TSTP Solution File: KLE148+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 02:15:34 EDT 2022
% Result : Theorem 0.69s 0.86s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 38
% Syntax : Number of formulae : 197 ( 120 unt; 0 def)
% Number of atoms : 306 ( 254 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 218 ( 109 ~; 90 |; 7 &)
% ( 5 <=>; 7 =>; 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 278 ( 8 sgn 92 !; 4 ?)
% 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_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(idempotence,axiom,
! [A] : addition(A,A) = A ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(distributivity1,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero ).
fof(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(goals,conjecture,
! [X0,X1] :
( ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) )
& leq(X0,multiplication(X0,strong_iteration(X1))) ) ).
fof(subgoal_0,plain,
! [X0,X1] :
( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) ),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0,X1] :
( ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) )
=> leq(X0,multiplication(X0,strong_iteration(X1))) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] :
( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] :
( ~ leq(multiplication(X0,strong_iteration(X1)),X0)
& multiplication(X0,X1) = zero ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ leq(multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0)
& multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = zero ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ leq(multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[distributivity1]) ).
fof(normalize_0_4,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[multiplicative_associativity]) ).
fof(normalize_0_6,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = zero,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_0_9,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_11,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(canonicalize,[],[infty_unfold1]) ).
fof(normalize_0_13,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_15,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_17,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_19,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[idempotence]) ).
fof(normalize_0_23,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_22]) ).
cnf(refute_0_0,plain,
~ leq(multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))) = addition(multiplication(skolemFOFtoCNF_X0,X_41),multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21))),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(X_41)),bind(C,$fot(multiplication(skolemFOFtoCNF_X1,X_21)))]]) ).
cnf(refute_0_3,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) = multiplication(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),X_21),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(skolemFOFtoCNF_X1)),bind(C,$fot(X_21))]]) ).
cnf(refute_0_5,plain,
multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = zero,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
( multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) != multiplication(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),X_21)
| multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != zero
| multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) = multiplication(zero,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)),multiplication(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),X_21)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_7,plain,
( multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) != multiplication(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),X_21)
| multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) = multiplication(zero,X_21) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),zero) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) = multiplication(zero,X_21),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)),multiplication(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),X_21)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
multiplication(zero,X_21) = zero,
inference(subst,[],[refute_0_9:[bind(A,$fot(X_21))]]) ).
cnf(refute_0_11,plain,
( multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) != multiplication(zero,X_21)
| multiplication(zero,X_21) != zero
| multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)),zero) ),[0],$fot(multiplication(zero,X_21))]]) ).
cnf(refute_0_12,plain,
( multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) != multiplication(zero,X_21)
| multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) = zero ),
inference(resolve,[$cnf( $equal(multiplication(zero,X_21),zero) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) = zero,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)),multiplication(zero,X_21)) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))) != addition(multiplication(skolemFOFtoCNF_X0,X_41),multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)))
| multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)) != zero
| multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))) = addition(multiplication(skolemFOFtoCNF_X0,X_41),zero) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))),addition(multiplication(skolemFOFtoCNF_X0,X_41),multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_15,plain,
( multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))) != addition(multiplication(skolemFOFtoCNF_X0,X_41),multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)))
| multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))) = addition(multiplication(skolemFOFtoCNF_X0,X_41),zero) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)),zero) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))) = addition(multiplication(skolemFOFtoCNF_X0,X_41),zero),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))),addition(multiplication(skolemFOFtoCNF_X0,X_41),multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1,X_21)))) )],[refute_0_2,refute_0_15]) ).
cnf(refute_0_17,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_18,plain,
addition(multiplication(skolemFOFtoCNF_X0,X_41),zero) = multiplication(skolemFOFtoCNF_X0,X_41),
inference(subst,[],[refute_0_17:[bind(A,$fot(multiplication(skolemFOFtoCNF_X0,X_41)))]]) ).
cnf(refute_0_19,plain,
( addition(multiplication(skolemFOFtoCNF_X0,X_41),zero) != multiplication(skolemFOFtoCNF_X0,X_41)
| multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))) != addition(multiplication(skolemFOFtoCNF_X0,X_41),zero)
| multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))) = multiplication(skolemFOFtoCNF_X0,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))),addition(multiplication(skolemFOFtoCNF_X0,X_41),zero)) ),[1],$fot(multiplication(skolemFOFtoCNF_X0,X_41))]]) ).
cnf(refute_0_20,plain,
( multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))) != addition(multiplication(skolemFOFtoCNF_X0,X_41),zero)
| multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))) = multiplication(skolemFOFtoCNF_X0,X_41) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,X_41),zero),multiplication(skolemFOFtoCNF_X0,X_41)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))) = multiplication(skolemFOFtoCNF_X0,X_41),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,addition(X_41,multiplication(skolemFOFtoCNF_X1,X_21))),addition(multiplication(skolemFOFtoCNF_X0,X_41),zero)) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
multiplication(skolemFOFtoCNF_X0,addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1)))) = multiplication(skolemFOFtoCNF_X0,one),
inference(subst,[],[refute_0_21:[bind(X_21,$fot(strong_iteration(skolemFOFtoCNF_X1))),bind(X_41,$fot(one))]]) ).
cnf(refute_0_23,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_24,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_25,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_26,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_27,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_29,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
addition(multiplication(A,strong_iteration(A)),one) = addition(one,multiplication(A,strong_iteration(A))),
inference(subst,[],[refute_0_29:[bind(A,$fot(one)),bind(B,$fot(multiplication(A,strong_iteration(A))))]]) ).
cnf(refute_0_31,plain,
( addition(multiplication(A,strong_iteration(A)),one) != addition(one,multiplication(A,strong_iteration(A)))
| strong_iteration(A) != addition(multiplication(A,strong_iteration(A)),one)
| strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))) ),
introduced(tautology,[equality,[$cnf( $equal(strong_iteration(A),addition(multiplication(A,strong_iteration(A)),one)) ),[1],$fot(addition(one,multiplication(A,strong_iteration(A))))]]) ).
cnf(refute_0_32,plain,
( strong_iteration(A) != addition(multiplication(A,strong_iteration(A)),one)
| strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,strong_iteration(A)),one),addition(one,multiplication(A,strong_iteration(A)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))),
inference(resolve,[$cnf( $equal(strong_iteration(A),addition(multiplication(A,strong_iteration(A)),one)) )],[refute_0_23,refute_0_32]) ).
cnf(refute_0_34,plain,
strong_iteration(skolemFOFtoCNF_X1) = addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1))),
inference(subst,[],[refute_0_33:[bind(A,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_35,plain,
( strong_iteration(skolemFOFtoCNF_X1) != addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1)))
| addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1))) = strong_iteration(skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(strong_iteration(skolemFOFtoCNF_X1))),bind(Y,$fot(addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1)))))]]) ).
cnf(refute_0_36,plain,
addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1))) = strong_iteration(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(strong_iteration(skolemFOFtoCNF_X1),addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1))) != strong_iteration(skolemFOFtoCNF_X1)
| multiplication(skolemFOFtoCNF_X0,addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1)))) != multiplication(skolemFOFtoCNF_X0,one)
| multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)) = multiplication(skolemFOFtoCNF_X0,one) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1)))),multiplication(skolemFOFtoCNF_X0,one)) ),[0,1],$fot(strong_iteration(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_38,plain,
( multiplication(skolemFOFtoCNF_X0,addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1)))) != multiplication(skolemFOFtoCNF_X0,one)
| multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)) = multiplication(skolemFOFtoCNF_X0,one) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1))),strong_iteration(skolemFOFtoCNF_X1)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)) = multiplication(skolemFOFtoCNF_X0,one),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,addition(one,multiplication(skolemFOFtoCNF_X1,strong_iteration(skolemFOFtoCNF_X1)))),multiplication(skolemFOFtoCNF_X0,one)) )],[refute_0_22,refute_0_38]) ).
cnf(refute_0_40,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_41,plain,
multiplication(skolemFOFtoCNF_X0,one) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_0_40:[bind(A,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_42,plain,
( multiplication(skolemFOFtoCNF_X0,one) != skolemFOFtoCNF_X0
| multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)) != multiplication(skolemFOFtoCNF_X0,one)
| multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)) = skolemFOFtoCNF_X0 ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,one)) ),[1],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_43,plain,
( multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)) != multiplication(skolemFOFtoCNF_X0,one)
| multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)) = skolemFOFtoCNF_X0 ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,one),skolemFOFtoCNF_X0) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)) = skolemFOFtoCNF_X0,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)),multiplication(skolemFOFtoCNF_X0,one)) )],[refute_0_39,refute_0_43]) ).
cnf(refute_0_45,plain,
( multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)) != skolemFOFtoCNF_X0
| ~ leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X0)
| leq(multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( ~ leq(multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0) ),[0],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_46,plain,
( ~ leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X0)
| leq(multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
~ leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X0),
inference(resolve,[$cnf( leq(multiplication(skolemFOFtoCNF_X0,strong_iteration(skolemFOFtoCNF_X1)),skolemFOFtoCNF_X0) )],[refute_0_46,refute_0_0]) ).
cnf(refute_0_48,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_49,plain,
( addition(X_13,X_13) != X_13
| leq(X_13,X_13) ),
inference(subst,[],[refute_0_48:[bind(A,$fot(X_13)),bind(B,$fot(X_13))]]) ).
cnf(refute_0_50,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_51,plain,
addition(X_13,X_13) = X_13,
inference(subst,[],[refute_0_50:[bind(A,$fot(X_13))]]) ).
cnf(refute_0_52,plain,
( X_13 != X_13
| addition(X_13,X_13) != X_13
| addition(X_13,X_13) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_13,X_13),X_13) ),[0,0],$fot(X_13)]]) ).
cnf(refute_0_53,plain,
( X_13 != X_13
| addition(X_13,X_13) = X_13 ),
inference(resolve,[$cnf( $equal(addition(X_13,X_13),X_13) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( X_13 != X_13
| leq(X_13,X_13) ),
inference(resolve,[$cnf( $equal(addition(X_13,X_13),X_13) )],[refute_0_53,refute_0_49]) ).
cnf(refute_0_55,plain,
X_13 = X_13,
introduced(tautology,[refl,[$fot(X_13)]]) ).
cnf(refute_0_56,plain,
leq(X_13,X_13),
inference(resolve,[$cnf( $equal(X_13,X_13) )],[refute_0_55,refute_0_54]) ).
cnf(refute_0_57,plain,
leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_56:[bind(X_13,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_58,plain,
$false,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X0) )],[refute_0_57,refute_0_47]) ).
fof(negate_1_0,plain,
~ ! [X0,X1] :
( ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) )
=> leq(X0,multiplication(X0,strong_iteration(X1))) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X0,X1] :
( ~ leq(X0,multiplication(X0,strong_iteration(X1)))
& ( multiplication(X0,X1) != zero
| leq(multiplication(X0,strong_iteration(X1)),X0) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ leq(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X0_1,strong_iteration(skolemFOFtoCNF_X1_1)))
& ( multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1) != zero
| leq(multiplication(skolemFOFtoCNF_X0_1,strong_iteration(skolemFOFtoCNF_X1_1)),skolemFOFtoCNF_X0_1) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ leq(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X0_1,strong_iteration(skolemFOFtoCNF_X1_1))),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_1_4,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_1_8,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[idempotence]) ).
fof(normalize_1_10,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[distributivity1]) ).
fof(normalize_1_12,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_1_14,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(canonicalize,[],[infty_unfold1]) ).
fof(normalize_1_16,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_1_18,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_1_17]) ).
cnf(refute_1_0,plain,
~ leq(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X0_1,strong_iteration(skolemFOFtoCNF_X1_1))),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( addition(A,addition(A,X_209)) != addition(A,X_209)
| leq(A,addition(A,X_209)) ),
inference(subst,[],[refute_1_1:[bind(B,$fot(addition(A,X_209)))]]) ).
cnf(refute_1_3,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_4,plain,
addition(X_62,addition(X_62,X_63)) = addition(addition(X_62,X_62),X_63),
inference(subst,[],[refute_1_3:[bind(A,$fot(X_62)),bind(B,$fot(X_62)),bind(C,$fot(X_63))]]) ).
cnf(refute_1_5,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_6,plain,
addition(X_62,X_62) = X_62,
inference(subst,[],[refute_1_5:[bind(A,$fot(X_62))]]) ).
cnf(refute_1_7,plain,
( addition(X_62,X_62) != X_62
| addition(X_62,addition(X_62,X_63)) != addition(addition(X_62,X_62),X_63)
| addition(X_62,addition(X_62,X_63)) = addition(X_62,X_63) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_62,addition(X_62,X_63)),addition(addition(X_62,X_62),X_63)) ),[1,0],$fot(X_62)]]) ).
cnf(refute_1_8,plain,
( addition(X_62,addition(X_62,X_63)) != addition(addition(X_62,X_62),X_63)
| addition(X_62,addition(X_62,X_63)) = addition(X_62,X_63) ),
inference(resolve,[$cnf( $equal(addition(X_62,X_62),X_62) )],[refute_1_6,refute_1_7]) ).
cnf(refute_1_9,plain,
addition(X_62,addition(X_62,X_63)) = addition(X_62,X_63),
inference(resolve,[$cnf( $equal(addition(X_62,addition(X_62,X_63)),addition(addition(X_62,X_62),X_63)) )],[refute_1_4,refute_1_8]) ).
cnf(refute_1_10,plain,
addition(A,addition(A,X_209)) = addition(A,X_209),
inference(subst,[],[refute_1_9:[bind(X_62,$fot(A)),bind(X_63,$fot(X_209))]]) ).
cnf(refute_1_11,plain,
( addition(A,X_209) != addition(A,X_209)
| addition(A,addition(A,X_209)) != addition(A,X_209)
| addition(A,addition(A,X_209)) = addition(A,X_209) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(A,X_209)),addition(A,X_209)) ),[0,1],$fot(addition(A,X_209))]]) ).
cnf(refute_1_12,plain,
( addition(A,X_209) != addition(A,X_209)
| addition(A,addition(A,X_209)) = addition(A,X_209) ),
inference(resolve,[$cnf( $equal(addition(A,addition(A,X_209)),addition(A,X_209)) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
( addition(A,X_209) != addition(A,X_209)
| leq(A,addition(A,X_209)) ),
inference(resolve,[$cnf( $equal(addition(A,addition(A,X_209)),addition(A,X_209)) )],[refute_1_12,refute_1_2]) ).
cnf(refute_1_14,plain,
addition(A,X_209) = addition(A,X_209),
introduced(tautology,[refl,[$fot(addition(A,X_209))]]) ).
cnf(refute_1_15,plain,
leq(A,addition(A,X_209)),
inference(resolve,[$cnf( $equal(addition(A,X_209),addition(A,X_209)) )],[refute_1_14,refute_1_13]) ).
cnf(refute_1_16,plain,
leq(X_210,addition(X_210,multiplication(X_210,strong_iteration(X_100)))),
inference(subst,[],[refute_1_15:[bind(A,$fot(X_210)),bind(X_209,$fot(multiplication(X_210,strong_iteration(X_100))))]]) ).
cnf(refute_1_17,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_18,plain,
multiplication(X_103,addition(one,X_105)) = addition(multiplication(X_103,one),multiplication(X_103,X_105)),
inference(subst,[],[refute_1_17:[bind(A,$fot(X_103)),bind(B,$fot(one)),bind(C,$fot(X_105))]]) ).
cnf(refute_1_19,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_20,plain,
multiplication(X_103,one) = X_103,
inference(subst,[],[refute_1_19:[bind(A,$fot(X_103))]]) ).
cnf(refute_1_21,plain,
( multiplication(X_103,addition(one,X_105)) != addition(multiplication(X_103,one),multiplication(X_103,X_105))
| multiplication(X_103,one) != X_103
| multiplication(X_103,addition(one,X_105)) = addition(X_103,multiplication(X_103,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_103,addition(one,X_105)),addition(multiplication(X_103,one),multiplication(X_103,X_105))) ),[1,0],$fot(X_103)]]) ).
cnf(refute_1_22,plain,
( multiplication(X_103,addition(one,X_105)) != addition(multiplication(X_103,one),multiplication(X_103,X_105))
| multiplication(X_103,addition(one,X_105)) = addition(X_103,multiplication(X_103,X_105)) ),
inference(resolve,[$cnf( $equal(multiplication(X_103,one),X_103) )],[refute_1_20,refute_1_21]) ).
cnf(refute_1_23,plain,
multiplication(X_103,addition(one,X_105)) = addition(X_103,multiplication(X_103,X_105)),
inference(resolve,[$cnf( $equal(multiplication(X_103,addition(one,X_105)),addition(multiplication(X_103,one),multiplication(X_103,X_105))) )],[refute_1_18,refute_1_22]) ).
cnf(refute_1_24,plain,
multiplication(X_108,addition(one,strong_iteration(X_100))) = addition(X_108,multiplication(X_108,strong_iteration(X_100))),
inference(subst,[],[refute_1_23:[bind(X_103,$fot(X_108)),bind(X_105,$fot(strong_iteration(X_100)))]]) ).
cnf(refute_1_25,plain,
addition(one,addition(multiplication(A,strong_iteration(A)),X_63)) = addition(addition(one,multiplication(A,strong_iteration(A))),X_63),
inference(subst,[],[refute_1_3:[bind(A,$fot(one)),bind(B,$fot(multiplication(A,strong_iteration(A)))),bind(C,$fot(X_63))]]) ).
cnf(refute_1_26,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_27,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_28,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_29,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_30,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_28,refute_1_29]) ).
cnf(refute_1_31,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_1_30:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_1_32,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_1_27,refute_1_31]) ).
cnf(refute_1_33,plain,
addition(multiplication(A,strong_iteration(A)),one) = addition(one,multiplication(A,strong_iteration(A))),
inference(subst,[],[refute_1_32:[bind(A,$fot(one)),bind(B,$fot(multiplication(A,strong_iteration(A))))]]) ).
cnf(refute_1_34,plain,
( addition(multiplication(A,strong_iteration(A)),one) != addition(one,multiplication(A,strong_iteration(A)))
| strong_iteration(A) != addition(multiplication(A,strong_iteration(A)),one)
| strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))) ),
introduced(tautology,[equality,[$cnf( $equal(strong_iteration(A),addition(multiplication(A,strong_iteration(A)),one)) ),[1],$fot(addition(one,multiplication(A,strong_iteration(A))))]]) ).
cnf(refute_1_35,plain,
( strong_iteration(A) != addition(multiplication(A,strong_iteration(A)),one)
| strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,strong_iteration(A)),one),addition(one,multiplication(A,strong_iteration(A)))) )],[refute_1_33,refute_1_34]) ).
cnf(refute_1_36,plain,
strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))),
inference(resolve,[$cnf( $equal(strong_iteration(A),addition(multiplication(A,strong_iteration(A)),one)) )],[refute_1_26,refute_1_35]) ).
cnf(refute_1_37,plain,
( strong_iteration(A) != addition(one,multiplication(A,strong_iteration(A)))
| addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A) ),
inference(subst,[],[refute_1_30:[bind(X,$fot(strong_iteration(A))),bind(Y,$fot(addition(one,multiplication(A,strong_iteration(A)))))]]) ).
cnf(refute_1_38,plain,
addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A),
inference(resolve,[$cnf( $equal(strong_iteration(A),addition(one,multiplication(A,strong_iteration(A)))) )],[refute_1_36,refute_1_37]) ).
cnf(refute_1_39,plain,
( addition(one,addition(multiplication(A,strong_iteration(A)),X_63)) != addition(addition(one,multiplication(A,strong_iteration(A))),X_63)
| addition(one,multiplication(A,strong_iteration(A))) != strong_iteration(A)
| addition(one,addition(multiplication(A,strong_iteration(A)),X_63)) = addition(strong_iteration(A),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,addition(multiplication(A,strong_iteration(A)),X_63)),addition(addition(one,multiplication(A,strong_iteration(A))),X_63)) ),[1,0],$fot(strong_iteration(A))]]) ).
cnf(refute_1_40,plain,
( addition(one,addition(multiplication(A,strong_iteration(A)),X_63)) != addition(addition(one,multiplication(A,strong_iteration(A))),X_63)
| addition(one,addition(multiplication(A,strong_iteration(A)),X_63)) = addition(strong_iteration(A),X_63) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(A,strong_iteration(A))),strong_iteration(A)) )],[refute_1_38,refute_1_39]) ).
cnf(refute_1_41,plain,
addition(one,addition(multiplication(A,strong_iteration(A)),X_63)) = addition(strong_iteration(A),X_63),
inference(resolve,[$cnf( $equal(addition(one,addition(multiplication(A,strong_iteration(A)),X_63)),addition(addition(one,multiplication(A,strong_iteration(A))),X_63)) )],[refute_1_25,refute_1_40]) ).
cnf(refute_1_42,plain,
addition(one,addition(multiplication(X_74,strong_iteration(X_74)),X_75)) = addition(strong_iteration(X_74),X_75),
inference(subst,[],[refute_1_41:[bind(A,$fot(X_74)),bind(X_63,$fot(X_75))]]) ).
cnf(refute_1_43,plain,
addition(X_75,multiplication(X_74,strong_iteration(X_74))) = addition(multiplication(X_74,strong_iteration(X_74)),X_75),
inference(subst,[],[refute_1_27:[bind(A,$fot(X_75)),bind(B,$fot(multiplication(X_74,strong_iteration(X_74))))]]) ).
cnf(refute_1_44,plain,
( addition(X_75,multiplication(X_74,strong_iteration(X_74))) != addition(multiplication(X_74,strong_iteration(X_74)),X_75)
| addition(multiplication(X_74,strong_iteration(X_74)),X_75) = addition(X_75,multiplication(X_74,strong_iteration(X_74))) ),
inference(subst,[],[refute_1_30:[bind(X,$fot(addition(X_75,multiplication(X_74,strong_iteration(X_74))))),bind(Y,$fot(addition(multiplication(X_74,strong_iteration(X_74)),X_75)))]]) ).
cnf(refute_1_45,plain,
addition(multiplication(X_74,strong_iteration(X_74)),X_75) = addition(X_75,multiplication(X_74,strong_iteration(X_74))),
inference(resolve,[$cnf( $equal(addition(X_75,multiplication(X_74,strong_iteration(X_74))),addition(multiplication(X_74,strong_iteration(X_74)),X_75)) )],[refute_1_43,refute_1_44]) ).
cnf(refute_1_46,plain,
( addition(multiplication(X_74,strong_iteration(X_74)),X_75) != addition(X_75,multiplication(X_74,strong_iteration(X_74)))
| addition(one,addition(multiplication(X_74,strong_iteration(X_74)),X_75)) != addition(strong_iteration(X_74),X_75)
| addition(one,addition(X_75,multiplication(X_74,strong_iteration(X_74)))) = addition(strong_iteration(X_74),X_75) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,addition(multiplication(X_74,strong_iteration(X_74)),X_75)),addition(strong_iteration(X_74),X_75)) ),[0,1],$fot(addition(X_75,multiplication(X_74,strong_iteration(X_74))))]]) ).
cnf(refute_1_47,plain,
( addition(one,addition(multiplication(X_74,strong_iteration(X_74)),X_75)) != addition(strong_iteration(X_74),X_75)
| addition(one,addition(X_75,multiplication(X_74,strong_iteration(X_74)))) = addition(strong_iteration(X_74),X_75) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_74,strong_iteration(X_74)),X_75),addition(X_75,multiplication(X_74,strong_iteration(X_74)))) )],[refute_1_45,refute_1_46]) ).
cnf(refute_1_48,plain,
addition(one,addition(X_75,multiplication(X_74,strong_iteration(X_74)))) = addition(strong_iteration(X_74),X_75),
inference(resolve,[$cnf( $equal(addition(one,addition(multiplication(X_74,strong_iteration(X_74)),X_75)),addition(strong_iteration(X_74),X_75)) )],[refute_1_42,refute_1_47]) ).
cnf(refute_1_49,plain,
addition(one,addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100)))) = addition(strong_iteration(X_100),strong_iteration(X_100)),
inference(subst,[],[refute_1_48:[bind(X_74,$fot(X_100)),bind(X_75,$fot(strong_iteration(X_100)))]]) ).
cnf(refute_1_50,plain,
addition(one,addition(multiplication(X_74,strong_iteration(X_74)),multiplication(X_74,strong_iteration(X_74)))) = addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74))),
inference(subst,[],[refute_1_41:[bind(A,$fot(X_74)),bind(X_63,$fot(multiplication(X_74,strong_iteration(X_74))))]]) ).
cnf(refute_1_51,plain,
addition(multiplication(X_74,strong_iteration(X_74)),multiplication(X_74,strong_iteration(X_74))) = multiplication(X_74,strong_iteration(X_74)),
inference(subst,[],[refute_1_5:[bind(A,$fot(multiplication(X_74,strong_iteration(X_74))))]]) ).
cnf(refute_1_52,plain,
( addition(multiplication(X_74,strong_iteration(X_74)),multiplication(X_74,strong_iteration(X_74))) != multiplication(X_74,strong_iteration(X_74))
| addition(one,addition(multiplication(X_74,strong_iteration(X_74)),multiplication(X_74,strong_iteration(X_74)))) != addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74)))
| addition(one,multiplication(X_74,strong_iteration(X_74))) = addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,addition(multiplication(X_74,strong_iteration(X_74)),multiplication(X_74,strong_iteration(X_74)))),addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74)))) ),[0,1],$fot(multiplication(X_74,strong_iteration(X_74)))]]) ).
cnf(refute_1_53,plain,
( addition(one,addition(multiplication(X_74,strong_iteration(X_74)),multiplication(X_74,strong_iteration(X_74)))) != addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74)))
| addition(one,multiplication(X_74,strong_iteration(X_74))) = addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_74,strong_iteration(X_74)),multiplication(X_74,strong_iteration(X_74))),multiplication(X_74,strong_iteration(X_74))) )],[refute_1_51,refute_1_52]) ).
cnf(refute_1_54,plain,
addition(one,multiplication(X_74,strong_iteration(X_74))) = addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74))),
inference(resolve,[$cnf( $equal(addition(one,addition(multiplication(X_74,strong_iteration(X_74)),multiplication(X_74,strong_iteration(X_74)))),addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74)))) )],[refute_1_50,refute_1_53]) ).
cnf(refute_1_55,plain,
addition(one,multiplication(X_74,strong_iteration(X_74))) = strong_iteration(X_74),
inference(subst,[],[refute_1_38:[bind(A,$fot(X_74))]]) ).
cnf(refute_1_56,plain,
( addition(one,multiplication(X_74,strong_iteration(X_74))) != addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74)))
| addition(one,multiplication(X_74,strong_iteration(X_74))) != strong_iteration(X_74)
| strong_iteration(X_74) = addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,multiplication(X_74,strong_iteration(X_74))),addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74)))) ),[0],$fot(strong_iteration(X_74))]]) ).
cnf(refute_1_57,plain,
( addition(one,multiplication(X_74,strong_iteration(X_74))) != addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74)))
| strong_iteration(X_74) = addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74))) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(X_74,strong_iteration(X_74))),strong_iteration(X_74)) )],[refute_1_55,refute_1_56]) ).
cnf(refute_1_58,plain,
strong_iteration(X_74) = addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74))),
inference(resolve,[$cnf( $equal(addition(one,multiplication(X_74,strong_iteration(X_74))),addition(strong_iteration(X_74),multiplication(X_74,strong_iteration(X_74)))) )],[refute_1_54,refute_1_57]) ).
cnf(refute_1_59,plain,
strong_iteration(X_100) = addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100))),
inference(subst,[],[refute_1_58:[bind(X_74,$fot(X_100))]]) ).
cnf(refute_1_60,plain,
( strong_iteration(X_100) != addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100)))
| addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100))) = strong_iteration(X_100) ),
inference(subst,[],[refute_1_30:[bind(X,$fot(strong_iteration(X_100))),bind(Y,$fot(addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100)))))]]) ).
cnf(refute_1_61,plain,
addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100))) = strong_iteration(X_100),
inference(resolve,[$cnf( $equal(strong_iteration(X_100),addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100)))) )],[refute_1_59,refute_1_60]) ).
cnf(refute_1_62,plain,
( addition(one,addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100)))) != addition(strong_iteration(X_100),strong_iteration(X_100))
| addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100))) != strong_iteration(X_100)
| addition(one,strong_iteration(X_100)) = addition(strong_iteration(X_100),strong_iteration(X_100)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100)))),addition(strong_iteration(X_100),strong_iteration(X_100))) ),[0,1],$fot(strong_iteration(X_100))]]) ).
cnf(refute_1_63,plain,
( addition(one,addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100)))) != addition(strong_iteration(X_100),strong_iteration(X_100))
| addition(one,strong_iteration(X_100)) = addition(strong_iteration(X_100),strong_iteration(X_100)) ),
inference(resolve,[$cnf( $equal(addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100))),strong_iteration(X_100)) )],[refute_1_61,refute_1_62]) ).
cnf(refute_1_64,plain,
addition(one,strong_iteration(X_100)) = addition(strong_iteration(X_100),strong_iteration(X_100)),
inference(resolve,[$cnf( $equal(addition(one,addition(strong_iteration(X_100),multiplication(X_100,strong_iteration(X_100)))),addition(strong_iteration(X_100),strong_iteration(X_100))) )],[refute_1_49,refute_1_63]) ).
cnf(refute_1_65,plain,
addition(strong_iteration(X_100),strong_iteration(X_100)) = strong_iteration(X_100),
inference(subst,[],[refute_1_5:[bind(A,$fot(strong_iteration(X_100)))]]) ).
cnf(refute_1_66,plain,
( addition(one,strong_iteration(X_100)) != addition(strong_iteration(X_100),strong_iteration(X_100))
| addition(strong_iteration(X_100),strong_iteration(X_100)) != strong_iteration(X_100)
| addition(one,strong_iteration(X_100)) = strong_iteration(X_100) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(one,strong_iteration(X_100)),strong_iteration(X_100)) ),[0],$fot(addition(strong_iteration(X_100),strong_iteration(X_100)))]]) ).
cnf(refute_1_67,plain,
( addition(one,strong_iteration(X_100)) != addition(strong_iteration(X_100),strong_iteration(X_100))
| addition(one,strong_iteration(X_100)) = strong_iteration(X_100) ),
inference(resolve,[$cnf( $equal(addition(strong_iteration(X_100),strong_iteration(X_100)),strong_iteration(X_100)) )],[refute_1_65,refute_1_66]) ).
cnf(refute_1_68,plain,
addition(one,strong_iteration(X_100)) = strong_iteration(X_100),
inference(resolve,[$cnf( $equal(addition(one,strong_iteration(X_100)),addition(strong_iteration(X_100),strong_iteration(X_100))) )],[refute_1_64,refute_1_67]) ).
cnf(refute_1_69,plain,
( addition(one,strong_iteration(X_100)) != strong_iteration(X_100)
| multiplication(X_108,addition(one,strong_iteration(X_100))) != addition(X_108,multiplication(X_108,strong_iteration(X_100)))
| multiplication(X_108,strong_iteration(X_100)) = addition(X_108,multiplication(X_108,strong_iteration(X_100))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_108,addition(one,strong_iteration(X_100))),addition(X_108,multiplication(X_108,strong_iteration(X_100)))) ),[0,1],$fot(strong_iteration(X_100))]]) ).
cnf(refute_1_70,plain,
( multiplication(X_108,addition(one,strong_iteration(X_100))) != addition(X_108,multiplication(X_108,strong_iteration(X_100)))
| multiplication(X_108,strong_iteration(X_100)) = addition(X_108,multiplication(X_108,strong_iteration(X_100))) ),
inference(resolve,[$cnf( $equal(addition(one,strong_iteration(X_100)),strong_iteration(X_100)) )],[refute_1_68,refute_1_69]) ).
cnf(refute_1_71,plain,
multiplication(X_108,strong_iteration(X_100)) = addition(X_108,multiplication(X_108,strong_iteration(X_100))),
inference(resolve,[$cnf( $equal(multiplication(X_108,addition(one,strong_iteration(X_100))),addition(X_108,multiplication(X_108,strong_iteration(X_100)))) )],[refute_1_24,refute_1_70]) ).
cnf(refute_1_72,plain,
multiplication(X_210,strong_iteration(X_100)) = addition(X_210,multiplication(X_210,strong_iteration(X_100))),
inference(subst,[],[refute_1_71:[bind(X_108,$fot(X_210))]]) ).
cnf(refute_1_73,plain,
( multiplication(X_210,strong_iteration(X_100)) != addition(X_210,multiplication(X_210,strong_iteration(X_100)))
| addition(X_210,multiplication(X_210,strong_iteration(X_100))) = multiplication(X_210,strong_iteration(X_100)) ),
inference(subst,[],[refute_1_30:[bind(X,$fot(multiplication(X_210,strong_iteration(X_100)))),bind(Y,$fot(addition(X_210,multiplication(X_210,strong_iteration(X_100)))))]]) ).
cnf(refute_1_74,plain,
addition(X_210,multiplication(X_210,strong_iteration(X_100))) = multiplication(X_210,strong_iteration(X_100)),
inference(resolve,[$cnf( $equal(multiplication(X_210,strong_iteration(X_100)),addition(X_210,multiplication(X_210,strong_iteration(X_100)))) )],[refute_1_72,refute_1_73]) ).
cnf(refute_1_75,plain,
( addition(X_210,multiplication(X_210,strong_iteration(X_100))) != multiplication(X_210,strong_iteration(X_100))
| ~ leq(X_210,addition(X_210,multiplication(X_210,strong_iteration(X_100))))
| leq(X_210,multiplication(X_210,strong_iteration(X_100))) ),
introduced(tautology,[equality,[$cnf( leq(X_210,addition(X_210,multiplication(X_210,strong_iteration(X_100)))) ),[1],$fot(multiplication(X_210,strong_iteration(X_100)))]]) ).
cnf(refute_1_76,plain,
( ~ leq(X_210,addition(X_210,multiplication(X_210,strong_iteration(X_100))))
| leq(X_210,multiplication(X_210,strong_iteration(X_100))) ),
inference(resolve,[$cnf( $equal(addition(X_210,multiplication(X_210,strong_iteration(X_100))),multiplication(X_210,strong_iteration(X_100))) )],[refute_1_74,refute_1_75]) ).
cnf(refute_1_77,plain,
leq(X_210,multiplication(X_210,strong_iteration(X_100))),
inference(resolve,[$cnf( leq(X_210,addition(X_210,multiplication(X_210,strong_iteration(X_100)))) )],[refute_1_16,refute_1_76]) ).
cnf(refute_1_78,plain,
leq(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X0_1,strong_iteration(skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_1_77:[bind(X_100,$fot(skolemFOFtoCNF_X1_1)),bind(X_210,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_79,plain,
$false,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X0_1,strong_iteration(skolemFOFtoCNF_X1_1))) )],[refute_1_78,refute_1_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n012.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 13:40:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.69/0.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.86
% 0.69/0.86 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.69/0.87
%------------------------------------------------------------------------------