TSTP Solution File: SWV962-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV962-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Thu Sep 29 15:25:05 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 41
% Syntax : Number of formulae : 71 ( 20 unt; 21 typ; 0 def)
% Number of atoms : 148 ( 37 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 173 ( 86 ~; 64 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 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 : 21 ( 9 >; 12 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-5 aty)
% Number of functors : 19 ( 19 usr; 12 con; 0-5 aty)
% Number of variables : 183 ( 162 !; 0 ?; 183 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Type_Oty_OVoid_type,type,
c_Type_Oty_OVoid: $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(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(tc_String_Ochar_type,type,
tc_String_Ochar: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(v_T_____type,type,
v_T____: $i ).
tff(c_WellTypeRT_OWTrt_type,type,
c_WellTypeRT_OWTrt: ( $i * $i * $i * $i * $i ) > $o ).
tff(c_Expr_Oexp_OFAss_type,type,
c_Expr_Oexp_OFAss: ( $i * $i * $i * $i * $i ) > $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(c_Expr_Oexp_OVal_type,type,
c_Expr_Oexp_OVal: ( $i * $i ) > $i ).
tff(v_v_____type,type,
v_v____: $i ).
tff(v_E_____type,type,
v_E____: $i ).
tff(v_ha_____type,type,
v_ha____: $i ).
tff(v_e_092_060_094isub_0622_H_____type,type,
v_e_092_060_094isub_0622_H____: $i ).
tff(v_h_Ha_____type,type,
v_h_Ha____: $i ).
tff(1,plain,
( c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____)
<=> c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt_0) ).
tff(3,plain,
c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
refl(
( ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
<=> ! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
<=> ! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
trans(
monotonicity(
rewrite(
( ( ( V_T = c_Type_Oty_OVoid )
| ( V_T = c_Type_Oty_OVoid ) )
<=> ( V_T = c_Type_Oty_OVoid ) )),
( ( ( V_T = c_Type_Oty_OVoid )
| ( V_T = c_Type_Oty_OVoid )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ( ( V_T = c_Type_Oty_OVoid )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T) ) )),
rewrite(
( ( ( V_T = c_Type_Oty_OVoid )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ) )),
( ( ( V_T = c_Type_Oty_OVoid )
| ( V_T = c_Type_Oty_OVoid )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ( V_T = c_Type_Oty_OVoid )
| ( V_T = c_Type_Oty_OVoid )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ( V_T = c_Type_Oty_OVoid )
| ( V_T = c_Type_Oty_OVoid )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_0) ).
tff(10,plain,
! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( v_T____ = c_Type_Oty_OVoid ) )
<=> ( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( v_T____ = c_Type_Oty_OVoid ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( v_T____ = c_Type_Oty_OVoid ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_F: $i,V_D: $i,V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAss(V_e,V_F,V_D,V_v,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( v_T____ = c_Type_Oty_OVoid ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
v_T____ = c_Type_Oty_OVoid,
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
c_Type_Oty_OVoid = v_T____,
inference(symmetry,[status(thm)],[17]) ).
tff(19,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),c_Type_Oty_OVoid) = 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(monotonicity,[status(thm)],[18]) ).
tff(20,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(monotonicity,[status(thm)],[19]) ).
tff(21,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(symmetry,[status(thm)],[20]) ).
tff(22,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)],[21]) ).
tff(23,plain,
^ [V_x: $i] :
refl(
( ( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(24,plain,
( ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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)],[23]) ).
tff(25,plain,
( ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(26,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,tc_List_Olist(tc_String_Ochar)),V_x) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(27,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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)],[26]) ).
tff(28,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,tc_List_Olist(tc_String_Ochar)),V_x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(29,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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)],[28,27]) ).
tff(30,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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)],[29,25]) ).
tff(31,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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)],[30]) ).
tff(32,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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)],[31,24]) ).
tff(33,plain,
( c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
<=> c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(35,plain,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( ( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(37,plain,
( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(38,plain,
( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_F____,v_D____,v_e_092_060_094isub_0622_H____,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)],[37,36]) ).
tff(39,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(unit_resolution,[status(thm)],[38,35,32]) ).
tff(40,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(modus_ponens,[status(thm)],[39,22]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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(45,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)],[44,43]) ).
tff(46,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)],[45]) ).
tff(47,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)],[46,42]) ).
tff(48,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(49,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)],[48,47]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV962-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 10:28:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------