%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT268-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:05 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 38
% Syntax : Number of formulae : 102 ( 76 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 132 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 44 ( 13 ~; 9 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-4 aty)
% Number of variables : 172 ( 156 !; 0 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
tff(true_type,type,
true: $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $i ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_r_type,type,
v_r: $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Tarski_Oglb_type,type,
c_Tarski_Oglb: ( $i * $i * $i ) > $i ).
tff(v_cl_type,type,
v_cl: $i ).
tff(v_S_type,type,
v_S: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $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(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(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(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $i ).
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(1,plain,
^ [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] :
refl(( ( ifeq(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)),true,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)),true) = true )
<=> ( ifeq(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)),true,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)),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] : ( ifeq(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)),true,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)),true) = true )
<=> ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] : ( ifeq(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)),true,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)),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] : ( ifeq(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)),true,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)),true) = true )
<=> ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] : ( ifeq(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)),true,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)),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] : ( ifeq(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)),true,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)),true) = true ),
file('/export/starexec/sandbox2/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(5,plain,
! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] : ( ifeq(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)),true,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)),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] : ( ifeq(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)),true,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)),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] : ( ifeq(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)),true,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)),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_x: $i,V_cl: $i,T_a: $i,V_y: $i] : ( ifeq(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)),true,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)),true) = true )
| ( ifeq(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)),true,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)),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(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)),true,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)),true) = true,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
tff(12,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(symmetry,[status(thm)],[12]) ).
tff(14,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(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) )
<=> ! [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)],[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) )
<=> ! [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(17,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/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
tff(18,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)],[17,16]) ).
tff(19,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)],[18]) ).
tff(20,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)],[19,15]) ).
tff(21,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(22,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)],[21,20]) ).
tff(23,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)],[22]) ).
tff(24,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)],[23]) ).
tff(25,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)],[24,13]) ).
tff(26,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)],[25]) ).
tff(27,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(31,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,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)),true) = 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(quant_inst,[status(thm)],[]) ).
tff(35,plain,
ifeq(true,true,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)),true) = 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)],[34,33]) ).
tff(36,plain,
( ( c_in(v_x,v_S,t_a) = true )
<=> ( c_in(v_x,v_S,t_a) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
c_in(v_x,v_S,t_a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(38,plain,
c_in(v_x,v_S,t_a) = true,
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
true = c_in(v_x,v_S,t_a),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
ifeq(true,true,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)),true) = ifeq(c_in(v_x,v_S,t_a),true,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)),true),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
ifeq(c_in(v_x,v_S,t_a),true,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)),true) = ifeq(true,true,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)),true),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true) = ifeq(c_in(v_x,v_S,t_a),true,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)),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
ifeq(true,true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true) = ifeq(c_in(v_x,v_S,t_a),true,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)),true),
inference(unit_resolution,[status(thm)],[42,33]) ).
tff(44,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)) = true )
<=> ( c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,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)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
tff(46,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)) = true,
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
true = 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(symmetry,[status(thm)],[46]) ).
tff(48,plain,
ifeq(true,true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true) = ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true) = ifeq(true,true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true) = ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true) = ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),
inference(unit_resolution,[status(thm)],[50,33]) ).
tff(52,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)) = true )
<=> ( c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,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)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
tff(54,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)) = true,
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
true = 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(symmetry,[status(thm)],[54]) ).
tff(56,plain,
ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true) = ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true) = ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),true) = ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),true) = ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),
inference(unit_resolution,[status(thm)],[58,33]) ).
tff(60,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(61,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
tff(62,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(symmetry,[status(thm)],[62]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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(67,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/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
tff(68,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)],[67,66]) ).
tff(69,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)],[68]) ).
tff(70,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)],[69,65]) ).
tff(71,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(72,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)],[71,70]) ).
tff(73,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit) = v_A,
inference(transitivity,[status(thm)],[72,63]) ).
tff(74,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)],[73]) ).
tff(75,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)],[74]) ).
tff(76,plain,
( ( c_lessequals(v_S,v_A,tc_set(t_a)) = true )
<=> ( c_lessequals(v_S,v_A,tc_set(t_a)) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(78,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
true = c_lessequals(v_S,v_A,tc_set(t_a)),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
true = 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(transitivity,[status(thm)],[79,75]) ).
tff(81,plain,
ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),true) = ifeq(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)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),true),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
ifeq(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)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),true) = ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),true),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
^ [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] :
refl(( ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true )
<=> ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] : ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true )
<=> ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] : ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] : ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true )
<=> ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] : ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,axiom,
! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] : ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
tff(87,plain,
! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] : ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] : ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] : ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
( ~ ! [V_x: $i,V_S: $i,V_cl: $i,T_a: $i] : ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true )
| ( ifeq(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)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
ifeq(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)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),true) = true,
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
true = ifeq(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)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,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)),true),true),true),true),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
true = 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(transitivity,[status(thm)],[92,82,59,57,51,49,43,41,35]) ).
tff(94,plain,
ifeq(true,true,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)),true) = ifeq(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)),true,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)),true),
inference(monotonicity,[status(thm)],[93,26]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,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)),true) = 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(quant_inst,[status(thm)],[]) ).
tff(96,plain,
ifeq(true,true,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)),true) = 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(unit_resolution,[status(thm)],[95,33]) ).
tff(97,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)) = ifeq(true,true,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)),true),
inference(symmetry,[status(thm)],[96]) ).
tff(98,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)) = true,
inference(transitivity,[status(thm)],[97,94,9]) ).
tff(99,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)) != true )
<=> ( 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)) != true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,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)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(101,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)) != true,
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
$false,
inference(unit_resolution,[status(thm)],[101,98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT268-10 : TPTP v9.0.0. Released v7.5.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:57:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% See solution above
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------