%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWX207+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n002.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 : 300s
% DateTime : Tue May 5 07:04:34 PM UTC 2026
% Result : Theorem 0.22s 0.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 45
% Syntax : Number of formulae : 177 ( 99 unt; 0 def)
% Number of atoms : 286 ( 285 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 225 ( 116 ~; 106 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 150 ( 3 sgn 34 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_008,axiom,
! [X] : aP(X) != pA ).
fof(axiom_017,axiom,
! [X,X2] : proj1C(c2(X,X2)) = X ).
fof(axiom_019,axiom,
! [Y] : append(nil,Y) = Y ).
fof(axiom_020,axiom,
! [Y,Z,Xs] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)) ).
fof(axiom_021,axiom,
! [P] : linP(aP(P)) = append(cons(a,nil),append(linP(P),cons(a,nil))) ).
fof(axiom_023,axiom,
linP(pA) = cons(a,nil) ).
fof(axiom_025,axiom,
linP(pE) = nil ).
fof(axiom_026,axiom,
! [P,Q] : linC(c2(P,Q)) = append(linP(P),linP(Q)) ).
fof(goal_027,conjecture,
? [U,V] :
~ ( linC(U) = linC(V)
=> U = V ) ).
fof(subgoal_0,plain,
? [U,V] :
~ ( linC(U) = linC(V)
=> U = V ),
inference(strip,[],[goal_027]) ).
fof(negate_0_0,plain,
~ ? [U,V] :
~ ( linC(U) = linC(V)
=> U = V ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,X2] : proj1C(c2(X,X2)) = X,
inference(canonicalize,[],[axiom_017]) ).
fof(normalize_0_1,plain,
! [X,X2] : proj1C(c2(X,X2)) = X,
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [U,V] :
( linC(U) != linC(V)
| U = V ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
! [U,V] :
( linC(U) != linC(V)
| U = V ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [P,Q] : linC(c2(P,Q)) = append(linP(P),linP(Q)),
inference(canonicalize,[],[axiom_026]) ).
fof(normalize_0_5,plain,
! [P,Q] : linC(c2(P,Q)) = append(linP(P),linP(Q)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Xs,Y,Z] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
inference(canonicalize,[],[axiom_020]) ).
fof(normalize_0_7,plain,
! [Xs,Y,Z] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [P] : linP(aP(P)) = append(cons(a,nil),append(linP(P),cons(a,nil))),
inference(canonicalize,[],[axiom_021]) ).
fof(normalize_0_9,plain,
! [P] : linP(aP(P)) = append(cons(a,nil),append(linP(P),cons(a,nil))),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [Y] : append(nil,Y) = Y,
inference(canonicalize,[],[axiom_019]) ).
fof(normalize_0_11,plain,
! [Y] : append(nil,Y) = Y,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
linP(pA) = cons(a,nil),
inference(canonicalize,[],[axiom_023]) ).
fof(normalize_0_13,plain,
linP(pE) = nil,
inference(canonicalize,[],[axiom_025]) ).
fof(normalize_0_14,plain,
! [X] : aP(X) != pA,
inference(canonicalize,[],[axiom_008]) ).
fof(normalize_0_15,plain,
! [X] : aP(X) != pA,
inference(specialize,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
proj1C(c2(X,X2)) = X,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
proj1C(c2(aP(pE),aP(pA))) = aP(pE),
inference(subst,[],[refute_0_0:[bind(X,$fot(aP(pE))),bind(X2,$fot(aP(pA)))]]) ).
cnf(refute_0_2,plain,
( linC(U) != linC(V)
| U = V ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( linC(U) != linC(c2(aP(pE),aP(pA)))
| U = c2(aP(pE),aP(pA)) ),
inference(subst,[],[refute_0_2:[bind(V,$fot(c2(aP(pE),aP(pA))))]]) ).
cnf(refute_0_4,plain,
linC(c2(P,Q)) = append(linP(P),linP(Q)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
linC(c2(aP(pE),Q)) = append(linP(aP(pE)),linP(Q)),
inference(subst,[],[refute_0_4:[bind(P,$fot(aP(pE)))]]) ).
cnf(refute_0_6,plain,
append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
append(cons(a,linP(pA)),X_36) = cons(a,append(linP(pA),X_36)),
inference(subst,[],[refute_0_6:[bind(Xs,$fot(linP(pA))),bind(Y,$fot(X_36)),bind(Z,$fot(a))]]) ).
cnf(refute_0_8,plain,
linP(aP(P)) = append(cons(a,nil),append(linP(P),cons(a,nil))),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
append(nil,Y) = Y,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
append(nil,append(linP(P),cons(a,nil))) = append(linP(P),cons(a,nil)),
inference(subst,[],[refute_0_9:[bind(Y,$fot(append(linP(P),cons(a,nil))))]]) ).
cnf(refute_0_11,plain,
cons(a,append(nil,append(linP(P),cons(a,nil)))) = cons(a,append(nil,append(linP(P),cons(a,nil)))),
introduced(tautology,[refl,[$fot(cons(a,append(nil,append(linP(P),cons(a,nil)))))]]) ).
cnf(refute_0_12,plain,
( cons(a,append(nil,append(linP(P),cons(a,nil)))) != cons(a,append(nil,append(linP(P),cons(a,nil))))
| append(nil,append(linP(P),cons(a,nil))) != append(linP(P),cons(a,nil))
| cons(a,append(nil,append(linP(P),cons(a,nil)))) = cons(a,append(linP(P),cons(a,nil))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(a,append(nil,append(linP(P),cons(a,nil)))),cons(a,append(nil,append(linP(P),cons(a,nil))))) ),[1,1],$fot(append(linP(P),cons(a,nil)))]]) ).
cnf(refute_0_13,plain,
( append(nil,append(linP(P),cons(a,nil))) != append(linP(P),cons(a,nil))
| cons(a,append(nil,append(linP(P),cons(a,nil)))) = cons(a,append(linP(P),cons(a,nil))) ),
inference(resolve,[$cnf( $equal(cons(a,append(nil,append(linP(P),cons(a,nil)))),cons(a,append(nil,append(linP(P),cons(a,nil))))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
cons(a,append(nil,append(linP(P),cons(a,nil)))) = cons(a,append(linP(P),cons(a,nil))),
inference(resolve,[$cnf( $equal(append(nil,append(linP(P),cons(a,nil))),append(linP(P),cons(a,nil))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
append(cons(a,nil),append(linP(P),cons(a,nil))) = cons(a,append(nil,append(linP(P),cons(a,nil)))),
inference(subst,[],[refute_0_6:[bind(Xs,$fot(nil)),bind(Y,$fot(append(linP(P),cons(a,nil)))),bind(Z,$fot(a))]]) ).
cnf(refute_0_16,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_17,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_18,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_20,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( cons(a,append(nil,append(linP(P),cons(a,nil)))) != cons(a,append(linP(P),cons(a,nil)))
| append(cons(a,nil),append(linP(P),cons(a,nil))) != cons(a,append(nil,append(linP(P),cons(a,nil))))
| append(cons(a,nil),append(linP(P),cons(a,nil))) = cons(a,append(linP(P),cons(a,nil))) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(append(cons(a,nil),append(linP(P),cons(a,nil))))),bind(Y0,$fot(cons(a,append(nil,append(linP(P),cons(a,nil)))))),bind(Z0,$fot(cons(a,append(linP(P),cons(a,nil)))))]]) ).
cnf(refute_0_22,plain,
( cons(a,append(nil,append(linP(P),cons(a,nil)))) != cons(a,append(linP(P),cons(a,nil)))
| append(cons(a,nil),append(linP(P),cons(a,nil))) = cons(a,append(linP(P),cons(a,nil))) ),
inference(resolve,[$cnf( $equal(append(cons(a,nil),append(linP(P),cons(a,nil))),cons(a,append(nil,append(linP(P),cons(a,nil))))) )],[refute_0_15,refute_0_21]) ).
cnf(refute_0_23,plain,
append(cons(a,nil),append(linP(P),cons(a,nil))) = cons(a,append(linP(P),cons(a,nil))),
inference(resolve,[$cnf( $equal(cons(a,append(nil,append(linP(P),cons(a,nil)))),cons(a,append(linP(P),cons(a,nil)))) )],[refute_0_14,refute_0_22]) ).
cnf(refute_0_24,plain,
( append(cons(a,nil),append(linP(P),cons(a,nil))) != cons(a,append(linP(P),cons(a,nil)))
| linP(aP(P)) != append(cons(a,nil),append(linP(P),cons(a,nil)))
| linP(aP(P)) = cons(a,append(linP(P),cons(a,nil))) ),
introduced(tautology,[equality,[$cnf( $equal(linP(aP(P)),append(cons(a,nil),append(linP(P),cons(a,nil)))) ),[1],$fot(cons(a,append(linP(P),cons(a,nil))))]]) ).
cnf(refute_0_25,plain,
( linP(aP(P)) != append(cons(a,nil),append(linP(P),cons(a,nil)))
| linP(aP(P)) = cons(a,append(linP(P),cons(a,nil))) ),
inference(resolve,[$cnf( $equal(append(cons(a,nil),append(linP(P),cons(a,nil))),cons(a,append(linP(P),cons(a,nil)))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
linP(aP(P)) = cons(a,append(linP(P),cons(a,nil))),
inference(resolve,[$cnf( $equal(linP(aP(P)),append(cons(a,nil),append(linP(P),cons(a,nil)))) )],[refute_0_8,refute_0_25]) ).
cnf(refute_0_27,plain,
( linC(c2(P,Q)) != append(linP(P),linP(Q))
| append(linP(P),linP(Q)) = linC(c2(P,Q)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(linC(c2(P,Q)))),bind(Y0,$fot(append(linP(P),linP(Q))))]]) ).
cnf(refute_0_28,plain,
append(linP(P),linP(Q)) = linC(c2(P,Q)),
inference(resolve,[$cnf( $equal(linC(c2(P,Q)),append(linP(P),linP(Q))) )],[refute_0_4,refute_0_27]) ).
cnf(refute_0_29,plain,
append(linP(P),linP(pA)) = linC(c2(P,pA)),
inference(subst,[],[refute_0_28:[bind(Q,$fot(pA))]]) ).
cnf(refute_0_30,plain,
linP(pA) = cons(a,nil),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_31,plain,
( linP(pA) != cons(a,nil)
| cons(a,nil) = linP(pA) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(linP(pA))),bind(Y0,$fot(cons(a,nil)))]]) ).
cnf(refute_0_32,plain,
cons(a,nil) = linP(pA),
inference(resolve,[$cnf( $equal(linP(pA),cons(a,nil)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
append(linP(P),cons(a,nil)) = append(linP(P),cons(a,nil)),
introduced(tautology,[refl,[$fot(append(linP(P),cons(a,nil)))]]) ).
cnf(refute_0_34,plain,
( cons(a,nil) != linP(pA)
| append(linP(P),cons(a,nil)) != append(linP(P),cons(a,nil))
| append(linP(P),cons(a,nil)) = append(linP(P),linP(pA)) ),
introduced(tautology,[equality,[$cnf( $equal(append(linP(P),cons(a,nil)),append(linP(P),cons(a,nil))) ),[1,1],$fot(linP(pA))]]) ).
cnf(refute_0_35,plain,
( cons(a,nil) != linP(pA)
| append(linP(P),cons(a,nil)) = append(linP(P),linP(pA)) ),
inference(resolve,[$cnf( $equal(append(linP(P),cons(a,nil)),append(linP(P),cons(a,nil))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
append(linP(P),cons(a,nil)) = append(linP(P),linP(pA)),
inference(resolve,[$cnf( $equal(cons(a,nil),linP(pA)) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
( append(linP(P),cons(a,nil)) != append(linP(P),linP(pA))
| append(linP(P),linP(pA)) != linC(c2(P,pA))
| append(linP(P),cons(a,nil)) = linC(c2(P,pA)) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(append(linP(P),cons(a,nil)))),bind(Y0,$fot(append(linP(P),linP(pA)))),bind(Z0,$fot(linC(c2(P,pA))))]]) ).
cnf(refute_0_38,plain,
( append(linP(P),linP(pA)) != linC(c2(P,pA))
| append(linP(P),cons(a,nil)) = linC(c2(P,pA)) ),
inference(resolve,[$cnf( $equal(append(linP(P),cons(a,nil)),append(linP(P),linP(pA))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
append(linP(P),cons(a,nil)) = linC(c2(P,pA)),
inference(resolve,[$cnf( $equal(append(linP(P),linP(pA)),linC(c2(P,pA))) )],[refute_0_29,refute_0_38]) ).
cnf(refute_0_40,plain,
cons(a,append(linP(P),cons(a,nil))) = cons(a,append(linP(P),cons(a,nil))),
introduced(tautology,[refl,[$fot(cons(a,append(linP(P),cons(a,nil))))]]) ).
cnf(refute_0_41,plain,
( cons(a,append(linP(P),cons(a,nil))) != cons(a,append(linP(P),cons(a,nil)))
| append(linP(P),cons(a,nil)) != linC(c2(P,pA))
| cons(a,append(linP(P),cons(a,nil))) = cons(a,linC(c2(P,pA))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(a,append(linP(P),cons(a,nil))),cons(a,append(linP(P),cons(a,nil)))) ),[1,1],$fot(linC(c2(P,pA)))]]) ).
cnf(refute_0_42,plain,
( append(linP(P),cons(a,nil)) != linC(c2(P,pA))
| cons(a,append(linP(P),cons(a,nil))) = cons(a,linC(c2(P,pA))) ),
inference(resolve,[$cnf( $equal(cons(a,append(linP(P),cons(a,nil))),cons(a,append(linP(P),cons(a,nil)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
cons(a,append(linP(P),cons(a,nil))) = cons(a,linC(c2(P,pA))),
inference(resolve,[$cnf( $equal(append(linP(P),cons(a,nil)),linC(c2(P,pA))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
( cons(a,append(linP(P),cons(a,nil))) != cons(a,linC(c2(P,pA)))
| linP(aP(P)) != cons(a,append(linP(P),cons(a,nil)))
| linP(aP(P)) = cons(a,linC(c2(P,pA))) ),
introduced(tautology,[equality,[$cnf( $equal(linP(aP(P)),cons(a,append(linP(P),cons(a,nil)))) ),[1],$fot(cons(a,linC(c2(P,pA))))]]) ).
cnf(refute_0_45,plain,
( linP(aP(P)) != cons(a,append(linP(P),cons(a,nil)))
| linP(aP(P)) = cons(a,linC(c2(P,pA))) ),
inference(resolve,[$cnf( $equal(cons(a,append(linP(P),cons(a,nil))),cons(a,linC(c2(P,pA)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
linP(aP(P)) = cons(a,linC(c2(P,pA))),
inference(resolve,[$cnf( $equal(linP(aP(P)),cons(a,append(linP(P),cons(a,nil)))) )],[refute_0_26,refute_0_45]) ).
cnf(refute_0_47,plain,
linP(aP(pE)) = cons(a,linC(c2(pE,pA))),
inference(subst,[],[refute_0_46:[bind(P,$fot(pE))]]) ).
cnf(refute_0_48,plain,
linC(c2(pE,X_30)) = append(linP(pE),linP(X_30)),
inference(subst,[],[refute_0_4:[bind(P,$fot(pE)),bind(Q,$fot(X_30))]]) ).
cnf(refute_0_49,plain,
linP(pE) = nil,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_50,plain,
( linC(c2(pE,X_30)) != append(linP(pE),linP(X_30))
| linP(pE) != nil
| linC(c2(pE,X_30)) = append(nil,linP(X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(linC(c2(pE,X_30)),append(linP(pE),linP(X_30))) ),[1,0],$fot(nil)]]) ).
cnf(refute_0_51,plain,
( linC(c2(pE,X_30)) != append(linP(pE),linP(X_30))
| linC(c2(pE,X_30)) = append(nil,linP(X_30)) ),
inference(resolve,[$cnf( $equal(linP(pE),nil) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
linC(c2(pE,X_30)) = append(nil,linP(X_30)),
inference(resolve,[$cnf( $equal(linC(c2(pE,X_30)),append(linP(pE),linP(X_30))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
append(nil,linP(X_30)) = linP(X_30),
inference(subst,[],[refute_0_9:[bind(Y,$fot(linP(X_30)))]]) ).
cnf(refute_0_54,plain,
( append(nil,linP(X_30)) != linP(X_30)
| linC(c2(pE,X_30)) != append(nil,linP(X_30))
| linC(c2(pE,X_30)) = linP(X_30) ),
introduced(tautology,[equality,[$cnf( $equal(linC(c2(pE,X_30)),append(nil,linP(X_30))) ),[1],$fot(linP(X_30))]]) ).
cnf(refute_0_55,plain,
( linC(c2(pE,X_30)) != append(nil,linP(X_30))
| linC(c2(pE,X_30)) = linP(X_30) ),
inference(resolve,[$cnf( $equal(append(nil,linP(X_30)),linP(X_30)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
linC(c2(pE,X_30)) = linP(X_30),
inference(resolve,[$cnf( $equal(linC(c2(pE,X_30)),append(nil,linP(X_30))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
linC(c2(pE,pA)) = linP(pA),
inference(subst,[],[refute_0_56:[bind(X_30,$fot(pA))]]) ).
cnf(refute_0_58,plain,
( linC(c2(pE,pA)) != linP(pA)
| linP(aP(pE)) != cons(a,linC(c2(pE,pA)))
| linP(aP(pE)) = cons(a,linP(pA)) ),
introduced(tautology,[equality,[$cnf( $equal(linP(aP(pE)),cons(a,linC(c2(pE,pA)))) ),[1,1],$fot(linP(pA))]]) ).
cnf(refute_0_59,plain,
( linP(aP(pE)) != cons(a,linC(c2(pE,pA)))
| linP(aP(pE)) = cons(a,linP(pA)) ),
inference(resolve,[$cnf( $equal(linC(c2(pE,pA)),linP(pA)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
linP(aP(pE)) = cons(a,linP(pA)),
inference(resolve,[$cnf( $equal(linP(aP(pE)),cons(a,linC(c2(pE,pA)))) )],[refute_0_47,refute_0_59]) ).
cnf(refute_0_61,plain,
( linP(aP(pE)) != cons(a,linP(pA))
| cons(a,linP(pA)) = linP(aP(pE)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(linP(aP(pE)))),bind(Y0,$fot(cons(a,linP(pA))))]]) ).
cnf(refute_0_62,plain,
cons(a,linP(pA)) = linP(aP(pE)),
inference(resolve,[$cnf( $equal(linP(aP(pE)),cons(a,linP(pA))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( cons(a,linP(pA)) != linP(aP(pE))
| append(cons(a,linP(pA)),X_36) != cons(a,append(linP(pA),X_36))
| append(linP(aP(pE)),X_36) = cons(a,append(linP(pA),X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(append(cons(a,linP(pA)),X_36),cons(a,append(linP(pA),X_36))) ),[0,0],$fot(linP(aP(pE)))]]) ).
cnf(refute_0_64,plain,
( append(cons(a,linP(pA)),X_36) != cons(a,append(linP(pA),X_36))
| append(linP(aP(pE)),X_36) = cons(a,append(linP(pA),X_36)) ),
inference(resolve,[$cnf( $equal(cons(a,linP(pA)),linP(aP(pE))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
append(linP(aP(pE)),X_36) = cons(a,append(linP(pA),X_36)),
inference(resolve,[$cnf( $equal(append(cons(a,linP(pA)),X_36),cons(a,append(linP(pA),X_36))) )],[refute_0_7,refute_0_64]) ).
cnf(refute_0_66,plain,
append(cons(a,nil),X_36) = cons(a,append(nil,X_36)),
inference(subst,[],[refute_0_6:[bind(Xs,$fot(nil)),bind(Y,$fot(X_36)),bind(Z,$fot(a))]]) ).
cnf(refute_0_67,plain,
( cons(a,nil) != linP(pA)
| append(cons(a,nil),X_36) != cons(a,append(nil,X_36))
| append(linP(pA),X_36) = cons(a,append(nil,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(append(cons(a,nil),X_36),cons(a,append(nil,X_36))) ),[0,0],$fot(linP(pA))]]) ).
cnf(refute_0_68,plain,
( append(cons(a,nil),X_36) != cons(a,append(nil,X_36))
| append(linP(pA),X_36) = cons(a,append(nil,X_36)) ),
inference(resolve,[$cnf( $equal(cons(a,nil),linP(pA)) )],[refute_0_32,refute_0_67]) ).
cnf(refute_0_69,plain,
append(linP(pA),X_36) = cons(a,append(nil,X_36)),
inference(resolve,[$cnf( $equal(append(cons(a,nil),X_36),cons(a,append(nil,X_36))) )],[refute_0_66,refute_0_68]) ).
cnf(refute_0_70,plain,
append(nil,X_36) = X_36,
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_36))]]) ).
cnf(refute_0_71,plain,
cons(a,append(nil,X_36)) = cons(a,append(nil,X_36)),
introduced(tautology,[refl,[$fot(cons(a,append(nil,X_36)))]]) ).
cnf(refute_0_72,plain,
( cons(a,append(nil,X_36)) != cons(a,append(nil,X_36))
| append(nil,X_36) != X_36
| cons(a,append(nil,X_36)) = cons(a,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(cons(a,append(nil,X_36)),cons(a,append(nil,X_36))) ),[1,1],$fot(X_36)]]) ).
cnf(refute_0_73,plain,
( append(nil,X_36) != X_36
| cons(a,append(nil,X_36)) = cons(a,X_36) ),
inference(resolve,[$cnf( $equal(cons(a,append(nil,X_36)),cons(a,append(nil,X_36))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
cons(a,append(nil,X_36)) = cons(a,X_36),
inference(resolve,[$cnf( $equal(append(nil,X_36),X_36) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
( cons(a,append(nil,X_36)) != cons(a,X_36)
| append(linP(pA),X_36) != cons(a,append(nil,X_36))
| append(linP(pA),X_36) = cons(a,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(append(linP(pA),X_36),cons(a,append(nil,X_36))) ),[1],$fot(cons(a,X_36))]]) ).
cnf(refute_0_76,plain,
( append(linP(pA),X_36) != cons(a,append(nil,X_36))
| append(linP(pA),X_36) = cons(a,X_36) ),
inference(resolve,[$cnf( $equal(cons(a,append(nil,X_36)),cons(a,X_36)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
append(linP(pA),X_36) = cons(a,X_36),
inference(resolve,[$cnf( $equal(append(linP(pA),X_36),cons(a,append(nil,X_36))) )],[refute_0_69,refute_0_76]) ).
cnf(refute_0_78,plain,
cons(a,append(linP(pA),X_36)) = cons(a,append(linP(pA),X_36)),
introduced(tautology,[refl,[$fot(cons(a,append(linP(pA),X_36)))]]) ).
cnf(refute_0_79,plain,
( cons(a,append(linP(pA),X_36)) != cons(a,append(linP(pA),X_36))
| append(linP(pA),X_36) != cons(a,X_36)
| cons(a,append(linP(pA),X_36)) = cons(a,cons(a,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(cons(a,append(linP(pA),X_36)),cons(a,append(linP(pA),X_36))) ),[1,1],$fot(cons(a,X_36))]]) ).
cnf(refute_0_80,plain,
( append(linP(pA),X_36) != cons(a,X_36)
| cons(a,append(linP(pA),X_36)) = cons(a,cons(a,X_36)) ),
inference(resolve,[$cnf( $equal(cons(a,append(linP(pA),X_36)),cons(a,append(linP(pA),X_36))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
cons(a,append(linP(pA),X_36)) = cons(a,cons(a,X_36)),
inference(resolve,[$cnf( $equal(append(linP(pA),X_36),cons(a,X_36)) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
( cons(a,append(linP(pA),X_36)) != cons(a,cons(a,X_36))
| append(linP(aP(pE)),X_36) != cons(a,append(linP(pA),X_36))
| append(linP(aP(pE)),X_36) = cons(a,cons(a,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(append(linP(aP(pE)),X_36),cons(a,append(linP(pA),X_36))) ),[1],$fot(cons(a,cons(a,X_36)))]]) ).
cnf(refute_0_83,plain,
( append(linP(aP(pE)),X_36) != cons(a,append(linP(pA),X_36))
| append(linP(aP(pE)),X_36) = cons(a,cons(a,X_36)) ),
inference(resolve,[$cnf( $equal(cons(a,append(linP(pA),X_36)),cons(a,cons(a,X_36))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
append(linP(aP(pE)),X_36) = cons(a,cons(a,X_36)),
inference(resolve,[$cnf( $equal(append(linP(aP(pE)),X_36),cons(a,append(linP(pA),X_36))) )],[refute_0_65,refute_0_83]) ).
cnf(refute_0_85,plain,
append(linP(aP(pE)),linP(Q)) = cons(a,cons(a,linP(Q))),
inference(subst,[],[refute_0_84:[bind(X_36,$fot(linP(Q)))]]) ).
cnf(refute_0_86,plain,
( append(linP(aP(pE)),linP(Q)) != cons(a,cons(a,linP(Q)))
| linC(c2(aP(pE),Q)) != append(linP(aP(pE)),linP(Q))
| linC(c2(aP(pE),Q)) = cons(a,cons(a,linP(Q))) ),
introduced(tautology,[equality,[$cnf( $equal(linC(c2(aP(pE),Q)),append(linP(aP(pE)),linP(Q))) ),[1],$fot(cons(a,cons(a,linP(Q))))]]) ).
cnf(refute_0_87,plain,
( linC(c2(aP(pE),Q)) != append(linP(aP(pE)),linP(Q))
| linC(c2(aP(pE),Q)) = cons(a,cons(a,linP(Q))) ),
inference(resolve,[$cnf( $equal(append(linP(aP(pE)),linP(Q)),cons(a,cons(a,linP(Q)))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
linC(c2(aP(pE),Q)) = cons(a,cons(a,linP(Q))),
inference(resolve,[$cnf( $equal(linC(c2(aP(pE),Q)),append(linP(aP(pE)),linP(Q))) )],[refute_0_5,refute_0_87]) ).
cnf(refute_0_89,plain,
linC(c2(pA,Q)) = append(linP(pA),linP(Q)),
inference(subst,[],[refute_0_4:[bind(P,$fot(pA))]]) ).
cnf(refute_0_90,plain,
append(linP(pA),linP(Q)) = cons(a,linP(Q)),
inference(subst,[],[refute_0_77:[bind(X_36,$fot(linP(Q)))]]) ).
cnf(refute_0_91,plain,
( append(linP(pA),linP(Q)) != cons(a,linP(Q))
| linC(c2(pA,Q)) != append(linP(pA),linP(Q))
| linC(c2(pA,Q)) = cons(a,linP(Q)) ),
introduced(tautology,[equality,[$cnf( $equal(linC(c2(pA,Q)),append(linP(pA),linP(Q))) ),[1],$fot(cons(a,linP(Q)))]]) ).
cnf(refute_0_92,plain,
( linC(c2(pA,Q)) != append(linP(pA),linP(Q))
| linC(c2(pA,Q)) = cons(a,linP(Q)) ),
inference(resolve,[$cnf( $equal(append(linP(pA),linP(Q)),cons(a,linP(Q))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
linC(c2(pA,Q)) = cons(a,linP(Q)),
inference(resolve,[$cnf( $equal(linC(c2(pA,Q)),append(linP(pA),linP(Q))) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
( linC(c2(pA,Q)) != cons(a,linP(Q))
| cons(a,linP(Q)) = linC(c2(pA,Q)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(linC(c2(pA,Q)))),bind(Y0,$fot(cons(a,linP(Q))))]]) ).
cnf(refute_0_95,plain,
cons(a,linP(Q)) = linC(c2(pA,Q)),
inference(resolve,[$cnf( $equal(linC(c2(pA,Q)),cons(a,linP(Q))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
cons(a,cons(a,linP(Q))) = cons(a,cons(a,linP(Q))),
introduced(tautology,[refl,[$fot(cons(a,cons(a,linP(Q))))]]) ).
cnf(refute_0_97,plain,
( cons(a,cons(a,linP(Q))) != cons(a,cons(a,linP(Q)))
| cons(a,linP(Q)) != linC(c2(pA,Q))
| cons(a,cons(a,linP(Q))) = cons(a,linC(c2(pA,Q))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(a,cons(a,linP(Q))),cons(a,cons(a,linP(Q)))) ),[1,1],$fot(linC(c2(pA,Q)))]]) ).
cnf(refute_0_98,plain,
( cons(a,linP(Q)) != linC(c2(pA,Q))
| cons(a,cons(a,linP(Q))) = cons(a,linC(c2(pA,Q))) ),
inference(resolve,[$cnf( $equal(cons(a,cons(a,linP(Q))),cons(a,cons(a,linP(Q)))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
cons(a,cons(a,linP(Q))) = cons(a,linC(c2(pA,Q))),
inference(resolve,[$cnf( $equal(cons(a,linP(Q)),linC(c2(pA,Q))) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
( cons(a,cons(a,linP(Q))) != cons(a,linC(c2(pA,Q)))
| linC(c2(aP(pE),Q)) != cons(a,cons(a,linP(Q)))
| linC(c2(aP(pE),Q)) = cons(a,linC(c2(pA,Q))) ),
introduced(tautology,[equality,[$cnf( $equal(linC(c2(aP(pE),Q)),cons(a,cons(a,linP(Q)))) ),[1],$fot(cons(a,linC(c2(pA,Q))))]]) ).
cnf(refute_0_101,plain,
( linC(c2(aP(pE),Q)) != cons(a,cons(a,linP(Q)))
| linC(c2(aP(pE),Q)) = cons(a,linC(c2(pA,Q))) ),
inference(resolve,[$cnf( $equal(cons(a,cons(a,linP(Q))),cons(a,linC(c2(pA,Q)))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
linC(c2(aP(pE),Q)) = cons(a,linC(c2(pA,Q))),
inference(resolve,[$cnf( $equal(linC(c2(aP(pE),Q)),cons(a,cons(a,linP(Q)))) )],[refute_0_88,refute_0_101]) ).
cnf(refute_0_103,plain,
linC(c2(aP(pE),aP(pA))) = cons(a,linC(c2(pA,aP(pA)))),
inference(subst,[],[refute_0_102:[bind(Q,$fot(aP(pA)))]]) ).
cnf(refute_0_104,plain,
linP(aP(aP(pE))) = cons(a,linC(c2(aP(pE),pA))),
inference(subst,[],[refute_0_46:[bind(P,$fot(aP(pE)))]]) ).
cnf(refute_0_105,plain,
linP(aP(pA)) = cons(a,linC(c2(pA,pA))),
inference(subst,[],[refute_0_46:[bind(P,$fot(pA))]]) ).
cnf(refute_0_106,plain,
linC(c2(aP(pE),pA)) = cons(a,linC(c2(pA,pA))),
inference(subst,[],[refute_0_102:[bind(Q,$fot(pA))]]) ).
cnf(refute_0_107,plain,
( linC(c2(aP(pE),pA)) != cons(a,linC(c2(pA,pA)))
| cons(a,linC(c2(pA,pA))) = linC(c2(aP(pE),pA)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(linC(c2(aP(pE),pA)))),bind(Y0,$fot(cons(a,linC(c2(pA,pA)))))]]) ).
cnf(refute_0_108,plain,
cons(a,linC(c2(pA,pA))) = linC(c2(aP(pE),pA)),
inference(resolve,[$cnf( $equal(linC(c2(aP(pE),pA)),cons(a,linC(c2(pA,pA)))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
( cons(a,linC(c2(pA,pA))) != linC(c2(aP(pE),pA))
| linP(aP(pA)) != cons(a,linC(c2(pA,pA)))
| linP(aP(pA)) = linC(c2(aP(pE),pA)) ),
introduced(tautology,[equality,[$cnf( $equal(linP(aP(pA)),cons(a,linC(c2(pA,pA)))) ),[1],$fot(linC(c2(aP(pE),pA)))]]) ).
cnf(refute_0_110,plain,
( linP(aP(pA)) != cons(a,linC(c2(pA,pA)))
| linP(aP(pA)) = linC(c2(aP(pE),pA)) ),
inference(resolve,[$cnf( $equal(cons(a,linC(c2(pA,pA))),linC(c2(aP(pE),pA))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
linP(aP(pA)) = linC(c2(aP(pE),pA)),
inference(resolve,[$cnf( $equal(linP(aP(pA)),cons(a,linC(c2(pA,pA)))) )],[refute_0_105,refute_0_110]) ).
cnf(refute_0_112,plain,
( linP(aP(pA)) != linC(c2(aP(pE),pA))
| linC(c2(aP(pE),pA)) = linP(aP(pA)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(linP(aP(pA)))),bind(Y0,$fot(linC(c2(aP(pE),pA))))]]) ).
cnf(refute_0_113,plain,
linC(c2(aP(pE),pA)) = linP(aP(pA)),
inference(resolve,[$cnf( $equal(linP(aP(pA)),linC(c2(aP(pE),pA))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( linC(c2(aP(pE),pA)) != linP(aP(pA))
| linP(aP(aP(pE))) != cons(a,linC(c2(aP(pE),pA)))
| linP(aP(aP(pE))) = cons(a,linP(aP(pA))) ),
introduced(tautology,[equality,[$cnf( $equal(linP(aP(aP(pE))),cons(a,linC(c2(aP(pE),pA)))) ),[1,1],$fot(linP(aP(pA)))]]) ).
cnf(refute_0_115,plain,
( linP(aP(aP(pE))) != cons(a,linC(c2(aP(pE),pA)))
| linP(aP(aP(pE))) = cons(a,linP(aP(pA))) ),
inference(resolve,[$cnf( $equal(linC(c2(aP(pE),pA)),linP(aP(pA))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
linP(aP(aP(pE))) = cons(a,linP(aP(pA))),
inference(resolve,[$cnf( $equal(linP(aP(aP(pE))),cons(a,linC(c2(aP(pE),pA)))) )],[refute_0_104,refute_0_115]) ).
cnf(refute_0_117,plain,
cons(a,linP(aP(pA))) = linC(c2(pA,aP(pA))),
inference(subst,[],[refute_0_95:[bind(Q,$fot(aP(pA)))]]) ).
cnf(refute_0_118,plain,
( cons(a,linP(aP(pA))) != linC(c2(pA,aP(pA)))
| linP(aP(aP(pE))) != cons(a,linP(aP(pA)))
| linP(aP(aP(pE))) = linC(c2(pA,aP(pA))) ),
introduced(tautology,[equality,[$cnf( $equal(linP(aP(aP(pE))),cons(a,linP(aP(pA)))) ),[1],$fot(linC(c2(pA,aP(pA))))]]) ).
cnf(refute_0_119,plain,
( linP(aP(aP(pE))) != cons(a,linP(aP(pA)))
| linP(aP(aP(pE))) = linC(c2(pA,aP(pA))) ),
inference(resolve,[$cnf( $equal(cons(a,linP(aP(pA))),linC(c2(pA,aP(pA)))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
linP(aP(aP(pE))) = linC(c2(pA,aP(pA))),
inference(resolve,[$cnf( $equal(linP(aP(aP(pE))),cons(a,linP(aP(pA)))) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
( linP(aP(aP(pE))) != linC(c2(pA,aP(pA)))
| linC(c2(pA,aP(pA))) = linP(aP(aP(pE))) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(linP(aP(aP(pE))))),bind(Y0,$fot(linC(c2(pA,aP(pA)))))]]) ).
cnf(refute_0_122,plain,
linC(c2(pA,aP(pA))) = linP(aP(aP(pE))),
inference(resolve,[$cnf( $equal(linP(aP(aP(pE))),linC(c2(pA,aP(pA)))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
( linC(c2(aP(pE),aP(pA))) != cons(a,linC(c2(pA,aP(pA))))
| linC(c2(pA,aP(pA))) != linP(aP(aP(pE)))
| linC(c2(aP(pE),aP(pA))) = cons(a,linP(aP(aP(pE)))) ),
introduced(tautology,[equality,[$cnf( $equal(linC(c2(aP(pE),aP(pA))),cons(a,linC(c2(pA,aP(pA))))) ),[1,1],$fot(linP(aP(aP(pE))))]]) ).
cnf(refute_0_124,plain,
( linC(c2(aP(pE),aP(pA))) != cons(a,linC(c2(pA,aP(pA))))
| linC(c2(aP(pE),aP(pA))) = cons(a,linP(aP(aP(pE)))) ),
inference(resolve,[$cnf( $equal(linC(c2(pA,aP(pA))),linP(aP(aP(pE)))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
linC(c2(aP(pE),aP(pA))) = cons(a,linP(aP(aP(pE)))),
inference(resolve,[$cnf( $equal(linC(c2(aP(pE),aP(pA))),cons(a,linC(c2(pA,aP(pA))))) )],[refute_0_103,refute_0_124]) ).
cnf(refute_0_126,plain,
cons(a,linP(aP(aP(pE)))) = linC(c2(pA,aP(aP(pE)))),
inference(subst,[],[refute_0_95:[bind(Q,$fot(aP(aP(pE))))]]) ).
cnf(refute_0_127,plain,
( cons(a,linP(aP(aP(pE)))) != linC(c2(pA,aP(aP(pE))))
| linC(c2(aP(pE),aP(pA))) != cons(a,linP(aP(aP(pE))))
| linC(c2(aP(pE),aP(pA))) = linC(c2(pA,aP(aP(pE)))) ),
introduced(tautology,[equality,[$cnf( $equal(linC(c2(aP(pE),aP(pA))),cons(a,linP(aP(aP(pE))))) ),[1],$fot(linC(c2(pA,aP(aP(pE)))))]]) ).
cnf(refute_0_128,plain,
( linC(c2(aP(pE),aP(pA))) != cons(a,linP(aP(aP(pE))))
| linC(c2(aP(pE),aP(pA))) = linC(c2(pA,aP(aP(pE)))) ),
inference(resolve,[$cnf( $equal(cons(a,linP(aP(aP(pE)))),linC(c2(pA,aP(aP(pE))))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
linC(c2(aP(pE),aP(pA))) = linC(c2(pA,aP(aP(pE)))),
inference(resolve,[$cnf( $equal(linC(c2(aP(pE),aP(pA))),cons(a,linP(aP(aP(pE))))) )],[refute_0_125,refute_0_128]) ).
cnf(refute_0_130,plain,
( linC(U) != linC(c2(pA,aP(aP(pE))))
| linC(c2(aP(pE),aP(pA))) != linC(c2(pA,aP(aP(pE))))
| linC(U) = linC(c2(aP(pE),aP(pA))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(linC(U),linC(c2(aP(pE),aP(pA)))) ),[1],$fot(linC(c2(pA,aP(aP(pE)))))]]) ).
cnf(refute_0_131,plain,
( linC(U) != linC(c2(pA,aP(aP(pE))))
| linC(U) = linC(c2(aP(pE),aP(pA))) ),
inference(resolve,[$cnf( $equal(linC(c2(aP(pE),aP(pA))),linC(c2(pA,aP(aP(pE))))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( linC(U) != linC(c2(pA,aP(aP(pE))))
| U = c2(aP(pE),aP(pA)) ),
inference(resolve,[$cnf( $equal(linC(U),linC(c2(aP(pE),aP(pA)))) )],[refute_0_131,refute_0_3]) ).
cnf(refute_0_133,plain,
( linC(c2(pA,aP(aP(pE)))) != linC(c2(pA,aP(aP(pE))))
| c2(pA,aP(aP(pE))) = c2(aP(pE),aP(pA)) ),
inference(subst,[],[refute_0_132:[bind(U,$fot(c2(pA,aP(aP(pE)))))]]) ).
cnf(refute_0_134,plain,
linC(c2(pA,aP(aP(pE)))) = linC(c2(pA,aP(aP(pE)))),
introduced(tautology,[refl,[$fot(linC(c2(pA,aP(aP(pE)))))]]) ).
cnf(refute_0_135,plain,
c2(pA,aP(aP(pE))) = c2(aP(pE),aP(pA)),
inference(resolve,[$cnf( $equal(linC(c2(pA,aP(aP(pE)))),linC(c2(pA,aP(aP(pE))))) )],[refute_0_134,refute_0_133]) ).
cnf(refute_0_136,plain,
( c2(pA,aP(aP(pE))) != c2(aP(pE),aP(pA))
| c2(aP(pE),aP(pA)) = c2(pA,aP(aP(pE))) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(c2(pA,aP(aP(pE))))),bind(Y0,$fot(c2(aP(pE),aP(pA))))]]) ).
cnf(refute_0_137,plain,
c2(aP(pE),aP(pA)) = c2(pA,aP(aP(pE))),
inference(resolve,[$cnf( $equal(c2(pA,aP(aP(pE))),c2(aP(pE),aP(pA))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( c2(aP(pE),aP(pA)) != c2(pA,aP(aP(pE)))
| proj1C(c2(aP(pE),aP(pA))) != aP(pE)
| proj1C(c2(pA,aP(aP(pE)))) = aP(pE) ),
introduced(tautology,[equality,[$cnf( $equal(proj1C(c2(aP(pE),aP(pA))),aP(pE)) ),[0,0],$fot(c2(pA,aP(aP(pE))))]]) ).
cnf(refute_0_139,plain,
( proj1C(c2(aP(pE),aP(pA))) != aP(pE)
| proj1C(c2(pA,aP(aP(pE)))) = aP(pE) ),
inference(resolve,[$cnf( $equal(c2(aP(pE),aP(pA)),c2(pA,aP(aP(pE)))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
proj1C(c2(pA,aP(aP(pE)))) = aP(pE),
inference(resolve,[$cnf( $equal(proj1C(c2(aP(pE),aP(pA))),aP(pE)) )],[refute_0_1,refute_0_139]) ).
cnf(refute_0_141,plain,
proj1C(c2(pA,aP(aP(pE)))) = pA,
inference(subst,[],[refute_0_0:[bind(X,$fot(pA)),bind(X2,$fot(aP(aP(pE))))]]) ).
cnf(refute_0_142,plain,
( proj1C(c2(pA,aP(aP(pE)))) != aP(pE)
| proj1C(c2(pA,aP(aP(pE)))) != pA
| pA = aP(pE) ),
introduced(tautology,[equality,[$cnf( $equal(proj1C(c2(pA,aP(aP(pE)))),aP(pE)) ),[0],$fot(pA)]]) ).
cnf(refute_0_143,plain,
( proj1C(c2(pA,aP(aP(pE)))) != aP(pE)
| pA = aP(pE) ),
inference(resolve,[$cnf( $equal(proj1C(c2(pA,aP(aP(pE)))),pA) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
pA = aP(pE),
inference(resolve,[$cnf( $equal(proj1C(c2(pA,aP(aP(pE)))),aP(pE)) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
aP(X) != pA,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_146,plain,
( pA != aP(X)
| aP(X) = pA ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(pA)),bind(Y0,$fot(aP(X)))]]) ).
cnf(refute_0_147,plain,
pA != aP(X),
inference(resolve,[$cnf( $equal(aP(X),pA) )],[refute_0_146,refute_0_145]) ).
cnf(refute_0_148,plain,
pA != aP(pE),
inference(subst,[],[refute_0_147:[bind(X,$fot(pE))]]) ).
cnf(refute_0_149,plain,
$false,
inference(resolve,[$cnf( $equal(pA,aP(pE)) )],[refute_0_144,refute_0_148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWX207+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.18/0.35 % Computer : n002.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue May 5 11:35:31 EDT 2026
% 0.18/0.35 % CPUTime :
% 0.22/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.41
% 0.22/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.22/0.43
%------------------------------------------------------------------------------