TSTP Solution File: KLE067+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE067+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 02:15:01 EDT 2022
% Result : Theorem 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 55 ( 36 unt; 0 def)
% Number of atoms : 82 ( 81 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 33 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 52 ( 0 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
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] : domain(addition(domain(X0),domain(X1))) = addition(domain(X0),domain(X1)) ).
fof(subgoal_0,plain,
! [X0,X1] : domain(addition(domain(X0),domain(X1))) = addition(domain(X0),domain(X1)),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] : domain(addition(domain(X0),domain(X1))) = addition(domain(X0),domain(X1)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] : domain(addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),
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,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[domain2]) ).
fof(normalize_0_5,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_7,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),
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,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_8,plain,
domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),
introduced(tautology,[refl,[$fot(domain(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))
| domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)))
| domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)))) ),[1,0],$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))
| domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),
inference(resolve,[$cnf( $equal(domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))
| domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))
| domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) ),[0],$fot(domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_13,plain,
( domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))
| domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) ),[1],$fot(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_15,plain,
( domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_7,refute_0_14]) ).
cnf(refute_0_16,plain,
( domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) )],[refute_0_15,refute_0_13]) ).
cnf(refute_0_17,plain,
domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(domain(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) )],[refute_0_16,refute_0_0]) ).
cnf(refute_0_18,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_19,plain,
domain(multiplication(one,X_15)) = domain(multiplication(one,domain(X_15))),
inference(subst,[],[refute_0_18:[bind(X0,$fot(one)),bind(X1,$fot(X_15))]]) ).
cnf(refute_0_20,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_21,plain,
multiplication(one,domain(X_15)) = domain(X_15),
inference(subst,[],[refute_0_20:[bind(A,$fot(domain(X_15)))]]) ).
cnf(refute_0_22,plain,
( domain(multiplication(one,X_15)) != domain(multiplication(one,domain(X_15)))
| multiplication(one,domain(X_15)) != domain(X_15)
| domain(multiplication(one,X_15)) = domain(domain(X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_15)),domain(multiplication(one,domain(X_15)))) ),[1,0],$fot(domain(X_15))]]) ).
cnf(refute_0_23,plain,
( domain(multiplication(one,X_15)) != domain(multiplication(one,domain(X_15)))
| domain(multiplication(one,X_15)) = domain(domain(X_15)) ),
inference(resolve,[$cnf( $equal(multiplication(one,domain(X_15)),domain(X_15)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
domain(multiplication(one,X_15)) = domain(domain(X_15)),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_15)),domain(multiplication(one,domain(X_15)))) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
multiplication(one,X_15) = X_15,
inference(subst,[],[refute_0_20:[bind(A,$fot(X_15))]]) ).
cnf(refute_0_26,plain,
domain(multiplication(one,X_15)) = domain(multiplication(one,X_15)),
introduced(tautology,[refl,[$fot(domain(multiplication(one,X_15)))]]) ).
cnf(refute_0_27,plain,
( domain(multiplication(one,X_15)) != domain(multiplication(one,X_15))
| multiplication(one,X_15) != X_15
| domain(multiplication(one,X_15)) = domain(X_15) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_15)),domain(multiplication(one,X_15))) ),[1,0],$fot(X_15)]]) ).
cnf(refute_0_28,plain,
( multiplication(one,X_15) != X_15
| domain(multiplication(one,X_15)) = domain(X_15) ),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_15)),domain(multiplication(one,X_15))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
domain(multiplication(one,X_15)) = domain(X_15),
inference(resolve,[$cnf( $equal(multiplication(one,X_15),X_15) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( domain(multiplication(one,X_15)) != domain(X_15)
| domain(multiplication(one,X_15)) != domain(domain(X_15))
| domain(X_15) = domain(domain(X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_15)),domain(domain(X_15))) ),[0],$fot(domain(X_15))]]) ).
cnf(refute_0_31,plain,
( domain(multiplication(one,X_15)) != domain(domain(X_15))
| domain(X_15) = domain(domain(X_15)) ),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_15)),domain(X_15)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
domain(X_15) = domain(domain(X_15)),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_15)),domain(domain(X_15))) )],[refute_0_24,refute_0_31]) ).
cnf(refute_0_33,plain,
( domain(X_15) != domain(domain(X_15))
| domain(domain(X_15)) = domain(X_15) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(domain(X_15))),bind(Y,$fot(domain(domain(X_15))))]]) ).
cnf(refute_0_34,plain,
domain(domain(X_15)) = domain(X_15),
inference(resolve,[$cnf( $equal(domain(X_15),domain(domain(X_15))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_34:[bind(X_15,$fot(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_36,plain,
( domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),[0,0],$fot(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_37,plain,
( domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) = domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) ),
inference(resolve,[$cnf( $equal(domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( $equal(domain(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_37,refute_0_17]) ).
cnf(refute_0_39,plain,
domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
introduced(tautology,[refl,[$fot(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( $equal(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_39,refute_0_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : KLE067+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 15:03:11 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.40
% 0.15/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.15/0.41
%------------------------------------------------------------------------------