%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT269-2 : TPTP v9.0.0. Released v3.2.0.
% 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 05:14:06 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 46 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 206 ( 54 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 267 ( 122 ~; 122 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-5 aty)
% Number of variables : 47 ( 42 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Tarski_Opotype_Opotype__ext__type_type,type,
tc_Tarski_Opotype_Opotype__ext__type: ( $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Tarski_OCompleteLattice_type,type,
c_Tarski_OCompleteLattice: $i ).
tff(c_Tarski_Opotype_Opotype__ext_type,type,
c_Tarski_Opotype_Opotype__ext: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Product__Type_OUnity_type,type,
c_Product__Type_OUnity: $i ).
tff(c_Tarski_Oinduced_type,type,
c_Tarski_Oinduced: ( $i * $i * $i ) > $i ).
tff(v_r_type,type,
v_r: $i ).
tff(c_Tarski_Ointerval_type,type,
c_Tarski_Ointerval: ( $i * $i * $i * $i ) > $i ).
tff(c_Tarski_OTop_type,type,
c_Tarski_OTop: ( $i * $i ) > $i ).
tff(v_cl_type,type,
v_cl: $i ).
tff(c_Tarski_Olub_type,type,
c_Tarski_Olub: ( $i * $i * $i ) > $i ).
tff(v_Y_type,type,
v_Y: $i ).
tff(v_intY1_type,type,
v_intY1: $i ).
tff(c_emptyset_type,type,
c_emptyset: $i ).
tff(v_A_type,type,
v_A: $i ).
tff(1,plain,
( ( v_intY1 = c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) )
<=> ( v_intY1 = c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
v_intY1 = c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0) ).
tff(3,plain,
v_intY1 = c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = v_intY1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a) = c_Tarski_Oinduced(v_intY1,v_r,t_a),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),
inference(monotonicity,[status(thm)],[4,5]) ).
tff(7,plain,
( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
<=> c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
<=> c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
<=> ~ c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
<=> ~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(12,plain,
~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
~ c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
^ [V_x: $i] :
refl(( ( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
<=> ( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
<=> ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
<=> ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0) ).
tff(18,plain,
! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
<=> c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0) ).
tff(23,plain,
c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
<=> ( ~ ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [V_x: $i] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset,
inference(unit_resolution,[status(thm)],[26,23,20]) ).
tff(28,plain,
^ [V_b: $i,V_a: $i] :
refl(( ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
<=> ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
<=> ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
<=> ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [V_b: $i,V_a: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a) )
<=> ( ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )
<=> ( ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ) )),
rewrite(( ( ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )
<=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )
<=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
<=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) ) )),
rewrite(( ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
<=> ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
<=> ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [V_b: $i,V_a: $i] :
( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
<=> ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [V_b: $i,V_a: $i] :
( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0) ).
tff(34,plain,
! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
<=> c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0) ).
tff(40,plain,
c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ( ~ ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) )
<=> ( ~ ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [V_b: $i,V_a: $i] :
( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
| ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(unit_resolution,[status(thm)],[43,40,37,23]) ).
tff(45,plain,
c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(unit_resolution,[status(thm)],[44,27]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT269-2 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % 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 19:58:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.36 % SZS status Unsatisfiable
% 0.18/0.36 % SZS output start Proof
% See solution above
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------