%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV963-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:36:24 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.65s
% Output : Proof 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 113 ( 54 ~; 50 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-5 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-5 aty)
% Number of variables : 17 ( 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(v_thesis_____type,type,
v_thesis____: $o ).
tff(c_WellTypeRT_OWTrt_type,type,
c_WellTypeRT_OWTrt: ( $i * $i * $i * $i * $i ) > $o ).
tff(v_sko__CHAINED__1_type,type,
v_sko__CHAINED__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_h_Ha_____type,type,
v_h_Ha____: $i ).
tff(v_e_092_060_094isub_0622_H_____type,type,
v_e_092_060_094isub_0622_H____: $i ).
tff(v_T_092_060_094isub_0622_____type,type,
v_T_092_060_094isub_0622____: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(v_E_____type,type,
v_E____: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $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(1,plain,
( ~ v_thesis____
<=> ~ v_thesis____ ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ v_thesis____,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,v_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____))
<=> c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,v_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,v_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(6,plain,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,v_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____)),
inference(modus_ponens,[status(thm)],[5,4]) ).
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_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____)),v_T_092_060_094isub_0622____))
<=> 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_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____)),v_T_092_060_094isub_0622____)) ),
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_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____)),v_T_092_060_094isub_0622____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
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_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____)),v_T_092_060_094isub_0622____)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_T_092_060_094isub_0622_H: $i] :
refl(( ( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) )
<=> ( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) )
<=> ! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) )
<=> ! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [V_T_092_060_094isub_0622_H: $i] :
rewrite(( ( v_thesis____
| ~ 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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____))
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_H) )
<=> ( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ 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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____))
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_H) )
<=> ! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ 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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____))
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
tff(16,plain,
! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) )
| v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,v_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____))
| ~ 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_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____)),v_T_092_060_094isub_0622____)) )
<=> ( ~ ! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) )
| v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,v_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____))
| ~ 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_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____)),v_T_092_060_094isub_0622____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) )
| v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,v_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____))
| ~ 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_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____)),v_T_092_060_094isub_0622____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_T_092_060_094isub_0622_H: $i] :
( v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,V_T_092_060_094isub_0622_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_092_060_094isub_0622_H),v_T_092_060_094isub_0622____)) )
| v_thesis____
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_092_060_094isub_0622_H____,v_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____))
| ~ 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_sko__CHAINED__1(v_E____,v_P,v_T_092_060_094isub_0622____,v_e_092_060_094isub_0622_H____,v_h_Ha____)),v_T_092_060_094isub_0622____)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV963-1 : TPTP v9.0.0. Released v4.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 11:09:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.48/0.65 % SZS status Unsatisfiable
% 0.48/0.65 % SZS output start Proof
% See solution above
% 0.55/0.74 % E exiting
%------------------------------------------------------------------------------