%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET845-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 Jun 21 05:26:30 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 74 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 226 ( 46 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 261 ( 120 ~; 109 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 159 ( 144 !; 0 ?; 159 :)
% 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_OTFin_type,type,
c_Zorn_OTFin: ( $i * $i ) > $i ).
tff(v_S_type,type,
v_S: $i ).
tff(c_Zorn_Osucc_type,type,
c_Zorn_Osucc: ( $i * $i * $i ) > $i ).
tff(v_m_type,type,
v_m: $i ).
tff(c_Union_type,type,
c_Union: ( $i * $i ) > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(1,plain,
( ( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) )
<=> ( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(3,plain,
v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) = c_Zorn_Osucc(v_S,v_m,t_a),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[5]) ).
tff(7,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(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( c_in(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),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)],[7]) ).
tff(9,plain,
( c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(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(10,plain,
( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
<=> c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(symmetry,[status(thm)],[9]) ).
tff(11,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(12,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(13,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
^ [V_x: $i,V_S: $i,T_a: $i] :
refl(( ( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,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)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
<=> ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
<=> ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin_OsuccI_0) ).
tff(19,plain,
! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
| ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )
<=> ( ~ ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
| ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
| ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [V_x: $i,V_S: $i,T_a: $i] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) )
| ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(unit_resolution,[status(thm)],[24,21]) ).
tff(26,plain,
c_in(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[25,14]) ).
tff(27,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)],[26,8]) ).
tff(28,plain,
( ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Zorn_Osucc(v_S,v_m,t_a) )
<=> ( v_m = c_Zorn_Osucc(v_S,v_m,t_a) ) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(29,plain,
( ( v_m = c_Zorn_Osucc(v_S,v_m,t_a) )
<=> ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Zorn_Osucc(v_S,v_m,t_a) ) ),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ( v_m != c_Zorn_Osucc(v_S,v_m,t_a) )
<=> ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != c_Zorn_Osucc(v_S,v_m,t_a) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,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(32,axiom,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(33,plain,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != c_Zorn_Osucc(v_S,v_m,t_a),
inference(modus_ponens,[status(thm)],[33,30]) ).
tff(35,plain,
( c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
<=> c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),tc_set(tc_set(t_a))) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(36,plain,
( c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),tc_set(tc_set(t_a)))
<=> c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) ),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
^ [V_x: $i,V_S: $i,T_a: $i] :
refl(( c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a)))
<=> c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a)))
<=> ! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a)))
<=> ! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
tff(41,plain,
! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [V_x: $i,V_S: $i,T_a: $i] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a)))
| c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[45,36]) ).
tff(47,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
trans(monotonicity(rewrite(( ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) )
<=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ( V_A = V_B ) ) )),
rewrite(( ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ( V_A = V_B ) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
tff(53,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
| ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Zorn_Osucc(v_S,v_m,t_a) )
| ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(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_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
| ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Zorn_Osucc(v_S,v_m,t_a) )
| ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(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_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
| ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Zorn_Osucc(v_S,v_m,t_a) )
| ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(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_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(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] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
| ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Zorn_Osucc(v_S,v_m,t_a) )
| ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(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_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Zorn_Osucc(v_S,v_m,t_a) )
| ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(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_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(unit_resolution,[status(thm)],[59,56]) ).
tff(61,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[60,46,34]) ).
tff(62,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) )
<=> ( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).
tff(66,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),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(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),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(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),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_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),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_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(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(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),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_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(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(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),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_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,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_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(unit_resolution,[status(thm)],[71,68]) ).
tff(73,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(unit_resolution,[status(thm)],[72,61]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET845-2 : TPTP v9.0.0. Released v3.2.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 05:45:48 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------