TSTP Solution File: SET852-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET852-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 05:08:22 EDT 2022
% Result : Unsatisfiable 1.97s 1.63s
% Output : Proof 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 91
% Syntax : Number of formulae : 189 ( 45 unt; 14 typ; 0 def)
% Number of atoms : 753 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 993 ( 433 ~; 488 |; 0 &)
% ( 72 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 10 >; 12 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 558 ( 508 !; 0 ?; 558 :)
% 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_Main_OUnionE__1_type,type,
c_Main_OUnionE__1: ( $i * $i * $i ) > $i ).
tff(v_Y_type,type,
v_Y: $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_Union_type,type,
c_Union: ( $i * $i ) > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_SetInterval_OatMost_type,type,
c_SetInterval_OatMost: ( $i * $i ) > $i ).
tff(c_Zorn_Osucc_type,type,
c_Zorn_Osucc: ( $i * $i * $i ) > $i ).
tff(v_S_type,type,
v_S: $i ).
tff(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(1,plain,
( ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
<=> ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(3,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,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/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_0) ).
tff(8,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)],[7,6]) ).
tff(9,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)],[8]) ).
tff(10,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)],[9,5]) ).
tff(11,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_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),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_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )
<=> ( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,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_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,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_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,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_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,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_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,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_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,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_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[16,10,3]) ).
tff(18,plain,
^ [T_a: $i,V_A: $i,V_C: $i] :
refl(
( ( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) )
<=> ( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) )
<=> ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) )
<=> ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OUnionE_1) ).
tff(22,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) )
<=> ( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,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(30,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)],[29]) ).
tff(31,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(32,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/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_1) ).
tff(33,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)],[32,31]) ).
tff(34,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)],[33]) ).
tff(35,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)],[34,30]) ).
tff(36,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_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,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_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,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_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,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_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a)),
inference(unit_resolution,[status(thm)],[38,35,3]) ).
tff(40,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
rewrite(
( ( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) )
<=> ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetD_0) ).
tff(46,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[52,49,39,28]) ).
tff(54,plain,
^ [T_a: $i,V_A: $i,V_C: $i] :
refl(
( ( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) )
<=> ( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OUnionE_0) ).
tff(58,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [T_a: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[63,60,17]) ).
tff(65,plain,
^ [V_U: $i] :
refl(
( ( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) )
<=> ( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
^ [V_U: $i] :
rewrite(
( ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,v_Y,tc_set(tc_set(t_a))) )
<=> ( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [V_U: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,v_Y,tc_set(tc_set(t_a))) )
<=> ! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [V_U: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,v_Y,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(71,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
( ( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) )
| ~ c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )
<=> ( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) )
| ~ c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) )
| ~ c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
( ~ ! [V_U: $i] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) )
| ~ c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(unit_resolution,[status(thm)],[77,74,64]) ).
tff(79,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[78,53]) ).
tff(80,plain,
^ [T_1: $i] :
refl(
( class_Orderings_Oord(tc_set(T_1))
<=> class_Orderings_Oord(tc_set(T_1)) )),
inference(bind,[status(th)],]) ).
tff(81,plain,
( ! [T_1: $i] : class_Orderings_Oord(tc_set(T_1))
<=> ! [T_1: $i] : class_Orderings_Oord(tc_set(T_1)) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [T_1: $i] : class_Orderings_Oord(tc_set(T_1))
<=> ! [T_1: $i] : class_Orderings_Oord(tc_set(T_1)) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
! [T_1: $i] : class_Orderings_Oord(tc_set(T_1)),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsarity_set_1) ).
tff(84,plain,
! [T_1: $i] : class_Orderings_Oord(tc_set(T_1)),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [T_1: $i] : class_Orderings_Oord(tc_set(T_1)),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [T_1: $i] : class_Orderings_Oord(tc_set(T_1)),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ~ ! [T_1: $i] : class_Orderings_Oord(tc_set(T_1))
| class_Orderings_Oord(tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
class_Orderings_Oord(tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
^ [V_i: $i,T_a: $i,V_k: $i] :
refl(
( ( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) )
<=> ( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [V_i: $i,T_a: $i,V_k: $i] :
rewrite(
( ( ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_i,V_k,T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
<=> ( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_i,V_k,T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_i,V_k,T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_SetInterval_OatMost__iff__iff2_0) ).
tff(95,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) )
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )
<=> ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) )
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) )
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| ~ c_lessequals(V_i,V_k,T_a) )
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[101,98,88,79]) ).
tff(103,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
<=> ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(104,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(105,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
^ [V_i: $i,T_a: $i,V_k: $i] :
refl(
( ( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
<=> ( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
^ [V_i: $i,T_a: $i,V_k: $i] :
rewrite(
( ( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| c_lessequals(V_i,V_k,T_a) )
<=> ( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| c_lessequals(V_i,V_k,T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,axiom,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a)
| c_lessequals(V_i,V_k,T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_SetInterval_OatMost__iff__iff1_0) ).
tff(112,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[114,107]) ).
tff(116,plain,
( ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))) )
<=> ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))) )
<=> ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))) )
<=> ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))) )
<=> ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,plain,
( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| c_lessequals(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OatMost(V_k,T_a),T_a) )
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
( ~ class_Orderings_Oord(tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))) ),
inference(unit_resolution,[status(thm)],[121,115,105]) ).
tff(123,plain,
~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[122,88]) ).
tff(124,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(tc_set(t_a)))) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(tc_set(t_a)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(tc_set(t_a)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(tc_set(t_a)))) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
~ c_lessequals(c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(tc_set(t_a)))),
inference(unit_resolution,[status(thm)],[126,49,123,102]) ).
tff(128,plain,
^ [T_1: $i] :
refl(
( class_Orderings_Oorder(tc_set(T_1))
<=> class_Orderings_Oorder(tc_set(T_1)) )),
inference(bind,[status(th)],]) ).
tff(129,plain,
( ! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1))
<=> ! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1)) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1))
<=> ! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1)) ),
inference(rewrite,[status(thm)],]) ).
tff(131,axiom,
! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1)),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsarity_set_2) ).
tff(132,plain,
! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1)),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1)),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1)),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
( ~ ! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1))
| class_Orderings_Oorder(tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(136,plain,
class_Orderings_Oorder(tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[135,134]) ).
tff(137,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) )
<=> ( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(138,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[137]) ).
tff(139,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) )
<=> ( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(141,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_SetInterval_OatMost__subset__iff__iff2_0) ).
tff(143,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[143,139]) ).
tff(145,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) ),
inference(skolemize,[status(sab)],[144]) ).
tff(146,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[145,138]) ).
tff(147,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) )
| ~ class_Orderings_Oorder(tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(tc_set(t_a)))) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) )
| ~ class_Orderings_Oorder(tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(tc_set(t_a)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) )
| ~ class_Orderings_Oorder(tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(tc_set(t_a)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(c_SetInterval_OatMost(V_x,T_a),c_SetInterval_OatMost(V_y,T_a),tc_set(T_a)) )
| ~ class_Orderings_Oorder(tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_SetInterval_OatMost(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),c_SetInterval_OatMost(c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),tc_set(tc_set(tc_set(t_a)))) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(unit_resolution,[status(thm)],[149,146,136,127]) ).
tff(151,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_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),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_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
( ( c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )
<=> ( c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(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_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) ) ),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(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_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) ) ),
inference(transitivity,[status(thm)],[153,151]) ).
tff(155,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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,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_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[156,10,150]) ).
tff(158,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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(159,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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
~ c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[160,35,150]) ).
tff(162,plain,
^ [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
refl(
( ( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) )
<=> ( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(163,plain,
( ! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) )
<=> ! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,plain,
( ! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) )
<=> ! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,plain,
^ [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
rewrite(
( ( ~ c_in(V_A,V_X,T_a)
| ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a) )
<=> ( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(166,plain,
( ! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,V_X,T_a)
| ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a) )
<=> ! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) ) ),
inference(quant_intro,[status(thm)],[165]) ).
tff(167,axiom,
! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_A,V_X,T_a)
| ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_Set_OUnionI_0) ).
tff(168,plain,
! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) ),
inference(modus_ponens,[status(thm)],[168,164]) ).
tff(170,plain,
! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) ),
inference(skolemize,[status(sab)],[169]) ).
tff(171,plain,
! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) ),
inference(modus_ponens,[status(thm)],[170,163]) ).
tff(172,plain,
( ( ~ ! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) )
| ~ c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) )
<=> ( ~ ! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) )
| ~ c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
( ~ ! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) )
| ~ c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
( ~ ! [T_a: $i,V_X: $i,V_A: $i,V_C: $i] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_A,V_X,T_a) )
| ~ c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
$false,
inference(unit_resolution,[status(thm)],[174,171,64,161,157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET852-1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.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 08:31:02 EDT 2022
% 0.13/0.35 % 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.
% 1.97/1.63 % SZS status Unsatisfiable
% 1.97/1.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------