TSTP Solution File: SYN072+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN072+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 : Thu Jul 21 08:59:18 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 68 ( 23 unt; 0 def)
% Number of atoms : 137 ( 107 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 115 ( 46 ~; 69 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 35 ( 0 sgn 7 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel49_1,axiom,
? [X0,Y0] :
! [Z] :
( Z = X0
| Z = Y0 ) ).
fof(pel49_2,axiom,
big_p(a) ).
fof(pel49_3,axiom,
big_p(b) ).
fof(pel49_4,axiom,
a != b ).
fof(pel49,conjecture,
! [X0] : big_p(X0) ).
fof(subgoal_0,plain,
! [X0] : big_p(X0),
inference(strip,[],[pel49]) ).
fof(negate_0_0,plain,
~ ! [X0] : big_p(X0),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : ~ big_p(X0),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ big_p(skolemFOFtoCNF_X_1),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
big_p(b),
inference(canonicalize,[],[pel49_3]) ).
fof(normalize_0_3,plain,
? [X0,Y0] :
! [Z] :
( Z = X0
| Z = Y0 ),
inference(canonicalize,[],[pel49_1]) ).
fof(normalize_0_4,plain,
! [Z] :
( Z = skolemFOFtoCNF_X
| Z = skolemFOFtoCNF_Y ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Z] :
( Z = skolemFOFtoCNF_X
| Z = skolemFOFtoCNF_Y ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
big_p(a),
inference(canonicalize,[],[pel49_2]) ).
fof(normalize_0_7,plain,
a != b,
inference(canonicalize,[],[pel49_4]) ).
cnf(refute_0_0,plain,
~ big_p(skolemFOFtoCNF_X_1),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
big_p(b),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( Z = skolemFOFtoCNF_X
| Z = skolemFOFtoCNF_Y ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( X_0 = skolemFOFtoCNF_X
| X_0 = skolemFOFtoCNF_Y ),
inference(subst,[],[refute_0_2:[bind(Z,$fot(X_0))]]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_6,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( X_0 != skolemFOFtoCNF_Y
| skolemFOFtoCNF_Y = X_0 ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_0)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_8,plain,
( X_0 = skolemFOFtoCNF_X
| skolemFOFtoCNF_Y = X_0 ),
inference(resolve,[$cnf( $equal(X_0,skolemFOFtoCNF_Y) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( Z != skolemFOFtoCNF_Y
| skolemFOFtoCNF_Y != X_0
| Z = X_0 ),
introduced(tautology,[equality,[$cnf( ~ $equal(Z,X_0) ),[0],$fot(skolemFOFtoCNF_Y)]]) ).
cnf(refute_0_10,plain,
( Z != skolemFOFtoCNF_Y
| Z = X_0
| X_0 = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,X_0) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( Z = X_0
| Z = skolemFOFtoCNF_X
| X_0 = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( $equal(Z,skolemFOFtoCNF_Y) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( X_2 = skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = X_2
| skolemFOFtoCNF_X_1 = skolemFOFtoCNF_X ),
inference(subst,[],[refute_0_11:[bind(Z,$fot(skolemFOFtoCNF_X_1)),bind(X_0,$fot(X_2))]]) ).
cnf(refute_0_13,plain,
( skolemFOFtoCNF_X_1 != X_2
| ~ big_p(X_2)
| big_p(skolemFOFtoCNF_X_1) ),
introduced(tautology,[equality,[$cnf( ~ big_p(skolemFOFtoCNF_X_1) ),[0],$fot(X_2)]]) ).
cnf(refute_0_14,plain,
( ~ big_p(X_2)
| X_2 = skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = skolemFOFtoCNF_X
| big_p(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,X_2) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ big_p(X_2)
| X_2 = skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_1) )],[refute_0_14,refute_0_0]) ).
cnf(refute_0_16,plain,
( ~ big_p(b)
| b = skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = skolemFOFtoCNF_X ),
inference(subst,[],[refute_0_15:[bind(X_2,$fot(b))]]) ).
cnf(refute_0_17,plain,
( b = skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( big_p(b) )],[refute_0_1,refute_0_16]) ).
cnf(refute_0_18,plain,
big_p(a),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_19,plain,
( ~ big_p(a)
| a = skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = skolemFOFtoCNF_X ),
inference(subst,[],[refute_0_15:[bind(X_2,$fot(a))]]) ).
cnf(refute_0_20,plain,
( a = skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( big_p(a) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
a != b,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_22,plain,
( X_2 = skolemFOFtoCNF_X
| a = X_2
| a = skolemFOFtoCNF_X ),
inference(subst,[],[refute_0_11:[bind(Z,$fot(a)),bind(X_0,$fot(X_2))]]) ).
cnf(refute_0_23,plain,
( X_2 != b
| a != X_2
| a = b ),
introduced(tautology,[equality,[$cnf( $equal(a,X_2) ),[1],$fot(b)]]) ).
cnf(refute_0_24,plain,
( X_2 != b
| X_2 = skolemFOFtoCNF_X
| a = b
| a = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( $equal(a,X_2) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( X_2 != b
| X_2 = skolemFOFtoCNF_X
| a = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( $equal(a,b) )],[refute_0_24,refute_0_21]) ).
cnf(refute_0_26,plain,
( b != b
| a = skolemFOFtoCNF_X
| b = skolemFOFtoCNF_X ),
inference(subst,[],[refute_0_25:[bind(X_2,$fot(b))]]) ).
cnf(refute_0_27,plain,
b = b,
introduced(tautology,[refl,[$fot(b)]]) ).
cnf(refute_0_28,plain,
( a = skolemFOFtoCNF_X
| b = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( $equal(b,b) )],[refute_0_27,refute_0_26]) ).
cnf(refute_0_29,plain,
( b != skolemFOFtoCNF_X
| skolemFOFtoCNF_X = b ),
inference(subst,[],[refute_0_6:[bind(X,$fot(b)),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_30,plain,
( a = skolemFOFtoCNF_X
| skolemFOFtoCNF_X = b ),
inference(resolve,[$cnf( $equal(b,skolemFOFtoCNF_X) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_X != b
| skolemFOFtoCNF_X_1 != skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = b ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X) ),[1],$fot(b)]]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_X_1 != skolemFOFtoCNF_X
| a = skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = b ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,b) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( a = skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = b ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X) )],[refute_0_20,refute_0_32]) ).
cnf(refute_0_34,plain,
( skolemFOFtoCNF_X_1 != b
| ~ big_p(b)
| big_p(skolemFOFtoCNF_X_1) ),
introduced(tautology,[equality,[$cnf( ~ big_p(skolemFOFtoCNF_X_1) ),[0],$fot(b)]]) ).
cnf(refute_0_35,plain,
( ~ big_p(b)
| a = skolemFOFtoCNF_X
| big_p(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,b) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ big_p(b)
| a = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_1) )],[refute_0_35,refute_0_0]) ).
cnf(refute_0_37,plain,
a = skolemFOFtoCNF_X,
inference(resolve,[$cnf( big_p(b) )],[refute_0_1,refute_0_36]) ).
cnf(refute_0_38,plain,
( a != skolemFOFtoCNF_X
| skolemFOFtoCNF_X = a ),
inference(subst,[],[refute_0_6:[bind(X,$fot(a)),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_39,plain,
skolemFOFtoCNF_X = a,
inference(resolve,[$cnf( $equal(a,skolemFOFtoCNF_X) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( b != skolemFOFtoCNF_X
| skolemFOFtoCNF_X != a
| b = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(b,a) ),[0],$fot(skolemFOFtoCNF_X)]]) ).
cnf(refute_0_41,plain,
( b != skolemFOFtoCNF_X
| b = a ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,a) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( b = a
| skolemFOFtoCNF_X_1 = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( $equal(b,skolemFOFtoCNF_X) )],[refute_0_17,refute_0_41]) ).
cnf(refute_0_43,plain,
( skolemFOFtoCNF_X != a
| skolemFOFtoCNF_X_1 != skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = a ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X) ),[1],$fot(a)]]) ).
cnf(refute_0_44,plain,
( skolemFOFtoCNF_X_1 != skolemFOFtoCNF_X
| skolemFOFtoCNF_X_1 = a ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,a) )],[refute_0_39,refute_0_43]) ).
cnf(refute_0_45,plain,
( b = a
| skolemFOFtoCNF_X_1 = a ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X) )],[refute_0_42,refute_0_44]) ).
cnf(refute_0_46,plain,
( b != a
| a = b ),
inference(subst,[],[refute_0_6:[bind(X,$fot(b)),bind(Y,$fot(a))]]) ).
cnf(refute_0_47,plain,
b != a,
inference(resolve,[$cnf( $equal(a,b) )],[refute_0_46,refute_0_21]) ).
cnf(refute_0_48,plain,
skolemFOFtoCNF_X_1 = a,
inference(resolve,[$cnf( $equal(b,a) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
( skolemFOFtoCNF_X_1 != a
| ~ big_p(a)
| big_p(skolemFOFtoCNF_X_1) ),
introduced(tautology,[equality,[$cnf( ~ big_p(skolemFOFtoCNF_X_1) ),[0],$fot(a)]]) ).
cnf(refute_0_50,plain,
( ~ big_p(a)
| big_p(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,a) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
~ big_p(a),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_1) )],[refute_0_50,refute_0_0]) ).
cnf(refute_0_52,plain,
$false,
inference(resolve,[$cnf( big_p(a) )],[refute_0_18,refute_0_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN072+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 12 01:04:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.38
% 0.19/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.38
%------------------------------------------------------------------------------