TSTP Solution File: SWV254-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Thu Sep 29 15:10:37 EDT 2022
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 35
% Syntax : Number of formulae : 77 ( 32 unt; 9 typ; 0 def)
% Number of atoms : 183 ( 84 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 208 ( 99 ~; 79 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 123 ( 111 !; 0 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_x_type,type,
v_x: $i > $i ).
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(v_nat_type,type,
v_nat: $i ).
tff(c_emptyset_type,type,
c_emptyset: $i ).
tff(c_SetInterval_OatLeastLessThan_type,type,
c_SetInterval_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(c_insert_type,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(1,plain,
^ [V_U: $i] :
refl(
( ( v_x(V_U) = v_nat )
<=> ( v_x(V_U) = v_nat ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_U: $i] : ( v_x(V_U) = v_nat )
<=> ! [V_U: $i] : ( v_x(V_U) = v_nat ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_U: $i] : ( v_x(V_U) = v_nat )
<=> ! [V_U: $i] : ( v_x(V_U) = v_nat ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_U: $i] : ( v_x(V_U) = v_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(5,plain,
! [V_U: $i] : ( v_x(V_U) = v_nat ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_U: $i] : ( v_x(V_U) = v_nat ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_U: $i] : ( v_x(V_U) = v_nat ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_U: $i] : ( v_x(V_U) = v_nat )
| ( v_x(c_Suc(v_nat)) = v_nat ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
v_x(c_Suc(v_nat)) = v_nat,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( c_lessequals(c_Suc(v_nat),v_x(c_Suc(v_nat)),tc_nat)
<=> c_lessequals(c_Suc(v_nat),v_nat,tc_nat) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( c_lessequals(c_Suc(v_nat),v_nat,tc_nat)
<=> c_lessequals(c_Suc(v_nat),v_x(c_Suc(v_nat)),tc_nat) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat)
<=> ~ c_lessequals(c_Suc(v_nat),v_x(c_Suc(v_nat)),tc_nat) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ( c_insert(v_nat,c_emptyset,tc_nat) = c_emptyset )
<=> ( c_emptyset = c_insert(v_nat,c_emptyset,tc_nat) ) ),
inference(commutativity,[status(thm)],]) ).
tff(14,plain,
^ [V_m: $i] :
refl(
( ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) )
<=> ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [V_m: $i] : ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) )
<=> ! [V_m: $i] : ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [V_m: $i] : ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) )
<=> ! [V_m: $i] : ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
! [V_m: $i] : ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
tff(18,plain,
! [V_m: $i] : ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [V_m: $i] : ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [V_m: $i] : ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [V_m: $i] : ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) )
| ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_insert(v_nat,c_emptyset,tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_insert(v_nat,c_emptyset,tc_nat),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
( ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
<=> ( c_insert(v_nat,c_emptyset,tc_nat) = c_emptyset ) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
<=> ( c_emptyset = c_insert(v_nat,c_emptyset,tc_nat) ) ),
inference(transitivity,[status(thm)],[23,13]) ).
tff(25,plain,
( ( c_emptyset = c_insert(v_nat,c_emptyset,tc_nat) )
<=> ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset ) ),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ( c_emptyset != c_insert(v_nat,c_emptyset,tc_nat) )
<=> ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) != c_emptyset ) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(
( ( c_emptyset != c_insert(V_a,V_A,T_a) )
<=> ( c_emptyset != c_insert(V_a,V_A,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] : ( c_emptyset != c_insert(V_a,V_A,T_a) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] : ( c_emptyset != c_insert(V_a,V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] : ( c_emptyset != c_insert(V_a,V_A,T_a) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] : ( c_emptyset != c_insert(V_a,V_A,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_emptyset != c_insert(V_a,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
tff(31,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_emptyset != c_insert(V_a,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_emptyset != c_insert(V_a,V_A,T_a) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_emptyset != c_insert(V_a,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] : ( c_emptyset != c_insert(V_a,V_A,T_a) )
| ( c_emptyset != c_insert(v_nat,c_emptyset,tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
c_emptyset != c_insert(v_nat,c_emptyset,tc_nat),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) != c_emptyset,
inference(modus_ponens,[status(thm)],[35,26]) ).
tff(37,plain,
( class_Orderings_Oorder(tc_nat)
<=> class_Orderings_Oorder(tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
tff(39,plain,
class_Orderings_Oorder(tc_nat),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
^ [V_n: $i,T_a: $i,V_m: $i] :
refl(
( ( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
^ [V_n: $i,T_a: $i,V_m: $i] :
rewrite(
( ( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_n,V_m,T_a)
| ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset ) )
<=> ( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [V_n: $i,T_a: $i,V_m: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_n,V_m,T_a)
| ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset ) )
<=> ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [V_n: $i,T_a: $i,V_m: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_n,V_m,T_a)
| ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
tff(46,plain,
! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ class_Orderings_Oorder(tc_nat)
| ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
| ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat) )
<=> ( ~ ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ class_Orderings_Oorder(tc_nat)
| ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
| ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
| ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat)
| ~ class_Orderings_Oorder(tc_nat) )
<=> ( ~ class_Orderings_Oorder(tc_nat)
| ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
| ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( ~ ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
| ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat)
| ~ class_Orderings_Oorder(tc_nat) )
<=> ( ~ ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ class_Orderings_Oorder(tc_nat)
| ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
| ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
| ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat)
| ~ class_Orderings_Oorder(tc_nat) )
<=> ( ~ ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ class_Orderings_Oorder(tc_nat)
| ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
| ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
| ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat)
| ~ class_Orderings_Oorder(tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [V_n: $i,T_a: $i,V_m: $i] :
( ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset )
| ~ c_lessequals(V_n,V_m,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ class_Orderings_Oorder(tc_nat)
| ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
| ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
( ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset )
| ~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat) ),
inference(unit_resolution,[status(thm)],[55,49,39]) ).
tff(57,plain,
~ c_lessequals(c_Suc(v_nat),v_nat,tc_nat),
inference(unit_resolution,[status(thm)],[56,36]) ).
tff(58,plain,
~ c_lessequals(c_Suc(v_nat),v_x(c_Suc(v_nat)),tc_nat),
inference(modus_ponens,[status(thm)],[57,12]) ).
tff(59,plain,
^ [V_U: $i] :
refl(
( c_lessequals(V_U,v_x(V_U),tc_nat)
<=> c_lessequals(V_U,v_x(V_U),tc_nat) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [V_U: $i] : c_lessequals(V_U,v_x(V_U),tc_nat)
<=> ! [V_U: $i] : c_lessequals(V_U,v_x(V_U),tc_nat) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [V_U: $i] : c_lessequals(V_U,v_x(V_U),tc_nat)
<=> ! [V_U: $i] : c_lessequals(V_U,v_x(V_U),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
! [V_U: $i] : c_lessequals(V_U,v_x(V_U),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(63,plain,
! [V_U: $i] : c_lessequals(V_U,v_x(V_U),tc_nat),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [V_U: $i] : c_lessequals(V_U,v_x(V_U),tc_nat),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [V_U: $i] : c_lessequals(V_U,v_x(V_U),tc_nat),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ~ ! [V_U: $i] : c_lessequals(V_U,v_x(V_U),tc_nat)
| c_lessequals(c_Suc(v_nat),v_x(c_Suc(v_nat)),tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
c_lessequals(c_Suc(v_nat),v_x(c_Suc(v_nat)),tc_nat),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
$false,
inference(unit_resolution,[status(thm)],[67,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 02:07:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------