TSTP Solution File: SEU150+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU150+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 12:38:47 EDT 2022
% Result : Theorem 0.18s 0.34s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 22 unt; 0 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 86 ( 43 ~; 37 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 3 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
fof(t8_zfmisc_1,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ) ).
fof(t9_zfmisc_1,conjecture,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
inference(strip,[],[t9_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( A = B
| ! [C] : singleton(A) != unordered_pair(B,C) ),
inference(canonicalize,[],[t8_zfmisc_1]) ).
fof(normalize_0_1,plain,
! [A,B] :
( A = B
| ! [C] : singleton(A) != unordered_pair(B,C) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( singleton(A) != unordered_pair(B,C)
| A = B ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(canonicalize,[],[commutativity_k2_tarski]) ).
fof(normalize_0_4,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [A,B,C] :
( B != C
& singleton(A) = unordered_pair(B,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_C
& singleton(skolemFOFtoCNF_A) = unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
singleton(skolemFOFtoCNF_A) = unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
skolemFOFtoCNF_B != skolemFOFtoCNF_C,
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( singleton(A) != unordered_pair(B,C)
| A = B ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( singleton(X_2) != unordered_pair(X_3,X_4)
| X_2 = X_3 ),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_2)),bind(B,$fot(X_3)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_2,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
unordered_pair(X_4,X_3) = unordered_pair(X_3,X_4),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_4)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( unordered_pair(X_4,X_3) != unordered_pair(X_3,X_4)
| unordered_pair(X_3,X_4) = unordered_pair(X_4,X_3) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(unordered_pair(X_4,X_3))),bind(Y,$fot(unordered_pair(X_3,X_4)))]]) ).
cnf(refute_0_8,plain,
unordered_pair(X_3,X_4) = unordered_pair(X_4,X_3),
inference(resolve,[$cnf( $equal(unordered_pair(X_4,X_3),unordered_pair(X_3,X_4)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( singleton(X_2) != unordered_pair(X_4,X_3)
| unordered_pair(X_3,X_4) != unordered_pair(X_4,X_3)
| singleton(X_2) = unordered_pair(X_3,X_4) ),
introduced(tautology,[equality,[$cnf( ~ $equal(singleton(X_2),unordered_pair(X_3,X_4)) ),[1],$fot(unordered_pair(X_4,X_3))]]) ).
cnf(refute_0_10,plain,
( singleton(X_2) != unordered_pair(X_4,X_3)
| singleton(X_2) = unordered_pair(X_3,X_4) ),
inference(resolve,[$cnf( $equal(unordered_pair(X_3,X_4),unordered_pair(X_4,X_3)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( singleton(X_2) != unordered_pair(X_4,X_3)
| X_2 = X_3 ),
inference(resolve,[$cnf( $equal(singleton(X_2),unordered_pair(X_3,X_4)) )],[refute_0_10,refute_0_1]) ).
cnf(refute_0_12,plain,
( singleton(X_6) != unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C)
| X_6 = skolemFOFtoCNF_C ),
inference(subst,[],[refute_0_11:[bind(X_2,$fot(X_6)),bind(X_3,$fot(skolemFOFtoCNF_C)),bind(X_4,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_13,plain,
singleton(skolemFOFtoCNF_A) = unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_14,plain,
( singleton(X_2) != unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| X_2 = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_15,plain,
( singleton(skolemFOFtoCNF_A) != unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(singleton(skolemFOFtoCNF_A))),bind(Y,$fot(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_16,plain,
unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A),unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( singleton(X_2) != singleton(skolemFOFtoCNF_A)
| unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A)
| singleton(X_2) = unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( ~ $equal(singleton(X_2),unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),[1],$fot(singleton(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_18,plain,
( singleton(X_2) != singleton(skolemFOFtoCNF_A)
| singleton(X_2) = unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( singleton(X_2) != singleton(skolemFOFtoCNF_A)
| X_2 = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(singleton(X_2),unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_18,refute_0_14]) ).
cnf(refute_0_20,plain,
( singleton(skolemFOFtoCNF_A) != singleton(skolemFOFtoCNF_A)
| skolemFOFtoCNF_A = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_19:[bind(X_2,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_21,plain,
singleton(skolemFOFtoCNF_A) = singleton(skolemFOFtoCNF_A),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_22,plain,
skolemFOFtoCNF_A = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A),singleton(skolemFOFtoCNF_A)) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
( skolemFOFtoCNF_A != skolemFOFtoCNF_B
| skolemFOFtoCNF_B = skolemFOFtoCNF_A ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_A)),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_24,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_A,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
introduced(tautology,[refl,[$fot(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_A
| unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C),unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),[1,0],$fot(skolemFOFtoCNF_A)]]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_A
| unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C),unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
( singleton(skolemFOFtoCNF_A) != unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C)
| singleton(skolemFOFtoCNF_A) = unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( ~ $equal(singleton(skolemFOFtoCNF_A),unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C)) ),[0],$fot(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_30,plain,
( singleton(skolemFOFtoCNF_A) != unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| singleton(skolemFOFtoCNF_A) = unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C),unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
singleton(skolemFOFtoCNF_A) = unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A),unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_13,refute_0_30]) ).
cnf(refute_0_32,plain,
( singleton(skolemFOFtoCNF_A) != unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(singleton(skolemFOFtoCNF_A))),bind(Y,$fot(unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_33,plain,
unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A),unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( singleton(X_6) != singleton(skolemFOFtoCNF_A)
| unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A)
| singleton(X_6) = unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( ~ $equal(singleton(X_6),unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C)) ),[1],$fot(singleton(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_35,plain,
( singleton(X_6) != singleton(skolemFOFtoCNF_A)
| singleton(X_6) = unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( singleton(X_6) != singleton(skolemFOFtoCNF_A)
| X_6 = skolemFOFtoCNF_C ),
inference(resolve,[$cnf( $equal(singleton(X_6),unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_C)) )],[refute_0_35,refute_0_12]) ).
cnf(refute_0_37,plain,
( singleton(skolemFOFtoCNF_A) != singleton(skolemFOFtoCNF_A)
| skolemFOFtoCNF_A = skolemFOFtoCNF_C ),
inference(subst,[],[refute_0_36:[bind(X_6,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_38,plain,
skolemFOFtoCNF_A = skolemFOFtoCNF_C,
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A),singleton(skolemFOFtoCNF_A)) )],[refute_0_21,refute_0_37]) ).
cnf(refute_0_39,plain,
skolemFOFtoCNF_B != skolemFOFtoCNF_C,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_40,plain,
( skolemFOFtoCNF_A != skolemFOFtoCNF_C
| skolemFOFtoCNF_B != skolemFOFtoCNF_A
| skolemFOFtoCNF_B = skolemFOFtoCNF_C ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),[1],$fot(skolemFOFtoCNF_C)]]) ).
cnf(refute_0_41,plain,
( skolemFOFtoCNF_A != skolemFOFtoCNF_C
| skolemFOFtoCNF_B = skolemFOFtoCNF_C ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_24,refute_0_40]) ).
cnf(refute_0_42,plain,
skolemFOFtoCNF_A != skolemFOFtoCNF_C,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_41,refute_0_39]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A,skolemFOFtoCNF_C) )],[refute_0_38,refute_0_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU150+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n005.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 : Sun Jun 19 11:46:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.34
% 0.18/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.34
%------------------------------------------------------------------------------