TSTP Solution File: KLE072+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE072+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 02:15:03 EDT 2022
% Result : Theorem 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 32 unt; 0 def)
% Number of atoms : 76 ( 75 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 31 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ).
fof(goals,conjecture,
! [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) = addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))) ).
fof(subgoal_0,plain,
! [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) = addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) = addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) != addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) != addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[domain2]) ).
fof(normalize_0_3,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_5,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[domain5]) ).
fof(normalize_0_7,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(specialize,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) != addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
domain(multiplication(X0,X1)) = domain(multiplication(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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( domain(multiplication(X0,X1)) != domain(multiplication(X0,domain(X1)))
| domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(domain(multiplication(X0,X1)))),bind(Y,$fot(domain(multiplication(X0,domain(X1)))))]]) ).
cnf(refute_0_6,plain,
domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(resolve,[$cnf( $equal(domain(multiplication(X0,X1)),domain(multiplication(X0,domain(X1)))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) = domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)),
inference(subst,[],[refute_0_6:[bind(X0,$fot(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),bind(X1,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_8,plain,
( domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) != domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))
| domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) != addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))
| domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) = addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))),addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))) ),[0],$fot(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_9,plain,
( domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) != addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))
| domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) = addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) ),
inference(resolve,[$cnf( $equal(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))),domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_11,plain,
( multiplication(addition(A,B),C) != addition(multiplication(A,C),multiplication(B,C))
| addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiplication(addition(A,B),C))),bind(Y,$fot(addition(multiplication(A,C),multiplication(B,C))))]]) ).
cnf(refute_0_12,plain,
addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C),
inference(resolve,[$cnf( $equal(multiplication(addition(A,B),C),addition(multiplication(A,C),multiplication(B,C))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))) = multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2)),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(skolemFOFtoCNF_X1)),bind(C,$fot(domain(skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_14,plain,
domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) = domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))),
introduced(tautology,[refl,[$fot(domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))))]]) ).
cnf(refute_0_15,plain,
( addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))) != multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))
| domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) != domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))
| domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) = domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))),domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))) ),[1,0],$fot(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_16,plain,
( addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))) != multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))
| domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) = domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) ),
inference(resolve,[$cnf( $equal(domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))),domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) = domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))),multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_19,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_18]) ).
cnf(refute_0_20,plain,
( domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) != domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2)))
| domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) != domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))
| domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) = domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))))),bind(Y,$fot(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))))),bind(Z,$fot(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_21,plain,
( domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) != domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))
| domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) = domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( $equal(domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))),domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2)))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) = domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))),domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))) )],[refute_0_7,refute_0_21]) ).
cnf(refute_0_23,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_24,plain,
( domain(addition(X0,X1)) != addition(domain(X0),domain(X1))
| addition(domain(X0),domain(X1)) = domain(addition(X0,X1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(domain(addition(X0,X1)))),bind(Y,$fot(addition(domain(X0),domain(X1))))]]) ).
cnf(refute_0_25,plain,
addition(domain(X0),domain(X1)) = domain(addition(X0,X1)),
inference(resolve,[$cnf( $equal(domain(addition(X0,X1)),addition(domain(X0),domain(X1))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) = domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))),
inference(subst,[],[refute_0_25:[bind(X0,$fot(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)))),bind(X1,$fot(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_27,plain,
( addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) != domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))
| domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) != domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))
| addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) = domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))))),bind(Y,$fot(domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))))),bind(Z,$fot(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_28,plain,
( domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) != domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))
| addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) = domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( $equal(addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))),domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) = domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(domain(addition(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))),domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))) )],[refute_0_22,refute_0_28]) ).
cnf(refute_0_30,plain,
( addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) != domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))
| domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) != domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))
| domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) = addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)),addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))) ),[1],$fot(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_31,plain,
( domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) != domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))
| domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) = addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) ),
inference(resolve,[$cnf( $equal(addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))),domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) != domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))
| domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))) = addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2)))) ),
inference(resolve,[$cnf( $equal(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)),addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))) )],[refute_0_31,refute_0_9]) ).
cnf(refute_0_33,plain,
domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) != domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X2))),addition(domain(multiplication(skolemFOFtoCNF_X0,domain(skolemFOFtoCNF_X2))),domain(multiplication(skolemFOFtoCNF_X1,domain(skolemFOFtoCNF_X2))))) )],[refute_0_32,refute_0_0]) ).
cnf(refute_0_34,plain,
domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)) = domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)),
introduced(tautology,[refl,[$fot(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( $equal(domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)),domain(multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))) )],[refute_0_34,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE072+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 09:17:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.37
% 0.20/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.38
%------------------------------------------------------------------------------