TSTP Solution File: KLE038+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE038+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 02:14:51 EDT 2022
% Result : Theorem 0.47s 0.66s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 42
% Syntax : Number of formulae : 225 ( 131 unt; 0 def)
% Number of atoms : 357 ( 312 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 268 ( 136 ~; 128 |; 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 : 362 ( 3 sgn 60 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ).
fof(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_left,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)) ).
fof(goals,conjecture,
! [X0] : leq(X0,star(X0)) ).
fof(subgoal_0,plain,
! [X0] : leq(X0,star(X0)),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : leq(X0,star(X0)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : ~ leq(X0,star(X0)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ leq(skolemFOFtoCNF_X0,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,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_11,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_13,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_15,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_17,plain,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(canonicalize,[],[star_unfold_left]) ).
fof(normalize_0_18,plain,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_20,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_22,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_21]) ).
cnf(refute_0_0,plain,
~ leq(skolemFOFtoCNF_X0,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_37,addition(X_37,X_16)) != addition(X_37,X_16)
| leq(X_37,addition(X_37,X_16)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_37)),bind(B,$fot(addition(X_37,X_16)))]]) ).
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_15,addition(X_15,X_16)) = addition(addition(X_15,X_15),X_16),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_15)),bind(B,$fot(X_15)),bind(C,$fot(X_16))]]) ).
cnf(refute_0_5,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
addition(X_15,X_15) = X_15,
inference(subst,[],[refute_0_5:[bind(A,$fot(X_15))]]) ).
cnf(refute_0_7,plain,
( addition(X_15,X_15) != X_15
| addition(X_15,addition(X_15,X_16)) != addition(addition(X_15,X_15),X_16)
| addition(X_15,addition(X_15,X_16)) = addition(X_15,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_15,addition(X_15,X_16)),addition(addition(X_15,X_15),X_16)) ),[1,0],$fot(X_15)]]) ).
cnf(refute_0_8,plain,
( addition(X_15,addition(X_15,X_16)) != addition(addition(X_15,X_15),X_16)
| addition(X_15,addition(X_15,X_16)) = addition(X_15,X_16) ),
inference(resolve,[$cnf( $equal(addition(X_15,X_15),X_15) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
addition(X_15,addition(X_15,X_16)) = addition(X_15,X_16),
inference(resolve,[$cnf( $equal(addition(X_15,addition(X_15,X_16)),addition(addition(X_15,X_15),X_16)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
addition(X_37,addition(X_37,X_16)) = addition(X_37,X_16),
inference(subst,[],[refute_0_9:[bind(X_15,$fot(X_37))]]) ).
cnf(refute_0_11,plain,
( addition(X_37,X_16) != addition(X_37,X_16)
| addition(X_37,addition(X_37,X_16)) != addition(X_37,X_16)
| addition(X_37,addition(X_37,X_16)) = addition(X_37,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_37,addition(X_37,X_16)),addition(X_37,X_16)) ),[0,1],$fot(addition(X_37,X_16))]]) ).
cnf(refute_0_12,plain,
( addition(X_37,X_16) != addition(X_37,X_16)
| addition(X_37,addition(X_37,X_16)) = addition(X_37,X_16) ),
inference(resolve,[$cnf( $equal(addition(X_37,addition(X_37,X_16)),addition(X_37,X_16)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( addition(X_37,X_16) != addition(X_37,X_16)
| leq(X_37,addition(X_37,X_16)) ),
inference(resolve,[$cnf( $equal(addition(X_37,addition(X_37,X_16)),addition(X_37,X_16)) )],[refute_0_12,refute_0_2]) ).
cnf(refute_0_14,plain,
addition(X_37,X_16) = addition(X_37,X_16),
introduced(tautology,[refl,[$fot(addition(X_37,X_16))]]) ).
cnf(refute_0_15,plain,
leq(X_37,addition(X_37,X_16)),
inference(resolve,[$cnf( $equal(addition(X_37,X_16),addition(X_37,X_16)) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
leq(X_37,addition(X_37,star(X_37))),
inference(subst,[],[refute_0_15:[bind(X_16,$fot(star(X_37)))]]) ).
cnf(refute_0_17,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_18,plain,
addition(addition(X_85,star(X_85)),one) = addition(one,addition(X_85,star(X_85))),
inference(subst,[],[refute_0_17:[bind(A,$fot(addition(X_85,star(X_85)))),bind(B,$fot(one))]]) ).
cnf(refute_0_19,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_20,plain,
multiplication(addition(one,X_29),X_30) = addition(multiplication(one,X_30),multiplication(X_29,X_30)),
inference(subst,[],[refute_0_19:[bind(A,$fot(one)),bind(B,$fot(X_29)),bind(C,$fot(X_30))]]) ).
cnf(refute_0_21,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_22,plain,
multiplication(one,X_30) = X_30,
inference(subst,[],[refute_0_21:[bind(A,$fot(X_30))]]) ).
cnf(refute_0_23,plain,
( multiplication(addition(one,X_29),X_30) != addition(multiplication(one,X_30),multiplication(X_29,X_30))
| multiplication(one,X_30) != X_30
| multiplication(addition(one,X_29),X_30) = addition(X_30,multiplication(X_29,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,X_29),X_30),addition(multiplication(one,X_30),multiplication(X_29,X_30))) ),[1,0],$fot(X_30)]]) ).
cnf(refute_0_24,plain,
( multiplication(addition(one,X_29),X_30) != addition(multiplication(one,X_30),multiplication(X_29,X_30))
| multiplication(addition(one,X_29),X_30) = addition(X_30,multiplication(X_29,X_30)) ),
inference(resolve,[$cnf( $equal(multiplication(one,X_30),X_30) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
multiplication(addition(one,X_29),X_30) = addition(X_30,multiplication(X_29,X_30)),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_29),X_30),addition(multiplication(one,X_30),multiplication(X_29,X_30))) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
multiplication(addition(one,star(X_84)),addition(one,X_84)) = addition(addition(one,X_84),multiplication(star(X_84),addition(one,X_84))),
inference(subst,[],[refute_0_25:[bind(X_29,$fot(star(X_84))),bind(X_30,$fot(addition(one,X_84)))]]) ).
cnf(refute_0_27,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_28,plain,
( ~ leq(multiplication(star(X_81),addition(one,X_81)),star(X_81))
| addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)) = star(X_81) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(multiplication(star(X_81),addition(one,X_81)))),bind(B,$fot(star(X_81)))]]) ).
cnf(refute_0_29,plain,
leq(X_42,addition(X_42,X_41)),
inference(subst,[],[refute_0_15:[bind(X_16,$fot(X_41)),bind(X_37,$fot(X_42))]]) ).
cnf(refute_0_30,plain,
addition(X_41,X_42) = addition(X_42,X_41),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_41)),bind(B,$fot(X_42))]]) ).
cnf(refute_0_31,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_32,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_33,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( addition(X_41,X_42) != addition(X_42,X_41)
| addition(X_42,X_41) = addition(X_41,X_42) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(addition(X_41,X_42))),bind(Y,$fot(addition(X_42,X_41)))]]) ).
cnf(refute_0_35,plain,
addition(X_42,X_41) = addition(X_41,X_42),
inference(resolve,[$cnf( $equal(addition(X_41,X_42),addition(X_42,X_41)) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
( addition(X_42,X_41) != addition(X_41,X_42)
| ~ leq(X_42,addition(X_42,X_41))
| leq(X_42,addition(X_41,X_42)) ),
introduced(tautology,[equality,[$cnf( leq(X_42,addition(X_42,X_41)) ),[1],$fot(addition(X_41,X_42))]]) ).
cnf(refute_0_37,plain,
( ~ leq(X_42,addition(X_42,X_41))
| leq(X_42,addition(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(addition(X_42,X_41),addition(X_41,X_42)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
leq(X_42,addition(X_41,X_42)),
inference(resolve,[$cnf( leq(X_42,addition(X_42,X_41)) )],[refute_0_29,refute_0_37]) ).
cnf(refute_0_39,plain,
leq(multiplication(star(X_56),addition(one,X_56)),addition(one,multiplication(star(X_56),addition(one,X_56)))),
inference(subst,[],[refute_0_38:[bind(X_41,$fot(one)),bind(X_42,$fot(multiplication(star(X_56),addition(one,X_56))))]]) ).
cnf(refute_0_40,plain,
leq(addition(one,multiplication(star(A),A)),star(A)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_41,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_27:[bind(A,$fot(addition(one,multiplication(star(A),A)))),bind(B,$fot(star(A)))]]) ).
cnf(refute_0_42,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = star(A),
inference(resolve,[$cnf( leq(addition(one,multiplication(star(A),A)),star(A)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
addition(A,addition(B,multiplication(B,X_27))) = addition(addition(A,B),multiplication(B,X_27)),
inference(subst,[],[refute_0_3:[bind(C,$fot(multiplication(B,X_27)))]]) ).
cnf(refute_0_44,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_45,plain,
multiplication(X_21,addition(one,X_23)) = addition(multiplication(X_21,one),multiplication(X_21,X_23)),
inference(subst,[],[refute_0_44:[bind(A,$fot(X_21)),bind(B,$fot(one)),bind(C,$fot(X_23))]]) ).
cnf(refute_0_46,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_47,plain,
multiplication(X_21,one) = X_21,
inference(subst,[],[refute_0_46:[bind(A,$fot(X_21))]]) ).
cnf(refute_0_48,plain,
( multiplication(X_21,addition(one,X_23)) != addition(multiplication(X_21,one),multiplication(X_21,X_23))
| multiplication(X_21,one) != X_21
| multiplication(X_21,addition(one,X_23)) = addition(X_21,multiplication(X_21,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_21,addition(one,X_23)),addition(multiplication(X_21,one),multiplication(X_21,X_23))) ),[1,0],$fot(X_21)]]) ).
cnf(refute_0_49,plain,
( multiplication(X_21,addition(one,X_23)) != addition(multiplication(X_21,one),multiplication(X_21,X_23))
| multiplication(X_21,addition(one,X_23)) = addition(X_21,multiplication(X_21,X_23)) ),
inference(resolve,[$cnf( $equal(multiplication(X_21,one),X_21) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
multiplication(X_21,addition(one,X_23)) = addition(X_21,multiplication(X_21,X_23)),
inference(resolve,[$cnf( $equal(multiplication(X_21,addition(one,X_23)),addition(multiplication(X_21,one),multiplication(X_21,X_23))) )],[refute_0_45,refute_0_49]) ).
cnf(refute_0_51,plain,
multiplication(B,addition(one,X_27)) = addition(B,multiplication(B,X_27)),
inference(subst,[],[refute_0_50:[bind(X_21,$fot(B)),bind(X_23,$fot(X_27))]]) ).
cnf(refute_0_52,plain,
( multiplication(B,addition(one,X_27)) != addition(B,multiplication(B,X_27))
| addition(B,multiplication(B,X_27)) = multiplication(B,addition(one,X_27)) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(multiplication(B,addition(one,X_27)))),bind(Y,$fot(addition(B,multiplication(B,X_27))))]]) ).
cnf(refute_0_53,plain,
addition(B,multiplication(B,X_27)) = multiplication(B,addition(one,X_27)),
inference(resolve,[$cnf( $equal(multiplication(B,addition(one,X_27)),addition(B,multiplication(B,X_27))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( addition(A,addition(B,multiplication(B,X_27))) != addition(addition(A,B),multiplication(B,X_27))
| addition(B,multiplication(B,X_27)) != multiplication(B,addition(one,X_27))
| addition(A,multiplication(B,addition(one,X_27))) = addition(addition(A,B),multiplication(B,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(B,multiplication(B,X_27))),addition(addition(A,B),multiplication(B,X_27))) ),[0,1],$fot(multiplication(B,addition(one,X_27)))]]) ).
cnf(refute_0_55,plain,
( addition(A,addition(B,multiplication(B,X_27))) != addition(addition(A,B),multiplication(B,X_27))
| addition(A,multiplication(B,addition(one,X_27))) = addition(addition(A,B),multiplication(B,X_27)) ),
inference(resolve,[$cnf( $equal(addition(B,multiplication(B,X_27)),multiplication(B,addition(one,X_27))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
addition(A,multiplication(B,addition(one,X_27))) = addition(addition(A,B),multiplication(B,X_27)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,multiplication(B,X_27))),addition(addition(A,B),multiplication(B,X_27))) )],[refute_0_43,refute_0_55]) ).
cnf(refute_0_57,plain,
( addition(A,addition(B,C)) != addition(addition(A,B),C)
| addition(addition(A,B),C) = addition(A,addition(B,C)) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(addition(A,addition(B,C)))),bind(Y,$fot(addition(addition(A,B),C)))]]) ).
cnf(refute_0_58,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,C)),addition(addition(A,B),C)) )],[refute_0_3,refute_0_57]) ).
cnf(refute_0_59,plain,
addition(addition(A,B),multiplication(B,X_27)) = addition(A,addition(B,multiplication(B,X_27))),
inference(subst,[],[refute_0_58:[bind(C,$fot(multiplication(B,X_27)))]]) ).
cnf(refute_0_60,plain,
( addition(A,multiplication(B,addition(one,X_27))) != addition(addition(A,B),multiplication(B,X_27))
| addition(addition(A,B),multiplication(B,X_27)) != addition(A,addition(B,multiplication(B,X_27)))
| addition(A,multiplication(B,addition(one,X_27))) = addition(A,addition(B,multiplication(B,X_27))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,multiplication(B,addition(one,X_27))),addition(A,addition(B,multiplication(B,X_27)))) ),[0],$fot(addition(addition(A,B),multiplication(B,X_27)))]]) ).
cnf(refute_0_61,plain,
( addition(A,multiplication(B,addition(one,X_27))) != addition(addition(A,B),multiplication(B,X_27))
| addition(A,multiplication(B,addition(one,X_27))) = addition(A,addition(B,multiplication(B,X_27))) ),
inference(resolve,[$cnf( $equal(addition(addition(A,B),multiplication(B,X_27)),addition(A,addition(B,multiplication(B,X_27)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
addition(A,multiplication(B,addition(one,X_27))) = addition(A,addition(B,multiplication(B,X_27))),
inference(resolve,[$cnf( $equal(addition(A,multiplication(B,addition(one,X_27))),addition(addition(A,B),multiplication(B,X_27))) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
( addition(A,multiplication(B,addition(one,X_27))) != addition(A,addition(B,multiplication(B,X_27)))
| addition(A,addition(B,multiplication(B,X_27))) = addition(A,multiplication(B,addition(one,X_27))) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(addition(A,multiplication(B,addition(one,X_27))))),bind(Y,$fot(addition(A,addition(B,multiplication(B,X_27)))))]]) ).
cnf(refute_0_64,plain,
addition(A,addition(B,multiplication(B,X_27))) = addition(A,multiplication(B,addition(one,X_27))),
inference(resolve,[$cnf( $equal(addition(A,multiplication(B,addition(one,X_27))),addition(A,addition(B,multiplication(B,X_27)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
addition(one,addition(star(A),multiplication(star(A),A))) = addition(one,multiplication(star(A),addition(one,A))),
inference(subst,[],[refute_0_64:[bind(A,$fot(one)),bind(B,$fot(star(A))),bind(X_27,$fot(A))]]) ).
cnf(refute_0_66,plain,
addition(X_14,addition(X_15,X_16)) = addition(addition(X_14,X_15),X_16),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_14)),bind(B,$fot(X_15)),bind(C,$fot(X_16))]]) ).
cnf(refute_0_67,plain,
addition(X_16,X_15) = addition(X_15,X_16),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_16)),bind(B,$fot(X_15))]]) ).
cnf(refute_0_68,plain,
( addition(X_16,X_15) != addition(X_15,X_16)
| addition(X_15,X_16) = addition(X_16,X_15) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(addition(X_16,X_15))),bind(Y,$fot(addition(X_15,X_16)))]]) ).
cnf(refute_0_69,plain,
addition(X_15,X_16) = addition(X_16,X_15),
inference(resolve,[$cnf( $equal(addition(X_16,X_15),addition(X_15,X_16)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( addition(X_14,addition(X_15,X_16)) != addition(addition(X_14,X_15),X_16)
| addition(X_15,X_16) != addition(X_16,X_15)
| addition(X_14,addition(X_16,X_15)) = addition(addition(X_14,X_15),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_14,addition(X_15,X_16)),addition(addition(X_14,X_15),X_16)) ),[0,1],$fot(addition(X_16,X_15))]]) ).
cnf(refute_0_71,plain,
( addition(X_14,addition(X_15,X_16)) != addition(addition(X_14,X_15),X_16)
| addition(X_14,addition(X_16,X_15)) = addition(addition(X_14,X_15),X_16) ),
inference(resolve,[$cnf( $equal(addition(X_15,X_16),addition(X_16,X_15)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
addition(X_14,addition(X_16,X_15)) = addition(addition(X_14,X_15),X_16),
inference(resolve,[$cnf( $equal(addition(X_14,addition(X_15,X_16)),addition(addition(X_14,X_15),X_16)) )],[refute_0_66,refute_0_71]) ).
cnf(refute_0_73,plain,
addition(addition(X_14,X_15),X_16) = addition(X_14,addition(X_15,X_16)),
inference(subst,[],[refute_0_58:[bind(A,$fot(X_14)),bind(B,$fot(X_15)),bind(C,$fot(X_16))]]) ).
cnf(refute_0_74,plain,
( addition(X_14,addition(X_16,X_15)) != addition(addition(X_14,X_15),X_16)
| addition(addition(X_14,X_15),X_16) != addition(X_14,addition(X_15,X_16))
| addition(X_14,addition(X_16,X_15)) = addition(X_14,addition(X_15,X_16)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_14,addition(X_16,X_15)),addition(X_14,addition(X_15,X_16))) ),[0],$fot(addition(addition(X_14,X_15),X_16))]]) ).
cnf(refute_0_75,plain,
( addition(X_14,addition(X_16,X_15)) != addition(addition(X_14,X_15),X_16)
| addition(X_14,addition(X_16,X_15)) = addition(X_14,addition(X_15,X_16)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_14,X_15),X_16),addition(X_14,addition(X_15,X_16))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
addition(X_14,addition(X_16,X_15)) = addition(X_14,addition(X_15,X_16)),
inference(resolve,[$cnf( $equal(addition(X_14,addition(X_16,X_15)),addition(addition(X_14,X_15),X_16)) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
( addition(X_14,addition(X_16,X_15)) != addition(X_14,addition(X_15,X_16))
| addition(X_14,addition(X_15,X_16)) = addition(X_14,addition(X_16,X_15)) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(addition(X_14,addition(X_16,X_15)))),bind(Y,$fot(addition(X_14,addition(X_15,X_16))))]]) ).
cnf(refute_0_78,plain,
addition(X_14,addition(X_15,X_16)) = addition(X_14,addition(X_16,X_15)),
inference(resolve,[$cnf( $equal(addition(X_14,addition(X_16,X_15)),addition(X_14,addition(X_15,X_16))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,addition(star(A),multiplication(star(A),A))),
inference(subst,[],[refute_0_78:[bind(X_14,$fot(one)),bind(X_15,$fot(multiplication(star(A),A))),bind(X_16,$fot(star(A)))]]) ).
cnf(refute_0_80,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_81,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_33,refute_0_80]) ).
cnf(refute_0_82,plain,
( addition(one,addition(multiplication(star(A),A),star(A))) != addition(one,addition(star(A),multiplication(star(A),A)))
| addition(one,addition(star(A),multiplication(star(A),A))) != addition(one,multiplication(star(A),addition(one,A)))
| addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,multiplication(star(A),addition(one,A))) ),
inference(subst,[],[refute_0_81:[bind(X,$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_83,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( $equal(addition(one,addition(multiplication(star(A),A),star(A))),addition(one,addition(star(A),multiplication(star(A),A)))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
addition(one,addition(multiplication(star(A),A),star(A))) = addition(one,multiplication(star(A),addition(one,A))),
inference(resolve,[$cnf( $equal(addition(one,addition(star(A),multiplication(star(A),A))),addition(one,multiplication(star(A),addition(one,A)))) )],[refute_0_65,refute_0_83]) ).
cnf(refute_0_85,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,addition(multiplication(star(A),A),star(A))),
inference(subst,[],[refute_0_58:[bind(A,$fot(one)),bind(B,$fot(multiplication(star(A),A))),bind(C,$fot(star(A)))]]) ).
cnf(refute_0_86,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_81:[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,$fot(addition(one,multiplication(star(A),addition(one,A)))))]]) ).
cnf(refute_0_87,plain,
( addition(one,addition(multiplication(star(A),A),star(A))) != addition(one,multiplication(star(A),addition(one,A)))
| addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,multiplication(star(A),addition(one,A))) ),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),addition(one,addition(multiplication(star(A),A),star(A)))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
addition(addition(one,multiplication(star(A),A)),star(A)) = addition(one,multiplication(star(A),addition(one,A))),
inference(resolve,[$cnf( $equal(addition(one,addition(multiplication(star(A),A),star(A))),addition(one,multiplication(star(A),addition(one,A)))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( addition(addition(one,multiplication(star(A),A)),star(A)) != addition(one,multiplication(star(A),addition(one,A)))
| addition(addition(one,multiplication(star(A),A)),star(A)) != star(A)
| addition(one,multiplication(star(A),addition(one,A))) = star(A) ),
introduced(tautology,[equality,[$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_90,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( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),addition(one,multiplication(star(A),addition(one,A)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
addition(one,multiplication(star(A),addition(one,A))) = star(A),
inference(resolve,[$cnf( $equal(addition(addition(one,multiplication(star(A),A)),star(A)),star(A)) )],[refute_0_42,refute_0_90]) ).
cnf(refute_0_92,plain,
addition(one,multiplication(star(X_56),addition(one,X_56))) = star(X_56),
inference(subst,[],[refute_0_91:[bind(A,$fot(X_56))]]) ).
cnf(refute_0_93,plain,
( addition(one,multiplication(star(X_56),addition(one,X_56))) != star(X_56)
| ~ leq(multiplication(star(X_56),addition(one,X_56)),addition(one,multiplication(star(X_56),addition(one,X_56))))
| leq(multiplication(star(X_56),addition(one,X_56)),star(X_56)) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(star(X_56),addition(one,X_56)),addition(one,multiplication(star(X_56),addition(one,X_56)))) ),[1],$fot(star(X_56))]]) ).
cnf(refute_0_94,plain,
( ~ leq(multiplication(star(X_56),addition(one,X_56)),addition(one,multiplication(star(X_56),addition(one,X_56))))
| leq(multiplication(star(X_56),addition(one,X_56)),star(X_56)) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(star(X_56),addition(one,X_56))),star(X_56)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
leq(multiplication(star(X_56),addition(one,X_56)),star(X_56)),
inference(resolve,[$cnf( leq(multiplication(star(X_56),addition(one,X_56)),addition(one,multiplication(star(X_56),addition(one,X_56)))) )],[refute_0_39,refute_0_94]) ).
cnf(refute_0_96,plain,
leq(multiplication(star(X_81),addition(one,X_81)),star(X_81)),
inference(subst,[],[refute_0_95:[bind(X_56,$fot(X_81))]]) ).
cnf(refute_0_97,plain,
addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)) = star(X_81),
inference(resolve,[$cnf( leq(multiplication(star(X_81),addition(one,X_81)),star(X_81)) )],[refute_0_96,refute_0_28]) ).
cnf(refute_0_98,plain,
multiplication(X_21,addition(X_22,one)) = addition(multiplication(X_21,X_22),multiplication(X_21,one)),
inference(subst,[],[refute_0_44:[bind(A,$fot(X_21)),bind(B,$fot(X_22)),bind(C,$fot(one))]]) ).
cnf(refute_0_99,plain,
( multiplication(X_21,addition(X_22,one)) != addition(multiplication(X_21,X_22),multiplication(X_21,one))
| multiplication(X_21,one) != X_21
| multiplication(X_21,addition(X_22,one)) = addition(multiplication(X_21,X_22),X_21) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_21,addition(X_22,one)),addition(multiplication(X_21,X_22),multiplication(X_21,one))) ),[1,1],$fot(X_21)]]) ).
cnf(refute_0_100,plain,
( multiplication(X_21,addition(X_22,one)) != addition(multiplication(X_21,X_22),multiplication(X_21,one))
| multiplication(X_21,addition(X_22,one)) = addition(multiplication(X_21,X_22),X_21) ),
inference(resolve,[$cnf( $equal(multiplication(X_21,one),X_21) )],[refute_0_47,refute_0_99]) ).
cnf(refute_0_101,plain,
multiplication(X_21,addition(X_22,one)) = addition(multiplication(X_21,X_22),X_21),
inference(resolve,[$cnf( $equal(multiplication(X_21,addition(X_22,one)),addition(multiplication(X_21,X_22),multiplication(X_21,one))) )],[refute_0_98,refute_0_100]) ).
cnf(refute_0_102,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_103,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_17,refute_0_102]) ).
cnf(refute_0_104,plain,
addition(multiplication(X_21,X_22),X_21) = addition(X_21,multiplication(X_21,X_22)),
inference(subst,[],[refute_0_103:[bind(A,$fot(X_21)),bind(B,$fot(multiplication(X_21,X_22)))]]) ).
cnf(refute_0_105,plain,
( addition(multiplication(X_21,X_22),X_21) != addition(X_21,multiplication(X_21,X_22))
| multiplication(X_21,addition(X_22,one)) != addition(multiplication(X_21,X_22),X_21)
| multiplication(X_21,addition(X_22,one)) = addition(X_21,multiplication(X_21,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_21,addition(X_22,one)),addition(multiplication(X_21,X_22),X_21)) ),[1],$fot(addition(X_21,multiplication(X_21,X_22)))]]) ).
cnf(refute_0_106,plain,
( multiplication(X_21,addition(X_22,one)) != addition(multiplication(X_21,X_22),X_21)
| multiplication(X_21,addition(X_22,one)) = addition(X_21,multiplication(X_21,X_22)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_21,X_22),X_21),addition(X_21,multiplication(X_21,X_22))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
multiplication(X_21,addition(X_22,one)) = addition(X_21,multiplication(X_21,X_22)),
inference(resolve,[$cnf( $equal(multiplication(X_21,addition(X_22,one)),addition(multiplication(X_21,X_22),X_21)) )],[refute_0_101,refute_0_106]) ).
cnf(refute_0_108,plain,
multiplication(X_24,addition(X_25,one)) = addition(X_24,multiplication(X_24,X_25)),
inference(subst,[],[refute_0_107:[bind(X_21,$fot(X_24)),bind(X_22,$fot(X_25))]]) ).
cnf(refute_0_109,plain,
addition(one,X_25) = addition(X_25,one),
inference(subst,[],[refute_0_17:[bind(A,$fot(one)),bind(B,$fot(X_25))]]) ).
cnf(refute_0_110,plain,
( addition(one,X_25) != addition(X_25,one)
| addition(X_25,one) = addition(one,X_25) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(addition(one,X_25))),bind(Y,$fot(addition(X_25,one)))]]) ).
cnf(refute_0_111,plain,
addition(X_25,one) = addition(one,X_25),
inference(resolve,[$cnf( $equal(addition(one,X_25),addition(X_25,one)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( addition(X_25,one) != addition(one,X_25)
| multiplication(X_24,addition(X_25,one)) != addition(X_24,multiplication(X_24,X_25))
| multiplication(X_24,addition(one,X_25)) = addition(X_24,multiplication(X_24,X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_24,addition(X_25,one)),addition(X_24,multiplication(X_24,X_25))) ),[0,1],$fot(addition(one,X_25))]]) ).
cnf(refute_0_113,plain,
( multiplication(X_24,addition(X_25,one)) != addition(X_24,multiplication(X_24,X_25))
| multiplication(X_24,addition(one,X_25)) = addition(X_24,multiplication(X_24,X_25)) ),
inference(resolve,[$cnf( $equal(addition(X_25,one),addition(one,X_25)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
multiplication(X_24,addition(one,X_25)) = addition(X_24,multiplication(X_24,X_25)),
inference(resolve,[$cnf( $equal(multiplication(X_24,addition(X_25,one)),addition(X_24,multiplication(X_24,X_25))) )],[refute_0_108,refute_0_113]) ).
cnf(refute_0_115,plain,
( multiplication(X_24,addition(one,X_25)) != addition(X_24,multiplication(X_24,X_25))
| addition(X_24,multiplication(X_24,X_25)) = multiplication(X_24,addition(one,X_25)) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(multiplication(X_24,addition(one,X_25)))),bind(Y,$fot(addition(X_24,multiplication(X_24,X_25))))]]) ).
cnf(refute_0_116,plain,
addition(X_24,multiplication(X_24,X_25)) = multiplication(X_24,addition(one,X_25)),
inference(resolve,[$cnf( $equal(multiplication(X_24,addition(one,X_25)),addition(X_24,multiplication(X_24,X_25))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
addition(star(X_81),multiplication(star(X_81),X_81)) = multiplication(star(X_81),addition(one,X_81)),
inference(subst,[],[refute_0_116:[bind(X_24,$fot(star(X_81))),bind(X_25,$fot(X_81))]]) ).
cnf(refute_0_118,plain,
addition(X_15,addition(X_15,multiplication(X_15,X_27))) = addition(X_15,multiplication(X_15,X_27)),
inference(subst,[],[refute_0_9:[bind(X_16,$fot(multiplication(X_15,X_27)))]]) ).
cnf(refute_0_119,plain,
multiplication(X_15,addition(one,X_27)) = addition(X_15,multiplication(X_15,X_27)),
inference(subst,[],[refute_0_50:[bind(X_21,$fot(X_15)),bind(X_23,$fot(X_27))]]) ).
cnf(refute_0_120,plain,
( multiplication(X_15,addition(one,X_27)) != addition(X_15,multiplication(X_15,X_27))
| addition(X_15,multiplication(X_15,X_27)) = multiplication(X_15,addition(one,X_27)) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(multiplication(X_15,addition(one,X_27)))),bind(Y,$fot(addition(X_15,multiplication(X_15,X_27))))]]) ).
cnf(refute_0_121,plain,
addition(X_15,multiplication(X_15,X_27)) = multiplication(X_15,addition(one,X_27)),
inference(resolve,[$cnf( $equal(multiplication(X_15,addition(one,X_27)),addition(X_15,multiplication(X_15,X_27))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
( addition(X_15,addition(X_15,multiplication(X_15,X_27))) != addition(X_15,multiplication(X_15,X_27))
| addition(X_15,multiplication(X_15,X_27)) != multiplication(X_15,addition(one,X_27))
| addition(X_15,multiplication(X_15,addition(one,X_27))) = addition(X_15,multiplication(X_15,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_15,addition(X_15,multiplication(X_15,X_27))),addition(X_15,multiplication(X_15,X_27))) ),[0,1],$fot(multiplication(X_15,addition(one,X_27)))]]) ).
cnf(refute_0_123,plain,
( addition(X_15,addition(X_15,multiplication(X_15,X_27))) != addition(X_15,multiplication(X_15,X_27))
| addition(X_15,multiplication(X_15,addition(one,X_27))) = addition(X_15,multiplication(X_15,X_27)) ),
inference(resolve,[$cnf( $equal(addition(X_15,multiplication(X_15,X_27)),multiplication(X_15,addition(one,X_27))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
addition(X_15,multiplication(X_15,addition(one,X_27))) = addition(X_15,multiplication(X_15,X_27)),
inference(resolve,[$cnf( $equal(addition(X_15,addition(X_15,multiplication(X_15,X_27))),addition(X_15,multiplication(X_15,X_27))) )],[refute_0_118,refute_0_123]) ).
cnf(refute_0_125,plain,
addition(star(X_81),multiplication(star(X_81),addition(one,X_81))) = addition(star(X_81),multiplication(star(X_81),X_81)),
inference(subst,[],[refute_0_124:[bind(X_15,$fot(star(X_81))),bind(X_27,$fot(X_81))]]) ).
cnf(refute_0_126,plain,
( addition(star(X_81),multiplication(star(X_81),X_81)) != multiplication(star(X_81),addition(one,X_81))
| addition(star(X_81),multiplication(star(X_81),addition(one,X_81))) != addition(star(X_81),multiplication(star(X_81),X_81))
| addition(star(X_81),multiplication(star(X_81),addition(one,X_81))) = multiplication(star(X_81),addition(one,X_81)) ),
inference(subst,[],[refute_0_81:[bind(X,$fot(addition(star(X_81),multiplication(star(X_81),addition(one,X_81))))),bind(Y,$fot(addition(star(X_81),multiplication(star(X_81),X_81)))),bind(Z,$fot(multiplication(star(X_81),addition(one,X_81))))]]) ).
cnf(refute_0_127,plain,
( addition(star(X_81),multiplication(star(X_81),X_81)) != multiplication(star(X_81),addition(one,X_81))
| addition(star(X_81),multiplication(star(X_81),addition(one,X_81))) = multiplication(star(X_81),addition(one,X_81)) ),
inference(resolve,[$cnf( $equal(addition(star(X_81),multiplication(star(X_81),addition(one,X_81))),addition(star(X_81),multiplication(star(X_81),X_81))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
addition(star(X_81),multiplication(star(X_81),addition(one,X_81))) = multiplication(star(X_81),addition(one,X_81)),
inference(resolve,[$cnf( $equal(addition(star(X_81),multiplication(star(X_81),X_81)),multiplication(star(X_81),addition(one,X_81))) )],[refute_0_117,refute_0_127]) ).
cnf(refute_0_129,plain,
addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)) = addition(star(X_81),multiplication(star(X_81),addition(one,X_81))),
inference(subst,[],[refute_0_103:[bind(A,$fot(star(X_81))),bind(B,$fot(multiplication(star(X_81),addition(one,X_81))))]]) ).
cnf(refute_0_130,plain,
( addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)) != addition(star(X_81),multiplication(star(X_81),addition(one,X_81)))
| addition(star(X_81),multiplication(star(X_81),addition(one,X_81))) != multiplication(star(X_81),addition(one,X_81))
| addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)) = multiplication(star(X_81),addition(one,X_81)) ),
inference(subst,[],[refute_0_81:[bind(X,$fot(addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)))),bind(Y,$fot(addition(star(X_81),multiplication(star(X_81),addition(one,X_81))))),bind(Z,$fot(multiplication(star(X_81),addition(one,X_81))))]]) ).
cnf(refute_0_131,plain,
( addition(star(X_81),multiplication(star(X_81),addition(one,X_81))) != multiplication(star(X_81),addition(one,X_81))
| addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)) = multiplication(star(X_81),addition(one,X_81)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)),addition(star(X_81),multiplication(star(X_81),addition(one,X_81)))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)) = multiplication(star(X_81),addition(one,X_81)),
inference(resolve,[$cnf( $equal(addition(star(X_81),multiplication(star(X_81),addition(one,X_81))),multiplication(star(X_81),addition(one,X_81))) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
( addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)) != multiplication(star(X_81),addition(one,X_81))
| addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)) != star(X_81)
| multiplication(star(X_81),addition(one,X_81)) = star(X_81) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)),star(X_81)) ),[0],$fot(multiplication(star(X_81),addition(one,X_81)))]]) ).
cnf(refute_0_134,plain,
( addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)) != star(X_81)
| multiplication(star(X_81),addition(one,X_81)) = star(X_81) ),
inference(resolve,[$cnf( $equal(addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)),multiplication(star(X_81),addition(one,X_81))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
multiplication(star(X_81),addition(one,X_81)) = star(X_81),
inference(resolve,[$cnf( $equal(addition(multiplication(star(X_81),addition(one,X_81)),star(X_81)),star(X_81)) )],[refute_0_97,refute_0_134]) ).
cnf(refute_0_136,plain,
multiplication(star(X_84),addition(one,X_84)) = star(X_84),
inference(subst,[],[refute_0_135:[bind(X_81,$fot(X_84))]]) ).
cnf(refute_0_137,plain,
( multiplication(addition(one,star(X_84)),addition(one,X_84)) != addition(addition(one,X_84),multiplication(star(X_84),addition(one,X_84)))
| multiplication(star(X_84),addition(one,X_84)) != star(X_84)
| multiplication(addition(one,star(X_84)),addition(one,X_84)) = addition(addition(one,X_84),star(X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,star(X_84)),addition(one,X_84)),addition(addition(one,X_84),multiplication(star(X_84),addition(one,X_84)))) ),[1,1],$fot(star(X_84))]]) ).
cnf(refute_0_138,plain,
( multiplication(addition(one,star(X_84)),addition(one,X_84)) != addition(addition(one,X_84),multiplication(star(X_84),addition(one,X_84)))
| multiplication(addition(one,star(X_84)),addition(one,X_84)) = addition(addition(one,X_84),star(X_84)) ),
inference(resolve,[$cnf( $equal(multiplication(star(X_84),addition(one,X_84)),star(X_84)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
multiplication(addition(one,star(X_84)),addition(one,X_84)) = addition(addition(one,X_84),star(X_84)),
inference(resolve,[$cnf( $equal(multiplication(addition(one,star(X_84)),addition(one,X_84)),addition(addition(one,X_84),multiplication(star(X_84),addition(one,X_84)))) )],[refute_0_26,refute_0_138]) ).
cnf(refute_0_140,plain,
addition(one,addition(one,multiplication(star(X_56),addition(one,X_56)))) = addition(one,multiplication(star(X_56),addition(one,X_56))),
inference(subst,[],[refute_0_9:[bind(X_15,$fot(one)),bind(X_16,$fot(multiplication(star(X_56),addition(one,X_56))))]]) ).
cnf(refute_0_141,plain,
( addition(one,addition(one,multiplication(star(X_56),addition(one,X_56)))) != addition(one,multiplication(star(X_56),addition(one,X_56)))
| addition(one,multiplication(star(X_56),addition(one,X_56))) != star(X_56)
| addition(one,star(X_56)) = addition(one,multiplication(star(X_56),addition(one,X_56))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,addition(one,multiplication(star(X_56),addition(one,X_56)))),addition(one,multiplication(star(X_56),addition(one,X_56)))) ),[0,1],$fot(star(X_56))]]) ).
cnf(refute_0_142,plain,
( addition(one,addition(one,multiplication(star(X_56),addition(one,X_56)))) != addition(one,multiplication(star(X_56),addition(one,X_56)))
| addition(one,star(X_56)) = addition(one,multiplication(star(X_56),addition(one,X_56))) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(star(X_56),addition(one,X_56))),star(X_56)) )],[refute_0_92,refute_0_141]) ).
cnf(refute_0_143,plain,
addition(one,star(X_56)) = addition(one,multiplication(star(X_56),addition(one,X_56))),
inference(resolve,[$cnf( $equal(addition(one,addition(one,multiplication(star(X_56),addition(one,X_56)))),addition(one,multiplication(star(X_56),addition(one,X_56)))) )],[refute_0_140,refute_0_142]) ).
cnf(refute_0_144,plain,
( addition(one,multiplication(star(X_56),addition(one,X_56))) != star(X_56)
| addition(one,star(X_56)) != addition(one,multiplication(star(X_56),addition(one,X_56)))
| addition(one,star(X_56)) = star(X_56) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,star(X_56)),addition(one,multiplication(star(X_56),addition(one,X_56)))) ),[1],$fot(star(X_56))]]) ).
cnf(refute_0_145,plain,
( addition(one,star(X_56)) != addition(one,multiplication(star(X_56),addition(one,X_56)))
| addition(one,star(X_56)) = star(X_56) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(star(X_56),addition(one,X_56))),star(X_56)) )],[refute_0_92,refute_0_144]) ).
cnf(refute_0_146,plain,
addition(one,star(X_56)) = star(X_56),
inference(resolve,[$cnf( $equal(addition(one,star(X_56)),addition(one,multiplication(star(X_56),addition(one,X_56)))) )],[refute_0_143,refute_0_145]) ).
cnf(refute_0_147,plain,
addition(one,star(X_84)) = star(X_84),
inference(subst,[],[refute_0_146:[bind(X_56,$fot(X_84))]]) ).
cnf(refute_0_148,plain,
multiplication(addition(one,star(X_84)),addition(one,X_84)) = multiplication(addition(one,star(X_84)),addition(one,X_84)),
introduced(tautology,[refl,[$fot(multiplication(addition(one,star(X_84)),addition(one,X_84)))]]) ).
cnf(refute_0_149,plain,
( addition(one,star(X_84)) != star(X_84)
| multiplication(addition(one,star(X_84)),addition(one,X_84)) != multiplication(addition(one,star(X_84)),addition(one,X_84))
| multiplication(addition(one,star(X_84)),addition(one,X_84)) = multiplication(star(X_84),addition(one,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,star(X_84)),addition(one,X_84)),multiplication(addition(one,star(X_84)),addition(one,X_84))) ),[1,0],$fot(star(X_84))]]) ).
cnf(refute_0_150,plain,
( addition(one,star(X_84)) != star(X_84)
| multiplication(addition(one,star(X_84)),addition(one,X_84)) = multiplication(star(X_84),addition(one,X_84)) ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,star(X_84)),addition(one,X_84)),multiplication(addition(one,star(X_84)),addition(one,X_84))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
multiplication(addition(one,star(X_84)),addition(one,X_84)) = multiplication(star(X_84),addition(one,X_84)),
inference(resolve,[$cnf( $equal(addition(one,star(X_84)),star(X_84)) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
( multiplication(addition(one,star(X_84)),addition(one,X_84)) != multiplication(star(X_84),addition(one,X_84))
| multiplication(star(X_84),addition(one,X_84)) != star(X_84)
| multiplication(addition(one,star(X_84)),addition(one,X_84)) = star(X_84) ),
inference(subst,[],[refute_0_81:[bind(X,$fot(multiplication(addition(one,star(X_84)),addition(one,X_84)))),bind(Y,$fot(multiplication(star(X_84),addition(one,X_84)))),bind(Z,$fot(star(X_84)))]]) ).
cnf(refute_0_153,plain,
( multiplication(star(X_84),addition(one,X_84)) != star(X_84)
| multiplication(addition(one,star(X_84)),addition(one,X_84)) = star(X_84) ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,star(X_84)),addition(one,X_84)),multiplication(star(X_84),addition(one,X_84))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
multiplication(addition(one,star(X_84)),addition(one,X_84)) = star(X_84),
inference(resolve,[$cnf( $equal(multiplication(star(X_84),addition(one,X_84)),star(X_84)) )],[refute_0_136,refute_0_153]) ).
cnf(refute_0_155,plain,
( multiplication(addition(one,star(X_84)),addition(one,X_84)) != addition(addition(one,X_84),star(X_84))
| multiplication(addition(one,star(X_84)),addition(one,X_84)) != star(X_84)
| star(X_84) = addition(addition(one,X_84),star(X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,star(X_84)),addition(one,X_84)),addition(addition(one,X_84),star(X_84))) ),[0],$fot(star(X_84))]]) ).
cnf(refute_0_156,plain,
( multiplication(addition(one,star(X_84)),addition(one,X_84)) != addition(addition(one,X_84),star(X_84))
| star(X_84) = addition(addition(one,X_84),star(X_84)) ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,star(X_84)),addition(one,X_84)),star(X_84)) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
addition(addition(one,X_84),star(X_84)) = addition(one,addition(X_84,star(X_84))),
inference(subst,[],[refute_0_58:[bind(A,$fot(one)),bind(B,$fot(X_84)),bind(C,$fot(star(X_84)))]]) ).
cnf(refute_0_158,plain,
( addition(addition(one,X_84),star(X_84)) != addition(one,addition(X_84,star(X_84)))
| star(X_84) != addition(addition(one,X_84),star(X_84))
| star(X_84) = addition(one,addition(X_84,star(X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(star(X_84),addition(addition(one,X_84),star(X_84))) ),[1],$fot(addition(one,addition(X_84,star(X_84))))]]) ).
cnf(refute_0_159,plain,
( star(X_84) != addition(addition(one,X_84),star(X_84))
| star(X_84) = addition(one,addition(X_84,star(X_84))) ),
inference(resolve,[$cnf( $equal(addition(addition(one,X_84),star(X_84)),addition(one,addition(X_84,star(X_84)))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( multiplication(addition(one,star(X_84)),addition(one,X_84)) != addition(addition(one,X_84),star(X_84))
| star(X_84) = addition(one,addition(X_84,star(X_84))) ),
inference(resolve,[$cnf( $equal(star(X_84),addition(addition(one,X_84),star(X_84))) )],[refute_0_156,refute_0_159]) ).
cnf(refute_0_161,plain,
star(X_84) = addition(one,addition(X_84,star(X_84))),
inference(resolve,[$cnf( $equal(multiplication(addition(one,star(X_84)),addition(one,X_84)),addition(addition(one,X_84),star(X_84))) )],[refute_0_139,refute_0_160]) ).
cnf(refute_0_162,plain,
star(X_85) = addition(one,addition(X_85,star(X_85))),
inference(subst,[],[refute_0_161:[bind(X_84,$fot(X_85))]]) ).
cnf(refute_0_163,plain,
( star(X_85) != addition(one,addition(X_85,star(X_85)))
| addition(one,addition(X_85,star(X_85))) = star(X_85) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(star(X_85))),bind(Y,$fot(addition(one,addition(X_85,star(X_85)))))]]) ).
cnf(refute_0_164,plain,
addition(one,addition(X_85,star(X_85))) = star(X_85),
inference(resolve,[$cnf( $equal(star(X_85),addition(one,addition(X_85,star(X_85)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
( addition(addition(X_85,star(X_85)),one) != addition(one,addition(X_85,star(X_85)))
| addition(one,addition(X_85,star(X_85))) != star(X_85)
| addition(addition(X_85,star(X_85)),one) = star(X_85) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(addition(X_85,star(X_85)),one),star(X_85)) ),[0],$fot(addition(one,addition(X_85,star(X_85))))]]) ).
cnf(refute_0_166,plain,
( addition(addition(X_85,star(X_85)),one) != addition(one,addition(X_85,star(X_85)))
| addition(addition(X_85,star(X_85)),one) = star(X_85) ),
inference(resolve,[$cnf( $equal(addition(one,addition(X_85,star(X_85))),star(X_85)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
addition(addition(X_85,star(X_85)),one) = star(X_85),
inference(resolve,[$cnf( $equal(addition(addition(X_85,star(X_85)),one),addition(one,addition(X_85,star(X_85)))) )],[refute_0_18,refute_0_166]) ).
cnf(refute_0_168,plain,
addition(one,star(X_85)) = star(X_85),
inference(subst,[],[refute_0_146:[bind(X_56,$fot(X_85))]]) ).
cnf(refute_0_169,plain,
addition(X_85,addition(one,star(X_85))) = addition(X_85,addition(one,star(X_85))),
introduced(tautology,[refl,[$fot(addition(X_85,addition(one,star(X_85))))]]) ).
cnf(refute_0_170,plain,
( addition(X_85,addition(one,star(X_85))) != addition(X_85,addition(one,star(X_85)))
| addition(one,star(X_85)) != star(X_85)
| addition(X_85,addition(one,star(X_85))) = addition(X_85,star(X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_85,addition(one,star(X_85))),addition(X_85,addition(one,star(X_85)))) ),[1,1],$fot(star(X_85))]]) ).
cnf(refute_0_171,plain,
( addition(one,star(X_85)) != star(X_85)
| addition(X_85,addition(one,star(X_85))) = addition(X_85,star(X_85)) ),
inference(resolve,[$cnf( $equal(addition(X_85,addition(one,star(X_85))),addition(X_85,addition(one,star(X_85)))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
addition(X_85,addition(one,star(X_85))) = addition(X_85,star(X_85)),
inference(resolve,[$cnf( $equal(addition(one,star(X_85)),star(X_85)) )],[refute_0_168,refute_0_171]) ).
cnf(refute_0_173,plain,
addition(X_85,addition(star(X_85),one)) = addition(X_85,addition(one,star(X_85))),
inference(subst,[],[refute_0_78:[bind(X_14,$fot(X_85)),bind(X_15,$fot(star(X_85))),bind(X_16,$fot(one))]]) ).
cnf(refute_0_174,plain,
addition(addition(X_85,star(X_85)),one) = addition(X_85,addition(star(X_85),one)),
inference(subst,[],[refute_0_58:[bind(A,$fot(X_85)),bind(B,$fot(star(X_85))),bind(C,$fot(one))]]) ).
cnf(refute_0_175,plain,
( addition(X_85,addition(star(X_85),one)) != addition(X_85,addition(one,star(X_85)))
| addition(addition(X_85,star(X_85)),one) != addition(X_85,addition(star(X_85),one))
| addition(addition(X_85,star(X_85)),one) = addition(X_85,addition(one,star(X_85))) ),
inference(subst,[],[refute_0_81:[bind(X,$fot(addition(addition(X_85,star(X_85)),one))),bind(Y,$fot(addition(X_85,addition(star(X_85),one)))),bind(Z,$fot(addition(X_85,addition(one,star(X_85)))))]]) ).
cnf(refute_0_176,plain,
( addition(X_85,addition(star(X_85),one)) != addition(X_85,addition(one,star(X_85)))
| addition(addition(X_85,star(X_85)),one) = addition(X_85,addition(one,star(X_85))) ),
inference(resolve,[$cnf( $equal(addition(addition(X_85,star(X_85)),one),addition(X_85,addition(star(X_85),one))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
addition(addition(X_85,star(X_85)),one) = addition(X_85,addition(one,star(X_85))),
inference(resolve,[$cnf( $equal(addition(X_85,addition(star(X_85),one)),addition(X_85,addition(one,star(X_85)))) )],[refute_0_173,refute_0_176]) ).
cnf(refute_0_178,plain,
( addition(X_85,addition(one,star(X_85))) != addition(X_85,star(X_85))
| addition(addition(X_85,star(X_85)),one) != addition(X_85,addition(one,star(X_85)))
| addition(addition(X_85,star(X_85)),one) = addition(X_85,star(X_85)) ),
inference(subst,[],[refute_0_81:[bind(X,$fot(addition(addition(X_85,star(X_85)),one))),bind(Y,$fot(addition(X_85,addition(one,star(X_85))))),bind(Z,$fot(addition(X_85,star(X_85))))]]) ).
cnf(refute_0_179,plain,
( addition(X_85,addition(one,star(X_85))) != addition(X_85,star(X_85))
| addition(addition(X_85,star(X_85)),one) = addition(X_85,star(X_85)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_85,star(X_85)),one),addition(X_85,addition(one,star(X_85)))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
addition(addition(X_85,star(X_85)),one) = addition(X_85,star(X_85)),
inference(resolve,[$cnf( $equal(addition(X_85,addition(one,star(X_85))),addition(X_85,star(X_85))) )],[refute_0_172,refute_0_179]) ).
cnf(refute_0_181,plain,
( addition(addition(X_85,star(X_85)),one) != addition(X_85,star(X_85))
| addition(addition(X_85,star(X_85)),one) != star(X_85)
| addition(X_85,star(X_85)) = star(X_85) ),
introduced(tautology,[equality,[$cnf( $equal(addition(addition(X_85,star(X_85)),one),star(X_85)) ),[0],$fot(addition(X_85,star(X_85)))]]) ).
cnf(refute_0_182,plain,
( addition(addition(X_85,star(X_85)),one) != star(X_85)
| addition(X_85,star(X_85)) = star(X_85) ),
inference(resolve,[$cnf( $equal(addition(addition(X_85,star(X_85)),one),addition(X_85,star(X_85))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
addition(X_85,star(X_85)) = star(X_85),
inference(resolve,[$cnf( $equal(addition(addition(X_85,star(X_85)),one),star(X_85)) )],[refute_0_167,refute_0_182]) ).
cnf(refute_0_184,plain,
addition(X_37,star(X_37)) = star(X_37),
inference(subst,[],[refute_0_183:[bind(X_85,$fot(X_37))]]) ).
cnf(refute_0_185,plain,
( addition(X_37,star(X_37)) != star(X_37)
| ~ leq(X_37,addition(X_37,star(X_37)))
| leq(X_37,star(X_37)) ),
introduced(tautology,[equality,[$cnf( leq(X_37,addition(X_37,star(X_37))) ),[1],$fot(star(X_37))]]) ).
cnf(refute_0_186,plain,
( ~ leq(X_37,addition(X_37,star(X_37)))
| leq(X_37,star(X_37)) ),
inference(resolve,[$cnf( $equal(addition(X_37,star(X_37)),star(X_37)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
leq(X_37,star(X_37)),
inference(resolve,[$cnf( leq(X_37,addition(X_37,star(X_37))) )],[refute_0_16,refute_0_186]) ).
cnf(refute_0_188,plain,
leq(skolemFOFtoCNF_X0,star(skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_187:[bind(X_37,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_189,plain,
$false,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,star(skolemFOFtoCNF_X0)) )],[refute_0_188,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE038+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n014.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 09:15:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.66
% 0.47/0.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.52/0.69
%------------------------------------------------------------------------------