TSTP Solution File: LAT263-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT263-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 Sep 17 18:32:30 EDT 2022
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 39
% Syntax : Number of formulae : 72 ( 28 unt; 15 typ; 0 def)
% Number of atoms : 185 ( 27 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 222 ( 104 ~; 92 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 8 >; 12 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 101 ( 90 !; 0 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Tarski_Opotype_Opset_type,type,
c_Tarski_Opotype_Opset: ( $i * $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(c_Tarski_Odual_type,type,
c_Tarski_Odual: ( $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_S_type,type,
v_S: $i ).
tff(c_Tarski_Oglb_type,type,
c_Tarski_Oglb: ( $i * $i * $i ) > $i ).
tff(v_A_type,type,
v_A: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(tc_Tarski_Opotype_Opotype__ext__type_type,type,
tc_Tarski_Opotype_Opotype__ext__type: ( $i * $i ) > $i ).
tff(c_Tarski_OPartialOrder_type,type,
c_Tarski_OPartialOrder: $i ).
tff(c_Tarski_OCompleteLattice_type,type,
c_Tarski_OCompleteLattice: $i ).
tff(1,plain,
^ [V_cl: $i,T_a: $i] :
refl(
( ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) )
<=> ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_cl: $i,T_a: $i] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) )
<=> ! [V_cl: $i,T_a: $i] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_cl: $i,T_a: $i] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) )
<=> ! [V_cl: $i,T_a: $i] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_cl: $i,T_a: $i] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
tff(5,plain,
! [V_cl: $i,T_a: $i] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_cl: $i,T_a: $i] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_cl: $i,T_a: $i] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_cl: $i,T_a: $i] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) )
| ( c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_S: $i,V_cl: $i,T_a: $i] :
refl(
( ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) )
<=> ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V_S: $i,V_cl: $i,T_a: $i] : ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) )
<=> ! [V_S: $i,V_cl: $i,T_a: $i] : ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_S: $i,V_cl: $i,T_a: $i] : ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) )
<=> ! [V_S: $i,V_cl: $i,T_a: $i] : ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [V_S: $i,V_cl: $i,T_a: $i] : ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
tff(14,plain,
! [V_S: $i,V_cl: $i,T_a: $i] : ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [V_S: $i,V_cl: $i,T_a: $i] : ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_S: $i,V_cl: $i,T_a: $i] : ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [V_S: $i,V_cl: $i,T_a: $i] : ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) )
| ( c_Tarski_Oglb(v_S,v_cl,t_a) = c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
c_Tarski_Oglb(v_S,v_cl,t_a) = c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a) = c_Tarski_Oglb(v_S,v_cl,t_a),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),t_a)
<=> c_in(c_Tarski_Oglb(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(monotonicity,[status(thm)],[19,9]) ).
tff(21,plain,
( c_in(c_Tarski_Oglb(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
<=> c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),t_a) ),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
<=> ~ c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),t_a) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a)
<=> ~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a)
<=> ~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(26,plain,
~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(modus_ponens,[status(thm)],[26,23]) ).
tff(28,plain,
~ c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),t_a),
inference(modus_ponens,[status(thm)],[27,22]) ).
tff(29,plain,
( c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a))
<=> c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(30,plain,
( c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
<=> c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) ),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( c_lessequals(v_S,v_A,tc_set(t_a))
<=> c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( c_lessequals(v_S,v_A,tc_set(t_a))
<=> c_lessequals(v_S,v_A,tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(34,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[34,31]) ).
tff(36,plain,
c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[35,30]) ).
tff(37,plain,
( c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
<=> c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
tff(39,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
<=> c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
tff(42,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
^ [V_S: $i,V_cl: $i,T_a: $i] :
refl(
( ( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) )
<=> ( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) )
<=> ! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) )
<=> ! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
^ [V_S: $i,V_cl: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)) )
<=> ( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ) )),
( ( ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a) )
<=> ( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a) ) )),
rewrite(
( ( ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a) )
<=> ( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ) )),
( ( ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a) )
<=> ( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [V_S: $i,V_cl: $i,T_a: $i] :
( ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a) )
<=> ! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [V_S: $i,V_cl: $i,T_a: $i] :
( ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__in__lattice_0) ).
tff(49,plain,
! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) )
| c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),t_a)
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )
<=> ( ~ ! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) )
| c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),t_a)
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) )
| c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),t_a)
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) )
| c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),t_a)
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
( c_in(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),t_a)
| ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) ),
inference(unit_resolution,[status(thm)],[55,52,42,39]) ).
tff(57,plain,
$false,
inference(unit_resolution,[status(thm)],[56,36,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT263-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 12:53:48 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------