TSTP Solution File: KLE069+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE069+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 02:15:02 EDT 2022
% Result : Theorem 1.18s 1.36s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 41
% Syntax : Number of formulae : 175 ( 110 unt; 0 def)
% Number of atoms : 264 ( 204 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 184 ( 95 ~; 85 |; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 289 ( 22 sgn 69 !; 2 ?)
% 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(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(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ).
fof(goals,conjecture,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0) ).
fof(subgoal_0,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) != domain(X0),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[domain5]) ).
fof(normalize_0_3,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
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,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_12,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_14,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[domain2]) ).
fof(normalize_0_16,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_18,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_20,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_22,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X0] : addition(domain(X0),one) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_24,plain,
! [X0] : addition(domain(X0),one) = one,
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_26,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_25]) ).
cnf(refute_0_0,plain,
multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( domain(addition(X0,X1)) != addition(domain(X0),domain(X1))
| addition(domain(X0),domain(X1)) = domain(addition(X0,X1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(domain(addition(X0,X1)))),bind(Y,$fot(addition(domain(X0),domain(X1))))]]) ).
cnf(refute_0_6,plain,
addition(domain(X0),domain(X1)) = domain(addition(X0,X1)),
inference(resolve,[$cnf( $equal(domain(addition(X0,X1)),addition(domain(X0),domain(X1))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) = domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_6:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_8,plain,
multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),
introduced(tautology,[refl,[$fot(multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_9,plain,
( addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)))
| multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)))) ),[1,1],$fot(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_10,plain,
( addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))
| multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) ),[0],$fot(multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_13,plain,
( multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) )],[refute_0_13,refute_0_0]) ).
cnf(refute_0_15,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_16,plain,
( ~ leq(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154))))
| addition(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))) = multiplication(domain(X_153),domain(addition(X_153,X_154))) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(domain(X_153))),bind(B,$fot(multiplication(domain(X_153),domain(addition(X_153,X_154)))))]]) ).
cnf(refute_0_17,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_18,plain,
( addition(X_47,addition(multiplication(domain(X_47),X_47),X_32)) != addition(multiplication(domain(X_47),X_47),X_32)
| leq(X_47,addition(multiplication(domain(X_47),X_47),X_32)) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_47)),bind(B,$fot(addition(multiplication(domain(X_47),X_47),X_32)))]]) ).
cnf(refute_0_19,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_20,plain,
addition(X_30,addition(multiplication(domain(X_30),X_30),X_32)) = addition(addition(X_30,multiplication(domain(X_30),X_30)),X_32),
inference(subst,[],[refute_0_19:[bind(A,$fot(X_30)),bind(B,$fot(multiplication(domain(X_30),X_30))),bind(C,$fot(X_32))]]) ).
cnf(refute_0_21,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_22,plain,
addition(X_30,multiplication(domain(X_30),X_30)) = multiplication(domain(X_30),X_30),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_30))]]) ).
cnf(refute_0_23,plain,
( addition(X_30,addition(multiplication(domain(X_30),X_30),X_32)) != addition(addition(X_30,multiplication(domain(X_30),X_30)),X_32)
| addition(X_30,multiplication(domain(X_30),X_30)) != multiplication(domain(X_30),X_30)
| addition(X_30,addition(multiplication(domain(X_30),X_30),X_32)) = addition(multiplication(domain(X_30),X_30),X_32) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_30,addition(multiplication(domain(X_30),X_30),X_32)),addition(addition(X_30,multiplication(domain(X_30),X_30)),X_32)) ),[1,0],$fot(multiplication(domain(X_30),X_30))]]) ).
cnf(refute_0_24,plain,
( addition(X_30,addition(multiplication(domain(X_30),X_30),X_32)) != addition(addition(X_30,multiplication(domain(X_30),X_30)),X_32)
| addition(X_30,addition(multiplication(domain(X_30),X_30),X_32)) = addition(multiplication(domain(X_30),X_30),X_32) ),
inference(resolve,[$cnf( $equal(addition(X_30,multiplication(domain(X_30),X_30)),multiplication(domain(X_30),X_30)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
addition(X_30,addition(multiplication(domain(X_30),X_30),X_32)) = addition(multiplication(domain(X_30),X_30),X_32),
inference(resolve,[$cnf( $equal(addition(X_30,addition(multiplication(domain(X_30),X_30),X_32)),addition(addition(X_30,multiplication(domain(X_30),X_30)),X_32)) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
addition(X_47,addition(multiplication(domain(X_47),X_47),X_32)) = addition(multiplication(domain(X_47),X_47),X_32),
inference(subst,[],[refute_0_25:[bind(X_30,$fot(X_47))]]) ).
cnf(refute_0_27,plain,
( addition(X_47,addition(multiplication(domain(X_47),X_47),X_32)) != addition(multiplication(domain(X_47),X_47),X_32)
| addition(multiplication(domain(X_47),X_47),X_32) != addition(multiplication(domain(X_47),X_47),X_32)
| addition(X_47,addition(multiplication(domain(X_47),X_47),X_32)) = addition(multiplication(domain(X_47),X_47),X_32) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_47,addition(multiplication(domain(X_47),X_47),X_32)),addition(multiplication(domain(X_47),X_47),X_32)) ),[0],$fot(addition(multiplication(domain(X_47),X_47),X_32))]]) ).
cnf(refute_0_28,plain,
( addition(multiplication(domain(X_47),X_47),X_32) != addition(multiplication(domain(X_47),X_47),X_32)
| addition(X_47,addition(multiplication(domain(X_47),X_47),X_32)) = addition(multiplication(domain(X_47),X_47),X_32) ),
inference(resolve,[$cnf( $equal(addition(X_47,addition(multiplication(domain(X_47),X_47),X_32)),addition(multiplication(domain(X_47),X_47),X_32)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( addition(multiplication(domain(X_47),X_47),X_32) != addition(multiplication(domain(X_47),X_47),X_32)
| leq(X_47,addition(multiplication(domain(X_47),X_47),X_32)) ),
inference(resolve,[$cnf( $equal(addition(X_47,addition(multiplication(domain(X_47),X_47),X_32)),addition(multiplication(domain(X_47),X_47),X_32)) )],[refute_0_28,refute_0_18]) ).
cnf(refute_0_30,plain,
addition(multiplication(domain(X_47),X_47),X_32) = addition(multiplication(domain(X_47),X_47),X_32),
introduced(tautology,[refl,[$fot(addition(multiplication(domain(X_47),X_47),X_32))]]) ).
cnf(refute_0_31,plain,
leq(X_47,addition(multiplication(domain(X_47),X_47),X_32)),
inference(resolve,[$cnf( $equal(addition(multiplication(domain(X_47),X_47),X_32),addition(multiplication(domain(X_47),X_47),X_32)) )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
leq(X_47,addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129))),
inference(subst,[],[refute_0_31:[bind(X_32,$fot(multiplication(domain(X_47),X_129)))]]) ).
cnf(refute_0_33,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_34,plain,
multiplication(domain(X_47),addition(X_47,X_129)) = addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129)),
inference(subst,[],[refute_0_33:[bind(A,$fot(domain(X_47))),bind(B,$fot(X_47)),bind(C,$fot(X_129))]]) ).
cnf(refute_0_35,plain,
( multiplication(domain(X_47),addition(X_47,X_129)) != addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129))
| addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129)) = multiplication(domain(X_47),addition(X_47,X_129)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiplication(domain(X_47),addition(X_47,X_129)))),bind(Y,$fot(addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129))))]]) ).
cnf(refute_0_36,plain,
addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129)) = multiplication(domain(X_47),addition(X_47,X_129)),
inference(resolve,[$cnf( $equal(multiplication(domain(X_47),addition(X_47,X_129)),addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129)) != multiplication(domain(X_47),addition(X_47,X_129))
| ~ leq(X_47,addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129)))
| leq(X_47,multiplication(domain(X_47),addition(X_47,X_129))) ),
introduced(tautology,[equality,[$cnf( leq(X_47,addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129))) ),[1],$fot(multiplication(domain(X_47),addition(X_47,X_129)))]]) ).
cnf(refute_0_38,plain,
( ~ leq(X_47,addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129)))
| leq(X_47,multiplication(domain(X_47),addition(X_47,X_129))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129)),multiplication(domain(X_47),addition(X_47,X_129))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
leq(X_47,multiplication(domain(X_47),addition(X_47,X_129))),
inference(resolve,[$cnf( leq(X_47,addition(multiplication(domain(X_47),X_47),multiplication(domain(X_47),X_129))) )],[refute_0_32,refute_0_38]) ).
cnf(refute_0_40,plain,
leq(domain(X0),multiplication(domain(domain(X0)),addition(domain(X0),domain(X1)))),
inference(subst,[],[refute_0_39:[bind(X_129,$fot(domain(X1))),bind(X_47,$fot(domain(X0)))]]) ).
cnf(refute_0_41,plain,
( addition(domain(X0),domain(X1)) != domain(addition(X0,X1))
| ~ leq(domain(X0),multiplication(domain(domain(X0)),addition(domain(X0),domain(X1))))
| leq(domain(X0),multiplication(domain(domain(X0)),domain(addition(X0,X1)))) ),
introduced(tautology,[equality,[$cnf( leq(domain(X0),multiplication(domain(domain(X0)),addition(domain(X0),domain(X1)))) ),[1,1],$fot(domain(addition(X0,X1)))]]) ).
cnf(refute_0_42,plain,
( ~ leq(domain(X0),multiplication(domain(domain(X0)),addition(domain(X0),domain(X1))))
| leq(domain(X0),multiplication(domain(domain(X0)),domain(addition(X0,X1)))) ),
inference(resolve,[$cnf( $equal(addition(domain(X0),domain(X1)),domain(addition(X0,X1))) )],[refute_0_6,refute_0_41]) ).
cnf(refute_0_43,plain,
leq(domain(X0),multiplication(domain(domain(X0)),domain(addition(X0,X1)))),
inference(resolve,[$cnf( leq(domain(X0),multiplication(domain(domain(X0)),addition(domain(X0),domain(X1)))) )],[refute_0_40,refute_0_42]) ).
cnf(refute_0_44,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_45,plain,
domain(multiplication(one,X_26)) = domain(multiplication(one,domain(X_26))),
inference(subst,[],[refute_0_44:[bind(X0,$fot(one)),bind(X1,$fot(X_26))]]) ).
cnf(refute_0_46,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_47,plain,
multiplication(one,domain(X_26)) = domain(X_26),
inference(subst,[],[refute_0_46:[bind(A,$fot(domain(X_26)))]]) ).
cnf(refute_0_48,plain,
( domain(multiplication(one,X_26)) != domain(multiplication(one,domain(X_26)))
| multiplication(one,domain(X_26)) != domain(X_26)
| domain(multiplication(one,X_26)) = domain(domain(X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_26)),domain(multiplication(one,domain(X_26)))) ),[1,0],$fot(domain(X_26))]]) ).
cnf(refute_0_49,plain,
( domain(multiplication(one,X_26)) != domain(multiplication(one,domain(X_26)))
| domain(multiplication(one,X_26)) = domain(domain(X_26)) ),
inference(resolve,[$cnf( $equal(multiplication(one,domain(X_26)),domain(X_26)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
domain(multiplication(one,X_26)) = domain(domain(X_26)),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_26)),domain(multiplication(one,domain(X_26)))) )],[refute_0_45,refute_0_49]) ).
cnf(refute_0_51,plain,
multiplication(one,X_26) = X_26,
inference(subst,[],[refute_0_46:[bind(A,$fot(X_26))]]) ).
cnf(refute_0_52,plain,
domain(multiplication(one,X_26)) = domain(multiplication(one,X_26)),
introduced(tautology,[refl,[$fot(domain(multiplication(one,X_26)))]]) ).
cnf(refute_0_53,plain,
( domain(multiplication(one,X_26)) != domain(multiplication(one,X_26))
| multiplication(one,X_26) != X_26
| domain(multiplication(one,X_26)) = domain(X_26) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_26)),domain(multiplication(one,X_26))) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_54,plain,
( multiplication(one,X_26) != X_26
| domain(multiplication(one,X_26)) = domain(X_26) ),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_26)),domain(multiplication(one,X_26))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
domain(multiplication(one,X_26)) = domain(X_26),
inference(resolve,[$cnf( $equal(multiplication(one,X_26),X_26) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
( domain(multiplication(one,X_26)) != domain(X_26)
| domain(multiplication(one,X_26)) != domain(domain(X_26))
| domain(X_26) = domain(domain(X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_26)),domain(domain(X_26))) ),[0],$fot(domain(X_26))]]) ).
cnf(refute_0_57,plain,
( domain(multiplication(one,X_26)) != domain(domain(X_26))
| domain(X_26) = domain(domain(X_26)) ),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_26)),domain(X_26)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
domain(X_26) = domain(domain(X_26)),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_26)),domain(domain(X_26))) )],[refute_0_50,refute_0_57]) ).
cnf(refute_0_59,plain,
( domain(X_26) != domain(domain(X_26))
| domain(domain(X_26)) = domain(X_26) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(domain(X_26))),bind(Y,$fot(domain(domain(X_26))))]]) ).
cnf(refute_0_60,plain,
domain(domain(X_26)) = domain(X_26),
inference(resolve,[$cnf( $equal(domain(X_26),domain(domain(X_26))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
domain(domain(X0)) = domain(X0),
inference(subst,[],[refute_0_60:[bind(X_26,$fot(X0))]]) ).
cnf(refute_0_62,plain,
multiplication(domain(domain(X0)),domain(addition(X0,X1))) = multiplication(domain(domain(X0)),domain(addition(X0,X1))),
introduced(tautology,[refl,[$fot(multiplication(domain(domain(X0)),domain(addition(X0,X1))))]]) ).
cnf(refute_0_63,plain,
( domain(domain(X0)) != domain(X0)
| multiplication(domain(domain(X0)),domain(addition(X0,X1))) != multiplication(domain(domain(X0)),domain(addition(X0,X1)))
| multiplication(domain(domain(X0)),domain(addition(X0,X1))) = multiplication(domain(X0),domain(addition(X0,X1))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(domain(X0)),domain(addition(X0,X1))),multiplication(domain(domain(X0)),domain(addition(X0,X1)))) ),[1,0],$fot(domain(X0))]]) ).
cnf(refute_0_64,plain,
( domain(domain(X0)) != domain(X0)
| multiplication(domain(domain(X0)),domain(addition(X0,X1))) = multiplication(domain(X0),domain(addition(X0,X1))) ),
inference(resolve,[$cnf( $equal(multiplication(domain(domain(X0)),domain(addition(X0,X1))),multiplication(domain(domain(X0)),domain(addition(X0,X1)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
multiplication(domain(domain(X0)),domain(addition(X0,X1))) = multiplication(domain(X0),domain(addition(X0,X1))),
inference(resolve,[$cnf( $equal(domain(domain(X0)),domain(X0)) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
( multiplication(domain(domain(X0)),domain(addition(X0,X1))) != multiplication(domain(X0),domain(addition(X0,X1)))
| ~ leq(domain(X0),multiplication(domain(domain(X0)),domain(addition(X0,X1))))
| leq(domain(X0),multiplication(domain(X0),domain(addition(X0,X1)))) ),
introduced(tautology,[equality,[$cnf( leq(domain(X0),multiplication(domain(domain(X0)),domain(addition(X0,X1)))) ),[1],$fot(multiplication(domain(X0),domain(addition(X0,X1))))]]) ).
cnf(refute_0_67,plain,
( ~ leq(domain(X0),multiplication(domain(domain(X0)),domain(addition(X0,X1))))
| leq(domain(X0),multiplication(domain(X0),domain(addition(X0,X1)))) ),
inference(resolve,[$cnf( $equal(multiplication(domain(domain(X0)),domain(addition(X0,X1))),multiplication(domain(X0),domain(addition(X0,X1)))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
leq(domain(X0),multiplication(domain(X0),domain(addition(X0,X1)))),
inference(resolve,[$cnf( leq(domain(X0),multiplication(domain(domain(X0)),domain(addition(X0,X1)))) )],[refute_0_43,refute_0_67]) ).
cnf(refute_0_69,plain,
leq(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))),
inference(subst,[],[refute_0_68:[bind(X0,$fot(X_153)),bind(X1,$fot(X_154))]]) ).
cnf(refute_0_70,plain,
addition(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))) = multiplication(domain(X_153),domain(addition(X_153,X_154))),
inference(resolve,[$cnf( leq(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))) )],[refute_0_69,refute_0_16]) ).
cnf(refute_0_71,plain,
( ~ leq(multiplication(X_150,domain(X_149)),X_150)
| addition(multiplication(X_150,domain(X_149)),X_150) = X_150 ),
inference(subst,[],[refute_0_15:[bind(A,$fot(multiplication(X_150,domain(X_149)))),bind(B,$fot(X_150))]]) ).
cnf(refute_0_72,plain,
( addition(X_47,addition(X_47,X_32)) != addition(X_47,X_32)
| leq(X_47,addition(X_47,X_32)) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_47)),bind(B,$fot(addition(X_47,X_32)))]]) ).
cnf(refute_0_73,plain,
addition(X_31,addition(X_31,X_32)) = addition(addition(X_31,X_31),X_32),
inference(subst,[],[refute_0_19:[bind(A,$fot(X_31)),bind(B,$fot(X_31)),bind(C,$fot(X_32))]]) ).
cnf(refute_0_74,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_75,plain,
addition(X_31,X_31) = X_31,
inference(subst,[],[refute_0_74:[bind(A,$fot(X_31))]]) ).
cnf(refute_0_76,plain,
( addition(X_31,X_31) != X_31
| addition(X_31,addition(X_31,X_32)) != addition(addition(X_31,X_31),X_32)
| addition(X_31,addition(X_31,X_32)) = addition(X_31,X_32) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_31,addition(X_31,X_32)),addition(addition(X_31,X_31),X_32)) ),[1,0],$fot(X_31)]]) ).
cnf(refute_0_77,plain,
( addition(X_31,addition(X_31,X_32)) != addition(addition(X_31,X_31),X_32)
| addition(X_31,addition(X_31,X_32)) = addition(X_31,X_32) ),
inference(resolve,[$cnf( $equal(addition(X_31,X_31),X_31) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
addition(X_31,addition(X_31,X_32)) = addition(X_31,X_32),
inference(resolve,[$cnf( $equal(addition(X_31,addition(X_31,X_32)),addition(addition(X_31,X_31),X_32)) )],[refute_0_73,refute_0_77]) ).
cnf(refute_0_79,plain,
addition(X_47,addition(X_47,X_32)) = addition(X_47,X_32),
inference(subst,[],[refute_0_78:[bind(X_31,$fot(X_47))]]) ).
cnf(refute_0_80,plain,
( addition(X_47,X_32) != addition(X_47,X_32)
| addition(X_47,addition(X_47,X_32)) != addition(X_47,X_32)
| addition(X_47,addition(X_47,X_32)) = addition(X_47,X_32) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_47,addition(X_47,X_32)),addition(X_47,X_32)) ),[0,1],$fot(addition(X_47,X_32))]]) ).
cnf(refute_0_81,plain,
( addition(X_47,X_32) != addition(X_47,X_32)
| addition(X_47,addition(X_47,X_32)) = addition(X_47,X_32) ),
inference(resolve,[$cnf( $equal(addition(X_47,addition(X_47,X_32)),addition(X_47,X_32)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( addition(X_47,X_32) != addition(X_47,X_32)
| leq(X_47,addition(X_47,X_32)) ),
inference(resolve,[$cnf( $equal(addition(X_47,addition(X_47,X_32)),addition(X_47,X_32)) )],[refute_0_81,refute_0_72]) ).
cnf(refute_0_83,plain,
addition(X_47,X_32) = addition(X_47,X_32),
introduced(tautology,[refl,[$fot(addition(X_47,X_32))]]) ).
cnf(refute_0_84,plain,
leq(X_47,addition(X_47,X_32)),
inference(resolve,[$cnf( $equal(addition(X_47,X_32),addition(X_47,X_32)) )],[refute_0_83,refute_0_82]) ).
cnf(refute_0_85,plain,
leq(X_54,addition(X_54,X_53)),
inference(subst,[],[refute_0_84:[bind(X_32,$fot(X_53)),bind(X_47,$fot(X_54))]]) ).
cnf(refute_0_86,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_87,plain,
addition(X_53,X_54) = addition(X_54,X_53),
inference(subst,[],[refute_0_86:[bind(A,$fot(X_53)),bind(B,$fot(X_54))]]) ).
cnf(refute_0_88,plain,
( addition(X_53,X_54) != addition(X_54,X_53)
| addition(X_54,X_53) = addition(X_53,X_54) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(X_53,X_54))),bind(Y,$fot(addition(X_54,X_53)))]]) ).
cnf(refute_0_89,plain,
addition(X_54,X_53) = addition(X_53,X_54),
inference(resolve,[$cnf( $equal(addition(X_53,X_54),addition(X_54,X_53)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( addition(X_54,X_53) != addition(X_53,X_54)
| ~ leq(X_54,addition(X_54,X_53))
| leq(X_54,addition(X_53,X_54)) ),
introduced(tautology,[equality,[$cnf( leq(X_54,addition(X_54,X_53)) ),[1],$fot(addition(X_53,X_54))]]) ).
cnf(refute_0_91,plain,
( ~ leq(X_54,addition(X_54,X_53))
| leq(X_54,addition(X_53,X_54)) ),
inference(resolve,[$cnf( $equal(addition(X_54,X_53),addition(X_53,X_54)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
leq(X_54,addition(X_53,X_54)),
inference(resolve,[$cnf( leq(X_54,addition(X_54,X_53)) )],[refute_0_85,refute_0_91]) ).
cnf(refute_0_93,plain,
leq(multiplication(X_127,X_129),addition(multiplication(X_127,X_128),multiplication(X_127,X_129))),
inference(subst,[],[refute_0_92:[bind(X_53,$fot(multiplication(X_127,X_128))),bind(X_54,$fot(multiplication(X_127,X_129)))]]) ).
cnf(refute_0_94,plain,
multiplication(X_127,addition(X_128,X_129)) = addition(multiplication(X_127,X_128),multiplication(X_127,X_129)),
inference(subst,[],[refute_0_33:[bind(A,$fot(X_127)),bind(B,$fot(X_128)),bind(C,$fot(X_129))]]) ).
cnf(refute_0_95,plain,
( multiplication(X_127,addition(X_128,X_129)) != addition(multiplication(X_127,X_128),multiplication(X_127,X_129))
| addition(multiplication(X_127,X_128),multiplication(X_127,X_129)) = multiplication(X_127,addition(X_128,X_129)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiplication(X_127,addition(X_128,X_129)))),bind(Y,$fot(addition(multiplication(X_127,X_128),multiplication(X_127,X_129))))]]) ).
cnf(refute_0_96,plain,
addition(multiplication(X_127,X_128),multiplication(X_127,X_129)) = multiplication(X_127,addition(X_128,X_129)),
inference(resolve,[$cnf( $equal(multiplication(X_127,addition(X_128,X_129)),addition(multiplication(X_127,X_128),multiplication(X_127,X_129))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( addition(multiplication(X_127,X_128),multiplication(X_127,X_129)) != multiplication(X_127,addition(X_128,X_129))
| ~ leq(multiplication(X_127,X_129),addition(multiplication(X_127,X_128),multiplication(X_127,X_129)))
| leq(multiplication(X_127,X_129),multiplication(X_127,addition(X_128,X_129))) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(X_127,X_129),addition(multiplication(X_127,X_128),multiplication(X_127,X_129))) ),[1],$fot(multiplication(X_127,addition(X_128,X_129)))]]) ).
cnf(refute_0_98,plain,
( ~ leq(multiplication(X_127,X_129),addition(multiplication(X_127,X_128),multiplication(X_127,X_129)))
| leq(multiplication(X_127,X_129),multiplication(X_127,addition(X_128,X_129))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_127,X_128),multiplication(X_127,X_129)),multiplication(X_127,addition(X_128,X_129))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
leq(multiplication(X_127,X_129),multiplication(X_127,addition(X_128,X_129))),
inference(resolve,[$cnf( leq(multiplication(X_127,X_129),addition(multiplication(X_127,X_128),multiplication(X_127,X_129))) )],[refute_0_93,refute_0_98]) ).
cnf(refute_0_100,plain,
leq(multiplication(X_136,domain(X0)),multiplication(X_136,addition(one,domain(X0)))),
inference(subst,[],[refute_0_99:[bind(X_127,$fot(X_136)),bind(X_128,$fot(one)),bind(X_129,$fot(domain(X0)))]]) ).
cnf(refute_0_101,plain,
addition(domain(X0),one) = one,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_102,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_103,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_86,refute_0_102]) ).
cnf(refute_0_104,plain,
addition(domain(X0),one) = addition(one,domain(X0)),
inference(subst,[],[refute_0_103:[bind(A,$fot(one)),bind(B,$fot(domain(X0)))]]) ).
cnf(refute_0_105,plain,
( addition(domain(X0),one) != addition(one,domain(X0))
| addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X0),one),one) ),[0],$fot(addition(one,domain(X0)))]]) ).
cnf(refute_0_106,plain,
( addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X0),one),addition(one,domain(X0))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
addition(one,domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(domain(X0),one),one) )],[refute_0_101,refute_0_106]) ).
cnf(refute_0_108,plain,
( addition(one,domain(X0)) != one
| ~ leq(multiplication(X_136,domain(X0)),multiplication(X_136,addition(one,domain(X0))))
| leq(multiplication(X_136,domain(X0)),multiplication(X_136,one)) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(X_136,domain(X0)),multiplication(X_136,addition(one,domain(X0)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_109,plain,
( ~ leq(multiplication(X_136,domain(X0)),multiplication(X_136,addition(one,domain(X0))))
| leq(multiplication(X_136,domain(X0)),multiplication(X_136,one)) ),
inference(resolve,[$cnf( $equal(addition(one,domain(X0)),one) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
leq(multiplication(X_136,domain(X0)),multiplication(X_136,one)),
inference(resolve,[$cnf( leq(multiplication(X_136,domain(X0)),multiplication(X_136,addition(one,domain(X0)))) )],[refute_0_100,refute_0_109]) ).
cnf(refute_0_111,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_112,plain,
multiplication(X_136,one) = X_136,
inference(subst,[],[refute_0_111:[bind(A,$fot(X_136))]]) ).
cnf(refute_0_113,plain,
( multiplication(X_136,one) != X_136
| ~ leq(multiplication(X_136,domain(X0)),multiplication(X_136,one))
| leq(multiplication(X_136,domain(X0)),X_136) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(X_136,domain(X0)),multiplication(X_136,one)) ),[1],$fot(X_136)]]) ).
cnf(refute_0_114,plain,
( ~ leq(multiplication(X_136,domain(X0)),multiplication(X_136,one))
| leq(multiplication(X_136,domain(X0)),X_136) ),
inference(resolve,[$cnf( $equal(multiplication(X_136,one),X_136) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
leq(multiplication(X_136,domain(X0)),X_136),
inference(resolve,[$cnf( leq(multiplication(X_136,domain(X0)),multiplication(X_136,one)) )],[refute_0_110,refute_0_114]) ).
cnf(refute_0_116,plain,
leq(multiplication(X_150,domain(X_149)),X_150),
inference(subst,[],[refute_0_115:[bind(X0,$fot(X_149)),bind(X_136,$fot(X_150))]]) ).
cnf(refute_0_117,plain,
addition(multiplication(X_150,domain(X_149)),X_150) = X_150,
inference(resolve,[$cnf( leq(multiplication(X_150,domain(X_149)),X_150) )],[refute_0_116,refute_0_71]) ).
cnf(refute_0_118,plain,
addition(multiplication(X_150,domain(X_149)),X_150) = addition(X_150,multiplication(X_150,domain(X_149))),
inference(subst,[],[refute_0_103:[bind(A,$fot(X_150)),bind(B,$fot(multiplication(X_150,domain(X_149))))]]) ).
cnf(refute_0_119,plain,
( addition(multiplication(X_150,domain(X_149)),X_150) != X_150
| addition(multiplication(X_150,domain(X_149)),X_150) != addition(X_150,multiplication(X_150,domain(X_149)))
| addition(X_150,multiplication(X_150,domain(X_149))) = X_150 ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(X_150,domain(X_149)),X_150),X_150) ),[0],$fot(addition(X_150,multiplication(X_150,domain(X_149))))]]) ).
cnf(refute_0_120,plain,
( addition(multiplication(X_150,domain(X_149)),X_150) != X_150
| addition(X_150,multiplication(X_150,domain(X_149))) = X_150 ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_150,domain(X_149)),X_150),addition(X_150,multiplication(X_150,domain(X_149)))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
addition(X_150,multiplication(X_150,domain(X_149))) = X_150,
inference(resolve,[$cnf( $equal(addition(multiplication(X_150,domain(X_149)),X_150),X_150) )],[refute_0_117,refute_0_120]) ).
cnf(refute_0_122,plain,
addition(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))) = domain(X_153),
inference(subst,[],[refute_0_121:[bind(X_149,$fot(addition(X_153,X_154))),bind(X_150,$fot(domain(X_153)))]]) ).
cnf(refute_0_123,plain,
( addition(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))) != domain(X_153)
| addition(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))) != multiplication(domain(X_153),domain(addition(X_153,X_154)))
| domain(X_153) = multiplication(domain(X_153),domain(addition(X_153,X_154))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))),multiplication(domain(X_153),domain(addition(X_153,X_154)))) ),[0],$fot(domain(X_153))]]) ).
cnf(refute_0_124,plain,
( addition(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))) != multiplication(domain(X_153),domain(addition(X_153,X_154)))
| domain(X_153) = multiplication(domain(X_153),domain(addition(X_153,X_154))) ),
inference(resolve,[$cnf( $equal(addition(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))),domain(X_153)) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
domain(X_153) = multiplication(domain(X_153),domain(addition(X_153,X_154))),
inference(resolve,[$cnf( $equal(addition(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))),multiplication(domain(X_153),domain(addition(X_153,X_154)))) )],[refute_0_70,refute_0_124]) ).
cnf(refute_0_126,plain,
( domain(X_153) != multiplication(domain(X_153),domain(addition(X_153,X_154)))
| multiplication(domain(X_153),domain(addition(X_153,X_154))) = domain(X_153) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(domain(X_153))),bind(Y,$fot(multiplication(domain(X_153),domain(addition(X_153,X_154)))))]]) ).
cnf(refute_0_127,plain,
multiplication(domain(X_153),domain(addition(X_153,X_154))) = domain(X_153),
inference(resolve,[$cnf( $equal(domain(X_153),multiplication(domain(X_153),domain(addition(X_153,X_154)))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_127:[bind(X_153,$fot(skolemFOFtoCNF_X0)),bind(X_154,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_129,plain,
( domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) ),[0,0],$fot(domain(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_130,plain,
( domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) )],[refute_0_130,refute_0_14]) ).
cnf(refute_0_132,plain,
domain(skolemFOFtoCNF_X0) = domain(skolemFOFtoCNF_X0),
introduced(tautology,[refl,[$fot(domain(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_133,plain,
$false,
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) )],[refute_0_132,refute_0_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE069+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 10:07:40 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.18/1.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.18/1.36
% 1.18/1.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.18/1.37
%------------------------------------------------------------------------------