TSTP Solution File: KLE052+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE052+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 02:14:56 EDT 2022
% Result : Theorem 0.52s 0.71s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 31
% Syntax : Number of formulae : 149 ( 89 unt; 0 def)
% Number of atoms : 232 ( 200 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 171 ( 88 ~; 79 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 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 : 287 ( 10 sgn 51 !; 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_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
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(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one ).
fof(goals,conjecture,
! [X0] : multiplication(domain(X0),X0) = X0 ).
fof(subgoal_0,plain,
! [X0] : multiplication(domain(X0),X0) = X0,
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : multiplication(domain(X0),X0) = X0,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : multiplication(domain(X0),X0) != X0,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_3,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_5,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_9,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_10,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_12,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_14,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_16,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X0] : addition(domain(X0),one) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_18,plain,
! [X0] : addition(domain(X0),one) = one,
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_20,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_19]) ).
cnf(refute_0_0,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ leq(multiplication(domain(X_109),X_110),X_110)
| addition(multiplication(domain(X_109),X_110),X_110) = X_110 ),
inference(subst,[],[refute_0_2:[bind(A,$fot(multiplication(domain(X_109),X_110))),bind(B,$fot(X_110))]]) ).
cnf(refute_0_4,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( addition(X_46,addition(X_21,X_46)) != addition(X_21,X_46)
| leq(X_46,addition(X_21,X_46)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_46)),bind(B,$fot(addition(X_21,X_46)))]]) ).
cnf(refute_0_6,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
addition(addition(X_21,X_22),addition(X_21,X_22)) = addition(addition(addition(X_21,X_22),X_21),X_22),
inference(subst,[],[refute_0_6:[bind(A,$fot(addition(X_21,X_22))),bind(B,$fot(X_21)),bind(C,$fot(X_22))]]) ).
cnf(refute_0_8,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
addition(addition(X_21,X_22),addition(X_21,X_22)) = addition(X_21,X_22),
inference(subst,[],[refute_0_8:[bind(A,$fot(addition(X_21,X_22)))]]) ).
cnf(refute_0_10,plain,
( addition(addition(X_21,X_22),addition(X_21,X_22)) != addition(X_21,X_22)
| addition(addition(X_21,X_22),addition(X_21,X_22)) != addition(addition(addition(X_21,X_22),X_21),X_22)
| addition(X_21,X_22) = addition(addition(addition(X_21,X_22),X_21),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(addition(addition(X_21,X_22),addition(X_21,X_22)),addition(addition(addition(X_21,X_22),X_21),X_22)) ),[0],$fot(addition(X_21,X_22))]]) ).
cnf(refute_0_11,plain,
( addition(addition(X_21,X_22),addition(X_21,X_22)) != addition(addition(addition(X_21,X_22),X_21),X_22)
| addition(X_21,X_22) = addition(addition(addition(X_21,X_22),X_21),X_22) ),
inference(resolve,[$cnf( $equal(addition(addition(X_21,X_22),addition(X_21,X_22)),addition(X_21,X_22)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
addition(X_21,X_22) = addition(addition(addition(X_21,X_22),X_21),X_22),
inference(resolve,[$cnf( $equal(addition(addition(X_21,X_22),addition(X_21,X_22)),addition(addition(addition(X_21,X_22),X_21),X_22)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
addition(X_20,addition(X_21,X_22)) = addition(addition(X_20,X_21),X_22),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_20)),bind(B,$fot(X_21)),bind(C,$fot(X_22))]]) ).
cnf(refute_0_14,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_15,plain,
addition(X_22,X_21) = addition(X_21,X_22),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_22)),bind(B,$fot(X_21))]]) ).
cnf(refute_0_16,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( addition(X_22,X_21) != addition(X_21,X_22)
| addition(X_21,X_22) = addition(X_22,X_21) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(addition(X_22,X_21))),bind(Y,$fot(addition(X_21,X_22)))]]) ).
cnf(refute_0_20,plain,
addition(X_21,X_22) = addition(X_22,X_21),
inference(resolve,[$cnf( $equal(addition(X_22,X_21),addition(X_21,X_22)) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
( addition(X_20,addition(X_21,X_22)) != addition(addition(X_20,X_21),X_22)
| addition(X_21,X_22) != addition(X_22,X_21)
| addition(X_20,addition(X_22,X_21)) = addition(addition(X_20,X_21),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_20,addition(X_21,X_22)),addition(addition(X_20,X_21),X_22)) ),[0,1],$fot(addition(X_22,X_21))]]) ).
cnf(refute_0_22,plain,
( addition(X_20,addition(X_21,X_22)) != addition(addition(X_20,X_21),X_22)
| addition(X_20,addition(X_22,X_21)) = addition(addition(X_20,X_21),X_22) ),
inference(resolve,[$cnf( $equal(addition(X_21,X_22),addition(X_22,X_21)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
addition(X_20,addition(X_22,X_21)) = addition(addition(X_20,X_21),X_22),
inference(resolve,[$cnf( $equal(addition(X_20,addition(X_21,X_22)),addition(addition(X_20,X_21),X_22)) )],[refute_0_13,refute_0_22]) ).
cnf(refute_0_24,plain,
( addition(A,addition(B,C)) != addition(addition(A,B),C)
| addition(addition(A,B),C) = addition(A,addition(B,C)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(addition(A,addition(B,C)))),bind(Y,$fot(addition(addition(A,B),C)))]]) ).
cnf(refute_0_25,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,C)),addition(addition(A,B),C)) )],[refute_0_6,refute_0_24]) ).
cnf(refute_0_26,plain,
addition(addition(X_20,X_21),X_22) = addition(X_20,addition(X_21,X_22)),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_20)),bind(B,$fot(X_21)),bind(C,$fot(X_22))]]) ).
cnf(refute_0_27,plain,
( addition(X_20,addition(X_22,X_21)) != addition(addition(X_20,X_21),X_22)
| addition(addition(X_20,X_21),X_22) != addition(X_20,addition(X_21,X_22))
| addition(X_20,addition(X_22,X_21)) = addition(X_20,addition(X_21,X_22)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_20,addition(X_22,X_21)),addition(X_20,addition(X_21,X_22))) ),[0],$fot(addition(addition(X_20,X_21),X_22))]]) ).
cnf(refute_0_28,plain,
( addition(X_20,addition(X_22,X_21)) != addition(addition(X_20,X_21),X_22)
| addition(X_20,addition(X_22,X_21)) = addition(X_20,addition(X_21,X_22)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_20,X_21),X_22),addition(X_20,addition(X_21,X_22))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
addition(X_20,addition(X_22,X_21)) = addition(X_20,addition(X_21,X_22)),
inference(resolve,[$cnf( $equal(addition(X_20,addition(X_22,X_21)),addition(addition(X_20,X_21),X_22)) )],[refute_0_23,refute_0_28]) ).
cnf(refute_0_30,plain,
( addition(X_20,addition(X_22,X_21)) != addition(X_20,addition(X_21,X_22))
| addition(X_20,addition(X_21,X_22)) = addition(X_20,addition(X_22,X_21)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(addition(X_20,addition(X_22,X_21)))),bind(Y,$fot(addition(X_20,addition(X_21,X_22))))]]) ).
cnf(refute_0_31,plain,
addition(X_20,addition(X_21,X_22)) = addition(X_20,addition(X_22,X_21)),
inference(resolve,[$cnf( $equal(addition(X_20,addition(X_22,X_21)),addition(X_20,addition(X_21,X_22))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
addition(X_22,addition(addition(X_21,X_22),X_21)) = addition(X_22,addition(X_21,addition(X_21,X_22))),
inference(subst,[],[refute_0_31:[bind(X_20,$fot(X_22)),bind(X_21,$fot(addition(X_21,X_22))),bind(X_22,$fot(X_21))]]) ).
cnf(refute_0_33,plain,
addition(A,addition(X_20,X_21)) = addition(addition(X_20,X_21),A),
inference(subst,[],[refute_0_14:[bind(B,$fot(addition(X_20,X_21)))]]) ).
cnf(refute_0_34,plain,
addition(X_20,addition(X_21,A)) = addition(addition(X_20,X_21),A),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_20)),bind(B,$fot(X_21)),bind(C,$fot(A))]]) ).
cnf(refute_0_35,plain,
( addition(X_20,addition(X_21,A)) != addition(addition(X_20,X_21),A)
| addition(addition(X_20,X_21),A) = addition(X_20,addition(X_21,A)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(addition(X_20,addition(X_21,A)))),bind(Y,$fot(addition(addition(X_20,X_21),A)))]]) ).
cnf(refute_0_36,plain,
addition(addition(X_20,X_21),A) = addition(X_20,addition(X_21,A)),
inference(resolve,[$cnf( $equal(addition(X_20,addition(X_21,A)),addition(addition(X_20,X_21),A)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( addition(A,addition(X_20,X_21)) != addition(addition(X_20,X_21),A)
| addition(addition(X_20,X_21),A) != addition(X_20,addition(X_21,A))
| addition(A,addition(X_20,X_21)) = addition(X_20,addition(X_21,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_20,X_21)),addition(X_20,addition(X_21,A))) ),[0],$fot(addition(addition(X_20,X_21),A))]]) ).
cnf(refute_0_38,plain,
( addition(A,addition(X_20,X_21)) != addition(addition(X_20,X_21),A)
| addition(A,addition(X_20,X_21)) = addition(X_20,addition(X_21,A)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_20,X_21),A),addition(X_20,addition(X_21,A))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
addition(A,addition(X_20,X_21)) = addition(X_20,addition(X_21,A)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_20,X_21)),addition(addition(X_20,X_21),A)) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
( addition(A,addition(X_20,X_21)) != addition(X_20,addition(X_21,A))
| addition(X_20,addition(X_21,A)) = addition(A,addition(X_20,X_21)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(addition(A,addition(X_20,X_21)))),bind(Y,$fot(addition(X_20,addition(X_21,A))))]]) ).
cnf(refute_0_41,plain,
addition(X_20,addition(X_21,A)) = addition(A,addition(X_20,X_21)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_20,X_21)),addition(X_20,addition(X_21,A))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
addition(addition(X_21,X_22),addition(X_21,X_22)) = addition(X_22,addition(addition(X_21,X_22),X_21)),
inference(subst,[],[refute_0_41:[bind(A,$fot(X_22)),bind(X_20,$fot(addition(X_21,X_22)))]]) ).
cnf(refute_0_43,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_44,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_18,refute_0_43]) ).
cnf(refute_0_45,plain,
( addition(X_22,addition(addition(X_21,X_22),X_21)) != addition(X_22,addition(X_21,addition(X_21,X_22)))
| addition(addition(X_21,X_22),addition(X_21,X_22)) != addition(X_22,addition(addition(X_21,X_22),X_21))
| addition(addition(X_21,X_22),addition(X_21,X_22)) = addition(X_22,addition(X_21,addition(X_21,X_22))) ),
inference(subst,[],[refute_0_44:[bind(X,$fot(addition(addition(X_21,X_22),addition(X_21,X_22)))),bind(Y,$fot(addition(X_22,addition(addition(X_21,X_22),X_21)))),bind(Z,$fot(addition(X_22,addition(X_21,addition(X_21,X_22)))))]]) ).
cnf(refute_0_46,plain,
( addition(X_22,addition(addition(X_21,X_22),X_21)) != addition(X_22,addition(X_21,addition(X_21,X_22)))
| addition(addition(X_21,X_22),addition(X_21,X_22)) = addition(X_22,addition(X_21,addition(X_21,X_22))) ),
inference(resolve,[$cnf( $equal(addition(addition(X_21,X_22),addition(X_21,X_22)),addition(X_22,addition(addition(X_21,X_22),X_21))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
addition(addition(X_21,X_22),addition(X_21,X_22)) = addition(X_22,addition(X_21,addition(X_21,X_22))),
inference(resolve,[$cnf( $equal(addition(X_22,addition(addition(X_21,X_22),X_21)),addition(X_22,addition(X_21,addition(X_21,X_22)))) )],[refute_0_32,refute_0_46]) ).
cnf(refute_0_48,plain,
addition(addition(addition(X_21,X_22),X_21),X_22) = addition(addition(X_21,X_22),addition(X_21,X_22)),
inference(subst,[],[refute_0_25:[bind(A,$fot(addition(X_21,X_22))),bind(B,$fot(X_21)),bind(C,$fot(X_22))]]) ).
cnf(refute_0_49,plain,
( addition(addition(X_21,X_22),addition(X_21,X_22)) != addition(X_22,addition(X_21,addition(X_21,X_22)))
| addition(addition(addition(X_21,X_22),X_21),X_22) != addition(addition(X_21,X_22),addition(X_21,X_22))
| addition(addition(addition(X_21,X_22),X_21),X_22) = addition(X_22,addition(X_21,addition(X_21,X_22))) ),
inference(subst,[],[refute_0_44:[bind(X,$fot(addition(addition(addition(X_21,X_22),X_21),X_22))),bind(Y,$fot(addition(addition(X_21,X_22),addition(X_21,X_22)))),bind(Z,$fot(addition(X_22,addition(X_21,addition(X_21,X_22)))))]]) ).
cnf(refute_0_50,plain,
( addition(addition(X_21,X_22),addition(X_21,X_22)) != addition(X_22,addition(X_21,addition(X_21,X_22)))
| addition(addition(addition(X_21,X_22),X_21),X_22) = addition(X_22,addition(X_21,addition(X_21,X_22))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(X_21,X_22),X_21),X_22),addition(addition(X_21,X_22),addition(X_21,X_22))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
addition(addition(addition(X_21,X_22),X_21),X_22) = addition(X_22,addition(X_21,addition(X_21,X_22))),
inference(resolve,[$cnf( $equal(addition(addition(X_21,X_22),addition(X_21,X_22)),addition(X_22,addition(X_21,addition(X_21,X_22)))) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
( addition(X_21,X_22) != addition(addition(addition(X_21,X_22),X_21),X_22)
| addition(addition(addition(X_21,X_22),X_21),X_22) != addition(X_22,addition(X_21,addition(X_21,X_22)))
| addition(X_21,X_22) = addition(X_22,addition(X_21,addition(X_21,X_22))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_21,X_22),addition(X_22,addition(X_21,addition(X_21,X_22)))) ),[0],$fot(addition(addition(addition(X_21,X_22),X_21),X_22))]]) ).
cnf(refute_0_53,plain,
( addition(X_21,X_22) != addition(addition(addition(X_21,X_22),X_21),X_22)
| addition(X_21,X_22) = addition(X_22,addition(X_21,addition(X_21,X_22))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(X_21,X_22),X_21),X_22),addition(X_22,addition(X_21,addition(X_21,X_22)))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
addition(X_21,X_22) = addition(X_22,addition(X_21,addition(X_21,X_22))),
inference(resolve,[$cnf( $equal(addition(X_21,X_22),addition(addition(addition(X_21,X_22),X_21),X_22)) )],[refute_0_12,refute_0_53]) ).
cnf(refute_0_55,plain,
addition(X_21,addition(X_21,X_22)) = addition(addition(X_21,X_21),X_22),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_21)),bind(B,$fot(X_21)),bind(C,$fot(X_22))]]) ).
cnf(refute_0_56,plain,
addition(X_21,X_21) = X_21,
inference(subst,[],[refute_0_8:[bind(A,$fot(X_21))]]) ).
cnf(refute_0_57,plain,
( addition(X_21,X_21) != X_21
| addition(X_21,addition(X_21,X_22)) != addition(addition(X_21,X_21),X_22)
| addition(X_21,addition(X_21,X_22)) = addition(X_21,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_21,addition(X_21,X_22)),addition(addition(X_21,X_21),X_22)) ),[1,0],$fot(X_21)]]) ).
cnf(refute_0_58,plain,
( addition(X_21,addition(X_21,X_22)) != addition(addition(X_21,X_21),X_22)
| addition(X_21,addition(X_21,X_22)) = addition(X_21,X_22) ),
inference(resolve,[$cnf( $equal(addition(X_21,X_21),X_21) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
addition(X_21,addition(X_21,X_22)) = addition(X_21,X_22),
inference(resolve,[$cnf( $equal(addition(X_21,addition(X_21,X_22)),addition(addition(X_21,X_21),X_22)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
addition(X_22,addition(X_21,addition(X_21,X_22))) = addition(X_22,addition(X_21,addition(X_21,X_22))),
introduced(tautology,[refl,[$fot(addition(X_22,addition(X_21,addition(X_21,X_22))))]]) ).
cnf(refute_0_61,plain,
( addition(X_21,addition(X_21,X_22)) != addition(X_21,X_22)
| addition(X_22,addition(X_21,addition(X_21,X_22))) != addition(X_22,addition(X_21,addition(X_21,X_22)))
| addition(X_22,addition(X_21,addition(X_21,X_22))) = addition(X_22,addition(X_21,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_22,addition(X_21,addition(X_21,X_22))),addition(X_22,addition(X_21,addition(X_21,X_22)))) ),[1,1],$fot(addition(X_21,X_22))]]) ).
cnf(refute_0_62,plain,
( addition(X_21,addition(X_21,X_22)) != addition(X_21,X_22)
| addition(X_22,addition(X_21,addition(X_21,X_22))) = addition(X_22,addition(X_21,X_22)) ),
inference(resolve,[$cnf( $equal(addition(X_22,addition(X_21,addition(X_21,X_22))),addition(X_22,addition(X_21,addition(X_21,X_22)))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
addition(X_22,addition(X_21,addition(X_21,X_22))) = addition(X_22,addition(X_21,X_22)),
inference(resolve,[$cnf( $equal(addition(X_21,addition(X_21,X_22)),addition(X_21,X_22)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( addition(X_21,X_22) != addition(X_22,addition(X_21,addition(X_21,X_22)))
| addition(X_22,addition(X_21,addition(X_21,X_22))) != addition(X_22,addition(X_21,X_22))
| addition(X_21,X_22) = addition(X_22,addition(X_21,X_22)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_21,X_22),addition(X_22,addition(X_21,X_22))) ),[0],$fot(addition(X_22,addition(X_21,addition(X_21,X_22))))]]) ).
cnf(refute_0_65,plain,
( addition(X_21,X_22) != addition(X_22,addition(X_21,addition(X_21,X_22)))
| addition(X_21,X_22) = addition(X_22,addition(X_21,X_22)) ),
inference(resolve,[$cnf( $equal(addition(X_22,addition(X_21,addition(X_21,X_22))),addition(X_22,addition(X_21,X_22))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
addition(X_21,X_22) = addition(X_22,addition(X_21,X_22)),
inference(resolve,[$cnf( $equal(addition(X_21,X_22),addition(X_22,addition(X_21,addition(X_21,X_22)))) )],[refute_0_54,refute_0_65]) ).
cnf(refute_0_67,plain,
addition(X_21,X_46) = addition(X_46,addition(X_21,X_46)),
inference(subst,[],[refute_0_66:[bind(X_22,$fot(X_46))]]) ).
cnf(refute_0_68,plain,
( addition(X_21,X_46) != addition(X_46,addition(X_21,X_46))
| addition(X_46,addition(X_21,X_46)) = addition(X_21,X_46) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(addition(X_21,X_46))),bind(Y,$fot(addition(X_46,addition(X_21,X_46))))]]) ).
cnf(refute_0_69,plain,
addition(X_46,addition(X_21,X_46)) = addition(X_21,X_46),
inference(resolve,[$cnf( $equal(addition(X_21,X_46),addition(X_46,addition(X_21,X_46))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( addition(X_21,X_46) != addition(X_21,X_46)
| addition(X_46,addition(X_21,X_46)) != addition(X_21,X_46)
| addition(X_46,addition(X_21,X_46)) = addition(X_21,X_46) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_46,addition(X_21,X_46)),addition(X_21,X_46)) ),[0,1],$fot(addition(X_21,X_46))]]) ).
cnf(refute_0_71,plain,
( addition(X_21,X_46) != addition(X_21,X_46)
| addition(X_46,addition(X_21,X_46)) = addition(X_21,X_46) ),
inference(resolve,[$cnf( $equal(addition(X_46,addition(X_21,X_46)),addition(X_21,X_46)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( addition(X_21,X_46) != addition(X_21,X_46)
| leq(X_46,addition(X_21,X_46)) ),
inference(resolve,[$cnf( $equal(addition(X_46,addition(X_21,X_46)),addition(X_21,X_46)) )],[refute_0_71,refute_0_5]) ).
cnf(refute_0_73,plain,
addition(X_21,X_46) = addition(X_21,X_46),
introduced(tautology,[refl,[$fot(addition(X_21,X_46))]]) ).
cnf(refute_0_74,plain,
leq(X_46,addition(X_21,X_46)),
inference(resolve,[$cnf( $equal(addition(X_21,X_46),addition(X_21,X_46)) )],[refute_0_73,refute_0_72]) ).
cnf(refute_0_75,plain,
leq(multiplication(X_89,X_90),addition(multiplication(X_88,X_90),multiplication(X_89,X_90))),
inference(subst,[],[refute_0_74:[bind(X_21,$fot(multiplication(X_88,X_90))),bind(X_46,$fot(multiplication(X_89,X_90)))]]) ).
cnf(refute_0_76,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_77,plain,
multiplication(addition(X_88,X_89),X_90) = addition(multiplication(X_88,X_90),multiplication(X_89,X_90)),
inference(subst,[],[refute_0_76:[bind(A,$fot(X_88)),bind(B,$fot(X_89)),bind(C,$fot(X_90))]]) ).
cnf(refute_0_78,plain,
( multiplication(addition(X_88,X_89),X_90) != addition(multiplication(X_88,X_90),multiplication(X_89,X_90))
| addition(multiplication(X_88,X_90),multiplication(X_89,X_90)) = multiplication(addition(X_88,X_89),X_90) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(multiplication(addition(X_88,X_89),X_90))),bind(Y,$fot(addition(multiplication(X_88,X_90),multiplication(X_89,X_90))))]]) ).
cnf(refute_0_79,plain,
addition(multiplication(X_88,X_90),multiplication(X_89,X_90)) = multiplication(addition(X_88,X_89),X_90),
inference(resolve,[$cnf( $equal(multiplication(addition(X_88,X_89),X_90),addition(multiplication(X_88,X_90),multiplication(X_89,X_90))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( addition(multiplication(X_88,X_90),multiplication(X_89,X_90)) != multiplication(addition(X_88,X_89),X_90)
| ~ leq(multiplication(X_89,X_90),addition(multiplication(X_88,X_90),multiplication(X_89,X_90)))
| leq(multiplication(X_89,X_90),multiplication(addition(X_88,X_89),X_90)) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(X_89,X_90),addition(multiplication(X_88,X_90),multiplication(X_89,X_90))) ),[1],$fot(multiplication(addition(X_88,X_89),X_90))]]) ).
cnf(refute_0_81,plain,
( ~ leq(multiplication(X_89,X_90),addition(multiplication(X_88,X_90),multiplication(X_89,X_90)))
| leq(multiplication(X_89,X_90),multiplication(addition(X_88,X_89),X_90)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_88,X_90),multiplication(X_89,X_90)),multiplication(addition(X_88,X_89),X_90)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
leq(multiplication(X_89,X_90),multiplication(addition(X_88,X_89),X_90)),
inference(resolve,[$cnf( leq(multiplication(X_89,X_90),addition(multiplication(X_88,X_90),multiplication(X_89,X_90))) )],[refute_0_75,refute_0_81]) ).
cnf(refute_0_83,plain,
leq(multiplication(domain(X0),X_108),multiplication(addition(one,domain(X0)),X_108)),
inference(subst,[],[refute_0_82:[bind(X_88,$fot(one)),bind(X_89,$fot(domain(X0))),bind(X_90,$fot(X_108))]]) ).
cnf(refute_0_84,plain,
addition(domain(X0),one) = one,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_85,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_86,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_14,refute_0_85]) ).
cnf(refute_0_87,plain,
addition(domain(X0),one) = addition(one,domain(X0)),
inference(subst,[],[refute_0_86:[bind(A,$fot(one)),bind(B,$fot(domain(X0)))]]) ).
cnf(refute_0_88,plain,
( addition(domain(X0),one) != addition(one,domain(X0))
| addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X0),one),one) ),[0],$fot(addition(one,domain(X0)))]]) ).
cnf(refute_0_89,plain,
( addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X0),one),addition(one,domain(X0))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
addition(one,domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(domain(X0),one),one) )],[refute_0_84,refute_0_89]) ).
cnf(refute_0_91,plain,
( addition(one,domain(X0)) != one
| ~ leq(multiplication(domain(X0),X_108),multiplication(addition(one,domain(X0)),X_108))
| leq(multiplication(domain(X0),X_108),multiplication(one,X_108)) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(domain(X0),X_108),multiplication(addition(one,domain(X0)),X_108)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_92,plain,
( ~ leq(multiplication(domain(X0),X_108),multiplication(addition(one,domain(X0)),X_108))
| leq(multiplication(domain(X0),X_108),multiplication(one,X_108)) ),
inference(resolve,[$cnf( $equal(addition(one,domain(X0)),one) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
leq(multiplication(domain(X0),X_108),multiplication(one,X_108)),
inference(resolve,[$cnf( leq(multiplication(domain(X0),X_108),multiplication(addition(one,domain(X0)),X_108)) )],[refute_0_83,refute_0_92]) ).
cnf(refute_0_94,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_95,plain,
multiplication(one,X_108) = X_108,
inference(subst,[],[refute_0_94:[bind(A,$fot(X_108))]]) ).
cnf(refute_0_96,plain,
( multiplication(one,X_108) != X_108
| ~ leq(multiplication(domain(X0),X_108),multiplication(one,X_108))
| leq(multiplication(domain(X0),X_108),X_108) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(domain(X0),X_108),multiplication(one,X_108)) ),[1],$fot(X_108)]]) ).
cnf(refute_0_97,plain,
( ~ leq(multiplication(domain(X0),X_108),multiplication(one,X_108))
| leq(multiplication(domain(X0),X_108),X_108) ),
inference(resolve,[$cnf( $equal(multiplication(one,X_108),X_108) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
leq(multiplication(domain(X0),X_108),X_108),
inference(resolve,[$cnf( leq(multiplication(domain(X0),X_108),multiplication(one,X_108)) )],[refute_0_93,refute_0_97]) ).
cnf(refute_0_99,plain,
leq(multiplication(domain(X_109),X_110),X_110),
inference(subst,[],[refute_0_98:[bind(X0,$fot(X_109)),bind(X_108,$fot(X_110))]]) ).
cnf(refute_0_100,plain,
addition(multiplication(domain(X_109),X_110),X_110) = X_110,
inference(resolve,[$cnf( leq(multiplication(domain(X_109),X_110),X_110) )],[refute_0_99,refute_0_3]) ).
cnf(refute_0_101,plain,
addition(multiplication(domain(X_109),X_110),X_110) = addition(X_110,multiplication(domain(X_109),X_110)),
inference(subst,[],[refute_0_86:[bind(A,$fot(X_110)),bind(B,$fot(multiplication(domain(X_109),X_110)))]]) ).
cnf(refute_0_102,plain,
( addition(multiplication(domain(X_109),X_110),X_110) != X_110
| addition(multiplication(domain(X_109),X_110),X_110) != addition(X_110,multiplication(domain(X_109),X_110))
| addition(X_110,multiplication(domain(X_109),X_110)) = X_110 ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(domain(X_109),X_110),X_110),X_110) ),[0],$fot(addition(X_110,multiplication(domain(X_109),X_110)))]]) ).
cnf(refute_0_103,plain,
( addition(multiplication(domain(X_109),X_110),X_110) != X_110
| addition(X_110,multiplication(domain(X_109),X_110)) = X_110 ),
inference(resolve,[$cnf( $equal(addition(multiplication(domain(X_109),X_110),X_110),addition(X_110,multiplication(domain(X_109),X_110))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
addition(X_110,multiplication(domain(X_109),X_110)) = X_110,
inference(resolve,[$cnf( $equal(addition(multiplication(domain(X_109),X_110),X_110),X_110) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
addition(X0,multiplication(domain(X0),X0)) = X0,
inference(subst,[],[refute_0_104:[bind(X_109,$fot(X0)),bind(X_110,$fot(X0))]]) ).
cnf(refute_0_106,plain,
( addition(X0,multiplication(domain(X0),X0)) != X0
| addition(X0,multiplication(domain(X0),X0)) != multiplication(domain(X0),X0)
| X0 = multiplication(domain(X0),X0) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X0,multiplication(domain(X0),X0)),multiplication(domain(X0),X0)) ),[0],$fot(X0)]]) ).
cnf(refute_0_107,plain,
( addition(X0,multiplication(domain(X0),X0)) != multiplication(domain(X0),X0)
| X0 = multiplication(domain(X0),X0) ),
inference(resolve,[$cnf( $equal(addition(X0,multiplication(domain(X0),X0)),X0) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
X0 = multiplication(domain(X0),X0),
inference(resolve,[$cnf( $equal(addition(X0,multiplication(domain(X0),X0)),multiplication(domain(X0),X0)) )],[refute_0_1,refute_0_107]) ).
cnf(refute_0_109,plain,
( X0 != multiplication(domain(X0),X0)
| multiplication(domain(X0),X0) = X0 ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X0)),bind(Y,$fot(multiplication(domain(X0),X0)))]]) ).
cnf(refute_0_110,plain,
multiplication(domain(X0),X0) = X0,
inference(resolve,[$cnf( $equal(X0,multiplication(domain(X0),X0)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_0_110:[bind(X0,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_112,plain,
( multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0
| skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) ),[0],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_113,plain,
( skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0
| multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0 ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0,
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) )],[refute_0_113,refute_0_0]) ).
cnf(refute_0_115,plain,
skolemFOFtoCNF_X0 = skolemFOFtoCNF_X0,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_116,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0,skolemFOFtoCNF_X0) )],[refute_0_115,refute_0_114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE052+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.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 13:46:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.52/0.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.52/0.71
% 0.52/0.71 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.52/0.73
%------------------------------------------------------------------------------