%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT268-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:14:06 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 34
% Syntax : Number of formulae : 81 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 338 ( 39 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 458 ( 218 ~; 203 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 186 ( 169 !; 0 ?; 186 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Tarski_Opotype_Oorder_type,type,
c_Tarski_Opotype_Oorder: ( $i * $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(v_cl_type,type,
v_cl: $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Tarski_Olub_type,type,
c_Tarski_Olub: ( $i * $i * $i ) > $i ).
tff(c_Tarski_Odual_type,type,
c_Tarski_Odual: ( $i * $i ) > $i ).
tff(v_S_type,type,
v_S: $i ).
tff(v_r_type,type,
v_r: $i ).
tff(c_Tarski_Oglb_type,type,
c_Tarski_Oglb: ( $i * $i * $i ) > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(c_Tarski_Opotype_Opset_type,type,
c_Tarski_Opotype_Opset: ( $i * $i * $i ) > $i ).
tff(v_A_type,type,
v_A: $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_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) )
<=> ( v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
tff(3,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(symmetry,[status(thm)],[3]) ).
tff(5,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(6,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)],[5]) ).
tff(7,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(8,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(9,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)],[8,7]) ).
tff(10,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)],[9]) ).
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) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
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) )
| ( 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(13,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)],[12,11]) ).
tff(14,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)],[13]) ).
tff(15,plain,
c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a) = c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
<=> c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(monotonicity,[status(thm)],[15,4]) ).
tff(17,plain,
( c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> ~ c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> ~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(21,plain,
~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
~ c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
( ( v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) )
<=> ( v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
tff(25,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(symmetry,[status(thm)],[25]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(30,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(31,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)],[30,29]) ).
tff(32,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)],[31]) ).
tff(33,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)],[32,28]) ).
tff(34,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(35,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)],[34,33]) ).
tff(36,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit) = v_A,
inference(transitivity,[status(thm)],[35,26]) ).
tff(37,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,v_A,tc_set(t_a)) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( c_lessequals(v_S,v_A,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)],[37]) ).
tff(39,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(40,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(41,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,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)],[41,38]) ).
tff(43,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(44,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(45,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)],[44,43]) ).
tff(46,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(47,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(48,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)],[47,46]) ).
tff(49,plain,
^ [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
refl(( ( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) )
<=> ( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) )
<=> ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) )
<=> ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ c_in(V_x,V_S,T_a)
| ~ 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_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_x,V_S,T_a) ) )),
( ( ~ c_in(V_x,V_S,T_a)
| ~ 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(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_x,V_S,T_a)
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)) ) )),
rewrite(( ( ~ 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_x,V_S,T_a)
| ~ 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_x,V_S,T_a) ) )),
( ( ~ c_in(V_x,V_S,T_a)
| ~ 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_x,V_S,T_a) ) )),
( ( ~ c_in(V_x,V_S,T_a)
| ~ 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_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a)
| c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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(V_x,V_S,T_a)
| c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) ) )),
( ( ~ c_in(V_x,V_S,T_a)
| ~ 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_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( ~ c_in(V_x,V_S,T_a)
| ~ 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_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) )
<=> ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( ~ c_in(V_x,V_S,T_a)
| ~ 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_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
tff(55,plain,
! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( c_in(v_x,v_S,t_a)
<=> c_in(v_x,v_S,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
c_in(v_x,v_S,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(61,plain,
c_in(v_x,v_S,t_a),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( ( ~ ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) )
| ~ c_in(v_x,v_S,t_a)
| c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,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_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) )
| ~ c_in(v_x,v_S,t_a)
| c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,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(63,plain,
( ( c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,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))
| ~ c_in(v_x,v_S,t_a) )
<=> ( ~ c_in(v_x,v_S,t_a)
| c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,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(64,plain,
( ( ~ ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) )
| c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,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))
| ~ c_in(v_x,v_S,t_a) )
<=> ( ~ ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) )
| ~ c_in(v_x,v_S,t_a)
| c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,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(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) )
| c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,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))
| ~ c_in(v_x,v_S,t_a) )
<=> ( ~ ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) )
| ~ c_in(v_x,v_S,t_a)
| c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,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(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) )
| c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,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))
| ~ c_in(v_x,v_S,t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,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_x,V_S,T_a) )
| ~ c_in(v_x,v_S,t_a)
| c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,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)],[66,65]) ).
tff(68,plain,
( c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,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)],[67,61,58,48,45]) ).
tff(69,plain,
c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[68,42]) ).
tff(70,plain,
^ [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
refl(( ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) )
<=> ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) )
<=> ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) ).
tff(74,plain,
! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ( ~ ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) )
| ~ c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[79,76,69]) ).
tff(81,plain,
$false,
inference(unit_resolution,[status(thm)],[80,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LAT268-2 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 19:57:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.41 % SZS status Unsatisfiable
% 0.22/0.41 % SZS output start Proof
% See solution above
% 0.22/0.44 % E exiting
%------------------------------------------------------------------------------