%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV943-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 90 ( 52 ~; 28 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-5 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 47 ( 42 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
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(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(c_WellTypeRT_OWTrt_type,type,
c_WellTypeRT_OWTrt: ( $i * $i * $i * $i * $i ) > $o ).
tff(c_Expr_Oexp_OBinOp_type,type,
c_Expr_Oexp_OBinOp: ( $i * $i * $i * $i ) > $i ).
tff(v_e_092_060_094isub_0622_____type,type,
v_e_092_060_094isub_0622____: $i ).
tff(v_bop_____type,type,
v_bop____: $i ).
tff(v_e_092_060_094isub_0621_H_____type,type,
v_e_092_060_094isub_0621_H____: $i ).
tff(v_E_____type,type,
v_E____: $i ).
tff(v_h_Ha_____type,type,
v_h_Ha____: $i ).
tff(1,plain,
^ [V_x: $i] :
refl(( ( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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(2,plain,
( ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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)],[1]) ).
tff(3,plain,
( ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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(4,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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(5,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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)],[4]) ).
tff(6,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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(7,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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)],[6,5]) ).
tff(8,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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)],[7,3]) ).
tff(9,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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)],[8]) ).
tff(10,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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)],[9,2]) ).
tff(11,plain,
( c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____)
<=> c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(13,plain,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),v_T____),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),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____),v_T____)) )
<=> ( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),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____),v_T____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),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____),v_T____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,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_OBinOp(v_e_092_060_094isub_0621_H____,v_bop____,v_e_092_060_094isub_0622____,tc_List_Olist(tc_String_Ochar)),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____),v_T____)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,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____),v_T____)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,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(22,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)],[21,20]) ).
tff(23,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)],[22]) ).
tff(24,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)],[23,19]) ).
tff(25,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)))),v_T____),v_T____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,24,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV943-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.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
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Fri Jun 20 11:05:33 EDT 2025
% 0.18/0.34 % CPUTime :
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48 % SZS output start Proof
% See solution above
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------