%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV951-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 1.29s 1.46s
% Output : Proof 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 40 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 169 ( 88 ~; 64 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 4 ( 4 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 : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 166 ( 154 !; 0 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_WellTypeRT_OWTrt_type,type,
c_WellTypeRT_OWTrt: ( $i * $i * $i * $i * $i ) > $o ).
tff(v_T_____type,type,
v_T____: $i ).
tff(c_Expr_Oexp_OFAcc_type,type,
c_Expr_Oexp_OFAcc: ( $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_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(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(1,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(2,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)],[1]) ).
tff(3,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(4,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/sandbox2/benchmark/theBenchmark.p',cls_widen__refl_0) ).
tff(5,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)],[4,3]) ).
tff(6,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)],[5]) ).
tff(7,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)],[6,2]) ).
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))
| 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(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____),v_T____)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_x: $i] :
refl(( ( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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_OFAcc(v_e_Ha____,v_F____,v_D____,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(11,plain,
( ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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_OFAcc(v_e_Ha____,v_F____,v_D____,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)],[10]) ).
tff(12,plain,
( ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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_OFAcc(v_e_Ha____,v_F____,v_D____,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(13,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_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),V_x) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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(14,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_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),V_x) )
<=> ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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)],[13]) ).
tff(15,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_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),V_x) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(16,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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)],[15,14]) ).
tff(17,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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)],[16,12]) ).
tff(18,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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)],[17]) ).
tff(19,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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_OFAcc(v_e_Ha____,v_F____,v_D____,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_OFAcc(v_e_Ha____,v_F____,v_D____,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_OFAcc(v_e_Ha____,v_F____,v_D____,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(21,plain,
( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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_OFAcc(v_e_Ha____,v_F____,v_D____,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(22,plain,
( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,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_OFAcc(v_e_Ha____,v_F____,v_D____,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)],[21,20]) ).
tff(23,plain,
~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),v_T____),
inference(unit_resolution,[status(thm)],[22,19,9]) ).
tff(24,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(25,axiom,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(26,plain,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
refl(( ( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) )
<=> ( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) )
<=> ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) )
<=> ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAccNT_0) ).
tff(31,plain,
! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ( ~ ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) )
| ~ 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_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),v_T____) )
<=> ( ~ ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) )
| ~ 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_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),v_T____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),v_T____)
| ~ 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)
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),v_T____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( ~ ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) )
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),v_T____)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT) )
<=> ( ~ ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) )
| ~ 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_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),v_T____) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) )
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),v_T____)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT) )
<=> ( ~ ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) )
| ~ 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_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),v_T____) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) )
| c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),v_T____)
| ~ c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,v_e_Ha____,c_Type_Oty_ONT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [V_F: $i,V_E: $i,V_D: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OFAcc(V_e,V_F,V_D,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) )
| ~ 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_OFAcc(v_e_Ha____,v_F____,v_D____,tc_List_Olist(tc_String_Ochar)),v_T____) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,33,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV951-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Fri Jun 20 11:06:56 EDT 2025
% 0.11/0.34 % CPUTime :
% 1.29/1.46 % SZS status Unsatisfiable
% 1.29/1.46 % SZS output start Proof
% See solution above
% 1.29/1.47 % E exiting
%------------------------------------------------------------------------------