%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ALG040+1 : TPTP v8.1.0. Released v2.7.0.
% 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 : Thu Jul 14 17:32:35 EDT 2022
% Result : Theorem 0.39s 0.57s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 24
% Syntax : Number of formulae : 124 ( 40 unt; 0 def)
% Number of atoms : 285 ( 156 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 282 ( 121 ~; 108 |; 24 &)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 55 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax3,axiom,
? [U] :
( sorti1(U)
& ! [V] :
( sorti1(V)
=> op1(V,V) = U ) ) ).
fof(ax4,axiom,
~ ? [U] :
( sorti2(U)
& ! [V] :
( sorti2(V)
=> op2(V,V) = U ) ) ).
fof(co1,conjecture,
( ( ! [U] :
( sorti1(U)
=> sorti2(h(U)) )
& ! [V] :
( sorti2(V)
=> sorti1(j(V)) ) )
=> ~ ( ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) )
& ! [Y0] :
( sorti2(Y0)
=> ! [Z0] :
( sorti2(Z0)
=> j(op2(Y0,Z0)) = op1(j(Y0),j(Z0)) ) )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 ) ) ) ).
fof(subgoal_0,plain,
( ( ! [U] :
( sorti1(U)
=> sorti2(h(U)) )
& ! [V] :
( sorti2(V)
=> sorti1(j(V)) )
& ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) )
& ! [Y0] :
( sorti2(Y0)
=> ! [Z0] :
( sorti2(Z0)
=> j(op2(Y0,Z0)) = op1(j(Y0),j(Z0)) ) )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 ) )
=> ~ ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 ) ),
inference(strip,[],[co1]) ).
fof(negate_0_0,plain,
~ ( ( ! [U] :
( sorti1(U)
=> sorti2(h(U)) )
& ! [V] :
( sorti2(V)
=> sorti1(j(V)) )
& ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) )
& ! [Y0] :
( sorti2(Y0)
=> ! [Z0] :
( sorti2(Z0)
=> j(op2(Y0,Z0)) = op1(j(Y0),j(Z0)) ) )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 ) )
=> ~ ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [U] :
( ~ sorti2(U)
| ? [V] :
( op2(V,V) != U
& sorti2(V) ) ),
inference(canonicalize,[],[ax4]) ).
fof(normalize_0_1,plain,
! [U] :
( ~ sorti2(U)
| ? [V] :
( op2(V,V) != U
& sorti2(V) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [U] :
( ( op2(skolemFOFtoCNF_V(U),skolemFOFtoCNF_V(U)) != U
| ~ sorti2(U) )
& ( ~ sorti2(U)
| sorti2(skolemFOFtoCNF_V(U)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [U] :
( op2(skolemFOFtoCNF_V(U),skolemFOFtoCNF_V(U)) != U
| ~ sorti2(U) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [U] :
( sorti1(U)
& ! [V] :
( ~ sorti1(V)
| op1(V,V) = U ) ),
inference(canonicalize,[],[ax3]) ).
fof(normalize_0_5,plain,
( sorti1(skolemFOFtoCNF_U)
& ! [V] :
( ~ sorti1(V)
| op1(V,V) = skolemFOFtoCNF_U ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
sorti1(skolemFOFtoCNF_U),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ! [U] :
( ~ sorti1(U)
| sorti2(h(U)) )
& ! [V] :
( ~ sorti2(V)
| sorti1(j(V)) )
& ! [W] :
( ~ sorti1(W)
| ! [X] :
( ~ sorti1(X)
| h(op1(W,X)) = op2(h(W),h(X)) ) )
& ! [X1] :
( ~ sorti2(X1)
| h(j(X1)) = X1 )
& ! [X2] :
( ~ sorti1(X2)
| j(h(X2)) = X2 )
& ! [Y0] :
( ~ sorti2(Y0)
| ! [Z0] :
( ~ sorti2(Z0)
| j(op2(Y0,Z0)) = op1(j(Y0),j(Z0)) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
! [U] :
( ~ sorti1(U)
| sorti2(h(U)) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [U] :
( ~ sorti1(U)
| sorti2(h(U)) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [U] :
( ~ sorti2(U)
| sorti2(skolemFOFtoCNF_V(U)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_11,plain,
! [V] :
( ~ sorti2(V)
| sorti1(j(V)) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_12,plain,
! [V] :
( ~ sorti2(V)
| sorti1(j(V)) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [W] :
( ~ sorti1(W)
| ! [X] :
( ~ sorti1(X)
| h(op1(W,X)) = op2(h(W),h(X)) ) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_14,plain,
! [W] :
( ~ sorti1(W)
| ! [X] :
( ~ sorti1(X)
| h(op1(W,X)) = op2(h(W),h(X)) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [W,X] :
( ~ sorti1(W)
| ~ sorti1(X)
| h(op1(W,X)) = op2(h(W),h(X)) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [V] :
( ~ sorti1(V)
| op1(V,V) = skolemFOFtoCNF_U ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_17,plain,
! [V] :
( ~ sorti1(V)
| op1(V,V) = skolemFOFtoCNF_U ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X1] :
( ~ sorti2(X1)
| h(j(X1)) = X1 ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_19,plain,
! [X1] :
( ~ sorti2(X1)
| h(j(X1)) = X1 ),
inference(specialize,[],[normalize_0_18]) ).
cnf(refute_0_0,plain,
( op2(skolemFOFtoCNF_V(U),skolemFOFtoCNF_V(U)) != U
| ~ sorti2(U) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) != h(skolemFOFtoCNF_U)
| ~ sorti2(h(skolemFOFtoCNF_U)) ),
inference(subst,[],[refute_0_0:[bind(U,$fot(h(skolemFOFtoCNF_U)))]]) ).
cnf(refute_0_2,plain,
sorti1(skolemFOFtoCNF_U),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ sorti1(U)
| sorti2(h(U)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( ~ sorti1(skolemFOFtoCNF_U)
| sorti2(h(skolemFOFtoCNF_U)) ),
inference(subst,[],[refute_0_3:[bind(U,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_5,plain,
sorti2(h(skolemFOFtoCNF_U)),
inference(resolve,[$cnf( sorti1(skolemFOFtoCNF_U) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ sorti2(U)
| sorti2(skolemFOFtoCNF_V(U)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ sorti2(h(skolemFOFtoCNF_U))
| sorti2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) ),
inference(subst,[],[refute_0_6:[bind(U,$fot(h(skolemFOFtoCNF_U)))]]) ).
cnf(refute_0_8,plain,
sorti2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),
inference(resolve,[$cnf( sorti2(h(skolemFOFtoCNF_U)) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ sorti2(V)
| sorti1(j(V)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ sorti2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))
| sorti1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) ),
inference(subst,[],[refute_0_9:[bind(V,$fot(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))]]) ).
cnf(refute_0_11,plain,
sorti1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),
inference(resolve,[$cnf( sorti2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ sorti1(W)
| ~ sorti1(X)
| h(op1(W,X)) = op2(h(W),h(X)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_13,plain,
( ~ sorti1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))
| h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) ),
inference(subst,[],[refute_0_12:[bind(W,$fot(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),bind(X,$fot(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))]]) ).
cnf(refute_0_14,plain,
h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),
inference(resolve,[$cnf( sorti1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ sorti1(V)
| op1(V,V) = skolemFOFtoCNF_U ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_16,plain,
( ~ sorti1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))
| op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_U ),
inference(subst,[],[refute_0_15:[bind(V,$fot(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))]]) ).
cnf(refute_0_17,plain,
op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_U,
inference(resolve,[$cnf( sorti1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) )],[refute_0_11,refute_0_16]) ).
cnf(refute_0_18,plain,
h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),
introduced(tautology,[refl,[$fot(h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))))]]) ).
cnf(refute_0_19,plain,
( h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) != h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))
| op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) != skolemFOFtoCNF_U
| h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = h(skolemFOFtoCNF_U) ),
introduced(tautology,[equality,[$cnf( $equal(h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))) ),[1,0],$fot(skolemFOFtoCNF_U)]]) ).
cnf(refute_0_20,plain,
( op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) != skolemFOFtoCNF_U
| h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = h(skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( $equal(h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = h(skolemFOFtoCNF_U),
inference(resolve,[$cnf( $equal(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),skolemFOFtoCNF_U) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) != h(skolemFOFtoCNF_U)
| h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) != op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))
| h(skolemFOFtoCNF_U) = op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) ),
introduced(tautology,[equality,[$cnf( $equal(h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))) ),[0],$fot(h(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_23,plain,
( h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) != op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))
| h(skolemFOFtoCNF_U) = op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) ),
inference(resolve,[$cnf( $equal(h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),h(skolemFOFtoCNF_U)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ sorti2(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))
| sorti2(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) ),
inference(subst,[],[refute_0_6:[bind(U,$fot(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))]]) ).
cnf(refute_0_25,plain,
( ~ sorti1(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))
| sorti2(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) ),
inference(subst,[],[refute_0_3:[bind(U,$fot(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))]]) ).
cnf(refute_0_26,plain,
( ~ sorti2(h(j(h(j(h(skolemFOFtoCNF_U))))))
| sorti1(j(h(j(h(j(h(skolemFOFtoCNF_U))))))) ),
inference(subst,[],[refute_0_9:[bind(V,$fot(h(j(h(j(h(skolemFOFtoCNF_U)))))))]]) ).
cnf(refute_0_27,plain,
( ~ sorti1(j(h(j(h(skolemFOFtoCNF_U)))))
| sorti2(h(j(h(j(h(skolemFOFtoCNF_U)))))) ),
inference(subst,[],[refute_0_3:[bind(U,$fot(j(h(j(h(skolemFOFtoCNF_U))))))]]) ).
cnf(refute_0_28,plain,
( ~ sorti2(h(j(h(skolemFOFtoCNF_U))))
| sorti1(j(h(j(h(skolemFOFtoCNF_U))))) ),
inference(subst,[],[refute_0_9:[bind(V,$fot(h(j(h(skolemFOFtoCNF_U)))))]]) ).
cnf(refute_0_29,plain,
( ~ sorti1(j(h(skolemFOFtoCNF_U)))
| sorti2(h(j(h(skolemFOFtoCNF_U)))) ),
inference(subst,[],[refute_0_3:[bind(U,$fot(j(h(skolemFOFtoCNF_U))))]]) ).
cnf(refute_0_30,plain,
( ~ sorti2(h(skolemFOFtoCNF_U))
| sorti1(j(h(skolemFOFtoCNF_U))) ),
inference(subst,[],[refute_0_9:[bind(V,$fot(h(skolemFOFtoCNF_U)))]]) ).
cnf(refute_0_31,plain,
sorti1(j(h(skolemFOFtoCNF_U))),
inference(resolve,[$cnf( sorti2(h(skolemFOFtoCNF_U)) )],[refute_0_5,refute_0_30]) ).
cnf(refute_0_32,plain,
sorti2(h(j(h(skolemFOFtoCNF_U)))),
inference(resolve,[$cnf( sorti1(j(h(skolemFOFtoCNF_U))) )],[refute_0_31,refute_0_29]) ).
cnf(refute_0_33,plain,
sorti1(j(h(j(h(skolemFOFtoCNF_U))))),
inference(resolve,[$cnf( sorti2(h(j(h(skolemFOFtoCNF_U)))) )],[refute_0_32,refute_0_28]) ).
cnf(refute_0_34,plain,
sorti2(h(j(h(j(h(skolemFOFtoCNF_U)))))),
inference(resolve,[$cnf( sorti1(j(h(j(h(skolemFOFtoCNF_U))))) )],[refute_0_33,refute_0_27]) ).
cnf(refute_0_35,plain,
sorti1(j(h(j(h(j(h(skolemFOFtoCNF_U))))))),
inference(resolve,[$cnf( sorti2(h(j(h(j(h(skolemFOFtoCNF_U)))))) )],[refute_0_34,refute_0_26]) ).
cnf(refute_0_36,plain,
sorti2(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))),
inference(resolve,[$cnf( sorti1(j(h(j(h(j(h(skolemFOFtoCNF_U))))))) )],[refute_0_35,refute_0_25]) ).
cnf(refute_0_37,plain,
sorti2(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))),
inference(resolve,[$cnf( sorti2(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) )],[refute_0_36,refute_0_24]) ).
cnf(refute_0_38,plain,
( ~ sorti2(X1)
| h(j(X1)) = X1 ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_39,plain,
( ~ sorti2(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))
| h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) = skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) ),
inference(subst,[],[refute_0_38:[bind(X1,$fot(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))))]]) ).
cnf(refute_0_40,plain,
h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) = skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))),
inference(resolve,[$cnf( sorti2(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) )],[refute_0_37,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ sorti2(h(skolemFOFtoCNF_U))
| h(j(h(skolemFOFtoCNF_U))) = h(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_38:[bind(X1,$fot(h(skolemFOFtoCNF_U)))]]) ).
cnf(refute_0_42,plain,
h(j(h(skolemFOFtoCNF_U))) = h(skolemFOFtoCNF_U),
inference(resolve,[$cnf( sorti2(h(skolemFOFtoCNF_U)) )],[refute_0_5,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ sorti2(h(j(h(skolemFOFtoCNF_U))))
| h(j(h(j(h(skolemFOFtoCNF_U))))) = h(j(h(skolemFOFtoCNF_U))) ),
inference(subst,[],[refute_0_38:[bind(X1,$fot(h(j(h(skolemFOFtoCNF_U)))))]]) ).
cnf(refute_0_44,plain,
h(j(h(j(h(skolemFOFtoCNF_U))))) = h(j(h(skolemFOFtoCNF_U))),
inference(resolve,[$cnf( sorti2(h(j(h(skolemFOFtoCNF_U)))) )],[refute_0_32,refute_0_43]) ).
cnf(refute_0_45,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_46,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_47,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( Y != X0
| Y != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_49,plain,
( X0 != Y
| Y != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( h(j(h(j(h(skolemFOFtoCNF_U))))) != h(j(h(skolemFOFtoCNF_U)))
| h(j(h(skolemFOFtoCNF_U))) != h(skolemFOFtoCNF_U)
| h(j(h(j(h(skolemFOFtoCNF_U))))) = h(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_49:[bind(X0,$fot(h(j(h(j(h(skolemFOFtoCNF_U))))))),bind(Y,$fot(h(j(h(skolemFOFtoCNF_U))))),bind(Z,$fot(h(skolemFOFtoCNF_U)))]]) ).
cnf(refute_0_51,plain,
( h(j(h(skolemFOFtoCNF_U))) != h(skolemFOFtoCNF_U)
| h(j(h(j(h(skolemFOFtoCNF_U))))) = h(skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( $equal(h(j(h(j(h(skolemFOFtoCNF_U))))),h(j(h(skolemFOFtoCNF_U)))) )],[refute_0_44,refute_0_50]) ).
cnf(refute_0_52,plain,
h(j(h(j(h(skolemFOFtoCNF_U))))) = h(skolemFOFtoCNF_U),
inference(resolve,[$cnf( $equal(h(j(h(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_U)) )],[refute_0_42,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ sorti2(h(j(h(j(h(skolemFOFtoCNF_U))))))
| h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))) = h(j(h(j(h(skolemFOFtoCNF_U))))) ),
inference(subst,[],[refute_0_38:[bind(X1,$fot(h(j(h(j(h(skolemFOFtoCNF_U)))))))]]) ).
cnf(refute_0_54,plain,
h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))) = h(j(h(j(h(skolemFOFtoCNF_U))))),
inference(resolve,[$cnf( sorti2(h(j(h(j(h(skolemFOFtoCNF_U)))))) )],[refute_0_34,refute_0_53]) ).
cnf(refute_0_55,plain,
( h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))) != h(j(h(j(h(skolemFOFtoCNF_U)))))
| h(j(h(j(h(skolemFOFtoCNF_U))))) != h(skolemFOFtoCNF_U)
| h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))) = h(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_49:[bind(X0,$fot(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))),bind(Y,$fot(h(j(h(j(h(skolemFOFtoCNF_U))))))),bind(Z,$fot(h(skolemFOFtoCNF_U)))]]) ).
cnf(refute_0_56,plain,
( h(j(h(j(h(skolemFOFtoCNF_U))))) != h(skolemFOFtoCNF_U)
| h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))) = h(skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( $equal(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))),h(j(h(j(h(skolemFOFtoCNF_U)))))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))) = h(skolemFOFtoCNF_U),
inference(resolve,[$cnf( $equal(h(j(h(j(h(skolemFOFtoCNF_U))))),h(skolemFOFtoCNF_U)) )],[refute_0_52,refute_0_56]) ).
cnf(refute_0_58,plain,
skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) = skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))]]) ).
cnf(refute_0_59,plain,
( h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))) != h(skolemFOFtoCNF_U)
| skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) != skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))
| skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) = skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))),skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) ),[1,0],$fot(h(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_60,plain,
( h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))) != h(skolemFOFtoCNF_U)
| skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) = skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))),skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) = skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),
inference(resolve,[$cnf( $equal(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))),h(skolemFOFtoCNF_U)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) = j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))),
introduced(tautology,[refl,[$fot(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))))]]) ).
cnf(refute_0_63,plain,
( j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) != j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))
| skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) != skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))
| j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) = j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) ),
introduced(tautology,[equality,[$cnf( $equal(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))),j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) ),[1,0],$fot(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))]]) ).
cnf(refute_0_64,plain,
( skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) != skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))
| j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) = j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) ),
inference(resolve,[$cnf( $equal(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))),j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) = j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) = h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))),
introduced(tautology,[refl,[$fot(h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))))]]) ).
cnf(refute_0_67,plain,
( h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) != h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))))
| j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) != j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))
| h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) = h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) ),
introduced(tautology,[equality,[$cnf( $equal(h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))),h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))))) ),[1,0],$fot(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))]]) ).
cnf(refute_0_68,plain,
( j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) != j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))
| h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) = h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) ),
inference(resolve,[$cnf( $equal(h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))),h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) = h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),
inference(resolve,[$cnf( $equal(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
( h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) != h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))
| h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) != skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))
| h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) ),
introduced(tautology,[equality,[$cnf( $equal(h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))),skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) ),[0],$fot(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))]]) ).
cnf(refute_0_71,plain,
( h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) != skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))
| h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) ),
inference(resolve,[$cnf( $equal(h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) != skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))
| skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))) != skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))
| h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) ),[0],$fot(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))]]) ).
cnf(refute_0_73,plain,
( h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) != skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))
| h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) )],[refute_0_61,refute_0_72]) ).
cnf(refute_0_74,plain,
( h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))) != skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))
| h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)) ),
inference(resolve,[$cnf( $equal(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) )],[refute_0_71,refute_0_73]) ).
cnf(refute_0_75,plain,
h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),
inference(resolve,[$cnf( $equal(h(j(skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U)))))))))),skolemFOFtoCNF_V(h(j(h(j(h(j(h(skolemFOFtoCNF_U))))))))) )],[refute_0_40,refute_0_74]) ).
cnf(refute_0_76,plain,
op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),
introduced(tautology,[refl,[$fot(op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))))]]) ).
cnf(refute_0_77,plain,
( h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) != skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))
| op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) != op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))
| op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) ),
introduced(tautology,[equality,[$cnf( $equal(op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))) ),[1,1],$fot(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))]]) ).
cnf(refute_0_78,plain,
( h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) != skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))
| op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) ),
inference(resolve,[$cnf( $equal(op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),
inference(resolve,[$cnf( $equal(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),
introduced(tautology,[refl,[$fot(op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))))]]) ).
cnf(refute_0_81,plain,
( h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) != skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))
| op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) != op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))
| op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) ),
introduced(tautology,[equality,[$cnf( $equal(op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))) ),[1,0],$fot(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))]]) ).
cnf(refute_0_82,plain,
( h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) != skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))
| op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) ),
inference(resolve,[$cnf( $equal(op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),
inference(resolve,[$cnf( $equal(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) )],[refute_0_75,refute_0_82]) ).
cnf(refute_0_84,plain,
( op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) != op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))
| op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) != op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))
| op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) ),
inference(subst,[],[refute_0_49:[bind(X0,$fot(op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))))),bind(Y,$fot(op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))))),bind(Z,$fot(op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))]]) ).
cnf(refute_0_85,plain,
( op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) != op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))
| op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) ),
inference(resolve,[$cnf( $equal(op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),
inference(resolve,[$cnf( $equal(op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) )],[refute_0_79,refute_0_85]) ).
cnf(refute_0_87,plain,
( h(skolemFOFtoCNF_U) != op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))
| op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) != op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))
| h(skolemFOFtoCNF_U) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(h(skolemFOFtoCNF_U),op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) ),[0],$fot(op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))))]]) ).
cnf(refute_0_88,plain,
( h(skolemFOFtoCNF_U) != op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))
| h(skolemFOFtoCNF_U) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) ),
inference(resolve,[$cnf( $equal(op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))) != op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))
| h(skolemFOFtoCNF_U) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) ),
inference(resolve,[$cnf( $equal(h(skolemFOFtoCNF_U),op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))) )],[refute_0_23,refute_0_88]) ).
cnf(refute_0_90,plain,
h(skolemFOFtoCNF_U) = op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),
inference(resolve,[$cnf( $equal(h(op1(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))))),op2(h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))) )],[refute_0_14,refute_0_89]) ).
cnf(refute_0_91,plain,
( h(skolemFOFtoCNF_U) != op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))
| op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) = h(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(h(skolemFOFtoCNF_U))),bind(Y,$fot(op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))))]]) ).
cnf(refute_0_92,plain,
op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) = h(skolemFOFtoCNF_U),
inference(resolve,[$cnf( $equal(h(skolemFOFtoCNF_U),op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( h(skolemFOFtoCNF_U) != h(skolemFOFtoCNF_U)
| op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) != h(skolemFOFtoCNF_U)
| op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) = h(skolemFOFtoCNF_U) ),
introduced(tautology,[equality,[$cnf( $equal(op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_U)) ),[0,0,0],$fot(h(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_94,plain,
( h(skolemFOFtoCNF_U) != h(skolemFOFtoCNF_U)
| op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))) = h(skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( $equal(op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_U)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( h(skolemFOFtoCNF_U) != h(skolemFOFtoCNF_U)
| ~ sorti2(h(skolemFOFtoCNF_U)) ),
inference(resolve,[$cnf( $equal(op2(skolemFOFtoCNF_V(h(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(h(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_U)) )],[refute_0_94,refute_0_1]) ).
cnf(refute_0_96,plain,
h(skolemFOFtoCNF_U) = h(skolemFOFtoCNF_U),
introduced(tautology,[refl,[$fot(h(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_97,plain,
~ sorti2(h(skolemFOFtoCNF_U)),
inference(resolve,[$cnf( $equal(h(skolemFOFtoCNF_U),h(skolemFOFtoCNF_U)) )],[refute_0_96,refute_0_95]) ).
cnf(refute_0_98,plain,
$false,
inference(resolve,[$cnf( sorti2(h(skolemFOFtoCNF_U)) )],[refute_0_5,refute_0_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG040+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 8 01:44:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.39/0.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.57
% 0.39/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.39/0.59
%------------------------------------------------------------------------------