TSTP Solution File: KLE085+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE085+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 02:15:09 EDT 2022
% Result : Theorem 0.18s 0.44s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 69 ( 48 unt; 0 def)
% Number of atoms : 99 ( 98 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 36 ~; 30 |; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 2 sgn 27 !; 1 ?)
% 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(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one ).
fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)) ).
fof(goals,conjecture,
! [X0] : addition(domain(X0),one) = one ).
fof(subgoal_0,plain,
! [X0] : addition(domain(X0),one) = one,
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : addition(domain(X0),one) = one,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : addition(domain(X0),one) != one,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
addition(domain(skolemFOFtoCNF_X0),one) != one,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_3,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_5,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_7,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[domain4]) ).
fof(normalize_0_9,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
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]) ).
cnf(refute_0_0,plain,
addition(domain(skolemFOFtoCNF_X0),one) != one,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
addition(A,B) = addition(B,A),
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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_6,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
addition(domain(skolemFOFtoCNF_X0),one) = addition(one,domain(skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_6:[bind(A,$fot(one)),bind(B,$fot(domain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_8,plain,
( addition(domain(skolemFOFtoCNF_X0),one) != addition(one,domain(skolemFOFtoCNF_X0))
| addition(one,domain(skolemFOFtoCNF_X0)) != one
| addition(domain(skolemFOFtoCNF_X0),one) = one ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(domain(skolemFOFtoCNF_X0),one),one) ),[0],$fot(addition(one,domain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_9,plain,
( addition(one,domain(skolemFOFtoCNF_X0)) != one
| addition(domain(skolemFOFtoCNF_X0),one) = one ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),one),addition(one,domain(skolemFOFtoCNF_X0))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
addition(one,domain(skolemFOFtoCNF_X0)) != one,
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),one),one) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_12,plain,
addition(antidomain(X0),addition(domain(X0),X_37)) = addition(addition(antidomain(X0),domain(X0)),X_37),
inference(subst,[],[refute_0_11:[bind(A,$fot(antidomain(X0))),bind(B,$fot(domain(X0))),bind(C,$fot(X_37))]]) ).
cnf(refute_0_13,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_14,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(subst,[],[refute_0_6:[bind(A,$fot(antidomain(X0))),bind(B,$fot(antidomain(antidomain(X0))))]]) ).
cnf(refute_0_15,plain,
( addition(antidomain(antidomain(X0)),antidomain(X0)) != addition(antidomain(X0),antidomain(antidomain(X0)))
| addition(antidomain(antidomain(X0)),antidomain(X0)) != one
| addition(antidomain(X0),antidomain(antidomain(X0))) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),one) ),[0],$fot(addition(antidomain(X0),antidomain(antidomain(X0))))]]) ).
cnf(refute_0_16,plain,
( addition(antidomain(antidomain(X0)),antidomain(X0)) != one
| addition(antidomain(X0),antidomain(antidomain(X0))) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),addition(antidomain(X0),antidomain(antidomain(X0)))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),one) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_19,plain,
( domain(X0) != antidomain(antidomain(X0))
| antidomain(antidomain(X0)) = domain(X0) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(domain(X0))),bind(Y,$fot(antidomain(antidomain(X0))))]]) ).
cnf(refute_0_20,plain,
antidomain(antidomain(X0)) = domain(X0),
inference(resolve,[$cnf( $equal(domain(X0),antidomain(antidomain(X0))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),antidomain(antidomain(X0))),
introduced(tautology,[refl,[$fot(addition(antidomain(X0),antidomain(antidomain(X0))))]]) ).
cnf(refute_0_22,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != addition(antidomain(X0),antidomain(antidomain(X0)))
| antidomain(antidomain(X0)) != domain(X0)
| addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),antidomain(antidomain(X0)))) ),[1,1],$fot(domain(X0))]]) ).
cnf(refute_0_23,plain,
( antidomain(antidomain(X0)) != domain(X0)
| addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),antidomain(antidomain(X0)))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)),
inference(resolve,[$cnf( $equal(antidomain(antidomain(X0)),domain(X0)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != addition(antidomain(X0),domain(X0))
| addition(antidomain(X0),antidomain(antidomain(X0))) != one
| addition(antidomain(X0),domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),one) ),[0],$fot(addition(antidomain(X0),domain(X0)))]]) ).
cnf(refute_0_26,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != one
| addition(antidomain(X0),domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),domain(X0))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
addition(antidomain(X0),domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),one) )],[refute_0_17,refute_0_26]) ).
cnf(refute_0_28,plain,
( addition(antidomain(X0),addition(domain(X0),X_37)) != addition(addition(antidomain(X0),domain(X0)),X_37)
| addition(antidomain(X0),domain(X0)) != one
| addition(antidomain(X0),addition(domain(X0),X_37)) = addition(one,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),addition(domain(X0),X_37)),addition(addition(antidomain(X0),domain(X0)),X_37)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_29,plain,
( addition(antidomain(X0),addition(domain(X0),X_37)) != addition(addition(antidomain(X0),domain(X0)),X_37)
| addition(antidomain(X0),addition(domain(X0),X_37)) = addition(one,X_37) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),domain(X0)),one) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
addition(antidomain(X0),addition(domain(X0),X_37)) = addition(one,X_37),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),addition(domain(X0),X_37)),addition(addition(antidomain(X0),domain(X0)),X_37)) )],[refute_0_12,refute_0_29]) ).
cnf(refute_0_31,plain,
addition(antidomain(X_38),addition(domain(X_38),domain(X_38))) = addition(one,domain(X_38)),
inference(subst,[],[refute_0_30:[bind(X0,$fot(X_38)),bind(X_37,$fot(domain(X_38)))]]) ).
cnf(refute_0_32,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_33,plain,
addition(domain(X_38),domain(X_38)) = domain(X_38),
inference(subst,[],[refute_0_32:[bind(A,$fot(domain(X_38)))]]) ).
cnf(refute_0_34,plain,
( addition(antidomain(X_38),addition(domain(X_38),domain(X_38))) != addition(one,domain(X_38))
| addition(domain(X_38),domain(X_38)) != domain(X_38)
| addition(antidomain(X_38),domain(X_38)) = addition(one,domain(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X_38),addition(domain(X_38),domain(X_38))),addition(one,domain(X_38))) ),[0,1],$fot(domain(X_38))]]) ).
cnf(refute_0_35,plain,
( addition(antidomain(X_38),addition(domain(X_38),domain(X_38))) != addition(one,domain(X_38))
| addition(antidomain(X_38),domain(X_38)) = addition(one,domain(X_38)) ),
inference(resolve,[$cnf( $equal(addition(domain(X_38),domain(X_38)),domain(X_38)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
addition(antidomain(X_38),domain(X_38)) = addition(one,domain(X_38)),
inference(resolve,[$cnf( $equal(addition(antidomain(X_38),addition(domain(X_38),domain(X_38))),addition(one,domain(X_38))) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
addition(antidomain(X_38),domain(X_38)) = one,
inference(subst,[],[refute_0_27:[bind(X0,$fot(X_38))]]) ).
cnf(refute_0_38,plain,
( addition(antidomain(X_38),domain(X_38)) != addition(one,domain(X_38))
| addition(antidomain(X_38),domain(X_38)) != one
| one = addition(one,domain(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X_38),domain(X_38)),addition(one,domain(X_38))) ),[0],$fot(one)]]) ).
cnf(refute_0_39,plain,
( addition(antidomain(X_38),domain(X_38)) != addition(one,domain(X_38))
| one = addition(one,domain(X_38)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X_38),domain(X_38)),one) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
one = addition(one,domain(X_38)),
inference(resolve,[$cnf( $equal(addition(antidomain(X_38),domain(X_38)),addition(one,domain(X_38))) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( one != addition(one,domain(X_38))
| addition(one,domain(X_38)) = one ),
inference(subst,[],[refute_0_4:[bind(X,$fot(one)),bind(Y,$fot(addition(one,domain(X_38))))]]) ).
cnf(refute_0_42,plain,
addition(one,domain(X_38)) = one,
inference(resolve,[$cnf( $equal(one,addition(one,domain(X_38))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
addition(one,domain(skolemFOFtoCNF_X0)) = one,
inference(subst,[],[refute_0_42:[bind(X_38,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_44,plain,
( addition(one,domain(skolemFOFtoCNF_X0)) != one
| one != one
| addition(one,domain(skolemFOFtoCNF_X0)) = one ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(one,domain(skolemFOFtoCNF_X0)),one) ),[0],$fot(one)]]) ).
cnf(refute_0_45,plain,
( one != one
| addition(one,domain(skolemFOFtoCNF_X0)) = one ),
inference(resolve,[$cnf( $equal(addition(one,domain(skolemFOFtoCNF_X0)),one) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
one != one,
inference(resolve,[$cnf( $equal(addition(one,domain(skolemFOFtoCNF_X0)),one) )],[refute_0_45,refute_0_10]) ).
cnf(refute_0_47,plain,
one = one,
introduced(tautology,[refl,[$fot(one)]]) ).
cnf(refute_0_48,plain,
$false,
inference(resolve,[$cnf( $equal(one,one) )],[refute_0_47,refute_0_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KLE085+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 16:07:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44
% 0.18/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.45
%------------------------------------------------------------------------------