%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET844-1 : 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 0.57s
% Output : Proof 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 60 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 267 ( 46 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 357 ( 160 ~; 169 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 10 ( 10 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 162 ( 148 !; 0 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Zorn_Osucc_type,type,
c_Zorn_Osucc: ( $i * $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_m_type,type,
v_m: $i ).
tff(v_S_type,type,
v_S: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(c_Main_OUnion__least__1_type,type,
c_Main_OUnion__least__1: ( $i * $i * $i ) > $i ).
tff(c_Zorn_OTFin_type,type,
c_Zorn_OTFin: ( $i * $i ) > $i ).
tff(c_Union_type,type,
c_Union: ( $i * $i ) > $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
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_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,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_Zorn_Osucc(v_S,v_m,t_a),t_a),
inference(symmetry,[status(thm)],[5]) ).
tff(7,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)),v_m,tc_set(tc_set(t_a))) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(8,plain,
( c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,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)],[7]) ).
tff(9,plain,
( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,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(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
<=> ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(12,plain,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,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)],[12,9]) ).
tff(14,plain,
^ [T_a: $i,V_A: $i,V_C: $i] :
refl(( ( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
<=> ( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__least_1) ).
tff(18,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
| ~ c_lessequals(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,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,v_m,t_a),tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
| ~ c_lessequals(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,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,v_m,t_a),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
| ~ c_lessequals(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,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,v_m,t_a),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(c_Main_OUnion__least__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
| ~ c_lessequals(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,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,v_m,t_a),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ~ c_lessequals(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,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,v_m,t_a),tc_set(tc_set(t_a))) ),
inference(unit_resolution,[status(thm)],[23,20]) ).
tff(25,plain,
~ c_lessequals(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[24,13]) ).
tff(26,plain,
^ [T_a: $i,V_A: $i,V_C: $i] :
refl(( ( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
<=> ( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__least_0) ).
tff(30,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
| c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,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))) )
<=> ( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
| c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,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(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
| c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,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(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( c_in(c_Main_OUnion__least__1(V_A,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(c_Union(V_A,T_a),V_C,tc_set(T_a)) )
| c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,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(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,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(unit_resolution,[status(thm)],[35,32]) ).
tff(37,plain,
c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[36,13]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,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(42,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,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)],[42,39]) ).
tff(44,plain,
^ [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
refl(( ( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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))) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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))) )
<=> ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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))) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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))) )
<=> ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
^ [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
trans(monotonicity(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)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,T_a) ) )
<=> ( ( V_m != c_Zorn_Osucc(V_S,V_m,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_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_m != c_Zorn_Osucc(V_S,V_m,T_a) )
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) )
<=> ( ( V_m != c_Zorn_Osucc(V_S,V_m,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))) ) )),
rewrite(( ( ( V_m != c_Zorn_Osucc(V_S,V_m,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)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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_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_m != c_Zorn_Osucc(V_S,V_m,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)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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))) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ~ 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_m != c_Zorn_Osucc(V_S,V_m,T_a) )
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) )
<=> ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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))) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( ~ 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_m != c_Zorn_Osucc(V_S,V_m,T_a) )
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Oeq__succ__upper_0) ).
tff(50,plain,
! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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))) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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))) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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))) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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))) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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_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_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_Osucc(v_S,v_m,t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) )
| ~ c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),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] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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_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_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_Osucc(v_S,v_m,t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) )
| ~ c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( c_lessequals(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_Osucc(v_S,v_m,t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) )
| ~ c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,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,v_m,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)))
| c_lessequals(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_Osucc(v_S,v_m,t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) )
| ~ c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( ~ ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_Osucc(v_S,v_m,t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) )
| ~ c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,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,v_m,t_a),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] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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_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_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_Osucc(v_S,v_m,t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) )
| ~ c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_Osucc(v_S,v_m,t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) )
| ~ c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,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,v_m,t_a),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] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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_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_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_Osucc(v_S,v_m,t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) )
| ~ c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_Osucc(v_S,v_m,t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) )
| ~ c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,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,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [V_n: $i,V_S: $i,T_a: $i,V_m: $i] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ( V_m != c_Zorn_Osucc(V_S,V_m,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_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_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_Osucc(v_S,v_m,t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) )
| ~ c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
$false,
inference(unit_resolution,[status(thm)],[59,53,43,37,25,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET844-1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:46:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.57 % SZS status Unsatisfiable
% 0.20/0.57 % SZS output start Proof
% See solution above
% 0.44/0.61 % E exiting
%------------------------------------------------------------------------------