TSTP Solution File: KLE002+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 02:14:29 EDT 2022
% Result : Theorem 15.71s 15.93s
% Output : CNFRefutation 15.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 60 ( 33 unt; 0 def)
% Number of atoms : 94 ( 52 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 35 ~; 25 |; 3 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 3 sgn 42 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ) ).
fof(subgoal_0,plain,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] :
( leq(X0,X1)
& ? [X2] : ~ leq(multiplication(X0,X2),multiplication(X1,X2)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)
& ? [X2] : ~ leq(multiplication(skolemFOFtoCNF_X0,X2),multiplication(skolemFOFtoCNF_X1,X2)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X2] : ~ leq(multiplication(skolemFOFtoCNF_X0,X2),multiplication(skolemFOFtoCNF_X1,X2)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ leq(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(skolemize,[],[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] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_9,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_11,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_13,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_15,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
~ leq(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( addition(X_23,addition(X_23,X_11)) != addition(X_23,X_11)
| leq(X_23,addition(X_23,X_11)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_23)),bind(B,$fot(addition(X_23,X_11)))]]) ).
cnf(refute_0_3,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
addition(X_10,addition(X_10,X_11)) = addition(addition(X_10,X_10),X_11),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_10)),bind(B,$fot(X_10)),bind(C,$fot(X_11))]]) ).
cnf(refute_0_5,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
addition(X_10,X_10) = X_10,
inference(subst,[],[refute_0_5:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_7,plain,
( addition(X_10,X_10) != X_10
| addition(X_10,addition(X_10,X_11)) != addition(addition(X_10,X_10),X_11)
| addition(X_10,addition(X_10,X_11)) = addition(X_10,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_10,addition(X_10,X_11)),addition(addition(X_10,X_10),X_11)) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_8,plain,
( addition(X_10,addition(X_10,X_11)) != addition(addition(X_10,X_10),X_11)
| addition(X_10,addition(X_10,X_11)) = addition(X_10,X_11) ),
inference(resolve,[$cnf( $equal(addition(X_10,X_10),X_10) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
addition(X_10,addition(X_10,X_11)) = addition(X_10,X_11),
inference(resolve,[$cnf( $equal(addition(X_10,addition(X_10,X_11)),addition(addition(X_10,X_10),X_11)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
addition(X_23,addition(X_23,X_11)) = addition(X_23,X_11),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(X_23))]]) ).
cnf(refute_0_11,plain,
( addition(X_23,X_11) != addition(X_23,X_11)
| addition(X_23,addition(X_23,X_11)) != addition(X_23,X_11)
| addition(X_23,addition(X_23,X_11)) = addition(X_23,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_23,addition(X_23,X_11)),addition(X_23,X_11)) ),[0,1],$fot(addition(X_23,X_11))]]) ).
cnf(refute_0_12,plain,
( addition(X_23,X_11) != addition(X_23,X_11)
| addition(X_23,addition(X_23,X_11)) = addition(X_23,X_11) ),
inference(resolve,[$cnf( $equal(addition(X_23,addition(X_23,X_11)),addition(X_23,X_11)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( addition(X_23,X_11) != addition(X_23,X_11)
| leq(X_23,addition(X_23,X_11)) ),
inference(resolve,[$cnf( $equal(addition(X_23,addition(X_23,X_11)),addition(X_23,X_11)) )],[refute_0_12,refute_0_2]) ).
cnf(refute_0_14,plain,
addition(X_23,X_11) = addition(X_23,X_11),
introduced(tautology,[refl,[$fot(addition(X_23,X_11))]]) ).
cnf(refute_0_15,plain,
leq(X_23,addition(X_23,X_11)),
inference(resolve,[$cnf( $equal(addition(X_23,X_11),addition(X_23,X_11)) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
leq(multiplication(X_71,X_73),addition(multiplication(X_71,X_73),multiplication(X_72,X_73))),
inference(subst,[],[refute_0_15:[bind(X_11,$fot(multiplication(X_72,X_73))),bind(X_23,$fot(multiplication(X_71,X_73)))]]) ).
cnf(refute_0_17,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
multiplication(addition(X_71,X_72),X_73) = addition(multiplication(X_71,X_73),multiplication(X_72,X_73)),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_71)),bind(B,$fot(X_72)),bind(C,$fot(X_73))]]) ).
cnf(refute_0_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( multiplication(addition(X_71,X_72),X_73) != addition(multiplication(X_71,X_73),multiplication(X_72,X_73))
| addition(multiplication(X_71,X_73),multiplication(X_72,X_73)) = multiplication(addition(X_71,X_72),X_73) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiplication(addition(X_71,X_72),X_73))),bind(Y,$fot(addition(multiplication(X_71,X_73),multiplication(X_72,X_73))))]]) ).
cnf(refute_0_23,plain,
addition(multiplication(X_71,X_73),multiplication(X_72,X_73)) = multiplication(addition(X_71,X_72),X_73),
inference(resolve,[$cnf( $equal(multiplication(addition(X_71,X_72),X_73),addition(multiplication(X_71,X_73),multiplication(X_72,X_73))) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( addition(multiplication(X_71,X_73),multiplication(X_72,X_73)) != multiplication(addition(X_71,X_72),X_73)
| ~ leq(multiplication(X_71,X_73),addition(multiplication(X_71,X_73),multiplication(X_72,X_73)))
| leq(multiplication(X_71,X_73),multiplication(addition(X_71,X_72),X_73)) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(X_71,X_73),addition(multiplication(X_71,X_73),multiplication(X_72,X_73))) ),[1],$fot(multiplication(addition(X_71,X_72),X_73))]]) ).
cnf(refute_0_25,plain,
( ~ leq(multiplication(X_71,X_73),addition(multiplication(X_71,X_73),multiplication(X_72,X_73)))
| leq(multiplication(X_71,X_73),multiplication(addition(X_71,X_72),X_73)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_71,X_73),multiplication(X_72,X_73)),multiplication(addition(X_71,X_72),X_73)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
leq(multiplication(X_71,X_73),multiplication(addition(X_71,X_72),X_73)),
inference(resolve,[$cnf( leq(multiplication(X_71,X_73),addition(multiplication(X_71,X_73),multiplication(X_72,X_73))) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
leq(multiplication(skolemFOFtoCNF_X0,X_394),multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),X_394)),
inference(subst,[],[refute_0_26:[bind(X_71,$fot(skolemFOFtoCNF_X0)),bind(X_72,$fot(skolemFOFtoCNF_X1)),bind(X_73,$fot(X_394))]]) ).
cnf(refute_0_28,plain,
leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_29,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_30,plain,
( ~ leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)
| addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_31,plain,
addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
( addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| ~ leq(multiplication(skolemFOFtoCNF_X0,X_394),multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),X_394))
| leq(multiplication(skolemFOFtoCNF_X0,X_394),multiplication(skolemFOFtoCNF_X1,X_394)) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(skolemFOFtoCNF_X0,X_394),multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),X_394)) ),[1,0],$fot(skolemFOFtoCNF_X1)]]) ).
cnf(refute_0_33,plain,
( ~ leq(multiplication(skolemFOFtoCNF_X0,X_394),multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),X_394))
| leq(multiplication(skolemFOFtoCNF_X0,X_394),multiplication(skolemFOFtoCNF_X1,X_394)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
leq(multiplication(skolemFOFtoCNF_X0,X_394),multiplication(skolemFOFtoCNF_X1,X_394)),
inference(resolve,[$cnf( leq(multiplication(skolemFOFtoCNF_X0,X_394),multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),X_394)) )],[refute_0_27,refute_0_33]) ).
cnf(refute_0_35,plain,
leq(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(subst,[],[refute_0_34:[bind(X_394,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( leq(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) )],[refute_0_35,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 13:05:30 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 15.71/15.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.71/15.93
% 15.71/15.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.77/15.93
%------------------------------------------------------------------------------