TSTP Solution File: REL049+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL049+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : Mon Jul 18 19:46:17 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 20 unt; 0 def)
% Number of atoms : 68 ( 67 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 26 ~; 20 |; 7 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( ( join(X0,X1) = X1
& join(X2,X1) = X1 )
=> join(join(X0,X2),X1) = X1 ) ).
fof(subgoal_0,plain,
! [X0,X1,X2] :
( ( join(X0,X1) = X1
& join(X2,X1) = X1 )
=> join(join(X0,X2),X1) = X1 ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2] :
( ( join(X0,X1) = X1
& join(X2,X1) = X1 )
=> join(join(X0,X2),X1) = X1 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1,X2] :
( join(join(X0,X2),X1) != X1
& join(X0,X1) = X1
& join(X2,X1) = X1 ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
& join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1
& join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_5,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[maddux2_join_associativity]) ).
fof(normalize_0_6,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(specialize,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1,
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),
introduced(tautology,[refl,[$fot(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_4,plain,
( join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) != join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1))
| join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1))) ),[1,1],$fot(skolemFOFtoCNF_X1)]]) ).
cnf(refute_0_5,plain,
( join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1))) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_8,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_9,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_11,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) != join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)
| join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = skolemFOFtoCNF_X1 ),
inference(subst,[],[refute_0_11:[bind(X,$fot(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)))),bind(Y,$fot(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),bind(Z,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_13,plain,
( join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = skolemFOFtoCNF_X1 ),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) )],[refute_0_6,refute_0_12]) ).
cnf(refute_0_14,plain,
join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) = skolemFOFtoCNF_X1,
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_1,refute_0_13]) ).
cnf(refute_0_15,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_16,plain,
( join(X0,join(X1,X2)) != join(join(X0,X1),X2)
| join(join(X0,X1),X2) = join(X0,join(X1,X2)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(join(X0,join(X1,X2)))),bind(Y,$fot(join(join(X0,X1),X2)))]]) ).
cnf(refute_0_17,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(resolve,[$cnf( $equal(join(X0,join(X1,X2)),join(join(X0,X1),X2)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_17:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(skolemFOFtoCNF_X2)),bind(X2,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_19,plain,
( join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) != join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1))
| join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) != skolemFOFtoCNF_X1
| join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
inference(subst,[],[refute_0_11:[bind(X,$fot(join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1))),bind(Y,$fot(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)))),bind(Z,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_20,plain,
( join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)) != skolemFOFtoCNF_X1
| join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
inference(resolve,[$cnf( $equal(join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1),join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1)),skolemFOFtoCNF_X1) )],[refute_0_14,refute_0_20]) ).
cnf(refute_0_22,plain,
( join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| skolemFOFtoCNF_X1 != skolemFOFtoCNF_X1
| join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) ),[0],$fot(skolemFOFtoCNF_X1)]]) ).
cnf(refute_0_23,plain,
( skolemFOFtoCNF_X1 != skolemFOFtoCNF_X1
| join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
inference(resolve,[$cnf( $equal(join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
skolemFOFtoCNF_X1 != skolemFOFtoCNF_X1,
inference(resolve,[$cnf( $equal(join(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_23,refute_0_0]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_X1 = skolemFOFtoCNF_X1,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X1)]]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1,skolemFOFtoCNF_X1) )],[refute_0_25,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL049+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 8 15:41:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------