%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV925-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:36:21 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 38 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 73 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 74 ( 38 ~; 24 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 66 ( 60 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(tc_Value_Oval_type,type,
tc_Value_Oval: $i ).
tff(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(v_ak_type,type,
v_ak: $i ).
tff(v_aj_type,type,
v_aj: $i ).
tff(tc_String_Ochar_type,type,
tc_String_Ochar: $i ).
tff(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
tff(tc_Type_Oty_type,type,
tc_Type_Oty: $i ).
tff(1,plain,
^ [T_a: $i] :
refl(( ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) )
<=> ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) )
<=> ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) )
<=> ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
tff(5,plain,
! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_a: $i] : ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)) )
<=> ( c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(12,plain,
c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_List_Olist(tc_String_Ochar))),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)) )
<=> ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(16,plain,
c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(transitivity,[status(thm)],[16,13,9]) ).
tff(18,plain,
^ [V_a_H: $i,V_list_H: $i,T_a: $i] :
refl(( ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) )
<=> ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) )
<=> ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) )
<=> ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
tff(22,plain,
! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [V_a_H: $i,V_list_H: $i,T_a: $i] : ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) )
| ( c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) != c_List_Olist_ONil(tc_Value_Oval) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) != c_List_Olist_ONil(tc_Value_Oval),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
^ [V_xs: $i,T_a: $i] :
refl(( ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) )
<=> ( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) )
<=> ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) )
<=> ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
tff(31,plain,
! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ( ~ ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) )
| ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) = c_List_Olist_ONil(tc_Value_Oval) ) )
<=> ( ~ ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) )
| ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) = c_List_Olist_ONil(tc_Value_Oval) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) )
| ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) = c_List_Olist_ONil(tc_Value_Oval) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_xs = c_List_Olist_ONil(T_a) ) )
| ( c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval) = c_List_Olist_ONil(tc_Value_Oval) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(unit_resolution,[status(thm)],[36,33,26]) ).
tff(38,plain,
$false,
inference(unit_resolution,[status(thm)],[37,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV925-1 : TPTP v9.0.0. Released v4.1.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.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
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 11:03:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% See solution above
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------