%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LDA003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of clauses : 66 ( 32 unt; 0 nHn; 56 RR)
% Number of literals : 115 ( 106 equ; 50 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a1,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ).
cnf(a2,axiom,
left(X,f(X,Y)) ).
cnf(clause_4,axiom,
n2 = f(n1,n1) ).
cnf(clause_5,axiom,
n3 = f(n2,n1) ).
cnf(clause_6,axiom,
u = f(n2,n2) ).
cnf(prove_equation,negated_conjecture,
~ left(n3,u) ).
cnf(refute_0_0,plain,
left(n3,f(n3,n3)),
inference(subst,[],[a2:[bind(X,$fot(n3)),bind(Y,$fot(n3))]]) ).
cnf(refute_0_1,plain,
f(n2,f(X_3,n1)) = f(f(n2,X_3),f(n2,n1)),
inference(subst,[],[a1:[bind(X,$fot(n2)),bind(Y,$fot(X_3)),bind(Z,$fot(n1))]]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( n3 != f(n2,n1)
| f(n2,n1) = n3 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(n3)),bind(Y0,$fot(f(n2,n1)))]]) ).
cnf(refute_0_6,plain,
f(n2,n1) = n3,
inference(resolve,[$cnf( $equal(n3,f(n2,n1)) )],[clause_5,refute_0_5]) ).
cnf(refute_0_7,plain,
( f(n2,f(X_3,n1)) != f(f(n2,X_3),f(n2,n1))
| f(n2,n1) != n3
| f(n2,f(X_3,n1)) = f(f(n2,X_3),n3) ),
introduced(tautology,[equality,[$cnf( $equal(f(n2,f(X_3,n1)),f(f(n2,X_3),f(n2,n1))) ),[1,1],$fot(n3)]]) ).
cnf(refute_0_8,plain,
( f(n2,f(X_3,n1)) != f(f(n2,X_3),f(n2,n1))
| f(n2,f(X_3,n1)) = f(f(n2,X_3),n3) ),
inference(resolve,[$cnf( $equal(f(n2,n1),n3) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
f(n2,f(X_3,n1)) = f(f(n2,X_3),n3),
inference(resolve,[$cnf( $equal(f(n2,f(X_3,n1)),f(f(n2,X_3),f(n2,n1))) )],[refute_0_1,refute_0_8]) ).
cnf(refute_0_10,plain,
f(n2,f(n1,n1)) = f(f(n2,n1),n3),
inference(subst,[],[refute_0_9:[bind(X_3,$fot(n1))]]) ).
cnf(refute_0_11,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_12,plain,
( f(n2,f(n1,n1)) != f(f(n2,n1),n3)
| f(n2,f(n1,n1)) = f(n3,n3) ),
inference(resolve,[$cnf( $equal(f(n2,n1),n3) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
f(n2,f(n1,n1)) = f(n3,n3),
inference(resolve,[$cnf( $equal(f(n2,f(n1,n1)),f(f(n2,n1),n3)) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
f(n1,f(X_3,n1)) = f(f(n1,X_3),f(n1,n1)),
inference(subst,[],[a1:[bind(X,$fot(n1)),bind(Y,$fot(X_3)),bind(Z,$fot(n1))]]) ).
cnf(refute_0_15,plain,
( n2 != f(n1,n1)
| f(n1,n1) = n2 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(n2)),bind(Y0,$fot(f(n1,n1)))]]) ).
cnf(refute_0_16,plain,
f(n1,n1) = n2,
inference(resolve,[$cnf( $equal(n2,f(n1,n1)) )],[clause_4,refute_0_15]) ).
cnf(refute_0_17,plain,
( f(n1,f(X_3,n1)) != f(f(n1,X_3),f(n1,n1))
| f(n1,n1) != n2
| f(n1,f(X_3,n1)) = f(f(n1,X_3),n2) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(X_3,n1)),f(f(n1,X_3),f(n1,n1))) ),[1,1],$fot(n2)]]) ).
cnf(refute_0_18,plain,
( f(n1,f(X_3,n1)) != f(f(n1,X_3),f(n1,n1))
| f(n1,f(X_3,n1)) = f(f(n1,X_3),n2) ),
inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
f(n1,f(X_3,n1)) = f(f(n1,X_3),n2),
inference(resolve,[$cnf( $equal(f(n1,f(X_3,n1)),f(f(n1,X_3),f(n1,n1))) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
f(n1,f(n1,n1)) = f(f(n1,n1),n2),
inference(subst,[],[refute_0_19:[bind(X_3,$fot(n1))]]) ).
cnf(refute_0_21,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_22,plain,
( f(n1,f(n1,n1)) != f(f(n1,n1),n2)
| f(n1,f(n1,n1)) = f(n2,n2) ),
inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
f(n1,f(n1,n1)) = f(n2,n2),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(f(n1,n1),n2)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
f(n1,f(n1,n1)) = f(n1,f(n1,n1)),
introduced(tautology,[refl,[$fot(f(n1,f(n1,n1)))]]) ).
cnf(refute_0_25,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_26,plain,
( f(n1,n1) != n2
| f(n1,f(n1,n1)) = f(n1,n2) ),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(n1,f(n1,n1))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
f(n1,f(n1,n1)) = f(n1,n2),
inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_16,refute_0_26]) ).
cnf(refute_0_28,plain,
( f(n1,f(n1,n1)) != f(n1,n2)
| f(n1,f(n1,n1)) != f(n2,n2)
| f(n1,n2) = f(n2,n2) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n1)),f(n2,n2)) ),[0],$fot(f(n1,n2))]]) ).
cnf(refute_0_29,plain,
( f(n1,f(n1,n1)) != f(n2,n2)
| f(n1,n2) = f(n2,n2) ),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(n1,n2)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( u != f(n2,n2)
| f(n2,n2) = u ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(u)),bind(Y0,$fot(f(n2,n2)))]]) ).
cnf(refute_0_31,plain,
f(n2,n2) = u,
inference(resolve,[$cnf( $equal(u,f(n2,n2)) )],[clause_6,refute_0_30]) ).
cnf(refute_0_32,plain,
( f(n1,n2) != f(n2,n2)
| f(n2,n2) != u
| f(n1,n2) = u ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(n1,n2),u) ),[0],$fot(f(n2,n2))]]) ).
cnf(refute_0_33,plain,
( f(n1,n2) != f(n2,n2)
| f(n1,n2) = u ),
inference(resolve,[$cnf( $equal(f(n2,n2),u) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( f(n1,f(n1,n1)) != f(n2,n2)
| f(n1,n2) = u ),
inference(resolve,[$cnf( $equal(f(n1,n2),f(n2,n2)) )],[refute_0_29,refute_0_33]) ).
cnf(refute_0_35,plain,
f(n1,n2) = u,
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(n2,n2)) )],[refute_0_23,refute_0_34]) ).
cnf(refute_0_36,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_37,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_4,refute_0_36]) ).
cnf(refute_0_38,plain,
( f(n1,f(n1,n1)) != f(n1,n2)
| f(n1,n2) != u
| f(n1,f(n1,n1)) = u ),
inference(subst,[],[refute_0_37:[bind(X0,$fot(f(n1,f(n1,n1)))),bind(Y0,$fot(f(n1,n2))),bind(Z0,$fot(u))]]) ).
cnf(refute_0_39,plain,
( f(n1,n2) != u
| f(n1,f(n1,n1)) = u ),
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(n1,n2)) )],[refute_0_27,refute_0_38]) ).
cnf(refute_0_40,plain,
f(n1,f(n1,n1)) = u,
inference(resolve,[$cnf( $equal(f(n1,n2),u) )],[refute_0_35,refute_0_39]) ).
cnf(refute_0_41,plain,
f(n1,f(n1,X_4)) = f(f(n1,n1),f(n1,X_4)),
inference(subst,[],[a1:[bind(X,$fot(n1)),bind(Y,$fot(n1)),bind(Z,$fot(X_4))]]) ).
cnf(refute_0_42,plain,
( f(n1,f(n1,X_4)) != f(f(n1,n1),f(n1,X_4))
| f(n1,n1) != n2
| f(n1,f(n1,X_4)) = f(n2,f(n1,X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,X_4)),f(f(n1,n1),f(n1,X_4))) ),[1,0],$fot(n2)]]) ).
cnf(refute_0_43,plain,
( f(n1,f(n1,X_4)) != f(f(n1,n1),f(n1,X_4))
| f(n1,f(n1,X_4)) = f(n2,f(n1,X_4)) ),
inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_16,refute_0_42]) ).
cnf(refute_0_44,plain,
f(n1,f(n1,X_4)) = f(n2,f(n1,X_4)),
inference(resolve,[$cnf( $equal(f(n1,f(n1,X_4)),f(f(n1,n1),f(n1,X_4))) )],[refute_0_41,refute_0_43]) ).
cnf(refute_0_45,plain,
( f(n1,f(n1,X_4)) != f(n2,f(n1,X_4))
| f(n2,f(n1,X_4)) = f(n1,f(n1,X_4)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(f(n1,f(n1,X_4)))),bind(Y0,$fot(f(n2,f(n1,X_4))))]]) ).
cnf(refute_0_46,plain,
f(n2,f(n1,X_4)) = f(n1,f(n1,X_4)),
inference(resolve,[$cnf( $equal(f(n1,f(n1,X_4)),f(n2,f(n1,X_4))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
f(n2,f(n1,n1)) = f(n1,f(n1,n1)),
inference(subst,[],[refute_0_46:[bind(X_4,$fot(n1))]]) ).
cnf(refute_0_48,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_37:[bind(X0,$fot(f(n2,f(n1,n1)))),bind(Y0,$fot(f(n1,f(n1,n1)))),bind(Z0,$fot(u))]]) ).
cnf(refute_0_49,plain,
( f(n1,f(n1,n1)) != u
| f(n2,f(n1,n1)) = u ),
inference(resolve,[$cnf( $equal(f(n2,f(n1,n1)),f(n1,f(n1,n1))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
f(n2,f(n1,n1)) = u,
inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),u) )],[refute_0_40,refute_0_49]) ).
cnf(refute_0_51,plain,
( f(n2,f(n1,n1)) != f(n3,n3)
| f(n2,f(n1,n1)) != u
| u = f(n3,n3) ),
introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n1,n1)),f(n3,n3)) ),[0],$fot(u)]]) ).
cnf(refute_0_52,plain,
( f(n2,f(n1,n1)) != f(n3,n3)
| u = f(n3,n3) ),
inference(resolve,[$cnf( $equal(f(n2,f(n1,n1)),u) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
u = f(n3,n3),
inference(resolve,[$cnf( $equal(f(n2,f(n1,n1)),f(n3,n3)) )],[refute_0_13,refute_0_52]) ).
cnf(refute_0_54,plain,
( u != f(n3,n3)
| f(n3,n3) = u ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(u)),bind(Y0,$fot(f(n3,n3)))]]) ).
cnf(refute_0_55,plain,
f(n3,n3) = u,
inference(resolve,[$cnf( $equal(u,f(n3,n3)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( f(n3,n3) != u
| ~ left(n3,f(n3,n3))
| left(n3,u) ),
introduced(tautology,[equality,[$cnf( left(n3,f(n3,n3)) ),[1],$fot(u)]]) ).
cnf(refute_0_57,plain,
( ~ left(n3,f(n3,n3))
| left(n3,u) ),
inference(resolve,[$cnf( $equal(f(n3,n3),u) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
left(n3,u),
inference(resolve,[$cnf( left(n3,f(n3,n3)) )],[refute_0_0,refute_0_57]) ).
cnf(refute_0_59,plain,
$false,
inference(resolve,[$cnf( left(n3,u) )],[refute_0_58,prove_equation]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LDA003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n024.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 May 30 04:10:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------