TSTP Solution File: SET841-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET841-2 : 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 05:08:17 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 25
% Syntax : Number of formulae : 58 ( 23 unt; 9 typ; 0 def)
% Number of atoms : 245 ( 38 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 310 ( 134 ~; 147 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 5 >; 7 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 68 ( 60 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_m_type,type,
v_m: $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_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(c_Zorn_OTFin_type,type,
c_Zorn_OTFin: ( $i * $i ) > $i ).
tff(1,plain,
( ( v_m = c_Zorn_Osucc(v_S,v_m,t_a) )
<=> ( v_m = c_Zorn_Osucc(v_S,v_m,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(3,plain,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
<=> c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
<=> c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
<=> c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(9,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( c_lessequals(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
<=> c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(12,plain,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
<=> c_lessequals(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
<=> c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(15,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
c_lessequals(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_m,t_a),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(monotonicity,[status(thm)],[4]) ).
tff(18,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),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) ),
inference(symmetry,[status(thm)],[17]) ).
tff(19,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),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,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(21,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(22,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)],[21,20]) ).
tff(23,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,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(25,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(26,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
refl(
( ( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
<=> ( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
<=> ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
<=> ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
<=> ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) )),
( ( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) )
<=> ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) ) )),
rewrite(
( ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) )
<=> ( ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) )),
( ( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) )
<=> ( ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) )),
( ( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a))) )
<=> ( ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a))) ) )),
rewrite(
( ( ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a))) )
<=> ( c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) )),
( ( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a))) )
<=> ( c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) )),
( ( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ( V_n = V_m ) )
<=> ( c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ( V_n = V_m ) ) )),
rewrite(
( ( c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ( V_n = V_m ) )
<=> ( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) )),
( ( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ( V_n = V_m ) )
<=> ( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ( V_n = V_m ) )
<=> ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ( V_n = V_m ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__subsetD_0) ).
tff(33,plain,
! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
| ( v_x = c_Zorn_Osucc(v_S,v_m,t_a) )
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),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))) )
<=> ( ~ ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
| ( v_x = c_Zorn_Osucc(v_S,v_m,t_a) )
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),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(38,plain,
( ~ ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
| ( v_x = c_Zorn_Osucc(v_S,v_m,t_a) )
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),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(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ( V_n = V_m )
| c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
| ( v_x = c_Zorn_Osucc(v_S,v_m,t_a) )
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),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(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( v_x = c_Zorn_Osucc(v_S,v_m,t_a) )
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(unit_resolution,[status(thm)],[39,36,26]) ).
tff(41,plain,
v_x = c_Zorn_Osucc(v_S,v_m,t_a),
inference(unit_resolution,[status(thm)],[40,23,16,10]) ).
tff(42,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_x,
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
v_x = v_m,
inference(transitivity,[status(thm)],[41,4]) ).
tff(44,plain,
c_Zorn_Osucc(v_S,v_x,t_a) = c_Zorn_Osucc(v_S,v_m,t_a),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
c_Zorn_Osucc(v_S,v_x,t_a) = v_x,
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a)))
<=> c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( c_lessequals(v_x,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(symmetry,[status(thm)],[46]) ).
tff(48,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)],[15,47]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[22,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET841-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 08:29:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------