%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV955-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 : Sat Jun 21 05:36:23 AM UTC 2025
% Result : Unsatisfiable 1.42s 1.63s
% Output : Proof 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 54 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 204 ( 5 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 277 ( 138 ~; 113 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-5 aty)
% Number of functors : 18 ( 18 usr; 12 con; 0-5 aty)
% Number of variables : 215 ( 194 !; 0 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_WellTypeRT_OWTrt_type,type,
c_WellTypeRT_OWTrt: ( $i * $i * $i * $i * $i ) > $o ).
tff(c_Type_Oty_OVoid_type,type,
c_Type_Oty_OVoid: $i ).
tff(c_Expr_Oexp_OFAss_type,type,
c_Expr_Oexp_OFAss: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(tc_String_Ochar_type,type,
tc_String_Ochar: $i ).
tff(v_e_092_060_094isub_0622_____type,type,
v_e_092_060_094isub_0622____: $i ).
tff(v_D_____type,type,
v_D____: $i ).
tff(v_F_____type,type,
v_F____: $i ).
tff(v_e_Ha_____type,type,
v_e_Ha____: $i ).
tff(v_E_____type,type,
v_E____: $i ).
tff(v_h_Ha_____type,type,
v_h_Ha____: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_T_____type,type,
v_T____: $i ).
tff(c_TypeRel_Owiden_type,type,
c_TypeRel_Owiden: ( $i * $i ) > $i ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(tc_Expr_Oexp_type,type,
tc_Expr_Oexp: $i > $i ).
tff(c_Type_Oty_ONT_type,type,
c_Type_Oty_ONT: $i ).
tff(v_T_092_060_094isub_0622_____type,type,
v_T_092_060_094isub_0622____: $i ).
tff(1,plain,
( ( v_T____ = c_Type_Oty_OVoid )
<=> ( v_T____ = c_Type_Oty_OVoid ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
v_T____ = c_Type_Oty_OVoid,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_void_0) ).
tff(3,plain,
v_T____ = c_Type_Oty_OVoid,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____) = hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),c_Type_Oty_OVoid),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____))
<=> hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),c_Type_Oty_OVoid)) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),c_Type_Oty_OVoid))
<=> hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
^ [V_T: $i,T_a: $i,V_P: $i] :
refl(( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T))
<=> hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T))
<=> ! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T))
<=> ! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__refl_0) ).
tff(11,plain,
! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
( ~ ! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),c_Type_Oty_OVoid)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),c_Type_Oty_OVoid)),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)),
inference(modus_ponens,[status(thm)],[15,6]) ).
tff(17,plain,
^ [V_x: $i] :
refl(( ( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
<=> ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
<=> ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
^ [V_x: $i] :
rewrite(( ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____))
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [V_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____))
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x) )
<=> ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [V_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____))
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(23,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
( ( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) )
<=> ( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) ),
inference(unit_resolution,[status(thm)],[29,26]) ).
tff(31,plain,
~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid),
inference(unit_resolution,[status(thm)],[30,16]) ).
tff(32,plain,
( c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT)
<=> c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
tff(34,plain,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____)
<=> c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
tff(37,plain,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
^ [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
refl(( ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
<=> ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
<=> ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
trans(monotonicity(rewrite(( ( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ) )),
( ( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT) ) )),
rewrite(( ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ) )),
( ( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT) )
<=> ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtFAssNT_0) ).
tff(44,plain,
! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT)
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
<=> ( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT)
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____)
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT)
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____)
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
<=> ( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT)
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____)
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
<=> ( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT)
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____)
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T_092_060_094isub_0622: $i,V_e_092_060_094isub_0622: $i,V_e_092_060_094isub_0621: $i,V_h: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,c_Type_Oty_ONT)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e_092_060_094isub_0621,V_F,V_D,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) )
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622____,v_T_092_060_094isub_0622____)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT)
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(v_e_Ha____,v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
$false,
inference(unit_resolution,[status(thm)],[53,47,37,34,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV955-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 11:07:07 EDT 2025
% 0.14/0.34 % CPUTime :
% 1.42/1.63 % SZS status Unsatisfiable
% 1.42/1.63 % SZS output start Proof
% See solution above
% 1.42/1.65 % E exiting
%------------------------------------------------------------------------------