TSTP Solution File: LAT273-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT273-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:32:35 EDT 2022
% Result : Unsatisfiable 0.16s 0.37s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 45
% Syntax : Number of formulae : 79 ( 17 unt; 16 typ; 0 def)
% Number of atoms : 476 ( 0 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 701 ( 318 ~; 340 |; 0 &)
% ( 43 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 30 ( 30 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 8 >; 16 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 252 ( 228 !; 0 ?; 252 :)
% 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(v_r_type,type,
v_r: $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_b_type,type,
v_b: $i ).
tff(v_sko__4mi_type,type,
v_sko__4mi: ( $i * $i * $i ) > $i ).
tff(v_S_type,type,
v_S: $i ).
tff(v_L_type,type,
v_L: $i ).
tff(c_Tarski_OisLub_type,type,
c_Tarski_OisLub: ( $i * $i * $i * $i ) > $o ).
tff(v_cl_type,type,
v_cl: $i ).
tff(v_A_type,type,
v_A: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(c_Tarski_Ointerval_type,type,
c_Tarski_Ointerval: ( $i * $i * $i * $i ) > $i ).
tff(v_a_type,type,
v_a: $i ).
tff(1,plain,
( ~ c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> ~ c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(3,plain,
~ c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
<=> c_Tarski_OisLub(v_S,v_cl,v_L,t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(6,plain,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( c_in(v_b,v_A,t_a)
<=> c_in(v_b,v_A,t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
c_in(v_b,v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(9,plain,
c_in(v_b,v_A,t_a),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_z: $i,V_S: $i,V_L: $i] :
refl(
( ( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [V_z: $i,V_S: $i,V_L: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a) )
<=> ( ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) )),
( ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) )),
rewrite(
( ( ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) )),
( ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) )),
( ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) )),
rewrite(
( ( ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) )),
( ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [V_z: $i,V_S: $i,V_L: $i] :
( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_z: $i,V_S: $i,V_L: $i] :
( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1) ).
tff(16,plain,
! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) )
<=> ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
tff(27,plain,
^ [V_z: $i,V_S: $i,V_L: $i] :
refl(
( ( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) )
<=> ( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) )
<=> ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) )
<=> ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [V_z: $i,V_S: $i,V_L: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a) )
<=> ( ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) )),
( ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) )),
rewrite(
( ( ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) )),
( ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
<=> ( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) )),
( ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a) )
<=> ( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a) ) )),
rewrite(
( ( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a) )
<=> ( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) )),
( ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a) )
<=> ( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [V_z: $i,V_S: $i,V_L: $i] :
( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a) )
<=> ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [V_z: $i,V_S: $i,V_L: $i] :
( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0) ).
tff(33,plain,
! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) )
<=> ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a) )
<=> ( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) )
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a) )
<=> ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) )
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a) )
<=> ( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) )
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [V_z: $i,V_S: $i,V_L: $i] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) )
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(v_b,v_A,t_a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a),
inference(unit_resolution,[status(thm)],[42,36,9,6,3]) ).
tff(44,plain,
( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
<=> c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(46,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
^ [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
refl(
( ( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
<=> ( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
<=> ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
<=> ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
^ [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
rewrite(
( ( ~ c_in(V_x,V_S,T_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( ~ c_in(V_x,V_S,T_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( ~ c_in(V_x,V_S,T_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0) ).
tff(53,plain,
! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( ( ~ ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) )
<=> ( ~ ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) )
<=> ( ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ~ ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) )
<=> ( ~ ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) )
<=> ( ~ ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [V_x: $i,V_r: $i,V_b: $i,V_S: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,56,46,43,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : LAT273-2 : TPTP v8.1.0. Released v3.2.0.
% 0.02/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.30 % Computer : n008.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Thu Sep 1 13:00:55 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.16/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.31 Usage: tptp [options] [-file:]file
% 0.16/0.31 -h, -? prints this message.
% 0.16/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.31 -m, -model generate model.
% 0.16/0.31 -p, -proof generate proof.
% 0.16/0.31 -c, -core generate unsat core of named formulas.
% 0.16/0.31 -st, -statistics display statistics.
% 0.16/0.31 -t:timeout set timeout (in second).
% 0.16/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.31 -<param>:<value> configuration parameter and value.
% 0.16/0.31 -o:<output-file> file to place output in.
% 0.16/0.37 % SZS status Unsatisfiable
% 0.16/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------