]]) ).
cnf(refute_0_29,plain,
( addition(A,addition(B,X_28)) != addition(addition(A,B),X_28)
| addition(addition(A,B),X_28) = addition(A,addition(B,X_28)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(A,addition(B,X_28)))),bind(Y,$fot(addition(addition(A,B),X_28)))]]) ).
cnf(refute_0_30,plain,
addition(addition(A,B),X_28) = addition(A,addition(B,X_28)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,X_28)),addition(addition(A,B),X_28)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( addition(addition(A,B),X_28) != addition(A,addition(B,X_28))
| ~ leq(X_28,addition(addition(A,B),X_28))
| leq(X_28,addition(A,addition(B,X_28))) ),
introduced(tautology,[equality,[$cnf( leq(X_28,addition(addition(A,B),X_28)) ),[1],$fot(addition(A,addition(B,X_28)))]]) ).
cnf(refute_0_32,plain,
( ~ leq(X_28,addition(addition(A,B),X_28))
| leq(X_28,addition(A,addition(B,X_28))) ),
inference(resolve,[$cnf( $equal(addition(addition(A,B),X_28),addition(A,addition(B,X_28))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
leq(X_28,addition(A,addition(B,X_28))),
inference(resolve,[$cnf( leq(X_28,addition(addition(A,B),X_28)) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
leq(X_31,addition(X_29,addition(X_30,X_31))),
inference(subst,[],[refute_0_33:[bind(A,$fot(X_29)),bind(B,$fot(X_30)),bind(X_28,$fot(X_31))]]) ).
cnf(refute_0_35,plain,
addition(X_31,X_30) = addition(X_30,X_31),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_31)),bind(B,$fot(X_30))]]) ).
cnf(refute_0_36,plain,
( addition(X_31,X_30) != addition(X_30,X_31)
| addition(X_30,X_31) = addition(X_31,X_30) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(X_31,X_30))),bind(Y,$fot(addition(X_30,X_31)))]]) ).
cnf(refute_0_37,plain,
addition(X_30,X_31) = addition(X_31,X_30),
inference(resolve,[$cnf( $equal(addition(X_31,X_30),addition(X_30,X_31)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( addition(X_30,X_31) != addition(X_31,X_30)
| ~ leq(X_31,addition(X_29,addition(X_30,X_31)))
| leq(X_31,addition(X_29,addition(X_31,X_30))) ),
introduced(tautology,[equality,[$cnf( leq(X_31,addition(X_29,addition(X_30,X_31))) ),[1,1],$fot(addition(X_31,X_30))]]) ).
cnf(refute_0_39,plain,
( ~ leq(X_31,addition(X_29,addition(X_30,X_31)))
| leq(X_31,addition(X_29,addition(X_31,X_30))) ),
inference(resolve,[$cnf( $equal(addition(X_30,X_31),addition(X_31,X_30)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
leq(X_31,addition(X_29,addition(X_31,X_30))),
inference(resolve,[$cnf( leq(X_31,addition(X_29,addition(X_30,X_31))) )],[refute_0_34,refute_0_39]) ).
cnf(refute_0_41,plain,
leq(multiplication(X_95,X_96),addition(X_29,addition(multiplication(X_95,X_96),multiplication(X_95,X_97)))),
inference(subst,[],[refute_0_40:[bind(X_30,$fot(multiplication(X_95,X_97))),bind(X_31,$fot(multiplication(X_95,X_96)))]]) ).
cnf(refute_0_42,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_43,plain,
multiplication(X_95,addition(X_96,X_97)) = addition(multiplication(X_95,X_96),multiplication(X_95,X_97)),
inference(subst,[],[refute_0_42:[bind(A,$fot(X_95)),bind(B,$fot(X_96)),bind(C,$fot(X_97))]]) ).
cnf(refute_0_44,plain,
( multiplication(X_95,addition(X_96,X_97)) != addition(multiplication(X_95,X_96),multiplication(X_95,X_97))
| addition(multiplication(X_95,X_96),multiplication(X_95,X_97)) = multiplication(X_95,addition(X_96,X_97)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiplication(X_95,addition(X_96,X_97)))),bind(Y,$fot(addition(multiplication(X_95,X_96),multiplication(X_95,X_97))))]]) ).
cnf(refute_0_45,plain,
addition(multiplication(X_95,X_96),multiplication(X_95,X_97)) = multiplication(X_95,addition(X_96,X_97)),
inference(resolve,[$cnf( $equal(multiplication(X_95,addition(X_96,X_97)),addition(multiplication(X_95,X_96),multiplication(X_95,X_97))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( addition(multiplication(X_95,X_96),multiplication(X_95,X_97)) != multiplication(X_95,addition(X_96,X_97))
| ~ leq(multiplication(X_95,X_96),addition(X_29,addition(multiplication(X_95,X_96),multiplication(X_95,X_97))))
| leq(multiplication(X_95,X_96),addition(X_29,multiplication(X_95,addition(X_96,X_97)))) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(X_95,X_96),addition(X_29,addition(multiplication(X_95,X_96),multiplication(X_95,X_97)))) ),[1,1],$fot(multiplication(X_95,addition(X_96,X_97)))]]) ).
cnf(refute_0_47,plain,
( ~ leq(multiplication(X_95,X_96),addition(X_29,addition(multiplication(X_95,X_96),multiplication(X_95,X_97))))
| leq(multiplication(X_95,X_96),addition(X_29,multiplication(X_95,addition(X_96,X_97)))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_95,X_96),multiplication(X_95,X_97)),multiplication(X_95,addition(X_96,X_97))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
leq(multiplication(X_95,X_96),addition(X_29,multiplication(X_95,addition(X_96,X_97)))),
inference(resolve,[$cnf( leq(multiplication(X_95,X_96),addition(X_29,addition(multiplication(X_95,X_96),multiplication(X_95,X_97)))) )],[refute_0_41,refute_0_47]) ).
cnf(refute_0_49,plain,
leq(multiplication(X_96,X_96),addition(star(X_96),multiplication(X_96,addition(X_96,one)))),
inference(subst,[],[refute_0_48:[bind(X_29,$fot(star(X_96))),bind(X_95,$fot(X_96)),bind(X_97,$fot(one))]]) ).
cnf(refute_0_50,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_51,plain,
multiplication(addition(X_120,star(X_98)),addition(X_98,one)) = addition(multiplication(X_120,addition(X_98,one)),multiplication(star(X_98),addition(X_98,one))),
inference(subst,[],[refute_0_50:[bind(A,$fot(X_120)),bind(B,$fot(star(X_98))),bind(C,$fot(addition(X_98,one)))]]) ).
cnf(refute_0_52,plain,
leq(addition(one,multiplication(star(A),A)),star(A)),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_53,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_54,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_53:[bind(A,$fot(addition(one,multiplication(star(A),A)))),bind(B,$fot(star(A)))]]) ).
cnf(refute_0_55,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = star(A),
inference(resolve,[$cnf( leq(addition(one,multiplication(star(A),A)),star(A)) )],[refute_0_52,refute_0_54]) ).
cnf(refute_0_56,plain,
addition(X_11,addition(X_12,X_13)) = addition(addition(X_11,X_12),X_13),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_11)),bind(B,$fot(X_12)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_57,plain,
addition(X_13,X_12) = addition(X_12,X_13),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_13)),bind(B,$fot(X_12))]]) ).
cnf(refute_0_58,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_21:[bind(X,$fot(addition(X_13,X_12))),bind(Y,$fot(addition(X_12,X_13)))]]) ).
cnf(refute_0_59,plain,
addition(X_12,X_13) = addition(X_13,X_12),
inference(resolve,[$cnf( $equal(addition(X_13,X_12),addition(X_12,X_13)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( addition(X_11,addition(X_12,X_13)) != addition(addition(X_11,X_12),X_13)
| addition(X_12,X_13) != addition(X_13,X_12)
| addition(X_11,addition(X_13,X_12)) = addition(addition(X_11,X_12),X_13) ),
introduced(tautology,[equality,[$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_61,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( $equal(addition(X_12,X_13),addition(X_13,X_12)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
addition(X_11,addition(X_13,X_12)) = addition(addition(X_11,X_12),X_13),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_12,X_13)),addition(addition(X_11,X_12),X_13)) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
( addition(A,addition(B,C)) != addition(addition(A,B),C)
| addition(addition(A,B),C) = addition(A,addition(B,C)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(A,addition(B,C)))),bind(Y,$fot(addition(addition(A,B),C)))]]) ).
cnf(refute_0_64,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,C)),addition(addition(A,B),C)) )],[refute_0_3,refute_0_63]) ).
cnf(refute_0_65,plain,
addition(addition(X_11,X_12),X_13) = addition(X_11,addition(X_12,X_13)),
inference(subst,[],[refute_0_64:[bind(A,$fot(X_11)),bind(B,$fot(X_12)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_66,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_67,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( $equal(addition(addition(X_11,X_12),X_13),addition(X_11,addition(X_12,X_13))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
addition(X_11,addition(X_13,X_12)) = addition(X_11,addition(X_12,X_13)),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_13,X_12)),addition(addition(X_11,X_12),X_13)) )],[refute_0_62,refute_0_67]) ).
cnf(refute_0_69,plain,
( addition(X_11,addition(X_13,X_12)) != addition(X_11,addition(X_12,X_13))
| addition(X_11,addition(X_12,X_13)) = addition(X_11,addition(X_13,X_12)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(X_11,addition(X_13,X_12)))),bind(Y,$fot(addition(X_11,addition(X_12,X_13))))]]) ).
cnf(refute_0_70,plain,
addition(X_11,addition(X_12,X_13)) = addition(X_11,addition(X_13,X_12)),
inference(resolve,[$cnf( $equal(addition(X_11,addition(X_13,X_12)),addition(X_11,addition(X_12,X_13))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,addition(star(A),multiplication(star(A),A))),
inference(subst,[],[refute_0_70:[bind(X_11,$fot(one)),bind(X_12,$fot(multiplication(star(A),A))),bind(X_13,$fot(star(A)))]]) ).
cnf(refute_0_72,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,addition(multiplication(star(A),A),star(A))),
inference(subst,[],[refute_0_64:[bind(A,$fot(one)),bind(B,$fot(multiplication(star(A),A))),bind(C,$fot(star(A)))]]) ).
cnf(refute_0_73,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_74,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_21,refute_0_73]) ).
cnf(refute_0_75,plain,
( addition(addition(one,multiplication(star(A),A)),star(A)) != addition(one,addition(multiplication(star(A),A),star(A)))
| addition(one,addition(multiplication(star(A),A),star(A))) != addition(one,addition(star(A),multiplication(star(A),A)))
| addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,addition(star(A),multiplication(star(A),A))) ),
inference(subst,[],[refute_0_74:[bind(X,$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,addition(star(A),multiplication(star(A),A)))))]]) ).
cnf(refute_0_76,plain,
( addition(one,addition(multiplication(star(A),A),star(A))) != addition(one,addition(star(A),multiplication(star(A),A)))
| addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,addition(star(A),multiplication(star(A),A))) ),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),addition(one,addition(multiplication(star(A),A),star(A)))) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,addition(star(A),multiplication(star(A),A))),
inference(resolve,[$cnf( $equal(addition(one,addition(multiplication(star(A),A),star(A))),addition(one,addition(star(A),multiplication(star(A),A)))) )],[refute_0_71,refute_0_76]) ).
cnf(refute_0_78,plain,
( addition(addition(one,multiplication(star(A),A)),star(A)) != addition(one,addition(star(A),multiplication(star(A),A)))
| addition(addition(one,multiplication(star(A),A)),star(A)) != star(A)
| addition(one,addition(star(A),multiplication(star(A),A))) = star(A) ),
introduced(tautology,[equality,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),star(A)) ),[0],$fot(addition(one,addition(star(A),multiplication(star(A),A))))]]) ).
cnf(refute_0_79,plain,
( addition(addition(one,multiplication(star(A),A)),star(A)) != star(A)
| addition(one,addition(star(A),multiplication(star(A),A))) = star(A) ),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),addition(one,addition(star(A),multiplication(star(A),A)))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
addition(one,addition(star(A),multiplication(star(A),A))) = star(A),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),star(A)) )],[refute_0_55,refute_0_79]) ).
cnf(refute_0_81,plain,
addition(one,addition(star(X_51),C)) = addition(addition(one,star(X_51)),C),
inference(subst,[],[refute_0_3:[bind(A,$fot(one)),bind(B,$fot(star(X_51)))]]) ).
cnf(refute_0_82,plain,
addition(one,addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))) = addition(one,addition(star(X_49),multiplication(star(X_49),X_49))),
inference(subst,[],[refute_0_9:[bind(X_12,$fot(one)),bind(X_13,$fot(addition(star(X_49),multiplication(star(X_49),X_49))))]]) ).
cnf(refute_0_83,plain,
addition(one,addition(star(X_49),multiplication(star(X_49),X_49))) = star(X_49),
inference(subst,[],[refute_0_80:[bind(A,$fot(X_49))]]) ).
cnf(refute_0_84,plain,
( addition(one,addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))) != addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))
| addition(one,addition(star(X_49),multiplication(star(X_49),X_49))) != star(X_49)
| addition(one,star(X_49)) = addition(one,addition(star(X_49),multiplication(star(X_49),X_49))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))),addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))) ),[0,1],$fot(star(X_49))]]) ).
cnf(refute_0_85,plain,
( addition(one,addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))) != addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))
| addition(one,star(X_49)) = addition(one,addition(star(X_49),multiplication(star(X_49),X_49))) ),
inference(resolve,[$cnf( $equal(addition(one,addition(star(X_49),multiplication(star(X_49),X_49))),star(X_49)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
addition(one,star(X_49)) = addition(one,addition(star(X_49),multiplication(star(X_49),X_49))),
inference(resolve,[$cnf( $equal(addition(one,addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))),addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
( addition(one,addition(star(X_49),multiplication(star(X_49),X_49))) != star(X_49)
| addition(one,star(X_49)) != addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))
| addition(one,star(X_49)) = star(X_49) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,star(X_49)),addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))) ),[1],$fot(star(X_49))]]) ).
cnf(refute_0_88,plain,
( addition(one,star(X_49)) != addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))
| addition(one,star(X_49)) = star(X_49) ),
inference(resolve,[$cnf( $equal(addition(one,addition(star(X_49),multiplication(star(X_49),X_49))),star(X_49)) )],[refute_0_83,refute_0_87]) ).
cnf(refute_0_89,plain,
addition(one,star(X_49)) = star(X_49),
inference(resolve,[$cnf( $equal(addition(one,star(X_49)),addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))) )],[refute_0_86,refute_0_88]) ).
cnf(refute_0_90,plain,
addition(one,star(X_51)) = star(X_51),
inference(subst,[],[refute_0_89:[bind(X_49,$fot(X_51))]]) ).
cnf(refute_0_91,plain,
( addition(one,addition(star(X_51),C)) != addition(addition(one,star(X_51)),C)
| addition(one,star(X_51)) != star(X_51)
| addition(one,addition(star(X_51),C)) = addition(star(X_51),C) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,addition(star(X_51),C)),addition(addition(one,star(X_51)),C)) ),[1,0],$fot(star(X_51))]]) ).
cnf(refute_0_92,plain,
( addition(one,addition(star(X_51),C)) != addition(addition(one,star(X_51)),C)
| addition(one,addition(star(X_51),C)) = addition(star(X_51),C) ),
inference(resolve,[$cnf( $equal(addition(one,star(X_51)),star(X_51)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
addition(one,addition(star(X_51),C)) = addition(star(X_51),C),
inference(resolve,[$cnf( $equal(addition(one,addition(star(X_51),C)),addition(addition(one,star(X_51)),C)) )],[refute_0_81,refute_0_92]) ).
cnf(refute_0_94,plain,
addition(one,addition(star(A),multiplication(star(A),A))) = addition(star(A),multiplication(star(A),A)),
inference(subst,[],[refute_0_93:[bind(C,$fot(multiplication(star(A),A))),bind(X_51,$fot(A))]]) ).
cnf(refute_0_95,plain,
( addition(one,addition(star(A),multiplication(star(A),A))) != addition(star(A),multiplication(star(A),A))
| addition(one,addition(star(A),multiplication(star(A),A))) != star(A)
| addition(star(A),multiplication(star(A),A)) = star(A) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,addition(star(A),multiplication(star(A),A))),star(A)) ),[0],$fot(addition(star(A),multiplication(star(A),A)))]]) ).
cnf(refute_0_96,plain,
( addition(one,addition(star(A),multiplication(star(A),A))) != star(A)
| addition(star(A),multiplication(star(A),A)) = star(A) ),
inference(resolve,[$cnf( $equal(addition(one,addition(star(A),multiplication(star(A),A))),addition(star(A),multiplication(star(A),A))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
addition(star(A),multiplication(star(A),A)) = star(A),
inference(resolve,[$cnf( $equal(addition(one,addition(star(A),multiplication(star(A),A))),star(A)) )],[refute_0_80,refute_0_96]) ).
cnf(refute_0_98,plain,
multiplication(X_95,addition(one,X_97)) = addition(multiplication(X_95,one),multiplication(X_95,X_97)),
inference(subst,[],[refute_0_42:[bind(A,$fot(X_95)),bind(B,$fot(one)),bind(C,$fot(X_97))]]) ).
cnf(refute_0_99,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_100,plain,
multiplication(X_95,one) = X_95,
inference(subst,[],[refute_0_99:[bind(A,$fot(X_95))]]) ).
cnf(refute_0_101,plain,
( multiplication(X_95,addition(one,X_97)) != addition(multiplication(X_95,one),multiplication(X_95,X_97))
| multiplication(X_95,one) != X_95
| multiplication(X_95,addition(one,X_97)) = addition(X_95,multiplication(X_95,X_97)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_95,addition(one,X_97)),addition(multiplication(X_95,one),multiplication(X_95,X_97))) ),[1,0],$fot(X_95)]]) ).
cnf(refute_0_102,plain,
( multiplication(X_95,addition(one,X_97)) != addition(multiplication(X_95,one),multiplication(X_95,X_97))
| multiplication(X_95,addition(one,X_97)) = addition(X_95,multiplication(X_95,X_97)) ),
inference(resolve,[$cnf( $equal(multiplication(X_95,one),X_95) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
multiplication(X_95,addition(one,X_97)) = addition(X_95,multiplication(X_95,X_97)),
inference(resolve,[$cnf( $equal(multiplication(X_95,addition(one,X_97)),addition(multiplication(X_95,one),multiplication(X_95,X_97))) )],[refute_0_98,refute_0_102]) ).
cnf(refute_0_104,plain,
( multiplication(X_95,addition(one,X_97)) != addition(X_95,multiplication(X_95,X_97))
| addition(X_95,multiplication(X_95,X_97)) = multiplication(X_95,addition(one,X_97)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiplication(X_95,addition(one,X_97)))),bind(Y,$fot(addition(X_95,multiplication(X_95,X_97))))]]) ).
cnf(refute_0_105,plain,
addition(X_95,multiplication(X_95,X_97)) = multiplication(X_95,addition(one,X_97)),
inference(resolve,[$cnf( $equal(multiplication(X_95,addition(one,X_97)),addition(X_95,multiplication(X_95,X_97))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
addition(star(A),multiplication(star(A),A)) = multiplication(star(A),addition(one,A)),
inference(subst,[],[refute_0_105:[bind(X_95,$fot(star(A))),bind(X_97,$fot(A))]]) ).
cnf(refute_0_107,plain,
( addition(star(A),multiplication(star(A),A)) != multiplication(star(A),addition(one,A))
| addition(star(A),multiplication(star(A),A)) != star(A)
| multiplication(star(A),addition(one,A)) = star(A) ),
introduced(tautology,[equality,[$cnf( $equal(addition(star(A),multiplication(star(A),A)),star(A)) ),[0],$fot(multiplication(star(A),addition(one,A)))]]) ).
cnf(refute_0_108,plain,
( addition(star(A),multiplication(star(A),A)) != star(A)
| multiplication(star(A),addition(one,A)) = star(A) ),
inference(resolve,[$cnf( $equal(addition(star(A),multiplication(star(A),A)),multiplication(star(A),addition(one,A))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
multiplication(star(A),addition(one,A)) = star(A),
inference(resolve,[$cnf( $equal(addition(star(A),multiplication(star(A),A)),star(A)) )],[refute_0_97,refute_0_108]) ).
cnf(refute_0_110,plain,
multiplication(star(X_98),addition(one,X_98)) = star(X_98),
inference(subst,[],[refute_0_109:[bind(A,$fot(X_98))]]) ).
cnf(refute_0_111,plain,
addition(X_98,one) = addition(one,X_98),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_98)),bind(B,$fot(one))]]) ).
cnf(refute_0_112,plain,
( addition(X_98,one) != addition(one,X_98)
| addition(one,X_98) = addition(X_98,one) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(X_98,one))),bind(Y,$fot(addition(one,X_98)))]]) ).
cnf(refute_0_113,plain,
addition(one,X_98) = addition(X_98,one),
inference(resolve,[$cnf( $equal(addition(X_98,one),addition(one,X_98)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( addition(one,X_98) != addition(X_98,one)
| multiplication(star(X_98),addition(one,X_98)) != star(X_98)
| multiplication(star(X_98),addition(X_98,one)) = star(X_98) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(star(X_98),addition(one,X_98)),star(X_98)) ),[0,1],$fot(addition(X_98,one))]]) ).
cnf(refute_0_115,plain,
( multiplication(star(X_98),addition(one,X_98)) != star(X_98)
| multiplication(star(X_98),addition(X_98,one)) = star(X_98) ),
inference(resolve,[$cnf( $equal(addition(one,X_98),addition(X_98,one)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
multiplication(star(X_98),addition(X_98,one)) = star(X_98),
inference(resolve,[$cnf( $equal(multiplication(star(X_98),addition(one,X_98)),star(X_98)) )],[refute_0_110,refute_0_115]) ).
cnf(refute_0_117,plain,
( multiplication(addition(X_120,star(X_98)),addition(X_98,one)) != addition(multiplication(X_120,addition(X_98,one)),multiplication(star(X_98),addition(X_98,one)))
| multiplication(star(X_98),addition(X_98,one)) != star(X_98)
| multiplication(addition(X_120,star(X_98)),addition(X_98,one)) = addition(multiplication(X_120,addition(X_98,one)),star(X_98)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(X_120,star(X_98)),addition(X_98,one)),addition(multiplication(X_120,addition(X_98,one)),multiplication(star(X_98),addition(X_98,one)))) ),[1,1],$fot(star(X_98))]]) ).
cnf(refute_0_118,plain,
( multiplication(addition(X_120,star(X_98)),addition(X_98,one)) != addition(multiplication(X_120,addition(X_98,one)),multiplication(star(X_98),addition(X_98,one)))
| multiplication(addition(X_120,star(X_98)),addition(X_98,one)) = addition(multiplication(X_120,addition(X_98,one)),star(X_98)) ),
inference(resolve,[$cnf( $equal(multiplication(star(X_98),addition(X_98,one)),star(X_98)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
multiplication(addition(X_120,star(X_98)),addition(X_98,one)) = addition(multiplication(X_120,addition(X_98,one)),star(X_98)),
inference(resolve,[$cnf( $equal(multiplication(addition(X_120,star(X_98)),addition(X_98,one)),addition(multiplication(X_120,addition(X_98,one)),multiplication(star(X_98),addition(X_98,one)))) )],[refute_0_51,refute_0_118]) ).
cnf(refute_0_120,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_121,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_17,refute_0_120]) ).
cnf(refute_0_122,plain,
addition(multiplication(X_120,addition(X_98,one)),star(X_98)) = addition(star(X_98),multiplication(X_120,addition(X_98,one))),
inference(subst,[],[refute_0_121:[bind(A,$fot(star(X_98))),bind(B,$fot(multiplication(X_120,addition(X_98,one))))]]) ).
cnf(refute_0_123,plain,
( addition(multiplication(X_120,addition(X_98,one)),star(X_98)) != addition(star(X_98),multiplication(X_120,addition(X_98,one)))
| multiplication(addition(X_120,star(X_98)),addition(X_98,one)) != addition(multiplication(X_120,addition(X_98,one)),star(X_98))
| multiplication(addition(X_120,star(X_98)),addition(X_98,one)) = addition(star(X_98),multiplication(X_120,addition(X_98,one))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(X_120,star(X_98)),addition(X_98,one)),addition(multiplication(X_120,addition(X_98,one)),star(X_98))) ),[1],$fot(addition(star(X_98),multiplication(X_120,addition(X_98,one))))]]) ).
cnf(refute_0_124,plain,
( multiplication(addition(X_120,star(X_98)),addition(X_98,one)) != addition(multiplication(X_120,addition(X_98,one)),star(X_98))
| multiplication(addition(X_120,star(X_98)),addition(X_98,one)) = addition(star(X_98),multiplication(X_120,addition(X_98,one))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_120,addition(X_98,one)),star(X_98)),addition(star(X_98),multiplication(X_120,addition(X_98,one)))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
multiplication(addition(X_120,star(X_98)),addition(X_98,one)) = addition(star(X_98),multiplication(X_120,addition(X_98,one))),
inference(resolve,[$cnf( $equal(multiplication(addition(X_120,star(X_98)),addition(X_98,one)),addition(multiplication(X_120,addition(X_98,one)),star(X_98))) )],[refute_0_119,refute_0_124]) ).
cnf(refute_0_126,plain,
multiplication(addition(X_207,star(X_207)),addition(X_207,one)) = addition(star(X_207),multiplication(X_207,addition(X_207,one))),
inference(subst,[],[refute_0_125:[bind(X_120,$fot(X_207)),bind(X_98,$fot(X_207))]]) ).
cnf(refute_0_127,plain,
multiplication(addition(one,X_123),addition(one,star(X_123))) = addition(addition(one,X_123),multiplication(addition(one,X_123),star(X_123))),
inference(subst,[],[refute_0_103:[bind(X_95,$fot(addition(one,X_123))),bind(X_97,$fot(star(X_123)))]]) ).
cnf(refute_0_128,plain,
leq(addition(one,multiplication(A,star(A))),star(A)),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_129,plain,
( ~ leq(addition(one,multiplication(A,star(A))),star(A))
| addition(addition(one,multiplication(A,star(A))),star(A)) = star(A) ),
inference(subst,[],[refute_0_53:[bind(A,$fot(addition(one,multiplication(A,star(A))))),bind(B,$fot(star(A)))]]) ).
cnf(refute_0_130,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[$cnf( leq(addition(one,multiplication(A,star(A))),star(A)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
addition(one,addition(multiplication(A,star(A)),star(A))) = addition(one,addition(star(A),multiplication(A,star(A)))),
inference(subst,[],[refute_0_70:[bind(X_11,$fot(one)),bind(X_12,$fot(multiplication(A,star(A)))),bind(X_13,$fot(star(A)))]]) ).
cnf(refute_0_132,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = addition(one,addition(multiplication(A,star(A)),star(A))),
inference(subst,[],[refute_0_64:[bind(A,$fot(one)),bind(B,$fot(multiplication(A,star(A)))),bind(C,$fot(star(A)))]]) ).
cnf(refute_0_133,plain,
( addition(addition(one,multiplication(A,star(A))),star(A)) != addition(one,addition(multiplication(A,star(A)),star(A)))
| addition(one,addition(multiplication(A,star(A)),star(A))) != addition(one,addition(star(A),multiplication(A,star(A))))
| addition(addition(one,multiplication(A,star(A))),star(A)) = addition(one,addition(star(A),multiplication(A,star(A)))) ),
inference(subst,[],[refute_0_74:[bind(X,$fot(addition(addition(one,multiplication(A,star(A))),star(A)))),bind(Y,$fot(addition(one,addition(multiplication(A,star(A)),star(A))))),bind(Z,$fot(addition(one,addition(star(A),multiplication(A,star(A))))))]]) ).
cnf(refute_0_134,plain,
( addition(one,addition(multiplication(A,star(A)),star(A))) != addition(one,addition(star(A),multiplication(A,star(A))))
| addition(addition(one,multiplication(A,star(A))),star(A)) = addition(one,addition(star(A),multiplication(A,star(A)))) ),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(A,star(A))),star(A)),addition(one,addition(multiplication(A,star(A)),star(A)))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = addition(one,addition(star(A),multiplication(A,star(A)))),
inference(resolve,[$cnf( $equal(addition(one,addition(multiplication(A,star(A)),star(A))),addition(one,addition(star(A),multiplication(A,star(A))))) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
( addition(addition(one,multiplication(A,star(A))),star(A)) != addition(one,addition(star(A),multiplication(A,star(A))))
| addition(addition(one,multiplication(A,star(A))),star(A)) != star(A)
| addition(one,addition(star(A),multiplication(A,star(A)))) = star(A) ),
introduced(tautology,[equality,[$cnf( $equal(addition(addition(one,multiplication(A,star(A))),star(A)),star(A)) ),[0],$fot(addition(one,addition(star(A),multiplication(A,star(A)))))]]) ).
cnf(refute_0_137,plain,
( addition(addition(one,multiplication(A,star(A))),star(A)) != star(A)
| addition(one,addition(star(A),multiplication(A,star(A)))) = star(A) ),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(A,star(A))),star(A)),addition(one,addition(star(A),multiplication(A,star(A))))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
addition(one,addition(star(A),multiplication(A,star(A)))) = star(A),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(A,star(A))),star(A)),star(A)) )],[refute_0_130,refute_0_137]) ).
cnf(refute_0_139,plain,
addition(one,addition(star(A),multiplication(A,star(A)))) = addition(star(A),multiplication(A,star(A))),
inference(subst,[],[refute_0_93:[bind(C,$fot(multiplication(A,star(A)))),bind(X_51,$fot(A))]]) ).
cnf(refute_0_140,plain,
( addition(one,addition(star(A),multiplication(A,star(A)))) != addition(star(A),multiplication(A,star(A)))
| addition(one,addition(star(A),multiplication(A,star(A)))) != star(A)
| addition(star(A),multiplication(A,star(A))) = star(A) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,addition(star(A),multiplication(A,star(A)))),star(A)) ),[0],$fot(addition(star(A),multiplication(A,star(A))))]]) ).
cnf(refute_0_141,plain,
( addition(one,addition(star(A),multiplication(A,star(A)))) != star(A)
| addition(star(A),multiplication(A,star(A))) = star(A) ),
inference(resolve,[$cnf( $equal(addition(one,addition(star(A),multiplication(A,star(A)))),addition(star(A),multiplication(A,star(A)))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
addition(star(A),multiplication(A,star(A))) = star(A),
inference(resolve,[$cnf( $equal(addition(one,addition(star(A),multiplication(A,star(A)))),star(A)) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
multiplication(addition(one,X_121),X_122) = addition(multiplication(one,X_122),multiplication(X_121,X_122)),
inference(subst,[],[refute_0_50:[bind(A,$fot(one)),bind(B,$fot(X_121)),bind(C,$fot(X_122))]]) ).
cnf(refute_0_144,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_145,plain,
multiplication(one,X_122) = X_122,
inference(subst,[],[refute_0_144:[bind(A,$fot(X_122))]]) ).
cnf(refute_0_146,plain,
( multiplication(addition(one,X_121),X_122) != addition(multiplication(one,X_122),multiplication(X_121,X_122))
| multiplication(one,X_122) != X_122
| multiplication(addition(one,X_121),X_122) = addition(X_122,multiplication(X_121,X_122)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,X_121),X_122),addition(multiplication(one,X_122),multiplication(X_121,X_122))) ),[1,0],$fot(X_122)]]) ).
cnf(refute_0_147,plain,
( multiplication(addition(one,X_121),X_122) != addition(multiplication(one,X_122),multiplication(X_121,X_122))
| multiplication(addition(one,X_121),X_122) = addition(X_122,multiplication(X_121,X_122)) ),
inference(resolve,[$cnf( $equal(multiplication(one,X_122),X_122) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
multiplication(addition(one,X_121),X_122) = addition(X_122,multiplication(X_121,X_122)),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_121),X_122),addition(multiplication(one,X_122),multiplication(X_121,X_122))) )],[refute_0_143,refute_0_147]) ).
cnf(refute_0_149,plain,
( multiplication(addition(one,X_121),X_122) != addition(X_122,multiplication(X_121,X_122))
| addition(X_122,multiplication(X_121,X_122)) = multiplication(addition(one,X_121),X_122) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiplication(addition(one,X_121),X_122))),bind(Y,$fot(addition(X_122,multiplication(X_121,X_122))))]]) ).
cnf(refute_0_150,plain,
addition(X_122,multiplication(X_121,X_122)) = multiplication(addition(one,X_121),X_122),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_121),X_122),addition(X_122,multiplication(X_121,X_122))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
addition(star(A),multiplication(A,star(A))) = multiplication(addition(one,A),star(A)),
inference(subst,[],[refute_0_150:[bind(X_121,$fot(A)),bind(X_122,$fot(star(A)))]]) ).
cnf(refute_0_152,plain,
( addition(star(A),multiplication(A,star(A))) != multiplication(addition(one,A),star(A))
| addition(star(A),multiplication(A,star(A))) != star(A)
| multiplication(addition(one,A),star(A)) = star(A) ),
introduced(tautology,[equality,[$cnf( $equal(addition(star(A),multiplication(A,star(A))),star(A)) ),[0],$fot(multiplication(addition(one,A),star(A)))]]) ).
cnf(refute_0_153,plain,
( addition(star(A),multiplication(A,star(A))) != star(A)
| multiplication(addition(one,A),star(A)) = star(A) ),
inference(resolve,[$cnf( $equal(addition(star(A),multiplication(A,star(A))),multiplication(addition(one,A),star(A))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(resolve,[$cnf( $equal(addition(star(A),multiplication(A,star(A))),star(A)) )],[refute_0_142,refute_0_153]) ).
cnf(refute_0_155,plain,
multiplication(addition(one,X_123),star(X_123)) = star(X_123),
inference(subst,[],[refute_0_154:[bind(A,$fot(X_123))]]) ).
cnf(refute_0_156,plain,
( multiplication(addition(one,X_123),addition(one,star(X_123))) != addition(addition(one,X_123),multiplication(addition(one,X_123),star(X_123)))
| multiplication(addition(one,X_123),star(X_123)) != star(X_123)
| multiplication(addition(one,X_123),addition(one,star(X_123))) = addition(addition(one,X_123),star(X_123)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,X_123),addition(one,star(X_123))),addition(addition(one,X_123),multiplication(addition(one,X_123),star(X_123)))) ),[1,1],$fot(star(X_123))]]) ).
cnf(refute_0_157,plain,
( multiplication(addition(one,X_123),addition(one,star(X_123))) != addition(addition(one,X_123),multiplication(addition(one,X_123),star(X_123)))
| multiplication(addition(one,X_123),addition(one,star(X_123))) = addition(addition(one,X_123),star(X_123)) ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_123),star(X_123)),star(X_123)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
multiplication(addition(one,X_123),addition(one,star(X_123))) = addition(addition(one,X_123),star(X_123)),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_123),addition(one,star(X_123))),addition(addition(one,X_123),multiplication(addition(one,X_123),star(X_123)))) )],[refute_0_127,refute_0_157]) ).
cnf(refute_0_159,plain,
addition(one,star(X_123)) = star(X_123),
inference(subst,[],[refute_0_89:[bind(X_49,$fot(X_123))]]) ).
cnf(refute_0_160,plain,
multiplication(addition(one,X_123),addition(one,star(X_123))) = multiplication(addition(one,X_123),addition(one,star(X_123))),
introduced(tautology,[refl,[$fot(multiplication(addition(one,X_123),addition(one,star(X_123))))]]) ).
cnf(refute_0_161,plain,
( addition(one,star(X_123)) != star(X_123)
| multiplication(addition(one,X_123),addition(one,star(X_123))) != multiplication(addition(one,X_123),addition(one,star(X_123)))
| multiplication(addition(one,X_123),addition(one,star(X_123))) = multiplication(addition(one,X_123),star(X_123)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,X_123),addition(one,star(X_123))),multiplication(addition(one,X_123),addition(one,star(X_123)))) ),[1,1],$fot(star(X_123))]]) ).
cnf(refute_0_162,plain,
( addition(one,star(X_123)) != star(X_123)
| multiplication(addition(one,X_123),addition(one,star(X_123))) = multiplication(addition(one,X_123),star(X_123)) ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_123),addition(one,star(X_123))),multiplication(addition(one,X_123),addition(one,star(X_123)))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
multiplication(addition(one,X_123),addition(one,star(X_123))) = multiplication(addition(one,X_123),star(X_123)),
inference(resolve,[$cnf( $equal(addition(one,star(X_123)),star(X_123)) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
( multiplication(addition(one,X_123),addition(one,star(X_123))) != multiplication(addition(one,X_123),star(X_123))
| multiplication(addition(one,X_123),star(X_123)) != star(X_123)
| multiplication(addition(one,X_123),addition(one,star(X_123))) = star(X_123) ),
inference(subst,[],[refute_0_74:[bind(X,$fot(multiplication(addition(one,X_123),addition(one,star(X_123))))),bind(Y,$fot(multiplication(addition(one,X_123),star(X_123)))),bind(Z,$fot(star(X_123)))]]) ).
cnf(refute_0_165,plain,
( multiplication(addition(one,X_123),star(X_123)) != star(X_123)
| multiplication(addition(one,X_123),addition(one,star(X_123))) = star(X_123) ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_123),addition(one,star(X_123))),multiplication(addition(one,X_123),star(X_123))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
multiplication(addition(one,X_123),addition(one,star(X_123))) = star(X_123),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_123),star(X_123)),star(X_123)) )],[refute_0_155,refute_0_165]) ).
cnf(refute_0_167,plain,
( multiplication(addition(one,X_123),addition(one,star(X_123))) != addition(addition(one,X_123),star(X_123))
| multiplication(addition(one,X_123),addition(one,star(X_123))) != star(X_123)
| star(X_123) = addition(addition(one,X_123),star(X_123)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,X_123),addition(one,star(X_123))),addition(addition(one,X_123),star(X_123))) ),[0],$fot(star(X_123))]]) ).
cnf(refute_0_168,plain,
( multiplication(addition(one,X_123),addition(one,star(X_123))) != addition(addition(one,X_123),star(X_123))
| star(X_123) = addition(addition(one,X_123),star(X_123)) ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_123),addition(one,star(X_123))),star(X_123)) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
( ~ leq(one,addition(X_52,star(X_53)))
| addition(one,addition(X_52,star(X_53))) = addition(X_52,star(X_53)) ),
inference(subst,[],[refute_0_53:[bind(A,$fot(one)),bind(B,$fot(addition(X_52,star(X_53))))]]) ).
cnf(refute_0_170,plain,
leq(one,addition(X_29,addition(one,addition(star(X_49),multiplication(star(X_49),X_49))))),
inference(subst,[],[refute_0_40:[bind(X_30,$fot(addition(star(X_49),multiplication(star(X_49),X_49)))),bind(X_31,$fot(one))]]) ).
cnf(refute_0_171,plain,
( addition(one,addition(star(X_49),multiplication(star(X_49),X_49))) != star(X_49)
| ~ leq(one,addition(X_29,addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))))
| leq(one,addition(X_29,star(X_49))) ),
introduced(tautology,[equality,[$cnf( leq(one,addition(X_29,addition(one,addition(star(X_49),multiplication(star(X_49),X_49))))) ),[1,1],$fot(star(X_49))]]) ).
cnf(refute_0_172,plain,
( ~ leq(one,addition(X_29,addition(one,addition(star(X_49),multiplication(star(X_49),X_49)))))
| leq(one,addition(X_29,star(X_49))) ),
inference(resolve,[$cnf( $equal(addition(one,addition(star(X_49),multiplication(star(X_49),X_49))),star(X_49)) )],[refute_0_83,refute_0_171]) ).
cnf(refute_0_173,plain,
leq(one,addition(X_29,star(X_49))),
inference(resolve,[$cnf( leq(one,addition(X_29,addition(one,addition(star(X_49),multiplication(star(X_49),X_49))))) )],[refute_0_170,refute_0_172]) ).
cnf(refute_0_174,plain,
leq(one,addition(X_52,star(X_53))),
inference(subst,[],[refute_0_173:[bind(X_29,$fot(X_52)),bind(X_49,$fot(X_53))]]) ).
cnf(refute_0_175,plain,
addition(one,addition(X_52,star(X_53))) = addition(X_52,star(X_53)),
inference(resolve,[$cnf( leq(one,addition(X_52,star(X_53))) )],[refute_0_174,refute_0_169]) ).
cnf(refute_0_176,plain,
addition(one,addition(X_123,star(X_123))) = addition(X_123,star(X_123)),
inference(subst,[],[refute_0_175:[bind(X_52,$fot(X_123)),bind(X_53,$fot(X_123))]]) ).
cnf(refute_0_177,plain,
addition(addition(one,X_123),star(X_123)) = addition(one,addition(X_123,star(X_123))),
inference(subst,[],[refute_0_64:[bind(A,$fot(one)),bind(B,$fot(X_123)),bind(C,$fot(star(X_123)))]]) ).
cnf(refute_0_178,plain,
( addition(addition(one,X_123),star(X_123)) != addition(one,addition(X_123,star(X_123)))
| addition(one,addition(X_123,star(X_123))) != addition(X_123,star(X_123))
| addition(addition(one,X_123),star(X_123)) = addition(X_123,star(X_123)) ),
inference(subst,[],[refute_0_74:[bind(X,$fot(addition(addition(one,X_123),star(X_123)))),bind(Y,$fot(addition(one,addition(X_123,star(X_123))))),bind(Z,$fot(addition(X_123,star(X_123))))]]) ).
cnf(refute_0_179,plain,
( addition(one,addition(X_123,star(X_123))) != addition(X_123,star(X_123))
| addition(addition(one,X_123),star(X_123)) = addition(X_123,star(X_123)) ),
inference(resolve,[$cnf( $equal(addition(addition(one,X_123),star(X_123)),addition(one,addition(X_123,star(X_123)))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
addition(addition(one,X_123),star(X_123)) = addition(X_123,star(X_123)),
inference(resolve,[$cnf( $equal(addition(one,addition(X_123,star(X_123))),addition(X_123,star(X_123))) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
( addition(addition(one,X_123),star(X_123)) != addition(X_123,star(X_123))
| star(X_123) != addition(addition(one,X_123),star(X_123))
| star(X_123) = addition(X_123,star(X_123)) ),
introduced(tautology,[equality,[$cnf( $equal(star(X_123),addition(addition(one,X_123),star(X_123))) ),[1],$fot(addition(X_123,star(X_123)))]]) ).
cnf(refute_0_182,plain,
( star(X_123) != addition(addition(one,X_123),star(X_123))
| star(X_123) = addition(X_123,star(X_123)) ),
inference(resolve,[$cnf( $equal(addition(addition(one,X_123),star(X_123)),addition(X_123,star(X_123))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
( multiplication(addition(one,X_123),addition(one,star(X_123))) != addition(addition(one,X_123),star(X_123))
| star(X_123) = addition(X_123,star(X_123)) ),
inference(resolve,[$cnf( $equal(star(X_123),addition(addition(one,X_123),star(X_123))) )],[refute_0_168,refute_0_182]) ).
cnf(refute_0_184,plain,
star(X_123) = addition(X_123,star(X_123)),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_123),addition(one,star(X_123))),addition(addition(one,X_123),star(X_123))) )],[refute_0_158,refute_0_183]) ).
cnf(refute_0_185,plain,
star(X_207) = addition(X_207,star(X_207)),
inference(subst,[],[refute_0_184:[bind(X_123,$fot(X_207))]]) ).
cnf(refute_0_186,plain,
( star(X_207) != addition(X_207,star(X_207))
| addition(X_207,star(X_207)) = star(X_207) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(star(X_207))),bind(Y,$fot(addition(X_207,star(X_207))))]]) ).
cnf(refute_0_187,plain,
addition(X_207,star(X_207)) = star(X_207),
inference(resolve,[$cnf( $equal(star(X_207),addition(X_207,star(X_207))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
( addition(X_207,star(X_207)) != star(X_207)
| multiplication(addition(X_207,star(X_207)),addition(X_207,one)) != addition(star(X_207),multiplication(X_207,addition(X_207,one)))
| multiplication(star(X_207),addition(X_207,one)) = addition(star(X_207),multiplication(X_207,addition(X_207,one))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(X_207,star(X_207)),addition(X_207,one)),addition(star(X_207),multiplication(X_207,addition(X_207,one)))) ),[0,0],$fot(star(X_207))]]) ).
cnf(refute_0_189,plain,
( multiplication(addition(X_207,star(X_207)),addition(X_207,one)) != addition(star(X_207),multiplication(X_207,addition(X_207,one)))
| multiplication(star(X_207),addition(X_207,one)) = addition(star(X_207),multiplication(X_207,addition(X_207,one))) ),
inference(resolve,[$cnf( $equal(addition(X_207,star(X_207)),star(X_207)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
multiplication(star(X_207),addition(X_207,one)) = addition(star(X_207),multiplication(X_207,addition(X_207,one))),
inference(resolve,[$cnf( $equal(multiplication(addition(X_207,star(X_207)),addition(X_207,one)),addition(star(X_207),multiplication(X_207,addition(X_207,one)))) )],[refute_0_126,refute_0_189]) ).
cnf(refute_0_191,plain,
multiplication(star(X_207),addition(X_207,one)) = star(X_207),
inference(subst,[],[refute_0_116:[bind(X_98,$fot(X_207))]]) ).
cnf(refute_0_192,plain,
( multiplication(star(X_207),addition(X_207,one)) != addition(star(X_207),multiplication(X_207,addition(X_207,one)))
| multiplication(star(X_207),addition(X_207,one)) != star(X_207)
| star(X_207) = addition(star(X_207),multiplication(X_207,addition(X_207,one))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(star(X_207),addition(X_207,one)),addition(star(X_207),multiplication(X_207,addition(X_207,one)))) ),[0],$fot(star(X_207))]]) ).
cnf(refute_0_193,plain,
( multiplication(star(X_207),addition(X_207,one)) != addition(star(X_207),multiplication(X_207,addition(X_207,one)))
| star(X_207) = addition(star(X_207),multiplication(X_207,addition(X_207,one))) ),
inference(resolve,[$cnf( $equal(multiplication(star(X_207),addition(X_207,one)),star(X_207)) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
star(X_207) = addition(star(X_207),multiplication(X_207,addition(X_207,one))),
inference(resolve,[$cnf( $equal(multiplication(star(X_207),addition(X_207,one)),addition(star(X_207),multiplication(X_207,addition(X_207,one)))) )],[refute_0_190,refute_0_193]) ).
cnf(refute_0_195,plain,
star(X_96) = addition(star(X_96),multiplication(X_96,addition(X_96,one))),
inference(subst,[],[refute_0_194:[bind(X_207,$fot(X_96))]]) ).
cnf(refute_0_196,plain,
( star(X_96) != addition(star(X_96),multiplication(X_96,addition(X_96,one)))
| addition(star(X_96),multiplication(X_96,addition(X_96,one))) = star(X_96) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(star(X_96))),bind(Y,$fot(addition(star(X_96),multiplication(X_96,addition(X_96,one)))))]]) ).
cnf(refute_0_197,plain,
addition(star(X_96),multiplication(X_96,addition(X_96,one))) = star(X_96),
inference(resolve,[$cnf( $equal(star(X_96),addition(star(X_96),multiplication(X_96,addition(X_96,one)))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
( addition(star(X_96),multiplication(X_96,addition(X_96,one))) != star(X_96)
| ~ leq(multiplication(X_96,X_96),addition(star(X_96),multiplication(X_96,addition(X_96,one))))
| leq(multiplication(X_96,X_96),star(X_96)) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(X_96,X_96),addition(star(X_96),multiplication(X_96,addition(X_96,one)))) ),[1],$fot(star(X_96))]]) ).
cnf(refute_0_199,plain,
( ~ leq(multiplication(X_96,X_96),addition(star(X_96),multiplication(X_96,addition(X_96,one))))
| leq(multiplication(X_96,X_96),star(X_96)) ),
inference(resolve,[$cnf( $equal(addition(star(X_96),multiplication(X_96,addition(X_96,one))),star(X_96)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
leq(multiplication(X_96,X_96),star(X_96)),
inference(resolve,[$cnf( leq(multiplication(X_96,X_96),addition(star(X_96),multiplication(X_96,addition(X_96,one)))) )],[refute_0_49,refute_0_199]) ).
cnf(refute_0_201,plain,
leq(multiplication(a,a),star(a)),
inference(subst,[],[refute_0_200:[bind(X_96,$fot(a))]]) ).
cnf(refute_0_202,plain,
$false,
inference(resolve,[$cnf( leq(multiplication(a,a),star(a)) )],[refute_0_201,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE170+1.002 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12 % 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 13:52:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.31/1.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.31/1.46
% 1.31/1.46 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.31/1.48
%------------------------------------------------------------------------------