TSTP Solution File: SET864-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET864-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 : Tue Sep 20 05:08:27 EDT 2022
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 37
% Syntax : Number of formulae : 71 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 284 ( 56 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 419 ( 210 ~; 179 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 13 ( 13 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 119 ( 106 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_S_type,type,
v_S: $i ).
tff(v_x_type,type,
v_x: $i > $i ).
tff(c_Union_type,type,
c_Union: ( $i * $i ) > $i ).
tff(v_c_type,type,
v_c: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Zorn_Omaxchain_type,type,
c_Zorn_Omaxchain: ( $i * $i ) > $i ).
tff(1,plain,
^ [V_U: $i] :
refl(
( ( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) )
<=> ( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [V_U: $i] :
rewrite(
( ( c_in(v_x(V_U),v_S,tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) )
<=> ( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_U: $i] :
( c_in(v_x(V_U),v_S,tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [V_U: $i] :
( c_in(v_x(V_U),v_S,tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(7,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
<=> c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(13,plain,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)) )
<=> ( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [V_U: $i] :
refl(
( ( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) )
<=> ( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) )
<=> ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) )
<=> ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(22,plain,
! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| ( c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)) ) )
<=> ( ~ ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| ( c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ( ( c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)) )
<=> ( ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| ( c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( ~ ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) )
| ( c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)) )
<=> ( ~ ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| ( c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)) ) ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( ~ ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) )
| ( c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)) )
<=> ( ~ ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| ( c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)) ) ) ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
( ~ ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) )
| ( c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [V_U: $i] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| ( c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)),
inference(unit_resolution,[status(thm)],[30,13,24]) ).
tff(32,plain,
^ [V_U: $i] :
refl(
( ( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) )
<=> ( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
^ [V_U: $i] :
rewrite(
( ( c_lessequals(V_U,v_x(V_U),tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) )
<=> ( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [V_U: $i] :
( c_lessequals(V_U,v_x(V_U),tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [V_U: $i] :
( c_lessequals(V_U,v_x(V_U),tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(38,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)) )
<=> ( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[44,13,41]) ).
tff(46,plain,
( c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
<=> c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(48,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
^ [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
refl(
( ( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) )
<=> ( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) )
<=> ! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) )
<=> ! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
^ [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( ~ c_in(V_u,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a)) )
<=> ( ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ) )),
( ( ~ c_in(V_u,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ( c_Union(V_c,T_a) = V_u ) )
<=> ( ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a))
| ( c_Union(V_c,T_a) = V_u ) ) )),
rewrite(
( ( ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a))
| ( c_Union(V_c,T_a) = V_u ) )
<=> ( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ) )),
( ( ~ c_in(V_u,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ( c_Union(V_c,T_a) = V_u ) )
<=> ( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_u,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ( c_Union(V_c,T_a) = V_u ) )
<=> ! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_u,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ( c_Union(V_c,T_a) = V_u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__Zorn_0) ).
tff(55,plain,
! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) )
| ( c_Union(v_c,t_a) = v_x(c_Union(v_c,t_a)) )
| ~ c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)) )
<=> ( ~ ! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) )
| ( c_Union(v_c,t_a) = v_x(c_Union(v_c,t_a)) )
| ~ c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) )
| ( c_Union(v_c,t_a) = v_x(c_Union(v_c,t_a)) )
| ~ c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [V_c: $i,V_u: $i,V_S: $i,T_a: $i] :
( ( c_Union(V_c,T_a) = V_u )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) )
| ( c_Union(v_c,t_a) = v_x(c_Union(v_c,t_a)) )
| ~ c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
$false,
inference(unit_resolution,[status(thm)],[61,58,48,45,31,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET864-2 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 08:39:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------