TSTP Solution File: SET903+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET903+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 : Tue Jul 19 03:38:13 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 21 unt; 0 def)
% Number of atoms : 156 ( 155 equ)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 170 ( 71 ~; 66 |; 31 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 5 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t43_zfmisc_1,axiom,
! [A,B,C] :
~ ( singleton(A) = set_union2(B,C)
& ~ ( B = singleton(A)
& C = singleton(A) )
& ~ ( B = empty_set
& C = singleton(A) )
& ~ ( B = singleton(A)
& C = empty_set ) ) ).
fof(t44_zfmisc_1,conjecture,
! [A,B,C] :
~ ( singleton(A) = set_union2(B,C)
& B != C
& B != empty_set
& C != empty_set ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( singleton(A) = set_union2(B,C)
& B != C
& B != empty_set )
=> C = empty_set ),
inference(strip,[],[t44_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( singleton(A) = set_union2(B,C)
& B != C
& B != empty_set )
=> C = empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C] :
( singleton(A) != set_union2(B,C)
| ( B = empty_set
& C = singleton(A) )
| ( B = singleton(A)
& C = empty_set )
| ( B = singleton(A)
& C = singleton(A) ) ),
inference(canonicalize,[],[t43_zfmisc_1]) ).
fof(normalize_0_1,plain,
! [A,B,C] :
( singleton(A) != set_union2(B,C)
| ( B = empty_set
& C = singleton(A) )
| ( B = singleton(A)
& C = empty_set )
| ( B = singleton(A)
& C = singleton(A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( singleton(A) != set_union2(B,C)
| B = empty_set
| B = singleton(A) )
& ( singleton(A) != set_union2(B,C)
| B = singleton(A)
| C = singleton(A) )
& ( singleton(A) != set_union2(B,C)
| C = empty_set
| C = singleton(A) )
& ( singleton(A) != set_union2(B,C)
| B = empty_set
| B = singleton(A)
| C = empty_set )
& ( singleton(A) != set_union2(B,C)
| B = empty_set
| B = singleton(A)
| C = singleton(A) )
& ( singleton(A) != set_union2(B,C)
| B = empty_set
| C = empty_set
| C = singleton(A) )
& ( singleton(A) != set_union2(B,C)
| B = singleton(A)
| C = empty_set
| C = singleton(A) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( singleton(A) != set_union2(B,C)
| C = empty_set
| C = singleton(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B,C] :
( B != C
& B != empty_set
& C != empty_set
& singleton(A) = set_union2(B,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( skolemFOFtoCNF_B != empty_set
& skolemFOFtoCNF_B != skolemFOFtoCNF_C
& skolemFOFtoCNF_C != empty_set
& singleton(skolemFOFtoCNF_A_2) = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
singleton(skolemFOFtoCNF_A_2) = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( singleton(A) != set_union2(B,C)
| B = empty_set
| B = singleton(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
skolemFOFtoCNF_B != empty_set,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
skolemFOFtoCNF_C != empty_set,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
skolemFOFtoCNF_B != skolemFOFtoCNF_C,
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( singleton(A) != set_union2(B,C)
| C = empty_set
| C = singleton(A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( singleton(X_10) != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| skolemFOFtoCNF_C = empty_set
| skolemFOFtoCNF_C = singleton(X_10) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_10)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_2,plain,
singleton(skolemFOFtoCNF_A_2) = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( singleton(A) != set_union2(B,C)
| B = empty_set
| B = singleton(A) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( singleton(X_7) != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| skolemFOFtoCNF_B = empty_set
| skolemFOFtoCNF_B = singleton(X_7) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_7)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( singleton(skolemFOFtoCNF_A_2) != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(singleton(skolemFOFtoCNF_A_2))),bind(Y,$fot(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_9,plain,
set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_2,refute_0_8]) ).
cnf(refute_0_10,plain,
( set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A_2)
| singleton(X_7) != singleton(skolemFOFtoCNF_A_2)
| singleton(X_7) = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( ~ $equal(singleton(X_7),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),[1],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_11,plain,
( singleton(X_7) != singleton(skolemFOFtoCNF_A_2)
| singleton(X_7) = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( singleton(X_7) != singleton(skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_B = empty_set
| skolemFOFtoCNF_B = singleton(X_7) ),
inference(resolve,[$cnf( $equal(singleton(X_7),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_11,refute_0_4]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_B != empty_set,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_14,plain,
( singleton(X_7) != singleton(skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_B = singleton(X_7) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_B = singleton(skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_14:[bind(X_7,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_16,plain,
singleton(skolemFOFtoCNF_A_2) = singleton(skolemFOFtoCNF_A_2),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_17,plain,
skolemFOFtoCNF_B = singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_16,refute_0_15]) ).
cnf(refute_0_18,plain,
( skolemFOFtoCNF_B != singleton(skolemFOFtoCNF_A_2)
| singleton(skolemFOFtoCNF_A_2) = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_19,plain,
singleton(skolemFOFtoCNF_A_2) = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( singleton(skolemFOFtoCNF_A_2) != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| singleton(skolemFOFtoCNF_A_2) != skolemFOFtoCNF_B
| skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),[0],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_21,plain,
( singleton(skolemFOFtoCNF_A_2) != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_2,refute_0_21]) ).
cnf(refute_0_23,plain,
( skolemFOFtoCNF_B != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_24,plain,
set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != skolemFOFtoCNF_B
| singleton(X_10) != skolemFOFtoCNF_B
| singleton(X_10) = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( ~ $equal(singleton(X_10),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),[1],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_26,plain,
( singleton(X_10) != skolemFOFtoCNF_B
| singleton(X_10) = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( singleton(X_10) != skolemFOFtoCNF_B
| skolemFOFtoCNF_C = empty_set
| skolemFOFtoCNF_C = singleton(X_10) ),
inference(resolve,[$cnf( $equal(singleton(X_10),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_26,refute_0_1]) ).
cnf(refute_0_28,plain,
( singleton(X_10) != skolemFOFtoCNF_B
| skolemFOFtoCNF_C != singleton(X_10)
| skolemFOFtoCNF_C = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_C,singleton(X_10)) ),[1],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_29,plain,
( singleton(X_10) != skolemFOFtoCNF_B
| skolemFOFtoCNF_C = empty_set
| skolemFOFtoCNF_C = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,singleton(X_10)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
skolemFOFtoCNF_C != empty_set,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_31,plain,
( singleton(X_10) != skolemFOFtoCNF_B
| skolemFOFtoCNF_C = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,empty_set) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
skolemFOFtoCNF_B != skolemFOFtoCNF_C,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_33,plain,
( skolemFOFtoCNF_C != skolemFOFtoCNF_B
| skolemFOFtoCNF_B = skolemFOFtoCNF_C ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_C)),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_34,plain,
skolemFOFtoCNF_C != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_33,refute_0_32]) ).
cnf(refute_0_35,plain,
singleton(X_10) != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,skolemFOFtoCNF_B) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
singleton(skolemFOFtoCNF_A_2) != skolemFOFtoCNF_B,
inference(subst,[],[refute_0_35:[bind(X_10,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_37,plain,
( singleton(skolemFOFtoCNF_A_2) != skolemFOFtoCNF_B
| skolemFOFtoCNF_B != skolemFOFtoCNF_B
| singleton(skolemFOFtoCNF_A_2) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( ~ $equal(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) ),[0],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_38,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| singleton(skolemFOFtoCNF_A_2) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) )],[refute_0_19,refute_0_37]) ).
cnf(refute_0_39,plain,
skolemFOFtoCNF_B != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) )],[refute_0_38,refute_0_36]) ).
cnf(refute_0_40,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_B,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_40,refute_0_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET903+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 17:42:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------