TSTP Solution File: SET018-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET018-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 03:31:15 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 32
% Syntax : Number of clauses : 118 ( 43 unt; 27 nHn; 106 RR)
% Number of literals : 226 ( 140 equ; 83 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(singleton_1,axiom,
member(X,singleton_set(X)) ).
cnf(singleton_2,axiom,
( ~ member(X,singleton_set(Y))
| X = Y ) ).
cnf(unordered_pair_1,axiom,
member(X,unordered_pair(X,Y)) ).
cnf(unordered_pair_2,axiom,
member(Y,unordered_pair(X,Y)) ).
cnf(unordered_pair_3,axiom,
( ~ member(X,unordered_pair(Y,Z))
| X = Y
| X = Z ) ).
cnf(ordered_pair,axiom,
ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)) ).
cnf(equal_ordered_pairs,hypothesis,
ordered_pair(m1,r1) = ordered_pair(m2,r2) ).
cnf(prove_second_components_equal,negated_conjecture,
r1 != r2 ).
cnf(refute_0_0,plain,
( ~ member(r1,unordered_pair(m1,m1))
| r1 = m1 ),
inference(subst,[],[unordered_pair_3:[bind(X,$fot(r1)),bind(Y,$fot(m1)),bind(Z,$fot(m1))]]) ).
cnf(refute_0_1,plain,
member(r1,unordered_pair(m1,r1)),
inference(subst,[],[unordered_pair_2:[bind(X,$fot(m1)),bind(Y,$fot(r1))]]) ).
cnf(refute_0_2,plain,
( ~ member(r1,singleton_set(m1))
| r1 = m1 ),
inference(subst,[],[singleton_2:[bind(X,$fot(r1)),bind(Y,$fot(m1))]]) ).
cnf(refute_0_3,plain,
( ~ member(X_21,unordered_pair(singleton_set(X),unordered_pair(X,Y)))
| X_21 = singleton_set(X)
| X_21 = unordered_pair(X,Y) ),
inference(subst,[],[unordered_pair_3:[bind(X,$fot(X_21)),bind(Y,$fot(singleton_set(X))),bind(Z,$fot(unordered_pair(X,Y)))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ordered_pair(X,Y) != unordered_pair(singleton_set(X),unordered_pair(X,Y))
| unordered_pair(singleton_set(X),unordered_pair(X,Y)) = ordered_pair(X,Y) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(ordered_pair(X,Y))),bind(Y0,$fot(unordered_pair(singleton_set(X),unordered_pair(X,Y))))]]) ).
cnf(refute_0_8,plain,
unordered_pair(singleton_set(X),unordered_pair(X,Y)) = ordered_pair(X,Y),
inference(resolve,[$cnf( $equal(ordered_pair(X,Y),unordered_pair(singleton_set(X),unordered_pair(X,Y))) )],[ordered_pair,refute_0_7]) ).
cnf(refute_0_9,plain,
( unordered_pair(singleton_set(X),unordered_pair(X,Y)) != ordered_pair(X,Y)
| ~ member(X_21,ordered_pair(X,Y))
| member(X_21,unordered_pair(singleton_set(X),unordered_pair(X,Y))) ),
introduced(tautology,[equality,[$cnf( ~ member(X_21,unordered_pair(singleton_set(X),unordered_pair(X,Y))) ),[1],$fot(ordered_pair(X,Y))]]) ).
cnf(refute_0_10,plain,
( ~ member(X_21,ordered_pair(X,Y))
| member(X_21,unordered_pair(singleton_set(X),unordered_pair(X,Y))) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton_set(X),unordered_pair(X,Y)),ordered_pair(X,Y)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ member(X_21,ordered_pair(X,Y))
| X_21 = singleton_set(X)
| X_21 = unordered_pair(X,Y) ),
inference(resolve,[$cnf( member(X_21,unordered_pair(singleton_set(X),unordered_pair(X,Y))) )],[refute_0_10,refute_0_3]) ).
cnf(refute_0_12,plain,
( ~ member(unordered_pair(m1,r1),ordered_pair(m1,m1))
| unordered_pair(m1,r1) = singleton_set(m1)
| unordered_pair(m1,r1) = unordered_pair(m1,m1) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(m1)),bind(Y,$fot(m1)),bind(X_21,$fot(unordered_pair(m1,r1)))]]) ).
cnf(refute_0_13,plain,
member(unordered_pair(X_5,X_6),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))),
inference(subst,[],[unordered_pair_2:[bind(X,$fot(singleton_set(X_5))),bind(Y,$fot(unordered_pair(X_5,X_6)))]]) ).
cnf(refute_0_14,plain,
ordered_pair(X_5,X_6) = unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)),
inference(subst,[],[ordered_pair:[bind(X,$fot(X_5)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_15,plain,
( ordered_pair(X_5,X_6) != unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))
| unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)) = ordered_pair(X_5,X_6) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(ordered_pair(X_5,X_6))),bind(Y0,$fot(unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))))]]) ).
cnf(refute_0_16,plain,
unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)) = ordered_pair(X_5,X_6),
inference(resolve,[$cnf( $equal(ordered_pair(X_5,X_6),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)) != ordered_pair(X_5,X_6)
| ~ member(unordered_pair(X_5,X_6),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)))
| member(unordered_pair(X_5,X_6),ordered_pair(X_5,X_6)) ),
introduced(tautology,[equality,[$cnf( member(unordered_pair(X_5,X_6),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))) ),[1],$fot(ordered_pair(X_5,X_6))]]) ).
cnf(refute_0_18,plain,
( ~ member(unordered_pair(X_5,X_6),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)))
| member(unordered_pair(X_5,X_6),ordered_pair(X_5,X_6)) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)),ordered_pair(X_5,X_6)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
member(unordered_pair(X_5,X_6),ordered_pair(X_5,X_6)),
inference(resolve,[$cnf( member(unordered_pair(X_5,X_6),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
member(unordered_pair(m1,r1),ordered_pair(m1,r1)),
inference(subst,[],[refute_0_19:[bind(X_5,$fot(m1)),bind(X_6,$fot(r1))]]) ).
cnf(refute_0_21,plain,
( ~ member(m2,singleton_set(m1))
| m2 = m1 ),
inference(subst,[],[singleton_2:[bind(X,$fot(m2)),bind(Y,$fot(m1))]]) ).
cnf(refute_0_22,plain,
member(m2,singleton_set(m2)),
inference(subst,[],[singleton_1:[bind(X,$fot(m2))]]) ).
cnf(refute_0_23,plain,
( ~ member(m1,singleton_set(m2))
| m1 = m2 ),
inference(subst,[],[singleton_2:[bind(X,$fot(m1)),bind(Y,$fot(m2))]]) ).
cnf(refute_0_24,plain,
member(m1,unordered_pair(m1,r1)),
inference(subst,[],[unordered_pair_1:[bind(X,$fot(m1)),bind(Y,$fot(r1))]]) ).
cnf(refute_0_25,plain,
member(singleton_set(X_5),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))),
inference(subst,[],[unordered_pair_1:[bind(X,$fot(singleton_set(X_5))),bind(Y,$fot(unordered_pair(X_5,X_6)))]]) ).
cnf(refute_0_26,plain,
( unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)) != ordered_pair(X_5,X_6)
| ~ member(singleton_set(X_5),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)))
| member(singleton_set(X_5),ordered_pair(X_5,X_6)) ),
introduced(tautology,[equality,[$cnf( member(singleton_set(X_5),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))) ),[1],$fot(ordered_pair(X_5,X_6))]]) ).
cnf(refute_0_27,plain,
( ~ member(singleton_set(X_5),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)))
| member(singleton_set(X_5),ordered_pair(X_5,X_6)) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)),ordered_pair(X_5,X_6)) )],[refute_0_16,refute_0_26]) ).
cnf(refute_0_28,plain,
member(singleton_set(X_5),ordered_pair(X_5,X_6)),
inference(resolve,[$cnf( member(singleton_set(X_5),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
member(singleton_set(m2),ordered_pair(m2,r2)),
inference(subst,[],[refute_0_28:[bind(X_5,$fot(m2)),bind(X_6,$fot(r2))]]) ).
cnf(refute_0_30,plain,
( ordered_pair(m1,r1) != ordered_pair(m2,r2)
| ordered_pair(m2,r2) = ordered_pair(m1,r1) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(ordered_pair(m1,r1))),bind(Y0,$fot(ordered_pair(m2,r2)))]]) ).
cnf(refute_0_31,plain,
ordered_pair(m2,r2) = ordered_pair(m1,r1),
inference(resolve,[$cnf( $equal(ordered_pair(m1,r1),ordered_pair(m2,r2)) )],[equal_ordered_pairs,refute_0_30]) ).
cnf(refute_0_32,plain,
( ordered_pair(m2,r2) != ordered_pair(m1,r1)
| ~ member(singleton_set(m2),ordered_pair(m2,r2))
| member(singleton_set(m2),ordered_pair(m1,r1)) ),
introduced(tautology,[equality,[$cnf( member(singleton_set(m2),ordered_pair(m2,r2)) ),[1],$fot(ordered_pair(m1,r1))]]) ).
cnf(refute_0_33,plain,
( ~ member(singleton_set(m2),ordered_pair(m2,r2))
| member(singleton_set(m2),ordered_pair(m1,r1)) ),
inference(resolve,[$cnf( $equal(ordered_pair(m2,r2),ordered_pair(m1,r1)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
member(singleton_set(m2),ordered_pair(m1,r1)),
inference(resolve,[$cnf( member(singleton_set(m2),ordered_pair(m2,r2)) )],[refute_0_29,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ member(singleton_set(m2),ordered_pair(m1,r1))
| singleton_set(m2) = singleton_set(m1)
| singleton_set(m2) = unordered_pair(m1,r1) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(m1)),bind(Y,$fot(r1)),bind(X_21,$fot(singleton_set(m2)))]]) ).
cnf(refute_0_36,plain,
( singleton_set(m2) = singleton_set(m1)
| singleton_set(m2) = unordered_pair(m1,r1) ),
inference(resolve,[$cnf( member(singleton_set(m2),ordered_pair(m1,r1)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( singleton_set(m2) != unordered_pair(m1,r1)
| unordered_pair(m1,r1) = singleton_set(m2) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(singleton_set(m2))),bind(Y0,$fot(unordered_pair(m1,r1)))]]) ).
cnf(refute_0_38,plain,
( singleton_set(m2) = singleton_set(m1)
| unordered_pair(m1,r1) = singleton_set(m2) ),
inference(resolve,[$cnf( $equal(singleton_set(m2),unordered_pair(m1,r1)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( unordered_pair(m1,r1) != singleton_set(m2)
| ~ member(m1,unordered_pair(m1,r1))
| member(m1,singleton_set(m2)) ),
introduced(tautology,[equality,[$cnf( member(m1,unordered_pair(m1,r1)) ),[1],$fot(singleton_set(m2))]]) ).
cnf(refute_0_40,plain,
( ~ member(m1,unordered_pair(m1,r1))
| singleton_set(m2) = singleton_set(m1)
| member(m1,singleton_set(m2)) ),
inference(resolve,[$cnf( $equal(unordered_pair(m1,r1),singleton_set(m2)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( singleton_set(m2) = singleton_set(m1)
| member(m1,singleton_set(m2)) ),
inference(resolve,[$cnf( member(m1,unordered_pair(m1,r1)) )],[refute_0_24,refute_0_40]) ).
cnf(refute_0_42,plain,
( m1 = m2
| singleton_set(m2) = singleton_set(m1) ),
inference(resolve,[$cnf( member(m1,singleton_set(m2)) )],[refute_0_41,refute_0_23]) ).
cnf(refute_0_43,plain,
( singleton_set(m2) != singleton_set(m1)
| ~ member(m2,singleton_set(m2))
| member(m2,singleton_set(m1)) ),
introduced(tautology,[equality,[$cnf( member(m2,singleton_set(m2)) ),[1],$fot(singleton_set(m1))]]) ).
cnf(refute_0_44,plain,
( ~ member(m2,singleton_set(m2))
| m1 = m2
| member(m2,singleton_set(m1)) ),
inference(resolve,[$cnf( $equal(singleton_set(m2),singleton_set(m1)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( m1 = m2
| member(m2,singleton_set(m1)) ),
inference(resolve,[$cnf( member(m2,singleton_set(m2)) )],[refute_0_22,refute_0_44]) ).
cnf(refute_0_46,plain,
( m1 = m2
| m2 = m1 ),
inference(resolve,[$cnf( member(m2,singleton_set(m1)) )],[refute_0_45,refute_0_21]) ).
cnf(refute_0_47,plain,
( m2 != m1
| m1 = m2 ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(m2)),bind(Y0,$fot(m1))]]) ).
cnf(refute_0_48,plain,
m1 = m2,
inference(resolve,[$cnf( $equal(m2,m1) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( m1 != m2
| m2 = m1 ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(m1)),bind(Y0,$fot(m2))]]) ).
cnf(refute_0_50,plain,
m2 = m1,
inference(resolve,[$cnf( $equal(m1,m2) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
ordered_pair(m2,r2) = ordered_pair(m2,r2),
introduced(tautology,[refl,[$fot(ordered_pair(m2,r2))]]) ).
cnf(refute_0_52,plain,
( m2 != m1
| ordered_pair(m2,r2) != ordered_pair(m2,r2)
| ordered_pair(m2,r2) = ordered_pair(m1,r2) ),
introduced(tautology,[equality,[$cnf( $equal(ordered_pair(m2,r2),ordered_pair(m2,r2)) ),[1,0],$fot(m1)]]) ).
cnf(refute_0_53,plain,
( m2 != m1
| ordered_pair(m2,r2) = ordered_pair(m1,r2) ),
inference(resolve,[$cnf( $equal(ordered_pair(m2,r2),ordered_pair(m2,r2)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
ordered_pair(m2,r2) = ordered_pair(m1,r2),
inference(resolve,[$cnf( $equal(m2,m1) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( ordered_pair(m1,r1) != ordered_pair(m2,r2)
| ordered_pair(m2,r2) != ordered_pair(m1,r2)
| ordered_pair(m1,r1) = ordered_pair(m1,r2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(ordered_pair(m1,r1),ordered_pair(m1,r2)) ),[0],$fot(ordered_pair(m2,r2))]]) ).
cnf(refute_0_56,plain,
( ordered_pair(m1,r1) != ordered_pair(m2,r2)
| ordered_pair(m1,r1) = ordered_pair(m1,r2) ),
inference(resolve,[$cnf( $equal(ordered_pair(m2,r2),ordered_pair(m1,r2)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
ordered_pair(m1,r1) = ordered_pair(m1,r2),
inference(resolve,[$cnf( $equal(ordered_pair(m1,r1),ordered_pair(m2,r2)) )],[equal_ordered_pairs,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ member(r2,singleton_set(m1))
| r2 = m1 ),
inference(subst,[],[singleton_2:[bind(X,$fot(r2)),bind(Y,$fot(m1))]]) ).
cnf(refute_0_59,plain,
member(r2,unordered_pair(m1,r2)),
inference(subst,[],[unordered_pair_2:[bind(X,$fot(m1)),bind(Y,$fot(r2))]]) ).
cnf(refute_0_60,plain,
( ~ member(r2,unordered_pair(m1,r1))
| r2 = m1
| r2 = r1 ),
inference(subst,[],[unordered_pair_3:[bind(X,$fot(r2)),bind(Y,$fot(m1)),bind(Z,$fot(r1))]]) ).
cnf(refute_0_61,plain,
member(r2,unordered_pair(m2,r2)),
inference(subst,[],[unordered_pair_2:[bind(X,$fot(m2)),bind(Y,$fot(r2))]]) ).
cnf(refute_0_62,plain,
member(unordered_pair(m2,r2),ordered_pair(m2,r2)),
inference(subst,[],[refute_0_19:[bind(X_5,$fot(m2)),bind(X_6,$fot(r2))]]) ).
cnf(refute_0_63,plain,
( ordered_pair(m2,r2) != ordered_pair(m1,r1)
| ~ member(unordered_pair(m2,r2),ordered_pair(m2,r2))
| member(unordered_pair(m2,r2),ordered_pair(m1,r1)) ),
introduced(tautology,[equality,[$cnf( member(unordered_pair(m2,r2),ordered_pair(m2,r2)) ),[1],$fot(ordered_pair(m1,r1))]]) ).
cnf(refute_0_64,plain,
( ~ member(unordered_pair(m2,r2),ordered_pair(m2,r2))
| member(unordered_pair(m2,r2),ordered_pair(m1,r1)) ),
inference(resolve,[$cnf( $equal(ordered_pair(m2,r2),ordered_pair(m1,r1)) )],[refute_0_31,refute_0_63]) ).
cnf(refute_0_65,plain,
member(unordered_pair(m2,r2),ordered_pair(m1,r1)),
inference(resolve,[$cnf( member(unordered_pair(m2,r2),ordered_pair(m2,r2)) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ member(unordered_pair(m2,r2),ordered_pair(m1,r1))
| unordered_pair(m2,r2) = singleton_set(m1)
| unordered_pair(m2,r2) = unordered_pair(m1,r1) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(m1)),bind(Y,$fot(r1)),bind(X_21,$fot(unordered_pair(m2,r2)))]]) ).
cnf(refute_0_67,plain,
( unordered_pair(m2,r2) = singleton_set(m1)
| unordered_pair(m2,r2) = unordered_pair(m1,r1) ),
inference(resolve,[$cnf( member(unordered_pair(m2,r2),ordered_pair(m1,r1)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( unordered_pair(m2,r2) != unordered_pair(m1,r1)
| ~ member(r2,unordered_pair(m2,r2))
| member(r2,unordered_pair(m1,r1)) ),
introduced(tautology,[equality,[$cnf( member(r2,unordered_pair(m2,r2)) ),[1],$fot(unordered_pair(m1,r1))]]) ).
cnf(refute_0_69,plain,
( ~ member(r2,unordered_pair(m2,r2))
| unordered_pair(m2,r2) = singleton_set(m1)
| member(r2,unordered_pair(m1,r1)) ),
inference(resolve,[$cnf( $equal(unordered_pair(m2,r2),unordered_pair(m1,r1)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( unordered_pair(m2,r2) = singleton_set(m1)
| member(r2,unordered_pair(m1,r1)) ),
inference(resolve,[$cnf( member(r2,unordered_pair(m2,r2)) )],[refute_0_61,refute_0_69]) ).
cnf(refute_0_71,plain,
( r2 = m1
| r2 = r1
| unordered_pair(m2,r2) = singleton_set(m1) ),
inference(resolve,[$cnf( member(r2,unordered_pair(m1,r1)) )],[refute_0_70,refute_0_60]) ).
cnf(refute_0_72,plain,
( r2 != r1
| r1 = r2 ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(r2)),bind(Y0,$fot(r1))]]) ).
cnf(refute_0_73,plain,
r2 != r1,
inference(resolve,[$cnf( $equal(r1,r2) )],[refute_0_72,prove_second_components_equal]) ).
cnf(refute_0_74,plain,
( r2 = m1
| unordered_pair(m2,r2) = singleton_set(m1) ),
inference(resolve,[$cnf( $equal(r2,r1) )],[refute_0_71,refute_0_73]) ).
cnf(refute_0_75,plain,
unordered_pair(m2,r2) = unordered_pair(m2,r2),
introduced(tautology,[refl,[$fot(unordered_pair(m2,r2))]]) ).
cnf(refute_0_76,plain,
( m2 != m1
| unordered_pair(m2,r2) != unordered_pair(m2,r2)
| unordered_pair(m2,r2) = unordered_pair(m1,r2) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(m2,r2),unordered_pair(m2,r2)) ),[1,0],$fot(m1)]]) ).
cnf(refute_0_77,plain,
( m2 != m1
| unordered_pair(m2,r2) = unordered_pair(m1,r2) ),
inference(resolve,[$cnf( $equal(unordered_pair(m2,r2),unordered_pair(m2,r2)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
unordered_pair(m2,r2) = unordered_pair(m1,r2),
inference(resolve,[$cnf( $equal(m2,m1) )],[refute_0_50,refute_0_77]) ).
cnf(refute_0_79,plain,
( unordered_pair(m2,r2) != singleton_set(m1)
| unordered_pair(m2,r2) != unordered_pair(m1,r2)
| unordered_pair(m1,r2) = singleton_set(m1) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(m2,r2),singleton_set(m1)) ),[0],$fot(unordered_pair(m1,r2))]]) ).
cnf(refute_0_80,plain,
( unordered_pair(m2,r2) != singleton_set(m1)
| unordered_pair(m1,r2) = singleton_set(m1) ),
inference(resolve,[$cnf( $equal(unordered_pair(m2,r2),unordered_pair(m1,r2)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( r2 = m1
| unordered_pair(m1,r2) = singleton_set(m1) ),
inference(resolve,[$cnf( $equal(unordered_pair(m2,r2),singleton_set(m1)) )],[refute_0_74,refute_0_80]) ).
cnf(refute_0_82,plain,
( unordered_pair(m1,r2) != singleton_set(m1)
| ~ member(r2,unordered_pair(m1,r2))
| member(r2,singleton_set(m1)) ),
introduced(tautology,[equality,[$cnf( member(r2,unordered_pair(m1,r2)) ),[1],$fot(singleton_set(m1))]]) ).
cnf(refute_0_83,plain,
( ~ member(r2,unordered_pair(m1,r2))
| r2 = m1
| member(r2,singleton_set(m1)) ),
inference(resolve,[$cnf( $equal(unordered_pair(m1,r2),singleton_set(m1)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( r2 = m1
| member(r2,singleton_set(m1)) ),
inference(resolve,[$cnf( member(r2,unordered_pair(m1,r2)) )],[refute_0_59,refute_0_83]) ).
cnf(refute_0_85,plain,
r2 = m1,
inference(resolve,[$cnf( member(r2,singleton_set(m1)) )],[refute_0_84,refute_0_58]) ).
cnf(refute_0_86,plain,
ordered_pair(m1,r2) = ordered_pair(m1,r2),
introduced(tautology,[refl,[$fot(ordered_pair(m1,r2))]]) ).
cnf(refute_0_87,plain,
( ordered_pair(m1,r2) != ordered_pair(m1,r2)
| r2 != m1
| ordered_pair(m1,r2) = ordered_pair(m1,m1) ),
introduced(tautology,[equality,[$cnf( $equal(ordered_pair(m1,r2),ordered_pair(m1,r2)) ),[1,1],$fot(m1)]]) ).
cnf(refute_0_88,plain,
( r2 != m1
| ordered_pair(m1,r2) = ordered_pair(m1,m1) ),
inference(resolve,[$cnf( $equal(ordered_pair(m1,r2),ordered_pair(m1,r2)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
ordered_pair(m1,r2) = ordered_pair(m1,m1),
inference(resolve,[$cnf( $equal(r2,m1) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
( ordered_pair(m1,r1) != ordered_pair(m1,r2)
| ordered_pair(m1,r2) != ordered_pair(m1,m1)
| ordered_pair(m1,r1) = ordered_pair(m1,m1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(ordered_pair(m1,r1),ordered_pair(m1,m1)) ),[0],$fot(ordered_pair(m1,r2))]]) ).
cnf(refute_0_91,plain,
( ordered_pair(m1,r1) != ordered_pair(m1,r2)
| ordered_pair(m1,r1) = ordered_pair(m1,m1) ),
inference(resolve,[$cnf( $equal(ordered_pair(m1,r2),ordered_pair(m1,m1)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
ordered_pair(m1,r1) = ordered_pair(m1,m1),
inference(resolve,[$cnf( $equal(ordered_pair(m1,r1),ordered_pair(m1,r2)) )],[refute_0_57,refute_0_91]) ).
cnf(refute_0_93,plain,
( ordered_pair(m1,r1) != ordered_pair(m1,m1)
| ~ member(unordered_pair(m1,r1),ordered_pair(m1,r1))
| member(unordered_pair(m1,r1),ordered_pair(m1,m1)) ),
introduced(tautology,[equality,[$cnf( member(unordered_pair(m1,r1),ordered_pair(m1,r1)) ),[1],$fot(ordered_pair(m1,m1))]]) ).
cnf(refute_0_94,plain,
( ~ member(unordered_pair(m1,r1),ordered_pair(m1,r1))
| member(unordered_pair(m1,r1),ordered_pair(m1,m1)) ),
inference(resolve,[$cnf( $equal(ordered_pair(m1,r1),ordered_pair(m1,m1)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
member(unordered_pair(m1,r1),ordered_pair(m1,m1)),
inference(resolve,[$cnf( member(unordered_pair(m1,r1),ordered_pair(m1,r1)) )],[refute_0_20,refute_0_94]) ).
cnf(refute_0_96,plain,
( unordered_pair(m1,r1) = singleton_set(m1)
| unordered_pair(m1,r1) = unordered_pair(m1,m1) ),
inference(resolve,[$cnf( member(unordered_pair(m1,r1),ordered_pair(m1,m1)) )],[refute_0_95,refute_0_12]) ).
cnf(refute_0_97,plain,
( unordered_pair(m1,r1) != singleton_set(m1)
| ~ member(r1,unordered_pair(m1,r1))
| member(r1,singleton_set(m1)) ),
introduced(tautology,[equality,[$cnf( member(r1,unordered_pair(m1,r1)) ),[1],$fot(singleton_set(m1))]]) ).
cnf(refute_0_98,plain,
( ~ member(r1,unordered_pair(m1,r1))
| unordered_pair(m1,r1) = unordered_pair(m1,m1)
| member(r1,singleton_set(m1)) ),
inference(resolve,[$cnf( $equal(unordered_pair(m1,r1),singleton_set(m1)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( unordered_pair(m1,r1) = unordered_pair(m1,m1)
| member(r1,singleton_set(m1)) ),
inference(resolve,[$cnf( member(r1,unordered_pair(m1,r1)) )],[refute_0_1,refute_0_98]) ).
cnf(refute_0_100,plain,
( r1 = m1
| unordered_pair(m1,r1) = unordered_pair(m1,m1) ),
inference(resolve,[$cnf( member(r1,singleton_set(m1)) )],[refute_0_99,refute_0_2]) ).
cnf(refute_0_101,plain,
( r1 != m1
| r2 != m1
| r1 = r2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(r1,r2) ),[1],$fot(m1)]]) ).
cnf(refute_0_102,plain,
( r1 != m1
| r1 = r2 ),
inference(resolve,[$cnf( $equal(r2,m1) )],[refute_0_85,refute_0_101]) ).
cnf(refute_0_103,plain,
r1 != m1,
inference(resolve,[$cnf( $equal(r1,r2) )],[refute_0_102,prove_second_components_equal]) ).
cnf(refute_0_104,plain,
unordered_pair(m1,r1) = unordered_pair(m1,m1),
inference(resolve,[$cnf( $equal(r1,m1) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
( unordered_pair(m1,r1) != unordered_pair(m1,m1)
| ~ member(r1,unordered_pair(m1,r1))
| member(r1,unordered_pair(m1,m1)) ),
introduced(tautology,[equality,[$cnf( member(r1,unordered_pair(m1,r1)) ),[1],$fot(unordered_pair(m1,m1))]]) ).
cnf(refute_0_106,plain,
( ~ member(r1,unordered_pair(m1,r1))
| member(r1,unordered_pair(m1,m1)) ),
inference(resolve,[$cnf( $equal(unordered_pair(m1,r1),unordered_pair(m1,m1)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
member(r1,unordered_pair(m1,m1)),
inference(resolve,[$cnf( member(r1,unordered_pair(m1,r1)) )],[refute_0_1,refute_0_106]) ).
cnf(refute_0_108,plain,
r1 = m1,
inference(resolve,[$cnf( member(r1,unordered_pair(m1,m1)) )],[refute_0_107,refute_0_0]) ).
cnf(refute_0_109,plain,
$false,
inference(resolve,[$cnf( $equal(r1,m1) )],[refute_0_108,refute_0_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n006.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 : Mon Jul 11 08:12:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48
% 0.20/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.49
%------------------------------------------------------------------------------