%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV939-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:36:22 AM UTC 2025
% Result : Unsatisfiable 0.42s 0.61s
% Output : Proof 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 25 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 5 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 72 ( 41 ~; 22 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-5 aty)
% Number of functors : 26 ( 26 usr; 16 con; 0-4 aty)
% Number of variables : 13 ( 12 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_T_H_____type,type,
v_T_H____: $i ).
tff(v_T_H_H_____type,type,
v_T_H_H____: $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_SmallStep_Oblocks_type,type,
c_SmallStep_Oblocks: $i > $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(tc_Value_Oval_type,type,
tc_Value_Oval: $i ).
tff(tc_Type_Oty_type,type,
tc_Type_Oty: $i ).
tff(v_body_____type,type,
v_body____: $i ).
tff(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(v_vs_____type,type,
v_vs____: $i ).
tff(c_Value_Oval_OAddr_type,type,
c_Value_Oval_OAddr: $i > $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(v_Ts_____type,type,
v_Ts____: $i ).
tff(c_Type_Oty_OClass_type,type,
c_Type_Oty_OClass: $i > $i ).
tff(v_D_____type,type,
v_D____: $i ).
tff(v_pns_____type,type,
v_pns____: $i ).
tff(c_Type_Othis_type,type,
c_Type_Othis: $i ).
tff(v_E_____type,type,
v_E____: $i ).
tff(v_ha_____type,type,
v_ha____: $i ).
tff(1,plain,
( ( v_T_H____ = v_T____ )
<=> ( v_T_H____ = v_T____ ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
v_T_H____ = v_T____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_HisT_0) ).
tff(3,plain,
v_T_H____ = v_T____,
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)))),v_T_H_H____),v_T_H____) = 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_T_H_H____),v_T____),
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)))),v_T_H_H____),v_T_H____))
<=> 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_T_H_H____),v_T____)) ),
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)))),v_T_H_H____),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)))),v_T_H_H____),v_T_H____)) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,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)))),v_T_H_H____),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)))),v_T_H_H____),v_T____)) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
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_T_H_H____),v_T____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_H_HsubT_0) ).
tff(9,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)))),v_T_H_H____),v_T____)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,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)))),v_T_H_H____),v_T_H____)),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
^ [V_x: $i] :
refl(( ( ~ 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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),V_x) ) )),
inference(bind,[status(th)],[]) ).
tff(12,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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),V_x) )
<=> ! [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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),V_x) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),V_x) )
<=> ! [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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),V_x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),V_x) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(15,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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),V_x) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),V_x) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),V_x) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),v_T_H_H____)
<=> c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),v_T_H_H____) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),v_T_H_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(20,plain,
c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),v_T_H_H____),
inference(modus_ponens,[status(thm)],[19,18]) ).
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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(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_T_H_H____),v_T_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),v_T_H_H____) )
<=> ( ~ ! [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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(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_T_H_H____),v_T_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),v_T_H_H____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(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_T_H_H____),v_T_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),v_T_H_H____) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,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_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(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_T_H_H____),v_T_H____))
| ~ c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_SmallStep_Oblocks(c_Pair(c_List_Olist_OCons(c_Type_Othis,v_pns____,tc_List_Olist(tc_String_Ochar)),c_Pair(c_List_Olist_OCons(c_Type_Oty_OClass(v_D____),v_Ts____,tc_Type_Oty),c_Pair(c_List_Olist_OCons(c_Value_Oval_OAddr(v_a____),v_vs____,tc_Value_Oval),v_body____,tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_List_Olist(tc_Type_Oty),tc_prod(tc_List_Olist(tc_Value_Oval),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),v_T_H_H____) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,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)))),v_T_H_H____),v_T_H____)),
inference(unit_resolution,[status(thm)],[23,20,17]) ).
tff(25,plain,
$false,
inference(unit_resolution,[status(thm)],[24,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV939-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 11:05:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.42/0.61 % SZS status Unsatisfiable
% 0.42/0.61 % SZS output start Proof
% See solution above
% 0.49/0.67 % E exiting
%------------------------------------------------------------------------------