TSTP Solution File: REL014+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL014+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 : Mon Jul 18 19:43:25 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 66 ( 43 unt; 0 def)
% Number of atoms : 97 ( 94 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 35 ~; 27 |; 2 &)
% ( 0 <=>; 2 =>; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0 ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0 ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ).
fof(goals,conjecture,
! [X0] :
( composition(X0,one) = X0
& composition(one,X0) = X0 ) ).
fof(subgoal_0,plain,
! [X0] : composition(X0,one) = X0,
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0] :
( composition(X0,one) = X0
=> composition(one,X0) = X0 ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : composition(X0,one) = X0,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : composition(X0,one) != X0,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X0] : composition(X0,one) = X0,
inference(canonicalize,[],[composition_identity]) ).
fof(normalize_0_2,plain,
! [X0] : composition(X0,one) = X0,
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
$false,
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
cnf(refute_0_0,plain,
$false,
inference(canonicalize,[],[normalize_0_3]) ).
fof(negate_1_0,plain,
~ ! [X0] :
( composition(X0,one) = X0
=> composition(one,X0) = X0 ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X0] :
( composition(one,X0) != X0
& composition(X0,one) = X0 ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [X0] : composition(X0,one) = X0,
inference(canonicalize,[],[composition_identity]) ).
fof(normalize_1_2,plain,
! [X0] : composition(X0,one) = X0,
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
? [X0] : composition(one,X0) != X0,
inference(simplify,[],[normalize_1_0,normalize_1_2]) ).
fof(normalize_1_4,plain,
composition(one,skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0,
inference(skolemize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[converse_multiplicativity]) ).
fof(normalize_1_6,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X0] : converse(converse(X0)) = X0,
inference(canonicalize,[],[converse_idempotence]) ).
fof(normalize_1_8,plain,
! [X0] : converse(converse(X0)) = X0,
inference(specialize,[],[normalize_1_7]) ).
cnf(refute_1_0,plain,
composition(one,skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0,
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_1,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
converse(composition(converse(X0),X_22)) = composition(converse(X_22),converse(converse(X0))),
inference(subst,[],[refute_1_1:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_22))]]) ).
cnf(refute_1_3,plain,
converse(converse(X0)) = X0,
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_4,plain,
( converse(composition(converse(X0),X_22)) != composition(converse(X_22),converse(converse(X0)))
| converse(converse(X0)) != X0
| converse(composition(converse(X0),X_22)) = composition(converse(X_22),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X0),X_22)),composition(converse(X_22),converse(converse(X0)))) ),[1,1],$fot(X0)]]) ).
cnf(refute_1_5,plain,
( converse(composition(converse(X0),X_22)) != composition(converse(X_22),converse(converse(X0)))
| converse(composition(converse(X0),X_22)) = composition(converse(X_22),X0) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_1_3,refute_1_4]) ).
cnf(refute_1_6,plain,
converse(composition(converse(X0),X_22)) = composition(converse(X_22),X0),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),X_22)),composition(converse(X_22),converse(converse(X0)))) )],[refute_1_2,refute_1_5]) ).
cnf(refute_1_7,plain,
converse(composition(converse(X_23),one)) = composition(converse(one),X_23),
inference(subst,[],[refute_1_6:[bind(X0,$fot(X_23)),bind(X_22,$fot(one))]]) ).
cnf(refute_1_8,plain,
composition(X0,one) = X0,
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_9,plain,
composition(converse(X_23),one) = converse(X_23),
inference(subst,[],[refute_1_8:[bind(X0,$fot(converse(X_23)))]]) ).
cnf(refute_1_10,plain,
( composition(converse(X_23),one) != converse(X_23)
| converse(composition(converse(X_23),one)) != composition(converse(one),X_23)
| converse(converse(X_23)) = composition(converse(one),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_23),one)),composition(converse(one),X_23)) ),[0,0],$fot(converse(X_23))]]) ).
cnf(refute_1_11,plain,
( converse(composition(converse(X_23),one)) != composition(converse(one),X_23)
| converse(converse(X_23)) = composition(converse(one),X_23) ),
inference(resolve,[$cnf( $equal(composition(converse(X_23),one),converse(X_23)) )],[refute_1_9,refute_1_10]) ).
cnf(refute_1_12,plain,
converse(converse(X_23)) = composition(converse(one),X_23),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_23),one)),composition(converse(one),X_23)) )],[refute_1_7,refute_1_11]) ).
cnf(refute_1_13,plain,
converse(converse(X_23)) = X_23,
inference(subst,[],[refute_1_3:[bind(X0,$fot(X_23))]]) ).
cnf(refute_1_14,plain,
( converse(converse(X_23)) != X_23
| converse(converse(X_23)) != composition(converse(one),X_23)
| X_23 = composition(converse(one),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_23)),composition(converse(one),X_23)) ),[0],$fot(X_23)]]) ).
cnf(refute_1_15,plain,
( converse(converse(X_23)) != composition(converse(one),X_23)
| X_23 = composition(converse(one),X_23) ),
inference(resolve,[$cnf( $equal(converse(converse(X_23)),X_23) )],[refute_1_13,refute_1_14]) ).
cnf(refute_1_16,plain,
X_23 = composition(converse(one),X_23),
inference(resolve,[$cnf( $equal(converse(converse(X_23)),composition(converse(one),X_23)) )],[refute_1_12,refute_1_15]) ).
cnf(refute_1_17,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[refute_1_8:[bind(X0,$fot(converse(one)))]]) ).
cnf(refute_1_18,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_1_16:[bind(X_23,$fot(one))]]) ).
cnf(refute_1_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_1_21:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_1_23,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_1_18,refute_1_22]) ).
cnf(refute_1_24,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_1_25,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_1_23,refute_1_24]) ).
cnf(refute_1_26,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_1_17,refute_1_25]) ).
cnf(refute_1_27,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_1_21:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_1_28,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_1_26,refute_1_27]) ).
cnf(refute_1_29,plain,
composition(converse(one),X_23) = composition(converse(one),X_23),
introduced(tautology,[refl,[$fot(composition(converse(one),X_23))]]) ).
cnf(refute_1_30,plain,
( composition(converse(one),X_23) != composition(converse(one),X_23)
| converse(one) != one
| composition(converse(one),X_23) = composition(one,X_23) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_23),composition(converse(one),X_23)) ),[1,0],$fot(one)]]) ).
cnf(refute_1_31,plain,
( converse(one) != one
| composition(converse(one),X_23) = composition(one,X_23) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_23),composition(converse(one),X_23)) )],[refute_1_29,refute_1_30]) ).
cnf(refute_1_32,plain,
composition(converse(one),X_23) = composition(one,X_23),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_1_28,refute_1_31]) ).
cnf(refute_1_33,plain,
( X_23 != composition(converse(one),X_23)
| composition(converse(one),X_23) != composition(one,X_23)
| X_23 = composition(one,X_23) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_23,composition(one,X_23)) ),[0],$fot(composition(converse(one),X_23))]]) ).
cnf(refute_1_34,plain,
( X_23 != composition(converse(one),X_23)
| X_23 = composition(one,X_23) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_23),composition(one,X_23)) )],[refute_1_32,refute_1_33]) ).
cnf(refute_1_35,plain,
X_23 = composition(one,X_23),
inference(resolve,[$cnf( $equal(X_23,composition(converse(one),X_23)) )],[refute_1_16,refute_1_34]) ).
cnf(refute_1_36,plain,
( X_23 != composition(one,X_23)
| composition(one,X_23) = X_23 ),
inference(subst,[],[refute_1_21:[bind(X,$fot(X_23)),bind(Y,$fot(composition(one,X_23)))]]) ).
cnf(refute_1_37,plain,
composition(one,X_23) = X_23,
inference(resolve,[$cnf( $equal(X_23,composition(one,X_23)) )],[refute_1_35,refute_1_36]) ).
cnf(refute_1_38,plain,
composition(one,skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_1_37:[bind(X_23,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_1_39,plain,
( composition(one,skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0
| skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0
| composition(one,skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0 ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(one,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) ),[0],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_1_40,plain,
( skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0
| composition(one,skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0 ),
inference(resolve,[$cnf( $equal(composition(one,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) )],[refute_1_38,refute_1_39]) ).
cnf(refute_1_41,plain,
skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0,
inference(resolve,[$cnf( $equal(composition(one,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) )],[refute_1_40,refute_1_0]) ).
cnf(refute_1_42,plain,
skolemFOFtoCNF_X0 = skolemFOFtoCNF_X0,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_1_43,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0,skolemFOFtoCNF_X0) )],[refute_1_42,refute_1_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL014+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 11:28:45 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.42
% 0.21/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.43
%------------------------------------------------------------------------------