TSTP Solution File: LAT269-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT269-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 Sep 17 18:32:33 EDT 2022
% Result : Unsatisfiable 0.94s 0.95s
% Output : Proof 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 41
% Syntax : Number of formulae : 65 ( 14 unt; 20 typ; 0 def)
% Number of atoms : 285 ( 72 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 391 ( 174 ~; 187 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 9 >; 17 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-5 aty)
% Number of variables : 67 ( 59 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_SetInterval_OlessThan_type,type,
c_SetInterval_OlessThan: ( $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Nat_Osize_type,type,
c_Nat_Osize: ( $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(c_Product__Type_OUnity_type,type,
c_Product__Type_OUnity: $i ).
tff(c_Tarski_Ointerval_type,type,
c_Tarski_Ointerval: ( $i * $i * $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Tarski_OTop_type,type,
c_Tarski_OTop: ( $i * $i ) > $i ).
tff(v_cl_type,type,
v_cl: $i ).
tff(c_Tarski_Olub_type,type,
c_Tarski_Olub: ( $i * $i * $i ) > $i ).
tff(v_Y_type,type,
v_Y: $i ).
tff(v_r_type,type,
v_r: $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(v_A_type,type,
v_A: $i ).
tff(c_emptyset_type,type,
c_emptyset: $i ).
tff(tc_Tarski_Opotype_Opotype__ext__type_type,type,
tc_Tarski_Opotype_Opotype__ext__type: ( $i * $i ) > $i ).
tff(c_Tarski_OCompleteLattice_type,type,
c_Tarski_OCompleteLattice: $i ).
tff(c_Tarski_Opotype_Opotype__ext_type,type,
c_Tarski_Opotype_Opotype__ext: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Tarski_Oinduced_type,type,
c_Tarski_Oinduced: ( $i * $i * $i ) > $i ).
tff(v_intY1_type,type,
v_intY1: $i ).
tff(1,plain,
^ [V_x: $i] :
refl(
( ( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
<=> ( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
<=> ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [V_x: $i] :
rewrite(
( ( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
<=> ( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
<=> ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
<=> ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0) ).
tff(7,plain,
! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
<=> c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0) ).
tff(13,plain,
c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
<=> ( ~ ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
( ~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
<=> ~ c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
<=> ~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(21,plain,
~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
~ c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
^ [V_b: $i,V_a: $i] :
refl(
( ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
<=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
<=> ! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
^ [V_b: $i,V_a: $i] :
trans(
monotonicity(
rewrite(
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
<=> ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )),
( ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
<=> ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
rewrite(
( ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
<=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) )),
( ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
<=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
<=> ! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
<=> ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
^ [V_b: $i,V_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a) )
<=> ( ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )
<=> ( ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ) )),
rewrite(
( ( ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )
<=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )
<=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
<=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) ) )),
rewrite(
( ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
<=> ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
<=> ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [V_b: $i,V_a: $i] :
( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
<=> ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,axiom,
! [V_b: $i,V_a: $i] :
( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0) ).
tff(31,plain,
! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[32,26]) ).
tff(34,plain,
! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[34,24]) ).
tff(36,plain,
( c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
<=> c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0) ).
tff(38,plain,
c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( ~ ! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
<=> ( ~ ! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
<=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ ! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
<=> ( ~ ! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
<=> ( ~ ! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [V_b: $i,V_a: $i] :
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_SetInterval_OlessThan(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,38,35,13,22,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT269-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 12:19:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.94/0.95 % SZS status Unsatisfiable
% 0.94/0.95 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------