TSTP Solution File: SET851-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET851-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 05:08:21 EDT 2022
% Result : Unsatisfiable 0.20s 0.60s
% Output : Proof 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 39
% Syntax : Number of formulae : 83 ( 19 unt; 10 typ; 0 def)
% Number of atoms : 297 ( 38 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 330 ( 123 ~; 177 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 6 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 147 ( 135 !; 0 ?; 147 :)
% 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(c_Zorn_Osucc_type,type,
c_Zorn_Osucc: ( $i * $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_S_type,type,
v_S: $i ).
tff(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).
tff(v_m_type,type,
v_m: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Zorn_OTFin_type,type,
c_Zorn_OTFin: ( $i * $i ) > $i ).
tff(1,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
<=> ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(3,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) )
<=> ( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) )
<=> ! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) )
<=> ! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
tff(8,plain,
! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) )
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )
<=> ( ~ ! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) )
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) )
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_x: $i,V_S: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) )
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) )
<=> ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(17,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[17,15]) ).
tff(19,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[20,15]) ).
tff(22,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[21,15]) ).
tff(23,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[23,15]) ).
tff(25,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[24,14]) ).
tff(26,plain,
^ [V_U: $i] :
refl(
( ( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) )
<=> ( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
^ [V_U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m ) )
<=> ( ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ) )),
( ( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a))) )
<=> ( ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a))) ) )),
rewrite(
( ( ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a))) )
<=> ( ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ) )),
( ( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a))) )
<=> ( ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ) )),
( ( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )
<=> ( ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) )),
rewrite(
( ( ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )
<=> ( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ) )),
( ( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )
<=> ( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [V_U: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [V_U: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(32,plain,
! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a)))
<=> ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(38,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
<=> c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(41,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( ~ ! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) )
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ( v_x = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) )
<=> ( ~ ! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) )
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ( v_x = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) )
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ( v_x = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [V_U: $i] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) )
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ( v_x = v_m )
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ( v_x = v_m ) ),
inference(unit_resolution,[status(thm)],[44,41,38,35]) ).
tff(46,plain,
v_x = v_m,
inference(unit_resolution,[status(thm)],[45,25]) ).
tff(47,plain,
c_Zorn_Osucc(v_S,v_x,t_a) = c_Zorn_Osucc(v_S,v_m,t_a),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a))
<=> c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a))
<=> c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)) ),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_0) ).
tff(54,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[59,56,3]) ).
tff(61,plain,
c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[60,49]) ).
tff(62,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_1) ).
tff(66,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
~ c_in(c_Main_OsubsetI__1(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[71,68,3]) ).
tff(73,plain,
$false,
inference(unit_resolution,[status(thm)],[72,61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET851-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 08:17:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.60 % SZS status Unsatisfiable
% 0.20/0.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------