TSTP Solution File: LDA001-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : Sun Jul 17 16:44:58 EDT 2022
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 42
% Syntax : Number of clauses : 155 ( 73 unt; 0 nHn; 134 RR)
% Number of literals : 273 ( 272 equ; 121 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a1,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ).
cnf(clause_2,axiom,
n2 = f(n1,n1) ).
cnf(clause_3,axiom,
n3 = f(n2,n1) ).
cnf(clause_4,axiom,
u = f(n2,n2) ).
cnf(prove_equation,negated_conjecture,
f(f(n3,n2),u) != f(f(u,u),u) ).
cnf(refute_0_0,plain,
f(n2,f(n1,X_2)) = f(f(n2,n1),f(n2,X_2)),
inference(subst,[],[a1:[bind(X,$fot(n2)),bind(Y,$fot(n1)),bind(Z,$fot(X_2))]]) ).
cnf(refute_0_1,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_2,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_3,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( n3 != f(n2,n1)
| f(n2,n1) = n3 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(n3)),bind(Y0,$fot(f(n2,n1)))]]) ).
cnf(refute_0_5,plain,
f(n2,n1) = n3,
inference(resolve,[$cnf( $equal(n3,f(n2,n1)) )],[clause_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( f(n2,f(n1,X_2)) != f(f(n2,n1),f(n2,X_2))
| f(n2,n1) != n3
| f(n2,f(n1,X_2)) = f(n3,f(n2,X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n1,X_2)),f(f(n2,n1),f(n2,X_2))) ),[1,0],$fot(n3)]]) ).
cnf(refute_0_7,plain,
( f(n2,f(n1,X_2)) != f(f(n2,n1),f(n2,X_2))
| f(n2,f(n1,X_2)) = f(n3,f(n2,X_2)) ),
inference(resolve,[$cnf( $equal(f(n2,n1),n3) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
f(n2,f(n1,X_2)) = f(n3,f(n2,X_2)),
inference(resolve,[$cnf( $equal(f(n2,f(n1,X_2)),f(f(n2,n1),f(n2,X_2))) )],[refute_0_0,refute_0_7]) ).
cnf(refute_0_9,plain,
f(n1,f(n1,X_2)) = f(f(n1,n1),f(n1,X_2)),
inference(subst,[],[a1:[bind(X,$fot(n1)),bind(Y,$fot(n1)),bind(Z,$fot(X_2))]]) ).
cnf(refute_0_10,plain,
( n2 != f(n1,n1)
| f(n1,n1) = n2 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(n2)),bind(Y0,$fot(f(n1,n1)))]]) ).
cnf(refute_0_11,plain,
f(n1,n1) = n2,
inference(resolve,[$cnf( $equal(n2,f(n1,n1)) )],[clause_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( f(n1,f(n1,X_2)) != f(f(n1,n1),f(n1,X_2))
| f(n1,n1) != n2
| f(n1,f(n1,X_2)) = f(n2,f(n1,X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,X_2)),f(f(n1,n1),f(n1,X_2))) ),[1,0],$fot(n2)]]) ).
cnf(refute_0_13,plain,
( f(n1,f(n1,X_2)) != f(f(n1,n1),f(n1,X_2))
| f(n1,f(n1,X_2)) = f(n2,f(n1,X_2)) ),
inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
f(n1,f(n1,X_2)) = f(n2,f(n1,X_2)),
inference(resolve,[$cnf( $equal(f(n1,f(n1,X_2)),f(f(n1,n1),f(n1,X_2))) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( f(n1,f(n1,X_2)) != f(n2,f(n1,X_2))
| f(n2,f(n1,X_2)) = f(n1,f(n1,X_2)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(f(n1,f(n1,X_2)))),bind(Y0,$fot(f(n2,f(n1,X_2))))]]) ).
cnf(refute_0_16,plain,
f(n2,f(n1,X_2)) = f(n1,f(n1,X_2)),
inference(resolve,[$cnf( $equal(f(n1,f(n1,X_2)),f(n2,f(n1,X_2))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( f(n2,f(n1,X_2)) != f(n1,f(n1,X_2))
| f(n2,f(n1,X_2)) != f(n3,f(n2,X_2))
| f(n1,f(n1,X_2)) = f(n3,f(n2,X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n1,X_2)),f(n3,f(n2,X_2))) ),[0],$fot(f(n1,f(n1,X_2)))]]) ).
cnf(refute_0_18,plain,
( f(n2,f(n1,X_2)) != f(n3,f(n2,X_2))
| f(n1,f(n1,X_2)) = f(n3,f(n2,X_2)) ),
inference(resolve,[$cnf( $equal(f(n2,f(n1,X_2)),f(n1,f(n1,X_2))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
f(n1,f(n1,X_2)) = f(n3,f(n2,X_2)),
inference(resolve,[$cnf( $equal(f(n2,f(n1,X_2)),f(n3,f(n2,X_2))) )],[refute_0_8,refute_0_18]) ).
cnf(refute_0_20,plain,
( f(n1,f(n1,X_2)) != f(n3,f(n2,X_2))
| f(n3,f(n2,X_2)) = f(n1,f(n1,X_2)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(f(n1,f(n1,X_2)))),bind(Y0,$fot(f(n3,f(n2,X_2))))]]) ).
cnf(refute_0_21,plain,
f(n3,f(n2,X_2)) = f(n1,f(n1,X_2)),
inference(resolve,[$cnf( $equal(f(n1,f(n1,X_2)),f(n3,f(n2,X_2))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
f(n3,f(n2,n3)) = f(n1,f(n1,n3)),
inference(subst,[],[refute_0_21:[bind(X_2,$fot(n3))]]) ).
cnf(refute_0_23,plain,
f(n3,f(Y,n3)) = f(f(n3,Y),f(n3,n3)),
inference(subst,[],[a1:[bind(X,$fot(n3)),bind(Z,$fot(n3))]]) ).
cnf(refute_0_24,plain,
f(n2,f(X_1,n1)) = f(f(n2,X_1),f(n2,n1)),
inference(subst,[],[a1:[bind(X,$fot(n2)),bind(Y,$fot(X_1)),bind(Z,$fot(n1))]]) ).
cnf(refute_0_25,plain,
( f(n2,f(X_1,n1)) != f(f(n2,X_1),f(n2,n1))
| f(n2,n1) != n3
| f(n2,f(X_1,n1)) = f(f(n2,X_1),n3) ),
introduced(tautology,[equality,[$cnf( $equal(f(n2,f(X_1,n1)),f(f(n2,X_1),f(n2,n1))) ),[1,1],$fot(n3)]]) ).
cnf(refute_0_26,plain,
( f(n2,f(X_1,n1)) != f(f(n2,X_1),f(n2,n1))
| f(n2,f(X_1,n1)) = f(f(n2,X_1),n3) ),
inference(resolve,[$cnf( $equal(f(n2,n1),n3) )],[refute_0_5,refute_0_25]) ).
cnf(refute_0_27,plain,
f(n2,f(X_1,n1)) = f(f(n2,X_1),n3),
inference(resolve,[$cnf( $equal(f(n2,f(X_1,n1)),f(f(n2,X_1),f(n2,n1))) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
f(n2,f(n1,n1)) = f(f(n2,n1),n3),
inference(subst,[],[refute_0_27:[bind(X_1,$fot(n1))]]) ).
cnf(refute_0_29,plain,
( f(n2,f(n1,n1)) != f(f(n2,n1),n3)
| f(n2,n1) != n3
| f(n2,f(n1,n1)) = f(n3,n3) ),
introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n1,n1)),f(f(n2,n1),n3)) ),[1,0],$fot(n3)]]) ).
cnf(refute_0_30,plain,
( f(n2,f(n1,n1)) != f(f(n2,n1),n3)
| f(n2,f(n1,n1)) = f(n3,n3) ),
inference(resolve,[$cnf( $equal(f(n2,n1),n3) )],[refute_0_5,refute_0_29]) ).
cnf(refute_0_31,plain,
f(n2,f(n1,n1)) = f(n3,n3),
inference(resolve,[$cnf( $equal(f(n2,f(n1,n1)),f(f(n2,n1),n3)) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
f(n1,f(X_1,n1)) = f(f(n1,X_1),f(n1,n1)),
inference(subst,[],[a1:[bind(X,$fot(n1)),bind(Y,$fot(X_1)),bind(Z,$fot(n1))]]) ).
cnf(refute_0_33,plain,
( f(n1,f(X_1,n1)) != f(f(n1,X_1),f(n1,n1))
| f(n1,n1) != n2
| f(n1,f(X_1,n1)) = f(f(n1,X_1),n2) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(X_1,n1)),f(f(n1,X_1),f(n1,n1))) ),[1,1],$fot(n2)]]) ).
cnf(refute_0_34,plain,
( f(n1,f(X_1,n1)) != f(f(n1,X_1),f(n1,n1))
| f(n1,f(X_1,n1)) = f(f(n1,X_1),n2) ),
inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_11,refute_0_33]) ).
cnf(refute_0_35,plain,
f(n1,f(X_1,n1)) = f(f(n1,X_1),n2),
inference(resolve,[$cnf( $equal(f(n1,f(X_1,n1)),f(f(n1,X_1),f(n1,n1))) )],[refute_0_32,refute_0_34]) ).
cnf(refute_0_36,plain,
f(n1,f(n1,n1)) = f(f(n1,n1),n2),
inference(subst,[],[refute_0_35:[bind(X_1,$fot(n1))]]) ).
cnf(refute_0_37,plain,
( f(n1,f(n1,n1)) != f(f(n1,n1),n2)
| f(n1,n1) != n2
| f(n1,f(n1,n1)) = f(n2,n2) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n1)),f(f(n1,n1),n2)) ),[1,0],$fot(n2)]]) ).
cnf(refute_0_38,plain,
( f(n1,f(n1,n1)) != f(f(n1,n1),n2)
| f(n1,f(n1,n1)) = f(n2,n2) ),
inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_11,refute_0_37]) ).
cnf(refute_0_39,plain,
f(n1,f(n1,n1)) = f(n2,n2),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(f(n1,n1),n2)) )],[refute_0_36,refute_0_38]) ).
cnf(refute_0_40,plain,
f(n1,f(n1,n1)) = f(n1,f(n1,n1)),
introduced(tautology,[refl,[$fot(f(n1,f(n1,n1)))]]) ).
cnf(refute_0_41,plain,
( f(n1,f(n1,n1)) != f(n1,f(n1,n1))
| f(n1,n1) != n2
| f(n1,f(n1,n1)) = f(n1,n2) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n1)),f(n1,f(n1,n1))) ),[1,1],$fot(n2)]]) ).
cnf(refute_0_42,plain,
( f(n1,n1) != n2
| f(n1,f(n1,n1)) = f(n1,n2) ),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(n1,f(n1,n1))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
f(n1,f(n1,n1)) = f(n1,n2),
inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_11,refute_0_42]) ).
cnf(refute_0_44,plain,
( f(n1,f(n1,n1)) != f(n1,n2)
| f(n1,f(n1,n1)) != f(n2,n2)
| f(n1,n2) = f(n2,n2) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n1)),f(n2,n2)) ),[0],$fot(f(n1,n2))]]) ).
cnf(refute_0_45,plain,
( f(n1,f(n1,n1)) != f(n2,n2)
| f(n1,n2) = f(n2,n2) ),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(n1,n2)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( u != f(n2,n2)
| f(n2,n2) = u ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(u)),bind(Y0,$fot(f(n2,n2)))]]) ).
cnf(refute_0_47,plain,
f(n2,n2) = u,
inference(resolve,[$cnf( $equal(u,f(n2,n2)) )],[clause_4,refute_0_46]) ).
cnf(refute_0_48,plain,
( f(n1,n2) != f(n2,n2)
| f(n2,n2) != u
| f(n1,n2) = u ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(n1,n2),u) ),[0],$fot(f(n2,n2))]]) ).
cnf(refute_0_49,plain,
( f(n1,n2) != f(n2,n2)
| f(n1,n2) = u ),
inference(resolve,[$cnf( $equal(f(n2,n2),u) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( f(n1,f(n1,n1)) != f(n2,n2)
| f(n1,n2) = u ),
inference(resolve,[$cnf( $equal(f(n1,n2),f(n2,n2)) )],[refute_0_45,refute_0_49]) ).
cnf(refute_0_51,plain,
f(n1,n2) = u,
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(n2,n2)) )],[refute_0_39,refute_0_50]) ).
cnf(refute_0_52,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_53,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_3,refute_0_52]) ).
cnf(refute_0_54,plain,
( f(n1,f(n1,n1)) != f(n1,n2)
| f(n1,n2) != u
| f(n1,f(n1,n1)) = u ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(f(n1,f(n1,n1)))),bind(Y0,$fot(f(n1,n2))),bind(Z0,$fot(u))]]) ).
cnf(refute_0_55,plain,
( f(n1,n2) != u
| f(n1,f(n1,n1)) = u ),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(n1,n2)) )],[refute_0_43,refute_0_54]) ).
cnf(refute_0_56,plain,
f(n1,f(n1,n1)) = u,
inference(resolve,[$cnf( $equal(f(n1,n2),u) )],[refute_0_51,refute_0_55]) ).
cnf(refute_0_57,plain,
f(n2,f(n1,n1)) = f(n1,f(n1,n1)),
inference(subst,[],[refute_0_16:[bind(X_2,$fot(n1))]]) ).
cnf(refute_0_58,plain,
( f(n1,f(n1,n1)) != u
| f(n2,f(n1,n1)) != f(n1,f(n1,n1))
| f(n2,f(n1,n1)) = u ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(f(n2,f(n1,n1)))),bind(Y0,$fot(f(n1,f(n1,n1)))),bind(Z0,$fot(u))]]) ).
cnf(refute_0_59,plain,
( f(n1,f(n1,n1)) != u
| f(n2,f(n1,n1)) = u ),
inference(resolve,[$cnf( $equal(f(n2,f(n1,n1)),f(n1,f(n1,n1))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
f(n2,f(n1,n1)) = u,
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),u) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
( f(n2,f(n1,n1)) != f(n3,n3)
| f(n2,f(n1,n1)) != u
| u = f(n3,n3) ),
introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n1,n1)),f(n3,n3)) ),[0],$fot(u)]]) ).
cnf(refute_0_62,plain,
( f(n2,f(n1,n1)) != f(n3,n3)
| u = f(n3,n3) ),
inference(resolve,[$cnf( $equal(f(n2,f(n1,n1)),u) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
u = f(n3,n3),
inference(resolve,[$cnf( $equal(f(n2,f(n1,n1)),f(n3,n3)) )],[refute_0_31,refute_0_62]) ).
cnf(refute_0_64,plain,
( u != f(n3,n3)
| f(n3,n3) = u ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(u)),bind(Y0,$fot(f(n3,n3)))]]) ).
cnf(refute_0_65,plain,
f(n3,n3) = u,
inference(resolve,[$cnf( $equal(u,f(n3,n3)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( f(n3,f(Y,n3)) != f(f(n3,Y),f(n3,n3))
| f(n3,n3) != u
| f(n3,f(Y,n3)) = f(f(n3,Y),u) ),
introduced(tautology,[equality,[$cnf( $equal(f(n3,f(Y,n3)),f(f(n3,Y),f(n3,n3))) ),[1,1],$fot(u)]]) ).
cnf(refute_0_67,plain,
( f(n3,f(Y,n3)) != f(f(n3,Y),f(n3,n3))
| f(n3,f(Y,n3)) = f(f(n3,Y),u) ),
inference(resolve,[$cnf( $equal(f(n3,n3),u) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
f(n3,f(Y,n3)) = f(f(n3,Y),u),
inference(resolve,[$cnf( $equal(f(n3,f(Y,n3)),f(f(n3,Y),f(n3,n3))) )],[refute_0_23,refute_0_67]) ).
cnf(refute_0_69,plain,
( f(n3,f(Y,n3)) != f(f(n3,Y),u)
| f(f(n3,Y),u) = f(n3,f(Y,n3)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(f(n3,f(Y,n3)))),bind(Y0,$fot(f(f(n3,Y),u)))]]) ).
cnf(refute_0_70,plain,
f(f(n3,Y),u) = f(n3,f(Y,n3)),
inference(resolve,[$cnf( $equal(f(n3,f(Y,n3)),f(f(n3,Y),u)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
f(f(n3,n2),u) = f(n3,f(n2,n3)),
inference(subst,[],[refute_0_70:[bind(Y,$fot(n2))]]) ).
cnf(refute_0_72,plain,
( f(f(n3,n2),u) != f(n3,f(n2,n3))
| f(n3,f(n2,n3)) != f(n1,f(n1,n3))
| f(f(n3,n2),u) = f(n1,f(n1,n3)) ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(f(f(n3,n2),u))),bind(Y0,$fot(f(n3,f(n2,n3)))),bind(Z0,$fot(f(n1,f(n1,n3))))]]) ).
cnf(refute_0_73,plain,
( f(n3,f(n2,n3)) != f(n1,f(n1,n3))
| f(f(n3,n2),u) = f(n1,f(n1,n3)) ),
inference(resolve,[$cnf( $equal(f(f(n3,n2),u),f(n3,f(n2,n3))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
f(f(n3,n2),u) = f(n1,f(n1,n3)),
inference(resolve,[$cnf( $equal(f(n3,f(n2,n3)),f(n1,f(n1,n3))) )],[refute_0_22,refute_0_73]) ).
cnf(refute_0_75,plain,
( f(f(n3,n2),u) != f(n1,f(n1,n3))
| f(n1,f(n1,n3)) != f(f(u,u),u)
| f(f(n3,n2),u) = f(f(u,u),u) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(f(n3,n2),u),f(f(u,u),u)) ),[0],$fot(f(n1,f(n1,n3)))]]) ).
cnf(refute_0_76,plain,
( f(n1,f(n1,n3)) != f(f(u,u),u)
| f(f(n3,n2),u) = f(f(u,u),u) ),
inference(resolve,[$cnf( $equal(f(f(n3,n2),u),f(n1,f(n1,n3))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
f(n1,f(n1,n3)) != f(f(u,u),u),
inference(resolve,[$cnf( $equal(f(f(n3,n2),u),f(f(u,u),u)) )],[refute_0_76,prove_equation]) ).
cnf(refute_0_78,plain,
f(n1,f(n2,n1)) = f(f(n1,n2),n2),
inference(subst,[],[refute_0_35:[bind(X_1,$fot(n2))]]) ).
cnf(refute_0_79,plain,
( f(n1,f(n2,n1)) != f(f(n1,n2),n2)
| f(n1,n2) != u
| f(n1,f(n2,n1)) = f(u,n2) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n2,n1)),f(f(n1,n2),n2)) ),[1,0],$fot(u)]]) ).
cnf(refute_0_80,plain,
( f(n1,f(n2,n1)) != f(f(n1,n2),n2)
| f(n1,f(n2,n1)) = f(u,n2) ),
inference(resolve,[$cnf( $equal(f(n1,n2),u) )],[refute_0_51,refute_0_79]) ).
cnf(refute_0_81,plain,
f(n1,f(n2,n1)) = f(u,n2),
inference(resolve,[$cnf( $equal(f(n1,f(n2,n1)),f(f(n1,n2),n2)) )],[refute_0_78,refute_0_80]) ).
cnf(refute_0_82,plain,
f(n1,f(n2,n1)) = f(n1,f(n2,n1)),
introduced(tautology,[refl,[$fot(f(n1,f(n2,n1)))]]) ).
cnf(refute_0_83,plain,
( f(n1,f(n2,n1)) != f(n1,f(n2,n1))
| f(n2,n1) != n3
| f(n1,f(n2,n1)) = f(n1,n3) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n2,n1)),f(n1,f(n2,n1))) ),[1,1],$fot(n3)]]) ).
cnf(refute_0_84,plain,
( f(n2,n1) != n3
| f(n1,f(n2,n1)) = f(n1,n3) ),
inference(resolve,[$cnf( $equal(f(n1,f(n2,n1)),f(n1,f(n2,n1))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
f(n1,f(n2,n1)) = f(n1,n3),
inference(resolve,[$cnf( $equal(f(n2,n1),n3) )],[refute_0_5,refute_0_84]) ).
cnf(refute_0_86,plain,
( f(n1,f(n2,n1)) != f(n1,n3)
| f(n1,f(n2,n1)) != f(u,n2)
| f(n1,n3) = f(u,n2) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n2,n1)),f(u,n2)) ),[0],$fot(f(n1,n3))]]) ).
cnf(refute_0_87,plain,
( f(n1,f(n2,n1)) != f(u,n2)
| f(n1,n3) = f(u,n2) ),
inference(resolve,[$cnf( $equal(f(n1,f(n2,n1)),f(n1,n3)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
f(n1,n3) = f(u,n2),
inference(resolve,[$cnf( $equal(f(n1,f(n2,n1)),f(u,n2)) )],[refute_0_81,refute_0_87]) ).
cnf(refute_0_89,plain,
( f(n1,n3) != f(u,n2)
| f(u,n2) = f(n1,n3) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(f(n1,n3))),bind(Y0,$fot(f(u,n2)))]]) ).
cnf(refute_0_90,plain,
f(u,n2) = f(n1,n3),
inference(resolve,[$cnf( $equal(f(n1,n3),f(u,n2)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
f(n1,f(u,n2)) = f(n1,f(u,n2)),
introduced(tautology,[refl,[$fot(f(n1,f(u,n2)))]]) ).
cnf(refute_0_92,plain,
( f(n1,f(u,n2)) != f(n1,f(u,n2))
| f(u,n2) != f(n1,n3)
| f(n1,f(u,n2)) = f(n1,f(n1,n3)) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(u,n2)),f(n1,f(u,n2))) ),[1,1],$fot(f(n1,n3))]]) ).
cnf(refute_0_93,plain,
( f(u,n2) != f(n1,n3)
| f(n1,f(u,n2)) = f(n1,f(n1,n3)) ),
inference(resolve,[$cnf( $equal(f(n1,f(u,n2)),f(n1,f(u,n2))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
f(n1,f(u,n2)) = f(n1,f(n1,n3)),
inference(resolve,[$cnf( $equal(f(u,n2),f(n1,n3)) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
f(n1,f(Y,n2)) = f(f(n1,Y),f(n1,n2)),
inference(subst,[],[a1:[bind(X,$fot(n1)),bind(Z,$fot(n2))]]) ).
cnf(refute_0_96,plain,
( f(n1,f(Y,n2)) != f(f(n1,Y),f(n1,n2))
| f(n1,n2) != u
| f(n1,f(Y,n2)) = f(f(n1,Y),u) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(Y,n2)),f(f(n1,Y),f(n1,n2))) ),[1,1],$fot(u)]]) ).
cnf(refute_0_97,plain,
( f(n1,f(Y,n2)) != f(f(n1,Y),f(n1,n2))
| f(n1,f(Y,n2)) = f(f(n1,Y),u) ),
inference(resolve,[$cnf( $equal(f(n1,n2),u) )],[refute_0_51,refute_0_96]) ).
cnf(refute_0_98,plain,
f(n1,f(Y,n2)) = f(f(n1,Y),u),
inference(resolve,[$cnf( $equal(f(n1,f(Y,n2)),f(f(n1,Y),f(n1,n2))) )],[refute_0_95,refute_0_97]) ).
cnf(refute_0_99,plain,
( f(n1,f(Y,n2)) != f(f(n1,Y),u)
| f(f(n1,Y),u) = f(n1,f(Y,n2)) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(f(n1,f(Y,n2)))),bind(Y0,$fot(f(f(n1,Y),u)))]]) ).
cnf(refute_0_100,plain,
f(f(n1,Y),u) = f(n1,f(Y,n2)),
inference(resolve,[$cnf( $equal(f(n1,f(Y,n2)),f(f(n1,Y),u)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
f(f(n1,u),u) = f(n1,f(u,n2)),
inference(subst,[],[refute_0_100:[bind(Y,$fot(u))]]) ).
cnf(refute_0_102,plain,
( f(f(n1,u),u) != f(n1,f(u,n2))
| f(n1,f(u,n2)) != f(n1,f(n1,n3))
| f(f(n1,u),u) = f(n1,f(n1,n3)) ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(f(f(n1,u),u))),bind(Y0,$fot(f(n1,f(u,n2)))),bind(Z0,$fot(f(n1,f(n1,n3))))]]) ).
cnf(refute_0_103,plain,
( f(n1,f(u,n2)) != f(n1,f(n1,n3))
| f(f(n1,u),u) = f(n1,f(n1,n3)) ),
inference(resolve,[$cnf( $equal(f(f(n1,u),u),f(n1,f(u,n2))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
f(f(n1,u),u) = f(n1,f(n1,n3)),
inference(resolve,[$cnf( $equal(f(n1,f(u,n2)),f(n1,f(n1,n3))) )],[refute_0_94,refute_0_103]) ).
cnf(refute_0_105,plain,
f(n2,f(X_1,n2)) = f(f(n2,X_1),f(n2,n2)),
inference(subst,[],[a1:[bind(X,$fot(n2)),bind(Y,$fot(X_1)),bind(Z,$fot(n2))]]) ).
cnf(refute_0_106,plain,
( f(n2,f(X_1,n2)) != f(f(n2,X_1),f(n2,n2))
| f(n2,n2) != u
| f(n2,f(X_1,n2)) = f(f(n2,X_1),u) ),
introduced(tautology,[equality,[$cnf( $equal(f(n2,f(X_1,n2)),f(f(n2,X_1),f(n2,n2))) ),[1,1],$fot(u)]]) ).
cnf(refute_0_107,plain,
( f(n2,f(X_1,n2)) != f(f(n2,X_1),f(n2,n2))
| f(n2,f(X_1,n2)) = f(f(n2,X_1),u) ),
inference(resolve,[$cnf( $equal(f(n2,n2),u) )],[refute_0_47,refute_0_106]) ).
cnf(refute_0_108,plain,
f(n2,f(X_1,n2)) = f(f(n2,X_1),u),
inference(resolve,[$cnf( $equal(f(n2,f(X_1,n2)),f(f(n2,X_1),f(n2,n2))) )],[refute_0_105,refute_0_107]) ).
cnf(refute_0_109,plain,
f(n2,f(n2,n2)) = f(f(n2,n2),u),
inference(subst,[],[refute_0_108:[bind(X_1,$fot(n2))]]) ).
cnf(refute_0_110,plain,
( f(n2,f(n2,n2)) != f(f(n2,n2),u)
| f(n2,n2) != u
| f(n2,f(n2,n2)) = f(u,u) ),
introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n2,n2)),f(f(n2,n2),u)) ),[1,0],$fot(u)]]) ).
cnf(refute_0_111,plain,
( f(n2,f(n2,n2)) != f(f(n2,n2),u)
| f(n2,f(n2,n2)) = f(u,u) ),
inference(resolve,[$cnf( $equal(f(n2,n2),u) )],[refute_0_47,refute_0_110]) ).
cnf(refute_0_112,plain,
f(n2,f(n2,n2)) = f(u,u),
inference(resolve,[$cnf( $equal(f(n2,f(n2,n2)),f(f(n2,n2),u)) )],[refute_0_109,refute_0_111]) ).
cnf(refute_0_113,plain,
f(n1,f(n1,n2)) = f(n2,f(n1,n2)),
inference(subst,[],[refute_0_14:[bind(X_2,$fot(n2))]]) ).
cnf(refute_0_114,plain,
( f(n1,f(n1,n2)) != f(n2,f(n1,n2))
| f(n1,n2) != u
| f(n1,f(n1,n2)) = f(n2,u) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n2)),f(n2,f(n1,n2))) ),[1,1],$fot(u)]]) ).
cnf(refute_0_115,plain,
( f(n1,f(n1,n2)) != f(n2,f(n1,n2))
| f(n1,f(n1,n2)) = f(n2,u) ),
inference(resolve,[$cnf( $equal(f(n1,n2),u) )],[refute_0_51,refute_0_114]) ).
cnf(refute_0_116,plain,
f(n1,f(n1,n2)) = f(n2,u),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n2)),f(n2,f(n1,n2))) )],[refute_0_113,refute_0_115]) ).
cnf(refute_0_117,plain,
f(n1,f(n1,n2)) = f(n1,f(n1,n2)),
introduced(tautology,[refl,[$fot(f(n1,f(n1,n2)))]]) ).
cnf(refute_0_118,plain,
( f(n1,f(n1,n2)) != f(n1,f(n1,n2))
| f(n1,n2) != u
| f(n1,f(n1,n2)) = f(n1,u) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n2)),f(n1,f(n1,n2))) ),[1,1],$fot(u)]]) ).
cnf(refute_0_119,plain,
( f(n1,n2) != u
| f(n1,f(n1,n2)) = f(n1,u) ),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n2)),f(n1,f(n1,n2))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
f(n1,f(n1,n2)) = f(n1,u),
inference(resolve,[$cnf( $equal(f(n1,n2),u) )],[refute_0_51,refute_0_119]) ).
cnf(refute_0_121,plain,
( f(n1,f(n1,n2)) != f(n1,u)
| f(n1,f(n1,n2)) != f(n2,u)
| f(n1,u) = f(n2,u) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n2)),f(n2,u)) ),[0],$fot(f(n1,u))]]) ).
cnf(refute_0_122,plain,
( f(n1,f(n1,n2)) != f(n2,u)
| f(n1,u) = f(n2,u) ),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n2)),f(n1,u)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
f(n1,u) = f(n2,u),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n2)),f(n2,u)) )],[refute_0_116,refute_0_122]) ).
cnf(refute_0_124,plain,
( f(n1,u) != f(n2,u)
| f(n2,u) = f(n1,u) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(f(n1,u))),bind(Y0,$fot(f(n2,u)))]]) ).
cnf(refute_0_125,plain,
f(n2,u) = f(n1,u),
inference(resolve,[$cnf( $equal(f(n1,u),f(n2,u)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
f(n2,f(n2,n2)) = f(n2,f(n2,n2)),
introduced(tautology,[refl,[$fot(f(n2,f(n2,n2)))]]) ).
cnf(refute_0_127,plain,
( f(n2,f(n2,n2)) != f(n2,f(n2,n2))
| f(n2,n2) != u
| f(n2,f(n2,n2)) = f(n2,u) ),
introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n2,n2)),f(n2,f(n2,n2))) ),[1,1],$fot(u)]]) ).
cnf(refute_0_128,plain,
( f(n2,n2) != u
| f(n2,f(n2,n2)) = f(n2,u) ),
inference(resolve,[$cnf( $equal(f(n2,f(n2,n2)),f(n2,f(n2,n2))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
f(n2,f(n2,n2)) = f(n2,u),
inference(resolve,[$cnf( $equal(f(n2,n2),u) )],[refute_0_47,refute_0_128]) ).
cnf(refute_0_130,plain,
( f(n2,f(n2,n2)) != f(n2,u)
| f(n2,u) != f(n1,u)
| f(n2,f(n2,n2)) = f(n1,u) ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(f(n2,f(n2,n2)))),bind(Y0,$fot(f(n2,u))),bind(Z0,$fot(f(n1,u)))]]) ).
cnf(refute_0_131,plain,
( f(n2,u) != f(n1,u)
| f(n2,f(n2,n2)) = f(n1,u) ),
inference(resolve,[$cnf( $equal(f(n2,f(n2,n2)),f(n2,u)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
f(n2,f(n2,n2)) = f(n1,u),
inference(resolve,[$cnf( $equal(f(n2,u),f(n1,u)) )],[refute_0_125,refute_0_131]) ).
cnf(refute_0_133,plain,
( f(n2,f(n2,n2)) != f(n1,u)
| f(n2,f(n2,n2)) != f(u,u)
| f(n1,u) = f(u,u) ),
introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n2,n2)),f(u,u)) ),[0],$fot(f(n1,u))]]) ).
cnf(refute_0_134,plain,
( f(n2,f(n2,n2)) != f(u,u)
| f(n1,u) = f(u,u) ),
inference(resolve,[$cnf( $equal(f(n2,f(n2,n2)),f(n1,u)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
f(n1,u) = f(u,u),
inference(resolve,[$cnf( $equal(f(n2,f(n2,n2)),f(u,u)) )],[refute_0_112,refute_0_134]) ).
cnf(refute_0_136,plain,
( f(n1,u) != f(u,u)
| f(u,u) = f(n1,u) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(f(n1,u))),bind(Y0,$fot(f(u,u)))]]) ).
cnf(refute_0_137,plain,
f(u,u) = f(n1,u),
inference(resolve,[$cnf( $equal(f(n1,u),f(u,u)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
f(f(u,u),u) = f(f(u,u),u),
introduced(tautology,[refl,[$fot(f(f(u,u),u))]]) ).
cnf(refute_0_139,plain,
( f(f(u,u),u) != f(f(u,u),u)
| f(u,u) != f(n1,u)
| f(f(u,u),u) = f(f(n1,u),u) ),
introduced(tautology,[equality,[$cnf( $equal(f(f(u,u),u),f(f(u,u),u)) ),[1,0],$fot(f(n1,u))]]) ).
cnf(refute_0_140,plain,
( f(u,u) != f(n1,u)
| f(f(u,u),u) = f(f(n1,u),u) ),
inference(resolve,[$cnf( $equal(f(f(u,u),u),f(f(u,u),u)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
f(f(u,u),u) = f(f(n1,u),u),
inference(resolve,[$cnf( $equal(f(u,u),f(n1,u)) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
( f(f(n1,u),u) != f(n1,f(n1,n3))
| f(f(u,u),u) != f(f(n1,u),u)
| f(f(u,u),u) = f(n1,f(n1,n3)) ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(f(f(u,u),u))),bind(Y0,$fot(f(f(n1,u),u))),bind(Z0,$fot(f(n1,f(n1,n3))))]]) ).
cnf(refute_0_143,plain,
( f(f(n1,u),u) != f(n1,f(n1,n3))
| f(f(u,u),u) = f(n1,f(n1,n3)) ),
inference(resolve,[$cnf( $equal(f(f(u,u),u),f(f(n1,u),u)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
f(f(u,u),u) = f(n1,f(n1,n3)),
inference(resolve,[$cnf( $equal(f(f(n1,u),u),f(n1,f(n1,n3))) )],[refute_0_104,refute_0_143]) ).
cnf(refute_0_145,plain,
( f(f(u,u),u) != f(n1,f(n1,n3))
| f(n1,f(n1,n3)) != f(n1,f(n1,n3))
| f(n1,f(n1,n3)) = f(f(u,u),u) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(n1,f(n1,n3)),f(f(u,u),u)) ),[1],$fot(f(n1,f(n1,n3)))]]) ).
cnf(refute_0_146,plain,
( f(n1,f(n1,n3)) != f(n1,f(n1,n3))
| f(n1,f(n1,n3)) = f(f(u,u),u) ),
inference(resolve,[$cnf( $equal(f(f(u,u),u),f(n1,f(n1,n3))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
f(n1,f(n1,n3)) != f(n1,f(n1,n3)),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n3)),f(f(u,u),u)) )],[refute_0_146,refute_0_77]) ).
cnf(refute_0_148,plain,
f(n1,f(n1,n3)) = f(n1,f(n1,n3)),
introduced(tautology,[refl,[$fot(f(n1,f(n1,n3)))]]) ).
cnf(refute_0_149,plain,
$false,
inference(resolve,[$cnf( $equal(f(n1,f(n1,n3)),f(n1,f(n1,n3))) )],[refute_0_148,refute_0_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.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 : Mon May 30 02:10:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.39
%------------------------------------------------------------------------------